Does Early Mathematics Intervention Change the Processes Underlying Children’s Learning?

PubMed Central

Watts, Tyler W.; Clements, Douglas H.; Sarama, Julie; Wolfe, Christopher B.; Spitler, Mary Elaine; Bailey, Drew H.

2017-01-01

Early educational intervention effects typically fade in the years following treatment, and few studies have investigated why achievement impacts diminish over time. The current study tested the effects of a preschool mathematics intervention on two aspects of children’s mathematical development. We tested for separate effects of the intervention on “state” (occasion-specific) and “trait” (relatively stable) variability in mathematics achievement. Results indicated that, although the treatment had a large impact on state mathematics, the treatment had no effect on trait mathematics, or the aspect of mathematics achievement that influences stable individual differences in mathematics achievement over time. Results did suggest, however, that the intervention could affect the underlying processes in children’s mathematical development by inducing more transfer of knowledge immediately following the intervention for students in the treated group. PMID:29399243

Interesting and Difficult Mathematical Problems: Changing Teachers' Views by Employing Multiple-Solution Tasks

ERIC Educational Resources Information Center

Guberman, Raisa; Leikin, Roza

2013-01-01

The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers' knowledge. It is aimed at exploring the development of teachers' mathematical and pedagogical conceptions…

The Prospective Mathematics Teachers' Thought Processes and Views about Using Problem-Based Learning in Statistics Education

ERIC Educational Resources Information Center

Canturk-Gunhan, Berna; Bukova-Guzel, Esra; Ozgur, Zekiye

2012-01-01

The purpose of this study is to determine prospective mathematics teachers' views about using problem-based learning (PBL) in statistics teaching and to examine their thought processes. It is a qualitative study conducted with 15 prospective mathematics teachers from a state university in Turkey. The data were collected via participant observation…

ICT integration in mathematics initial teacher training and its impact on visualization: the case of GeoGebra

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Dockendorff, Monika; Solar, Horacio

2018-01-01

This case study investigates the impact of the integration of information and communications technology (ICT) in mathematics visualization skills and initial teacher education programmes. It reports on the influence GeoGebra dynamic software use has on promoting mathematical learning at secondary school and on its impact on teachers' conceptions about teaching and learning mathematics. This paper describes how GeoGebra-based dynamic applets - designed and used in an exploratory manner - promote mathematical processes such as conjectures. It also refers to the changes prospective teachers experience regarding the relevance visual dynamic representations acquire in teaching mathematics. This study observes a shift in school routines when incorporating technology into the mathematics classroom. Visualization appears as a basic competence associated to key mathematical processes. Implications of an early integration of ICT in mathematics initial teacher training and its impact on developing technological pedagogical content knowledge (TPCK) are drawn.

An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

ERIC Educational Resources Information Center

Bukova-Guzel, Esra

2011-01-01

This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

Emotions and Heuristics: The State of Perplexity in Mathematics

ERIC Educational Resources Information Center

Gómez-Chacón, Inés M.

2017-01-01

Using data provided by an empirical exploratory study with mathematics undergraduates, this paper discusses some key variables in the interaction between affective and cognitive dimensions in the perplexity state in problem solving. These variables are as follows: heuristics, mathematical processes, appraisal processes [pleasantness, attentional…

Secondary School Students' Understanding of Mathematical Induction: Structural Characteristics and the Process of Proof Construction

ERIC Educational Resources Information Center

Palla, Marina; Potari, Despina; Spyrou, Panagiotis

2012-01-01

In this study, we investigate the meaning students attribute to the structure of mathematical induction (MI) and the process of proof construction using mathematical induction in the context of a geometric recursion problem. Two hundred and thirteen 17-year-old students of an upper secondary school in Greece participated in the study. Students'…

An Emergent Framework: Views of Mathematical Processes

ERIC Educational Resources Information Center

Sanchez, Wendy B.; Lischka, Alyson E.; Edenfield, Kelly W.; Gammill, Rebecca

2015-01-01

The findings reported in this paper were generated from a case study of teacher leaders at a state-level mathematics conference. Investigation focused on how participants viewed the mathematical processes of communication, connections, representations, problem solving, and reasoning and proof. Purposeful sampling was employed to select nine…

Professional Development Processes That Promote Teacher Change: The Case of a Video-Based Program Focused on Leveraging Students' Mathematical Errors

ERIC Educational Resources Information Center

Santagata, Rossella; Bray, Wendy

2016-01-01

This study examined processes at the core of teacher professional development (PD) experiences that might positively impact teacher learning and more specifically teacher change. Four processes were considered in the context of a PD program focused on student mathematical errors: analysis of students' mathematical misconceptions as a lever for…

Distinct and Overlapping Brain Areas Engaged during Value-Based, Mathematical, and Emotional Decision Processing

PubMed Central

Hsu, Chun-Wei; Goh, Joshua O. S.

2016-01-01

When comparing between the values of different choices, human beings can rely on either more cognitive processes, such as using mathematical computation, or more affective processes, such as using emotion. However, the neural correlates of how these two types of processes operate during value-based decision-making remain unclear. In this study, we investigated the extent to which neural regions engaged during value-based decision-making overlap with those engaged during mathematical and emotional processing in a within-subject manner. In a functional magnetic resonance imaging experiment, participants viewed stimuli that always consisted of numbers and emotional faces that depicted two choices. Across tasks, participants decided between the two choices based on the expected value of the numbers, a mathematical result of the numbers, or the emotional face stimuli. We found that all three tasks commonly involved various cortical areas including frontal, parietal, motor, somatosensory, and visual regions. Critically, the mathematical task shared common areas with the value but not emotion task in bilateral striatum. Although the emotion task overlapped with the value task in parietal, motor, and sensory areas, the mathematical task also evoked responses in other areas within these same cortical structures. Minimal areas were uniquely engaged for the value task apart from the other two tasks. The emotion task elicited a more expansive area of neural activity whereas value and mathematical task responses were in more focal regions. Whole-brain spatial correlation analysis showed that valuative processing engaged functional brain responses more similarly to mathematical processing than emotional processing. While decisions on expected value entail both mathematical and emotional processing regions, mathematical processes have a more prominent contribution particularly in subcortical processes. PMID:27375466

Distinct and Overlapping Brain Areas Engaged during Value-Based, Mathematical, and Emotional Decision Processing.

PubMed

Hsu, Chun-Wei; Goh, Joshua O S

2016-01-01

When comparing between the values of different choices, human beings can rely on either more cognitive processes, such as using mathematical computation, or more affective processes, such as using emotion. However, the neural correlates of how these two types of processes operate during value-based decision-making remain unclear. In this study, we investigated the extent to which neural regions engaged during value-based decision-making overlap with those engaged during mathematical and emotional processing in a within-subject manner. In a functional magnetic resonance imaging experiment, participants viewed stimuli that always consisted of numbers and emotional faces that depicted two choices. Across tasks, participants decided between the two choices based on the expected value of the numbers, a mathematical result of the numbers, or the emotional face stimuli. We found that all three tasks commonly involved various cortical areas including frontal, parietal, motor, somatosensory, and visual regions. Critically, the mathematical task shared common areas with the value but not emotion task in bilateral striatum. Although the emotion task overlapped with the value task in parietal, motor, and sensory areas, the mathematical task also evoked responses in other areas within these same cortical structures. Minimal areas were uniquely engaged for the value task apart from the other two tasks. The emotion task elicited a more expansive area of neural activity whereas value and mathematical task responses were in more focal regions. Whole-brain spatial correlation analysis showed that valuative processing engaged functional brain responses more similarly to mathematical processing than emotional processing. While decisions on expected value entail both mathematical and emotional processing regions, mathematical processes have a more prominent contribution particularly in subcortical processes.

The semantic system is involved in mathematical problem solving.

PubMed

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

Role of Visualization in Mathematical Abstraction: The Case of Congruence Concept

ERIC Educational Resources Information Center

Yilmaz, Rezan; Argun, Ziya

2018-01-01

Mathematical abstraction is an important process in mathematical thinking. Also, visualization is a strong tool for searching mathematical problems, giving meaning to mathematical concepts and the relationships between them. In this paper, we aim to investigate the role of visualizations in mathematical abstraction through a case study on five…

The Cognitive Profile of Chinese Children with Mathematics Difficulties

ERIC Educational Resources Information Center

Chan, Becky Mee-yin; Ho, Connie Suk-han

2010-01-01

This study examined how four domain-specific skills (arithmetic procedural skills, number fact retrieval, place value concept, and number sense) and two domain-general processing skills (working memory and processing speed) may account for Chinese children's mathematics learning difficulties. Children with mathematics difficulties (MD) of two age…

Contextual approach using VBA learning media to improve students’ mathematical displacement and disposition ability

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Chotimah, Siti; Bernard, M.; Wulandari, S. M.

2018-01-01

The main problems of the research were the lack of reasoning ability and mathematical disposition of students to the learning of mathematics in high school students in Cimahi - West Java. The lack of mathematical reasoning ability in students was caused by the process of learning. The teachers did not train the students to do the problems of reasoning ability. The students still depended on each other. Sometimes, one of patience teacher was still guiding his students. In addition, the basic ability aspects of students also affected the ability the mathematics skill. Furthermore, the learning process with contextual approach aided by VBA Learning Media (Visual Basic Application for Excel) gave the positive influence to the students’ mathematical disposition. The students are directly involved in learning process. The population of the study was all of the high school students in Cimahi. The samples were the students of SMA Negeri 4 Cimahi class XIA and XIB. There were both of tested and non-tested instruments. The test instrument was a description test of mathematical reasoning ability. The non-test instruments were questionnaire-scale attitudes about students’ mathematical dispositions. This instrument was used to obtain data about students’ mathematical reasoning and disposition of mathematics learning with contextual approach supported by VBA (Visual Basic Application for Excel) and by conventional learning. The data processed in this study was from the post-test score. These scores appeared from both of the experimental class group and the control class group. Then, performing data was processed by using SPSS 22 and Microsoft Excel. The data was analyzed using t-test statistic. The final result of this study concluded the achievement and improvement of reasoning ability and mathematical disposition of students whose learning with contextual approach supported by learning media of VBA (Visual Basic Application for Excel) was better than students who got conventional learning.

Improving students’ mathematical representational ability through RME-based progressive mathematization

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Warsito; Darhim; Herman, T.

2018-01-01

This study aims to determine the differences in the improving of mathematical representation ability based on progressive mathematization with realistic mathematics education (PMR-MP) with conventional learning approach (PB). The method of research is quasi-experiments with non-equivalent control group designs. The study population is all students of class VIII SMPN 2 Tangerang consisting of 6 classes, while the sample was taken two classes with purposive sampling technique. The experimental class is treated with PMR-MP while the control class is treated with PB. The instruments used are test of mathematical representation ability. Data analysis was done by t-test, ANOVA test, post hoc test, and descriptive analysis. The result of analysis can be concluded that: 1) there are differences of mathematical representation ability improvement between students treated by PMR-MP and PB, 2) no interaction between learning approach (PMR-MP, PB) and prior mathematics knowledge (PAM) to improve students’ mathematical representation; 3) Students’ mathematical representation improvement in the level of higher PAM is better than medium, and low PAM students. Thus, based on the process of mathematization, it is very important when the learning direction of PMR-MP emphasizes on the process of building mathematics through a mathematical model.

Second International Mathematics Study; Longitudinal, Classroom Process Surveys for Population A: Students, Teachers, and Schools, 1981-1982 [machine-readable data file].

ERIC Educational Resources Information Center

Wolfe, Richard G.

The Second International Mathematics Study (SIMS) of the International Association for the Evaluation of Educational Achievement (IEA) was conducted in 20 countries on two sampled populations: Population A of 13-year-olds and Population B of students studying mathematics in their final year of secondary school. Mathematics achievement was measured…

Forschung Zum Prozess des Mathematiklernens. Reihe: Materialien und Studien, Band 2. (Research on the Process of Mathematics Learning. Series: Materials and Studies, Volume 2.)

ERIC Educational Resources Information Center

Bielefeld Univ. (West Germany).

The ten papers in this document were developed for a meeting prepared for the Third International Congress on Mathematical Education. Each paper is concerned with research from 1970-1975 related to the mathematical learning process. The first paper describes projects conducted in England on both content and process learning. The second paper…

Pre-service mathematics teachers’ ability in solving well-structured problem

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Paradesa, R.

2018-01-01

This study aimed to describe the mathematical problem-solving ability of undergraduate students of mathematics education in solving the well-structured problem. The type of this study was qualitative descriptive. The subjects in this study were 100 undergraduate students of Mathematics Education at one of the private universities in Palembang city. The data in this study was collected through two test items with essay form. The results of this study showed that, from the first problem, only 8% students can solve it, but do not check back again to validate the process. Based on a scoring rubric that follows Polya strategy, their answer satisfied 2 4 2 0 patterns. But, from the second problem, 45% students satisfied it. This is because the second problem imitated from the example that was given in learning process. The average score of undergraduate students mathematical problem-solving ability in solving well-structured problems showed 56.00 with standard deviation was 13.22. It means that, from 0 - 100 scale, undergraduate students mathematical problem-solving ability can be categorized low. From this result, the conclusion was undergraduate students of mathematics education in Palembang still have a problem in solving mathematics well-structured problem.

Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem

ERIC Educational Resources Information Center

Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova

2017-01-01

The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…

Mathematics Placement Test: Typical Results with Unexpected Outcomes

ERIC Educational Resources Information Center

Ingalls, Victoria

2011-01-01

Based on the results of a prior case-study analysis of mathematics placement at one university, the mathematics department developed and piloted a mathematics placement test. This article describes the implementation process for a mathematics placement test and further analyzes the test results for the pilot group. As an unexpected result, the…

Mathematical History, Philosophy and Education

ERIC Educational Resources Information Center

Otte, Michael

2007-01-01

History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necessitate ever greater particularity whereas mathematics and…

Mathematical modeling of heat treatment processes conserving biological activity of plant bioresources

NASA Astrophysics Data System (ADS)

Rodionova, N. S.; Popov, E. S.; Pozhidaeva, E. A.; Pynzar, S. S.; Ryaskina, L. O.

2018-05-01

The aim of this study is to develop a mathematical model of the heat exchange process of LT-processing to estimate the dynamics of temperature field changes and optimize the regime parameters, due to the non-stationarity process, the physicochemical and thermophysical properties of food systems. The application of LT-processing, based on the use of low-temperature modes in thermal culinary processing of raw materials with preliminary vacuum packaging in a polymer heat- resistant film is a promising trend in the development of technics and technology in the catering field. LT-processing application of food raw materials guarantees the preservation of biologically active substances in food environments, which are characterized by a certain thermolability, as well as extend the shelf life and high consumer characteristics of food systems that are capillary-porous bodies. When performing the mathematical modeling of the LT-processing process, the packet of symbolic mathematics “Maple” was used, as well as the mathematical packet flexPDE that uses the finite element method for modeling objects with distributed parameters. The processing of experimental results was evaluated with the help of the developed software in the programming language Python 3.4. To calculate and optimize the parameters of the LT processing process of polycomponent food systems, the differential equation of non-stationary thermal conductivity was used, the solution of which makes it possible to identify the temperature change at any point of the solid at different moments. The present study specifies data on the thermophysical characteristics of the polycomponent food system based on plant raw materials, with the help of which the physico-mathematical model of the LT- processing process has been developed. The obtained mathematical model allows defining of the dynamics of the temperature field in different sections of the LT-processed polycomponent food systems on the basis of calculating the evolution profiles of temperature fields, which enable one to analyze the efficiency of the regime parameters of heat treatment.

Development Mathematic Assessment to Increase Mathematical Prerequisite Ability on The Student with Learning Disabilities in Inclusive Elementary School

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Robiansyah, S. T. U.; Nanang, F.; Hidayat

2018-01-01

The purpose of this study was to introduce about mathematic assessment is a process of obtaining data or information about the mastery of a student's mathematical skills as an ingredient in preparing a learning program. With this mathematics assessment can be known obstacles, difficulties and needs of students especially in the field of mathematic, so that the learning program will be in accordance with the potential students because it is tailored to what is required of students. This research study was conducted at elementary school of inclusive precisely at SDN Sukagalih I Bandung City based learning in setting of inclusive education. This research study is motivated by the existence of a first-grade student who has disabilities learning in mathematics, the ability of the mathematical prerequisite mastery of the classification of objects by color. The results of the research can provide a profile picture of student data information, the data obtained from the results of the development of systematic and formal mathematical assessment. After doing the development of mathematics assessment then the teacher gets important related information: 1. process the analysis of students’ learning needs, especially in the field of mathematics, 2. preparing the learning program planning according to student learning needs, 3. Designing procedural of method remedial program.

Processes involved in solving mathematical problems

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Shahrill, Masitah; Putri, Ratu Ilma Indra; Zulkardi, Prahmana, Rully Charitas Indra

2018-04-01

This study examines one of the instructional practices features utilized within the Year 8 mathematics lessons in Brunei Darussalam. The codes from the TIMSS 1999 Video Study were applied and strictly followed, and from the 183 mathematics problems recorded, there were 95 problems with a solution presented during the public segments of the video-recorded lesson sequences of the four sampled teachers. The analyses involved firstly, identifying the processes related to mathematical problem statements, and secondly, examining the different processes used in solving the mathematical problems for each problem publicly completed during the lessons. The findings revealed that for three of the teachers, their problem statements coded as `using procedures' ranged from 64% to 83%, while the remaining teacher had 40% of his problem statements coded as `making connections.' The processes used when solving the problems were mainly `using procedures', and none of the problems were coded as `giving results only'. Furthermore, all four teachers made use of making the relevant connections in solving the problems given to their respective students.

Students' Activity in Computer-Supported Collaborative Problem Solving in Mathematics

ERIC Educational Resources Information Center

Hurme, Tarja-riitta; Jarvela, Sanna

2005-01-01

The purpose of this study was to analyse secondary school students' (N = 16) computer-supported collaborative mathematical problem solving. The problem addressed in the study was: What kinds of metacognitive processes appear during computer-supported collaborative learning in mathematics? Another aim of the study was to consider the applicability…

Defining Mathematical Giftedness

ERIC Educational Resources Information Center

Parish, Linda

2014-01-01

This theoretical paper outlines the process of defining "mathematical giftedness" for a present study on how primary school teaching shapes the mindsets of children who are mathematically gifted. Mathematical giftedness is not a badge of honour or some special value attributed to a child who has achieved something exceptional.…

Mathematics Pedagogical Standards: A Suggested Model of Instruction in Enhancing the Mathematics Teacher’s Quality of Instruction

NASA Astrophysics Data System (ADS)

Saad, N. S.; Jemali, M.; Zakaria, Z. Hj; Yusof, Q.

2018-01-01

The paper aims at identifying the standards for teaching and learning of mathematics based on National Council of Teacher of Mathematics (NCTM, 2000), The Australian Association of Mathematics Teachers (AAMT, 2006) and Training and Development Agency for School (TDA, 2007). These known standards were used as a guide in identifying the constructs of the mathematics teacher’s instruction in the classroom. The survey method used in which a questionnaire instrument encompassed on the four identified constructs on the standards for teaching and learning of mathematics, namely professional practices, professional attributes, professional knowledge, and professional instructional processes. The instrument was tested during a pilot study and a Cronbach’s Alpha reliability index of greater than 0.85 was obtained. The actual research was carried out in Peninsular Malaysia involving 224 secondary schools with 1.120 mathematics teachers and 108 primary schools with 540 mathematics teachers. From the selected schools, only 820 secondary mathematics teachers (73.2%) and 361 primary teachers (66.9%) gave a response to the mailed questionnaires. The findings of the study revealed that the secondary and primary mathematics teachers strongly agreed on three constructs; professional practices, professional attributes and professional instructional processes.

Promoting Creativity and Self-Efficacy of Elementary Students through a Collaborative Research Task in Mathematics: A Case Study

ERIC Educational Resources Information Center

Katz, Sara; Stupel, Moshe

2015-01-01

There is a consensus among mathematicians and mathematics educators that creativity plays an essential role in doing mathematics. Creative students are self-regulated students who take control over processes and experience high self-efficacy beliefs. The aim of this case study was to promote mathematical creativity and self-efficacy of elementary…

New Materialist Ontologies in Mathematics Education: The Body in/of Mathematics

ERIC Educational Resources Information Center

de Freitas, Elizabeth; Sinclair, Nathalie

2013-01-01

In this paper we study the mathematical body as an assemblage of human and non-human mathematical concepts. We argue that learners' bodies are always in the process of becoming assemblages of diverse and dynamic materialities. Following the work of the historian of science Karen Barad, we argue that mathematical concepts must be considered dynamic…

Examining the Mathematical Modeling Processes of Primary School 4th-Grade Students: Shopping Problem

ERIC Educational Resources Information Center

Ulu, Mustafa

2017-01-01

The purpose of this study is to identify primary school students' thinking processes within the mathematical modeling process and the challenges they encounter, if any. This is a basic qualitative research study conducted in a primary school in the city of Kütahya in the academic year of 2015-2016. The study group of the research was composed of…

Teachers' Perception of Social Justice in Mathematics Classrooms

ERIC Educational Resources Information Center

Panthi, Ram Krishna; Luitel, Bal Chandra; Belbase, Shashidhar

2017-01-01

The purpose of this study was to explore mathematics teachers' perception of social justice in mathematics classrooms. We applied interpretive qualitative method for data collection, analysis, and interpretation through iterative process. We administered in-depth semi-structured interviews to capture the perceptions of three mathematics teachers…

Student Teachers' Mathematics Attitudes, Authentic Investigations and Use of Metacognitive Tools

ERIC Educational Resources Information Center

Afamasaga-Fuata'i, Karoline; Sooaemalelagi, Lumaava

2014-01-01

Based on findings from a semester-long study, this article examines the development of Samoan prospective teachers' mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The…

Teachers' Perception of Social Justice in Mathematics Classrooms

ERIC Educational Resources Information Center

Panthi, Ram Krishna; Luitel, Bal Chandra; Belbase, Shashidhar

2018-01-01

The purpose of this study was to explore mathematics teachers' perception of social justice in mathematics classrooms. We applied interpretive qualitative method for data collection, analysis, and interpretation through iterative process. We administered in-depth semi-structured interviews to capture the perceptions of three mathematics teachers…

Brain Correlates of Mathematical Competence in Processing Mathematical Representations

PubMed Central

Grabner, Roland H.; Reishofer, Gernot; Koschutnig, Karl; Ebner, Franz

2011-01-01

The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams) is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus (AG) activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left AG activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left AG activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance. PMID:22069387

Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation.

PubMed

Rodic, Maja; Cui, Jiaxin; Malykh, Sergey; Zhou, Xinlin; Gynku, Elena I; Bogdanova, Elena L; Zueva, Dina Y; Y Bogdanova, Olga; Kovas, Yulia

2018-06-01

The study investigated cross-cultural differences in variability and average performance in arithmetic, mathematical reasoning, symbolic and non-symbolic magnitude processing, intelligence, spatial ability, and mathematical anxiety in 890 6- to 9-year-old children from the United Kingdom, Russia, and China. Cross-cultural differences explained 28% of the variance in arithmetic and 17.3% of the variance in mathematical reasoning, with Chinese children outperforming the other two groups. No cross-cultural differences were observed for spatial ability and mathematical anxiety. In all samples, symbolic magnitude processing and mathematical reasoning were independently related to early arithmetic. Other factors, such as non-symbolic magnitude processing, mental rotation, intelligence, and mathematical anxiety, produced differential patterns across the populations. The results are discussed in relation to potential influences of parental practice, school readiness, and linguistic factors on individual differences in early mathematics. Statement of contribution What is already known on this subject? Cross-cultural differences in mathematical ability are present in preschool children. Similar mechanisms of mathematical development operate in preschool children from the United Kingdom, Russia, and China. Tasks that require understanding of numbers are best predictors of arithmetic in preschool children. What does this study add? Cross-cultural differences in mathematical ability become greater with age/years of formal education. Similar mechanisms of mathematical development operate in early primary school children from the United Kingdom, Russia, and China. Symbolic number magnitude and mathematical reasoning are the main predictors of arithmetic in all three populations. © 2018 The Authors British Journal of Developmental Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

Examining the Changes in Novice and Experienced Mathematics Teachers' Questioning Techniques through the Lesson Study Process

ERIC Educational Resources Information Center

Ong, Ewe Gnoh; Lim, Chap Sam; Ghazali, Munirah

2010-01-01

The purpose of this study was to examine the changes in novice and experienced mathematics teachers' questioning techniques. This study was conducted in Sarawak where ten (experienced and novice) teachers from two schools underwent the lesson study process for fifteen months. Four data collection methods namely, observation, interview, lesson…

Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

ERIC Educational Resources Information Center

Czocher, Jennifer A.

2016-01-01

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

Mathematics & Economics: Connections for Life, Grades 6-8.

ERIC Educational Resources Information Center

Hoff, Jody; McCorkle, Sarapage; Suiter, Mary; Bettendorf, James; Breidenbach, Lisa; Cornwell, Pamela

This book contains a set of 12 lessons for middle school students that demonstrate how mathematical processes and concepts may be applied to the study of economics and personal finance. Mathematics educators can find lessons connecting mathematics instruction to practical problems and issues that students encounter throughout their life. The…

Effects of Gender-Based Instruction on Fifth Graders' Attitudes toward Mathematics

ERIC Educational Resources Information Center

Oswald, Deborah R.

2009-01-01

Differences in male and female brains may impact the way girls and boys process mathematics and underscores the need for research that examines modification of mathematics instruction according to gender differences. Based in constructivist theory, this mixed-methods study investigated the effect of mathematics instruction modified according to…

Profile of mathematics anxiety of 7th graders

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Udil, Patrisius Afrisno; Kusmayadi, Tri Atmojo; Riyadi

2017-08-01

Mathematics anxiety is one of the important factors affect students mathematics achievement. This present research investigates profile of students' mathematics anxiety. This research focuses on analysis and description of students' mathematics anxiety level generally and its dominant domain and aspect. Qualitative research with case study strategy was used in this research. Subject in this research involved 15 students of 7th grade chosen with purposive sampling. Data in this research were students' mathematics anxiety scale result, interview record, and observation result during both mathematics learning activity and test. They were asked to complete mathematics anxiety scale before interviewed and observed. The results show that generally students' mathematics anxiety was identified in the moderate level. In addition, students' mathematics anxiety during mathematics test was identified in the high level, but it was in the moderate level during mathematics learning process. Based on the anxiety domain, students have a high mathematics anxiety on cognitive domain, while it was in the moderate level for psychological and physiological domains. On the other hand, it was identified in low level for psychological domain during mathematics learning process. Therefore, it can be concluded that students have serious and high anxiety regarding mathematics on the cognitive domain and mathematics test aspect.

Evaluating the Suitability of Mathematical Thinking Problems for Senior High-School Students by Including Mathematical Sense Making and Global Planning

ERIC Educational Resources Information Center

van Velzen, Joke H.

2016-01-01

The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

Frequencies as Proportions: Using a Teaching Model Based on Pirie and Kieren's Model of Mathematical Understanding

ERIC Educational Resources Information Center

Wright, Vince

2014-01-01

Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

A Multiple Case Study of College-Contextualized Mathematics Curriculum

ERIC Educational Resources Information Center

Valenzuela, Hector

2018-01-01

Contextualization is a method used for mathematics curriculum design within lesson plans and as a pedagogical practice in face-to-face classes. Many researchers are studying the effects of using contextualization in the teaching and the learning process for mathematics (Bottge & Cho, 2013; Perin, 2011; Young, Hodge, Edwards, & Leising,…

Establishing Mathematics for Teaching within Classroom Interactions in Teacher Education

ERIC Educational Resources Information Center

Ryve, Andreas; Nilsson, Per; Mason, John

2012-01-01

Teacher educators' processes of establishing "mathematics for teaching" in teacher education programs have been recognized as an important area for further research. In this study, we examine how two teacher educators establish and make explicit features of mathematics for teaching within classroom interactions. The study shows how the…

The Development of a Student Survey on Attitudes towards Mathematics Teaching-Learning Processes

ERIC Educational Resources Information Center

Mutohir, Toho Cholik; Lowrie, Tom; Patahuddin, Sitti Maesuri

2018-01-01

This study aimed to develop a survey instrument to measure student attitudes towards mathematics teaching-learning processes that is appropriate for the Indonesian context. This study consisted of two phases: Phase 1 (n = 320) was a pilot study to assess the suitability of the instrument items for Indonesian students. Phase 2 (n = 1001) was…

Semantic Processing of Mathematical Gestures

ERIC Educational Resources Information Center

Lim, Vanessa K.; Wilson, Anna J.; Hamm, Jeff P.; Phillips, Nicola; Iwabuchi, Sarina J.; Corballis, Michael C.; Arzarello, Ferdinando; Thomas, Michael O. J.

2009-01-01

Objective: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. Results: The N400 effect elicited by words primed with mathematical gestures…

Gaining control: changing relations between executive control and processing speed and their relevance for mathematics achievement over course of the preschool period

PubMed Central

Clark, Caron A. C.; Nelson, Jennifer Mize; Garza, John; Sheffield, Tiffany D.; Wiebe, Sandra A.; Espy, Kimberly Andrews

2014-01-01

Early executive control (EC) predicts a range of academic outcomes and shows particularly strong associations with children's mathematics achievement. Nonetheless, a major challenge for EC research lies in distinguishing EC from related cognitive constructs that also are linked to achievement outcomes. Developmental cascade models suggest that children's information processing speed is a driving mechanism in cognitive development that supports gains in working memory, inhibitory control and associated cognitive abilities. Accordingly, individual differences in early executive task performance and their relation to mathematics may reflect, at least in part, underlying variation in children's processing speed. The aims of this study were to: (1) examine the degree of overlap between EC and processing speed at different preschool age points; and (2) determine whether EC uniquely predicts children's mathematics achievement after accounting for individual differences in processing speed. As part of a longitudinal, cohort-sequential study, 388 children (50% boys; 44% from low income households) completed the same battery of EC tasks at ages 3, 3.75, 4.5, and 5.25 years. Several of the tasks incorporated baseline speeded naming conditions with minimal EC demands. Multidimensional latent models were used to isolate the variance in executive task performance that did not overlap with baseline processing speed, covarying for child language proficiency. Models for separate age points showed that, while EC did not form a coherent latent factor independent of processing speed at age 3 years, it did emerge as a distinct factor by age 5.25. Although EC at age 3 showed no distinct relation with mathematics achievement independent of processing speed, EC at ages 3.75, 4.5, and 5.25 showed independent, prospective links with mathematics achievement. Findings suggest that EC and processing speed are tightly intertwined in early childhood. As EC becomes progressively decoupled from processing speed with age, it begins to take on unique, discriminative importance for children's mathematics achievement. PMID:24596563

Enhancing Students’ Interest through Mathematics Learning

NASA Astrophysics Data System (ADS)

Azmidar, A.; Darhim, D.; Dahlan, J. A.

2017-09-01

A number of previous researchers indicated that students’ mathematics interest still low because most of them have perceived that mathematics is very difficult, boring, not very practical, and have many abstract theorems that were very hard to understand. Another cause is the teaching and learning process used, which is mechanistic without considering students’ needs. Learning is more known as the process of transferring the knowledge to the students. Let students construct their own knowledge with the physical and mental reflection that is done by activity in the new knowledge. This article is literature study. The purpose of this article is to examine the Concrete-Pictorial-Abstract approach in theoretically to improve students’ mathematics interest. The conclusion of this literature study is the Concrete-Pictorial-Abstract approach can be used as an alternative to improve students’ mathematics interest.

Teachers' Influence on Integration of Tools into Mathematics Teaching

ERIC Educational Resources Information Center

Yesildere, Sibel

2010-01-01

This paper examines the process through which three pre-service teachers learn to use mathematical tools; it also looks at pre-service teachers' instrumentation of tools into mathematics teaching. Three pre-service teachers were studying at a primary mathematics teacher training program at Dokuz Eylul University in Turkey. During an eight-week…

A Study of Prospective Secondary Mathematics Teachers' Evolving Understanding of Reasoning-and-Proving

ERIC Educational Resources Information Center

Boyle, Justin D.

2012-01-01

Proof is a foundational mathematical activity that has been underrepresented in school mathematics. The recently adopted Common Core State Standards in Mathematics includes eight process standards, several of which promote the inclusion of reasoning and proof across all grades, courses, and students. If students are to reach the expectations…

Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

2017-01-01

This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

An Analysis of the Reasoning Skills of Pre-Service Teachers in the Context of Mathematical Thinking

ERIC Educational Resources Information Center

Yavuz Mumcu, Hayal; Aktürk, Tolga

2017-01-01

The aim of this study is to address and analyse pre-service teachers' mathematical reasoning skills in relation to mathematical thinking processes. For these purposes, pre-service teachers' mathematical reasoning skills namely generalising/abstraction/modelling, ratiocination, development and creative thinking skills and the relationships among…

Student-Teachers in Higher Education Institutions' (HEIs) Emotional Intelligence and Mathematical Competencies

ERIC Educational Resources Information Center

Eustaquio, William Rafael

2015-01-01

As manifested by various studies conducted, the present state of Mathematics education in the teaching-learning process is relatively declining and the existing effort to identify emotional intelligence and mathematics competencies of Mathematics major student-teachers at Higher Education Institutions in Isabela is an attempt to help alleviate the…

Understanding Expertise-Based Training Effects on the Software Evaluation Process of Mathematics Education Teachers

ERIC Educational Resources Information Center

Incikabi, Lutfi; Sancar Tokmak, Hatice

2012-01-01

This case study examined the educational software evaluation processes of pre-service teachers who attended either expertise-based training (XBT) or traditional training in conjunction with a Software-Evaluation checklist. Forty-three mathematics teacher candidates and three experts participated in the study. All participants evaluated educational…

The Essential Role of Curricular Analyses in Comparative Studies of Mathematics Achievement: Developing "Fair" Tests

ERIC Educational Resources Information Center

Chavez, Oscar; Papick, Ira; Ross, Dan J.; Grouws, Douglas A.

2010-01-01

The purpose of this paper was to describe the process of development of assessment instruments for the Comparing Options in Secondary Mathematics: Investigating Curriculum (COSMIC) project. The COSMIC project was a three-year longitudinal comparative study focusing on evaluating high school students' mathematics learning from two distinct…

On the Four Types of Characteristics of Super Mathematically Gifted Students

ERIC Educational Resources Information Center

Leikin, Roza; Leikin, Mark; Paz-Baruch, Nurit; Waisman, Ilana; Lev, Miri

2017-01-01

In order to achieve the present study's goal--to understand better the phenomenon of mathematical giftedness--we performed a multidimensional examination of the mental processing in students who exhibited mathematical expertise (EM) at the secondary school level. The study included participants from the three groups: students who excelled in…

Cognitive Processing and Mathematical Achievement: A Study with Schoolchildren between Fourth and Sixth Grade of Primary Education

ERIC Educational Resources Information Center

Iglesias-Sarmiento, Valentin; Deano, Manuel

2011-01-01

This investigation analyzed the relation between cognitive functioning and mathematical achievement in 114 students in fourth, fifth, and sixth grades. Differences in cognitive performance were studied concurrently in three selected achievement groups: mathematical learning disability group (MLD), low achieving group (LA), and typically achieving…

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

ERIC Educational Resources Information Center

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…

Creative and algorithmic mathematical reasoning: effects of transfer-appropriate processing and effortful struggle

NASA Astrophysics Data System (ADS)

Jonsson, Bert; Kulaksiz, Yagmur C.; Lithner, Johan

2016-11-01

Two separate studies, Jonsson et al. (J. Math Behav. 2014;36: 20-32) and Karlsson Wirebring et al. (Trends Neurosci Educ. 2015;4(1-2):6-14), showed that learning mathematics using creative mathematical reasoning and constructing their own solution methods can be more efficient than if students use algorithmic reasoning and are given the solution procedures. It was argued that effortful struggle was the key that explained this difference. It was also argued that the results could not be explained by the effects of transfer-appropriate processing, although this was not empirically investigated. This study evaluated the hypotheses of transfer-appropriate processing and effortful struggle in relation to the specific characteristics associated with algorithmic reasoning task and creative mathematical reasoning task. In a between-subjects design, upper-secondary students were matched according to their working memory capacity.

The Characterization of Cognitive Processes Involved in Chemical Kinetics Using a Blended Processing Framework

ERIC Educational Resources Information Center

Bain, Kinsey; Rodriguez, Jon-Marc G.; Moon, Alena; Towns, Marcy H.

2018-01-01

Chemical kinetics is a highly quantitative content area that involves the use of multiple mathematical representations to model processes and is a context that is under-investigated in the literature. This qualitative study explored undergraduate student integration of chemistry and mathematics during problem solving in the context of chemical…

Transition Process of Procedural to Conceptual Understanding in Solving Mathematical Problems

ERIC Educational Resources Information Center

Fatqurhohman

2016-01-01

This article aims to describe the transition process from procedural understanding to conceptual understanding in solving mathematical problems. Subjects in this study were three students from 20 fifth grade students of SDN 01 Sumberberas Banyuwangi selected based on the results of the students' answers. The transition process from procedural to…

Numerical magnitude processing in abacus-trained children with superior mathematical ability: an EEG study*

PubMed Central

Huang, Jian; Du, Feng-lei; Yao, Yuan; Wan, Qun; Wang, Xiao-song; Chen, Fei-yan

2015-01-01

Distance effect has been regarded as the best established marker of basic numerical magnitude processes and is related to individual mathematical abilities. A larger behavioral distance effect is suggested to be concomitant with lower mathematical achievement in children. However, the relationship between distance effect and superior mathematical abilities is unclear. One could get superior mathematical abilities by acquiring the skill of abacus-based mental calculation (AMC), which can be used to solve calculation problems with exceptional speed and high accuracy. In the current study, we explore the relationship between distance effect and superior mathematical abilities by examining whether and how the AMC training modifies numerical magnitude processing. Thus, mathematical competencies were tested in 18 abacus-trained children (who accepted the AMC training) and 18 non-trained children. Electroencephalography (EEG) waveforms were recorded when these children executed numerical comparison tasks in both Arabic digit and dot array forms. We found that: (a) the abacus-trained group had superior mathematical abilities than their peers; (b) distance effects were found both in behavioral results and on EEG waveforms; (c) the distance effect size of the average amplitude on the late negative-going component was different between groups in the digit task, with a larger effect size for abacus-trained children; (d) both the behavioral and EEG distance effects were modulated by the notation. These results revealed that the neural substrates of magnitude processing were modified by AMC training, and suggested that the mechanism of the representation of numerical magnitude for children with superior mathematical abilities was different from their peers. In addition, the results provide evidence for a view of non-abstract numerical representation. PMID:26238541

Mathematizing Process of Junior High School Students to Improve Mathematics Literacy Refers PISA on RCP Learning

NASA Astrophysics Data System (ADS)

Wardono; Mariani, S.; Hendikawati, P.; Ikayani

2017-04-01

Mathematizing process (MP) is the process of modeling a phenomenon mathematically or establish the concept of a phenomenon. There are two mathematizing that is Mathematizing Horizontal (MH) and Mathematizing Vertical (MV). MH as events changes contextual problems into mathematical problems, while MV is the process of formulation of the problem into a variety of settlement mathematics by using some appropriate rules. Mathematics Literacy (ML) is the ability to formulate, implement and interpret mathematics in various contexts, including the capacity to perform reasoning mathematically and using the concepts, procedures, and facts to describe, explain or predict phenomena incident. If junior high school students are conditioned continuously to conduct mathematizing activities on RCP (RME-Card Problem) learning, it will be able to improve ML that refers PISA. The purpose of this research is to know the capability of the MP grade VIII on ML content shape and space with the matter of the cube and beams with RCP learning better than the scientific learning, upgrade MP grade VIII in the issue of the cube and beams with RCP learning better than the scientific learning in terms of cognitive styles reflective and impulsive the MP grade VIII with the approach of the RCP learning in terms of cognitive styles reflective and impulsive This research is the mixed methods model concurrent embedded. The population in this study, i.e., class VIII SMPN 1 Batang with sample two class. Data were taken with the observation, interviews, and tests and analyzed with a different test average of one party the right qualitative and descriptive. The results of this study demonstrate the capability of the MP student with RCP learning better than the scientific learning, upgrade MP with RCP learning better compare with scientific learning in term cognitive style of reflective and impulsive. The subject of the reflective group top, middle, and bottom can meet all the process of MH indicators are then the subject of the reflective upper and intermediate group can meet all the MV indicators but to lower groups can only fulfill some MV indicators. The subject is impulsive upper and middle group can meet all the MH indicators but to lower groups can only meet some MH indicator, then the subject is impulsive group can meet all the MV indicators but for middle and the bottom group can only fulfill some MV indicators.

The Development of Mathematical Knowledge for Teaching of Mathematics Teachers in Lesson Analysis Process

ERIC Educational Resources Information Center

Baki, Mujgan

2015-01-01

This study aims to explore the role of lesson analysis in the development of mathematical knowledge for teaching. For this purpose, a graduate course based on lesson analysis was designed for novice mathematics teachers. Throughout the course the teachers watched videos of group-mates and discussed the issues they identified in terms of…

Salient Beliefs of Secondary School Mathematics Teachers Using Dynamic Geometry Software

ERIC Educational Resources Information Center

Chan, Kan Kan

2015-01-01

Even though dynamic geometry software (DGS) is becoming an emergent instructional tool for mathematics teachers, many teachers are still in the process of consideration about whether to use it. In order to encourage teachers to use DGS, this study seeks to discover mathematics teachers' salient beliefs about the use of DGS in mathematics class.…

Is rapid automatized naming related to reading and mathematics for the same reason(s)? A follow-up study from kindergarten to Grade 1.

PubMed

Georgiou, George K; Tziraki, Niki; Manolitsis, George; Fella, Argyro

2013-07-01

We examined (a) what rapid automatized naming (RAN) components (articulation time and/or pause time) predict reading and mathematics ability and (b) what processing skills involved in RAN (speed of processing, response inhibition, working memory, and/or phonological awareness) may explain its relationship with reading and mathematics. A sample of 72 children were followed from the beginning of kindergarten until the end of Grade 1 and were assessed on measures of RAN, general cognitive ability, speed of processing, attention, working memory, phonological awareness, reading, and mathematics. The results indicated that pause time was the critical component in both the RAN-reading and RAN-mathematics relationships and that it shared most of its predictive variance in reading and mathematics with speed of processing and working memory. Our findings further suggested that, unlike the relationship between RAN and reading fluency in Grade 1, there is nothing in the RAN task that is uniquely related to math. Copyright © 2013 Elsevier Inc. All rights reserved.

The study of thermal processes in control systems of heat consumption of buildings

NASA Astrophysics Data System (ADS)

Tsynaeva, E.; A, Tsynaeva

2017-11-01

The article discusses the main thermal processes in the automated control systems for heat consumption (ACSHC) of buildings, schematic diagrams of these systems, mathematical models used for description of thermal processes in ACSHC. Conducted verification represented by mathematical models. It was found that the efficiency of the operation of ACSHC depend from the external and internal factors. Numerical study of dynamic modes of operation of ACSHC.

Mathematical Modelling as a Professional Task

ERIC Educational Resources Information Center

Frejd, Peter; Bergsten, Christer

2016-01-01

Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…

Cognitive components of a mathematical processing network in 9-year-old children.

PubMed

Szűcs, Dénes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2014-07-01

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo-spatial short-term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short-term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non-verbal intelligence measures were also non-significant predictors when added to our model. Number sense variables were non-significant predictors in the model and they were also non-significant predictors when entered into regression analysis with only a single visuo-spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular 'number sense'. We suggest an 'executive memory function centric' model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors.

Cognitive components of a mathematical processing network in 9-year-old children

PubMed Central

Szűcs, Dénes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2014-01-01

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo-spatial short-term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short-term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non-verbal intelligence measures were also non-significant predictors when added to our model. Number sense variables were non-significant predictors in the model and they were also non-significant predictors when entered into regression analysis with only a single visuo-spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular ‘number sense’. We suggest an ‘executive memory function centric’ model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors. PMID:25089322

Abstraction and Concreteness in the Everyday Mathematics of Structural Engineers.

ERIC Educational Resources Information Center

Gainsburg, Julie

The everyday mathematics processes of structural engineers were studied and analyzed in terms of abstraction. A main purpose of the study was to explore the degree to which the notion of a gap between school and everyday mathematics holds when the scope of practices considered "everyday" is extended. J. Lave (1988) promoted a methodology…

The Interaction between Intuitive and Formal Mathematical Thinking: A Case Study

ERIC Educational Resources Information Center

Farmaki, V.; Paschos, T.

2007-01-01

This paper reports studies of the interaction between the intuitive, the formal and the procedural aspects in the processes of mathematical understanding of Peter, a first-year undergraduate of Mathematics. Using an activity and an interview, an attempt is made to analyse his mental operations. The way in which he handles visual-graphic…

Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

Mathematical Thinking Process of Autistic Students in Terms of Representational Gesture

ERIC Educational Resources Information Center

Mustafa, Sriyanti; Nusantara, Toto; Subanji; Irawati, Santi

2016-01-01

The aim of this study is to describe the mathematical thinking process of autistic students in terms of gesture, using a qualitative approach. Data collecting is conducted by using 3 (three) audio-visual cameras. During the learning process, both teacher and students' activity are recorded using handy cam and digital camera (full HD capacity).…

Developmental Relations Among Motor and Cognitive Processes and Mathematics Skills.

PubMed

Kim, Helyn; Duran, Chelsea A K; Cameron, Claire E; Grissmer, David

2018-03-01

This study explored transactional associations among visuomotor integration, attention, fine motor coordination, and mathematics skills in a diverse sample of one hundred thirty-five 5-year-olds (kindergarteners) and one hundred nineteen 6-year-olds (first graders) in the United States who were followed over the course of 2 school years. Associations were dynamic, with more reciprocal transactions occurring in kindergarten than in the later grades. Specifically, visuomotor integration and mathematics exhibited ongoing reciprocity in kindergarten and first grade, attention contributed to mathematics in kindergarten and first grade, mathematics contributed to attention across the kindergarten year only, and fine motor coordination contributed to mathematics indirectly, through visuomotor integration, across kindergarten and first grade. Implications of examining the hierarchical interrelations among processes underlying the development of children's mathematics skills are discussed. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.

A mathematical study of a random process proposed as an atmospheric turbulence model

NASA Technical Reports Server (NTRS)

Sidwell, K.

1977-01-01

A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.

Visuospatial and Mathematical Dysfunction in Major Depressive Disorder and/or Panic Disorder: A Study of Parietal Functioning

PubMed Central

Nelson, Brady D.; Shankman, Stewart A.

2015-01-01

The parietal cortex is critical for several different cognitive functions, including visuospatial processing and mathematical abilities. There is strong evidence indicating parietal dysfunction in depression. However, it is less clear whether anxiety is associated with parietal dysfunction, and whether comorbid depression and anxiety is associated with greater impairment. The present study compared participants with major depression (MDD), panic disorder (PD), comorbid MDD/PD, and controls on neuropsychological measures of visuospatial processing, Judgment of Line Orientation (JLO), and mathematical abilities, Wide Range Achievement Arithmetic (WRAT-Arithmetic). Only comorbid MDD/PD was associated with decreased performance on JLO, whereas all psychopathological groups exhibited comparably decreased performance on WRAT-Arithmetic. Furthermore, the results were not accounted for by other comorbid disorders, medication use, or psychopathology severity. The present study suggests comorbid depression and anxious arousal is associated with impairment in visuospatial processing and provides novel evidence indicating mathematical deficits across depression and/or anxiety. Implications for understanding parietal dysfunction in internalizing psychopathology are discussed. PMID:25707308

Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

NASA Astrophysics Data System (ADS)

Misu, La; Ketut Budayasa, I.; Lukito, Agung

2018-03-01

This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

Avoiding Mathematics Trauma: Alternative Teaching Methods.

ERIC Educational Resources Information Center

Ufuktepe, Unal; Ozel, Claire Thomas

Children in primary education often encounter mathematics having picked up a general fear of mathematics from the society around them. This results in lack of confidence, avoidance of non-standard thought processes, weakness in problem solving strategies, and other negative consequences. This study offers an alternative approach: presenting…

Mathematics Learning Development: The Role of Long-Term Retrieval

ERIC Educational Resources Information Center

Calderón-Tena, Carlos O.; Caterino, Linda C.

2016-01-01

This study assessed the relation between long-term memory retrieval and mathematics calculation and mathematics problem solving achievement among elementary, middle, and high school students in nationally representative sample of US students, when controlling for fluid and crystallized intelligence, short-term memory, and processing speed. As…

The Mathematical Miseducation of America's Youth: Ignoring Research and Scientific Study in Education.

ERIC Educational Resources Information Center

Battista, Michael T.

1999-01-01

Because traditional instruction ignores students' personal construction of mathematical meaning, mathematical thought development is not properly nurtured. Several issues must be addressed, including adults' ignorance of math- and student-learning processes, identification of math-education research specialists, the myth of coverage, testing…

Mathematical Problem Solving through Sequential Process Analysis

ERIC Educational Resources Information Center

Codina, A.; Cañadas, M. C.; Castro, E.

2015-01-01

Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…

The Process of Making Meaning: The Interplay between Teachers' Knowledge of Mathematical Proofs and Their Classroom Practices

ERIC Educational Resources Information Center

Paddack, Megan

2009-01-01

The purpose of this study was to investigate and describe how middle school mathematics teachers "make meaning" of proofs and the process of proving in the context of their classroom practices. A framework of "making meaning," created by the researcher, guided the data collection and analysis phases of the study. This framework…

Teacher Knowledge That Supports Student Processes in Learning Mathematics: A Study at All-Female Middle Schools in Saudi Arabia

ERIC Educational Resources Information Center

Alsaeed, Maha Saad

2012-01-01

Teachers in Saudi Arabia are attempting to advance their teaching in mathematics to address specific reforms by the Ministry of Education. Saudi teachers must improve their students' thinking through engagement in problem solving. This qualitative study investigated how teachers use knowledge of student mathematical learning and how they promote…

Teacher and Student Use of Gesture and Access to Secondary Mathematics for Students with Learning Disabilities: An Exploratory Study

ERIC Educational Resources Information Center

Hord, Casey; Marita, Samantha; Walsh, Jennifer B.; Tomaro, Taylor-Marie; Gordon, Kiyana; Saldanha, Rene L.

2016-01-01

The researchers conducted an exploratory qualitative case study to describe the gesturing processes of tutors and students when engaging in secondary mathematics. The use of gestures ranged in complexity from simple gestures, such as pointing and moving the pointing finger in an arching motion to demonstrate mathematics relationships within…

Connecting Biology and Mathematics: First Prepare the Teachers

PubMed Central

2010-01-01

Developing the connection between biology and mathematics is one of the most important ways to shift the paradigms of both established science disciplines. However, adding some mathematic content to biology or biology content to mathematics is not enough but must be accompanied by development of suitable pedagogical models. I propose a model of pedagogical mathematical biological content knowledge as a feasible starting point for connecting biology and mathematics in schools and universities. The process of connecting these disciplines should start as early as possible in the educational process, in order to produce prepared minds that will be able to combine both disciplines at graduate and postgraduate levels of study. Because teachers are a crucial factor in introducing innovations in education, the first step toward such a goal should be the education of prospective and practicing elementary and secondary school teachers. PMID:20810951

The Effects of Using Exploratory Computerized Environments in Grades 1 to 8 Mathematics: A Meta-Analysis of Research

ERIC Educational Resources Information Center

Sokolowski, Andrzej; Li, Yeping; Willson, Victor

2015-01-01

Background: The process of problem solving is difficult for students; thus, mathematics educators have made multiple attempts to seek ways of making this process more accessible to learners. The purpose of this study was to examine the effect size statistic of utilizing exploratory computerized environments (ECEs) to support the process of word…

Construction Process of the Length of [cube root of 2] by Paper Folding

ERIC Educational Resources Information Center

Guler, Hatice Kubra; Gurbuz, Mustafa Cagri

2018-01-01

The main purpose of this study is to investigate mathematics teachers' mathematical thinking process while they are constructing the length of [cube root of 2] by paper folding. To carry out this aim, two teachers--who are PhD. students--were interviewed one by one. During the construction, it was possible to observe the consolidation process of…

Classroom-Based Integration of Text-Messaging in Mathematics Teaching-Learning Process

ERIC Educational Resources Information Center

Aunzo, Rodulfo T., Jr.

2017-01-01

A lot of teachers are complaining that students are "texting" inside the classroom even during class hours. With this, this research study "on students' perception before the integration and the students' attitude after the integration of text messaging inside the classroom during the mathematics teaching-learning process was…

Changing Mathematics Teaching Practices and Improving Student Outcomes through Collaborative Evaluation

ERIC Educational Resources Information Center

Thomas, Kelli

2013-01-01

This longitudinal study examines the effects of a collaborative evaluation process on mathematics instruction and student outcomes in an elementary school serving a low-resource community. Thirty-two elementary teachers participated in a 3-year collaborative evaluation professional development process that contributed to improved mathematics…

Birth and Death Process Modeling Leads to the Poisson Distribution: A Journey Worth Taking

ERIC Educational Resources Information Center

Rash, Agnes M.; Winkel, Brian J.

2009-01-01

This paper describes details of development of the general birth and death process from which we can extract the Poisson process as a special case. This general process is appropriate for a number of courses and units in courses and can enrich the study of mathematics for students as it touches and uses a diverse set of mathematical topics, e.g.,…

Didactital design of mathematics teaching in primary school

NASA Astrophysics Data System (ADS)

Nur’aeni, E.; Muharram, M. R. W.

2018-05-01

The fact that the low ability of geometrical understanding of primary school students is what triggers this study to be conducted. Thus, this research aimed to find out how to create a didactical design of students' mathematical understanding, particularly on one of geometry materials that is unit of length. A qualitative approach promoting Didactical Design Research (DDR) was administered in this study. Participants of the study were primary school students in Tasikmalaya, an city in West Java Province, Indonesia. The results show that there was a learning design based on learning obstacles found in the mathematics teaching and learning processes. The learning obstacles comprised students' difficulties in memorizing, relating, and operating the standards of unit of lengths. It has been proven that the most influential factor in the success of mathematics teaching and learning processes is the use of creative media.

Workbook, Basic Mathematics and Wastewater Processing Calculations.

ERIC Educational Resources Information Center

New York State Dept. of Environmental Conservation, Albany.

This workbook serves as a self-learning guide to basic mathematics and treatment plant calculations and also as a reference and source book for the mathematics of sewage treatment and processing. In addition to basic mathematics, the workbook discusses processing and process control, laboratory calculations and efficiency calculations necessary in…

Mathematical Strengths and Weaknesses of Preservice Agricultural Education Teachers

ERIC Educational Resources Information Center

Stripling, Christopher T.; Roberts, T. Grady; Stephens, Carrie A.

2014-01-01

The purpose of this study was to describe the mathematics ability of preservice agricultural education teachers related to each of the National Council of Teachers of Mathematics (NCTM) content/process areas and their corresponding sub-standards that are cross-referenced with the National Agriculture, Food and Natural Resources Career Cluster…

Deepening Prospective Mathematics Teachers' Diagnostic Judgments: Interplay of Videos, Focus Questions and Didactic Categories

ERIC Educational Resources Information Center

Prediger, Susanne; Zindel, Carina

2017-01-01

This article combines different conceptualizations of teachers' diagnostic competence in listening to students' mathematical thinking processes on the levels of general perspectives, noticed aspects and activated didactic categories. An empirical study of 159 prospective mathematics teachers' diagnostic judgments investigated how these levels are…

A Protocol-Analytic Study of Metacognition in Mathematical Problem Solving.

ERIC Educational Resources Information Center

Cai, Jinfa

1994-01-01

Metacognitive behaviors of subjects having high (n=2) and low (n=2) levels of mathematical experience were compared across four cognitive processes in mathematical problem solving: orientation, organization, execution, and verification. High-experience subjects engaged in self-regulation and spent more time on orientation and organization. (36…

Development process of in-service training intended for teachers to perform teaching of mathematics with computer algebra systems

NASA Astrophysics Data System (ADS)

Ardıç, Mehmet Alper; Işleyen, Tevfik

2018-01-01

In this study, we deal with the development process of in-service training activities designed in order for mathematics teachers of secondary education to realize teaching of mathematics, utilizing computer algebra systems. In addition, the results obtained from the researches carried out during and after the in-service training were summarized. Last section focuses on suggestions any teacher can use to carry out activities aimed at using computer algebra systems in teaching environments.

Six to Ten Digits Multiplication Fun Learning Using Puppet Prototype

NASA Astrophysics Data System (ADS)

Islamiah Rosli, D.'oria; Ali, Azita; Peng, Lim Soo; Sujardi, Imam; Usodo, Budi; Adie Perdana, Fengky

2017-01-01

Logic and technical subjects require students to understand basic knowledge in mathematic. For instance, addition, minus, division and multiplication operations need to be mastered by students due to mathematic complexity as the learning mathematic grows higher. Weak foundation in mathematic also contribute to high failure rate in mathematic subjects in schools. In fact, students in primary schools are struggling to learn mathematic because they need to memorize formulas, multiplication or division operations. To date, this study will develop a puppet prototyping for learning mathematic for six to ten digits multiplication. Ten participants involved in the process of developing the prototype in this study. Students involved in the study were those from the intermediate class students whilst teachers were selected based on their vast knowledge and experiences and have more than five years of experience in teaching mathematic. Close participatory analysis will be used in the prototyping process as to fulfil the requirements of the students and teachers whom will use the puppet in learning six to ten digit multiplication in mathematic. Findings showed that, the students had a great time and fun learning experience in learning multiplication and they able to understand the concept of multiplication using puppet. Colour and materials of the puppet also help to attract student attention during learning. Additionally, students able to visualized and able to calculate accurate multiplication value and the puppet help them to recall in multiplying and adding the digits accordingly.

Pre-Service Mathematics Teachers' Views about GeoGebra and Its Use

ERIC Educational Resources Information Center

Horzum, Tugba; Ünlü, Melihan

2017-01-01

The purpose of this study was to determine the views of pre-service Mathematics teachers' (PMTs) about GeoGebra and its use after being exposed to GeoGebra activities designing processes. This is a case study which was conducted with 36 PMTs. Three open-ended questions were used, after the completion of the 14-week process of GeoGebra training and…

Cognitive analysis as a way to understand students' problem-solving process in BODMAS rule

NASA Astrophysics Data System (ADS)

Ung, Ting Su; Kiong, Paul Lau Ngee; Manaf, Badron bin; Hamdan, Anniza Binti; Khium, Chen Chee

2017-04-01

Students tend to make lots of careless mistake during the process of mathematics solving. To facilitate effective learning, educators have to understand which cognitive processes are used by students and how these processes help them to solve problems. This paper is only aimed to determine the common errors in mathematics by pre-diploma students that took Intensive Mathematics I (MAT037) in UiTM Sarawak. Then, concentrate on the errors did by the students on the topic of BODMAS rule and the mental processes corresponding to these errors that been developed by students. One class of pre-diploma students taking MAT037 taught by the researchers was selected because they performed poorly in SPM mathematics. It is inevitable that they finished secondary education with many misconceptions in mathematics. The solution scripts for all the tutorials of the participants were collected. This study was predominately qualitative and the solution scripts were content analyzed to identify the common errors committed by the participants, and to generate possible mental processes to these errors. Selected students were interviewed by the researchers during the progress. BODMAS rule could be further divided into Numerical Simplification and Powers Simplification. Furthermore, the erroneous processes could be attributed to categories of Basic Arithmetic Rules, Negative Numbers and Powers.

Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

Milestones of mathematical model for business process management related to cost estimate documentation in petroleum industry

NASA Astrophysics Data System (ADS)

Khamidullin, R. I.

2018-05-01

The paper is devoted to milestones of the optimal mathematical model for a business process related to cost estimate documentation compiled during construction and reconstruction of oil and gas facilities. It describes the study and analysis of fundamental issues in petroleum industry, which are caused by economic instability and deterioration of a business strategy. Business process management is presented as business process modeling aimed at the improvement of the studied business process, namely main criteria of optimization and recommendations for the improvement of the above-mentioned business model.

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

PubMed Central

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930

Improving of prospective elementary teachers' reasoning: Learning geometry through mathematical investigation

NASA Astrophysics Data System (ADS)

Sumarna, Nana; Sentryo, Izlan

2017-08-01

This research applies mathematical investigation approach in teaching geometry to improve mathematical reasoning abilities of prospective elementary teachers. Mathematical investigation in this study involved non-routine tasks through a mathematical investigation process, namely through a series of activities as an attribute of mathematical investigation. Developing the ability of mathematical reasoning of research subjects obtained through capability of research subjects in the analysis, generalization, synthesis, justify, and resolve non-routine, which is operationally constructed as an indicator of research and is used as a criterion for measuring the ability of mathematical reasoning. Research design using Quasi-Experimental design. Based on this type, the researchers apply a pre-and posttest design, which is divided into two study groups: control group and the treatment group. The number of research subjects were 111 students consisting of 56 students in the experimental group and 55 students in the control group. The conclusion of this study stated that (1) Investigation of mathematics as an approach to learning is able to give a positive response to the increasing ability of mathematical reasoning, and (2) There is no interaction effect of the factors of learning and prior knowledge of mathematics to the increased ability of mathematical reasoning.

Associations of Non-Symbolic and Symbolic Numerical Magnitude Processing with Mathematical Competence: A Meta-Analysis

ERIC Educational Resources Information Center

Schneider, Michael; Beeres, Kassandra; Coban, Leyla; Merz, Simon; Schmidt, S. Susan; Stricker, Johannes; De Smedt, Bert

2017-01-01

Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent…

Shape Up: An Eye-Tracking Study of Preschoolers' Shape Name Processing and Spatial Development

ERIC Educational Resources Information Center

Verdine, Brian N.; Bunger, Ann; Athanasopoulou, Angeliki; Golinkoff, Roberta Michnick; Hirsh-Pasek, Kathy

2017-01-01

Learning the names of geometric shapes is at the intersection of early spatial, mathematical, and language skills, all important for school-readiness and predictors of later abilities in science, technology, engineering, and mathematics (STEM). We investigated whether socioeconomic status (SES) influenced children's processing of shape names and…

Socially Shared Metacognition of Dyads of Pupils in Collaborative Mathematical Problem-Solving Processes

ERIC Educational Resources Information Center

Iiskala, Tuike; Vauras, Marja; Lehtinen, Erno; Salonen, Pekka

2011-01-01

This study investigated how metacognition appears as a socially shared phenomenon within collaborative mathematical word-problem solving processes of dyads of high-achieving pupils. Four dyads solved problems of different difficulty levels. The pupils were 10 years old. The problem-solving activities were videotaped and transcribed in terms of…

Mathematical Development: The Role of Broad Cognitive Processes

ERIC Educational Resources Information Center

Calderón-Tena, Carlos O.

2016-01-01

This study investigated the role of broad cognitive processes in the development of mathematics skills among children and adolescents. Four hundred and forty-seven students (age mean [M] = 10.23 years, 73% boys and 27% girls) from an elementary school district in the US southwest participated. Structural equation modelling tests indicated that…

The Development and Validation of Scores on the Mathematics Information Processing Scale (MIPS).

ERIC Educational Resources Information Center

Bessant, Kenneth C.

1997-01-01

This study reports on the development and psychometric properties of a new 87-item Mathematics Information Processing Scale that explores learning strategies, metacognitive problem-solving skills, and attentional deployment. Results with 340 college students support the use of the instrument, for which factor analysis identified five theoretically…

Categorization and analysis of explanatory writing in mathematics

NASA Astrophysics Data System (ADS)

Craig, Tracy S.

2011-10-01

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to mathematical problem-solving processes. The rationale for the study was the recognized importance of mathematical problem-solving, the widely acknowledged challenge of teaching problem-solving skills directly and the evidence in the literature that writing in mathematics provides a tool for learning. The study was carried out in a first-year mathematics course at the University of Cape Town, South Africa. Students' written submissions were categorized and analysed through use of an adaptation of a journal entry classification scheme. The scheme successfully observed positive changes over the experimental period in students' level of engagement with the mathematical material and with their stance towards knowledge.

Action-Based Digital Tools: Mathematics Learning in 6-Year-Old Children

ERIC Educational Resources Information Center

Dejonckheere, Peter J. N.; Desoete, Annemie; Fonck, Nathalie; Roderiguez, Dave; Six, Leen; Vermeersch, Tine; Vermeulen, Lies

2014-01-01

Introduction: In the present study we used a metaphorical representation in order to stimulate the numerical competences of six-year-olds. It was expected that when properties of physical action are used for mathematical thinking or when abstract mathematical thinking is grounded in sensorimotor processes, learning gains should be more pronounced…

What Happens When Teachers and Students Are Introduced to Mathematical Investigations: An Exploratory Study

ERIC Educational Resources Information Center

Nivera, Gladys C.

2017-01-01

A mathematical investigation (MI) encapsulates the reform movement in mathematics education by addressing content and process simultaneously and providing a novel opportunity for students to develop thinking skills and good mental habits. However, introducing MI to teachers and students who are used to routinised teaching approaches and…

Mathematical modeling of forest fire initiation in three dimensional setting

Treesearch

Valeriy Perminov

2007-01-01

In this study, the assignment and theoretical investigations of the problems of forest fire initiation were carried out, including development of a mathematical model for description of heat and mass transfer processes in overterrestrial layer of atmosphere at crown forest fire initiation, taking into account their mutual influence. Mathematical model of forest fire...

Mathematical form models of tree trunks

Treesearch

Rudolfs Ozolins

2000-01-01

Assortment structure analysis of tree trunks is a characteristic and proper problem that can be solved by using mathematical modeling and standard computer programs. Mathematical form model of tree trunks consists of tapering curve equations and their parameters. Parameters for nine species were obtained by processing measurements of 2,794 model trees and studying the...

Methodological Potential of Computer Experiment in Teaching Mathematics at University

ERIC Educational Resources Information Center

Lin, Kequan; Sokolova, Anna Nikolaevna; Vlasova, Vera K.

2017-01-01

The study is relevant due to the opportunity of increasing efficiency of teaching mathematics at university through integration of students of computer experiment conducted with the use of IT in this process. The problem of there search is defined by a contradiction between great potential opportunities of mathematics experiment for motivating and…

Mathematical values in the processing of Chinese numeral classifiers and measure words.

PubMed

Her, One-Soon; Chen, Ying-Chun; Yen, Nai-Shing

2017-01-01

A numeral classifier is required between a numeral and a noun in Chinese, which comes in two varieties, sortal classifer (C) and measural classifier (M), also known as 'classifier' and 'measure word', respectively. Cs categorize objects based on semantic attributes and Cs and Ms both denote quantity in terms of mathematical values. The aim of this study was to conduct a psycholinguistic experiment to examine whether participants process C/Ms based on their mathematical values with a semantic distance comparison task, where participants judged which of the two C/M phrases was semantically closer to the target C/M. Results showed that participants performed more accurately and faster for C/Ms with fixed values than the ones with variable values. These results demonstrated that mathematical values do play an important role in the processing of C/Ms. This study may thus shed light on the influence of the linguistic system of C/Ms on magnitude cognition.

Thinking and Content Learning of Mathematics and Science as Cognitional Development in Content and Language Integrated Learning (CLIL): Teaching Through a Foreign Language in Finland

ERIC Educational Resources Information Center

Jappinen, Aini-Kristiina

2005-01-01

This paper presents a study on thinking and learning processes of mathematics and science in teaching through a foreign language, in Finland. The entity of thinking and content learning processes is, in this study, considered as cognitional development. Teaching through a foreign language is here called Content and Language Integrated Learning or…

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Structuring students’ analogical reasoning in solving algebra problem

NASA Astrophysics Data System (ADS)

Lailiyah, S.; Nusantara, T.; Sa'dijah, C.; Irawan, E. B.; Kusaeri; Asyhar, A. H.

2018-01-01

The average achievement of Indonesian students’ mathematics skills according to Benchmark International Trends in Mathematics and Science Study (TIMSS) is ranked at the 38th out of 42 countries and according to the survey result in Program for International Student Assessment (PISA) is ranked at the 64th out of 65 countries. The low mathematics skill of Indonesian student has become an important reason to research more deeply about reasoning and algebra in mathematics. Analogical reasoning is a very important component in mathematics because it is the key to creativity and it can make the learning process in the classroom become effective. The major part of the analogical reasoning is about structuring including the processes of inferencing and decision-making happens. Those processes involve base domain and target domain. Methodologically, the subjects of this research were 42 students from class XII. The sources of data were derived from the results of thinks aloud, the transcribed interviews, and the videos taken while the subject working on the instruments and interviews. The collected data were analyzed using qualitative techniques. The result of this study described the structuring characteristics of students’ analogical reasoning in solving algebra problems from all the research subjects.

Working Memory in Students with Mathematical Difficulties

NASA Astrophysics Data System (ADS)

Nur, I. R. D.; Herman, T.; Ningsih, S.

2018-04-01

Learning process is the activities that has important role because this process is one of the all factors that establish students success in learning. oftentimes we find so many students get the difficulties when they study mathematics. This condition is not only because of the outside factor but also it comes from the inside. The purpose of this research is to analyze and give the representation how students working memory happened in physical education students for basic statistics subjects which have mathematical difficulties. The subjects are 4 students which have a mathematical difficulties. The research method is case study and when the describe about students working memory are explanated deeply with naturalistic observation. Based on this research, it was founded that 4 students have a working memory deficit in three components. The components are phonological loop, visuospatial sketchpad, dan episodic buffer.

Parental Support of Numeracy during a Cooking Activity with Four-Year-Olds

ERIC Educational Resources Information Center

Vandermaas-Peeler, Maureen; Boomgarden, Erin; Finn, Lauren; Pittard, Caroline

2012-01-01

While research demonstrates the importance of numeracy-related activities performed at home for young children's mathematics achievement, few studies involve observational studies of the processes which support children's mathematical learning at home. On this premise, this study reports evidence from numeracy-related interactions between parents…

Improving Mathematics Achievement of Indonesian 5th Grade Students through Guided Discovery Learning

ERIC Educational Resources Information Center

Yurniwati; Hanum, Latipa

2017-01-01

This research aims to find information about the improvement of mathematics achievement of grade five student through guided discovery learning. This research method is classroom action research using Kemmis and Taggart model consists of three cycles. Data used in this study is learning process and learning results. Learning process data is…

Number Magnitude Processing and Basic Cognitive Functions in Children with Mathematical Learning Disabilities

ERIC Educational Resources Information Center

Andersson, Ulf; Ostergren, Rickard

2012-01-01

The study sought out to extend our knowledge regarding the origin of mathematical learning disabilities (MLD) in children by testing different hypotheses in the same samples of children. Different aspects of cognitive functions and number processing were assessed in fifth- and sixth-graders (11-13 years old) with MLD and compared to controls. The…

The Answering Process for Multiple-Choice Questions in Collaborative Learning: A Mathematical Learning Model Analysis

ERIC Educational Resources Information Center

Nakamura, Yasuyuki; Nishi, Shinnosuke; Muramatsu, Yuta; Yasutake, Koichi; Yamakawa, Osamu; Tagawa, Takahiro

2014-01-01

In this paper, we introduce a mathematical model for collaborative learning and the answering process for multiple-choice questions. The collaborative learning model is inspired by the Ising spin model and the model for answering multiple-choice questions is based on their difficulty level. An intensive simulation study predicts the possibility of…

Numerical Magnitude Processing Impairments in Genetic Syndromes: A Cross-Syndrome Comparison of Turner and 22Q11.2 Deletion Syndromes

ERIC Educational Resources Information Center

Brankaer, Carmen; Ghesquière, Pol; De Wel, Anke; Swillen, Ann; De Smedt, Bert

2017-01-01

Cross-syndrome comparisons offer an important window onto understanding heterogeneity in mathematical learning disabilities or dyscalculia. The present study therefore investigated symbolic numerical magnitude processing in two genetic syndromes that are both characterized by mathematical learning disabilities: Turner syndrome and 22q11.2 deletion…

Trends in TIMSS Responses over Time: Evidence of Global Forces in Education?

ERIC Educational Resources Information Center

Rutkowski, Leslie; Rutkowski, David

2009-01-01

In this article, the influence of global processes on international mathematics curricula as evidenced by item responses to 3 Trends in International Mathematics and Science Study (TIMSS) administrations (1995, 1999, and 2003) is considered. Based on Dale's (2000) argument, we set out to test 2 plausible impacts of global processes on education.…

How to Classify the Diversity of Seventh Grade Students' Mathematical Process Skills: An Application of Latent Profile Analysis

ERIC Educational Resources Information Center

Kaosa-ard, Chanapat; Erawan, Waraporn; Damrongpanit, Suntonrapot; Suksawang, Poonpong

2015-01-01

The researcher applied latent profile analysis to study the difference of the students' mathematical process skill. These skills are problem solving skills, reasoning skills, communication and presentation skills, connection knowledge skills, and creativity skills. Samples were 2,485 seventh-grade students obtained from Multi-stage Random…

Use of Words and Visuals in Modelling Context of Annual Plant

ERIC Educational Resources Information Center

Park, Jungeun; DiNapoli, Joseph; Mixell, Robert A.; Flores, Alfinio

2017-01-01

This study looks at the various verbal and non-verbal representations used in a process of modelling the number of annual plants over time. Analysis focuses on how various representations such as words, diagrams, letters and mathematical equations evolve in the mathematization process of the modelling context. Our results show that (1) visual…

Tablets and Applications to Tell Mathematics' History in High School

ERIC Educational Resources Information Center

Dias, Eduardo Jesus; Araujo, Carlos Fernando, Jr.; Ota, Marcos Andrei

2017-01-01

In this article, we suggest that the history in Mathematics Education combined with mobile technology, can provide analysis of concepts, theories and significant logical structures in the process of teaching and learning of Mathematics, as the main objective of this study is to analyze the students' motivation and learning using tablets in the…

Growing Mathematical Understanding through Collective Image Making, Collective Image Having, and Collective Property Noticing

ERIC Educational Resources Information Center

Martin, Lyndon C.; Towers, Jo

2015-01-01

In the research reported in this paper, we develop a theoretical perspective to describe and account for the growth of collective mathematical understanding. We discuss collective processes in mathematics, drawing in particular on theoretical work in the domains of improvisational jazz and theatre. Using examples of data from a study of elementary…

Creative and Algorithmic Mathematical Reasoning: Effects of Transfer-Appropriate Processing and Effortful Struggle

ERIC Educational Resources Information Center

Jonsson, Bert; Kulaksiz, Yagmur C.; Lithner, Johan

2016-01-01

Two separate studies, Jonsson et al. ("J. Math Behav." 2014;36: 20-32) and Karlsson Wirebring et al. ("Trends Neurosci Educ." 2015;4(1-2):6-14), showed that learning mathematics using creative mathematical reasoning and constructing their own solution methods can be more efficient than if students use algorithmic reasoning and…

Meta Didactic-Mathematical Knowledge of Teachers: Criteria for the Reflection and Assessment on Teaching Practice

ERIC Educational Resources Information Center

Breda, Adriana; Pino-Fan, Luis Roberto; Font, Vicenç

2017-01-01

The objective of this study is to demonstrate that the criteria of didactical suitability, proposed by the theoretical framework known as the Onto-Semiotic Approach (OSA) of mathematical knowledge and instruction, are powerful tools for organizing the reflection and assessment of instruction processes carried out by mathematics teachers. To this…

Interest in Mathematics = Interest in Mathematics? What General Measures of Interest Reflect When the Object of Interest Changes

ERIC Educational Resources Information Center

Ufer, Stefan; Rach, Stefanie; Kosiol, Timo

2017-01-01

Students' motivational characteristics, e.g., subject-related interest, are considered important predictors for successful learning processes. However, few empirical studies provide evidence for the assumed chain of effects between high interest and high achievement in mathematics. One reason for this result might be that the applied measures of…

Models of Individual Trajectories in Computer-Assisted Instruction for Deaf Students. Technical Report No. 214.

ERIC Educational Resources Information Center

Suppes, P.; And Others

From some simple and schematic assumptions about information processing, a stochastic differential equation is derived for the motion of a student through a computer-assisted elementary mathematics curriculum. The mathematics strands curriculum of the Institute for Mathematical Studies in the Social Sciences is used to test: (1) the theory and (2)…

An Example of Using History of Mathematics in Classes

ERIC Educational Resources Information Center

Goktepe, Sevda; Ozdemir, Ahmet Sukru

2013-01-01

In recent years, the topic of integrating history to mathematics lessons in teaching-learning processes has been frequently discussed among researchers. The main aim of this study is to present an example activity which enriched with history of mathematics and to take the views of students about teaching course in this way. In addition, to create…

The Impacts of a Service-Learning Experience on Pre-Service Mathematics Teachers

ERIC Educational Resources Information Center

Lee, Kyong-Hee; Statham, Anne

2010-01-01

This study examines the benefits that can be achieved by pre-service teachers tutoring mathematics in after school programs. Analysis of student journal entries show enhanced ability to meet National Council of Teachers of Mathematics' (NCTM) process standards and methods of assessment, as well as greater awareness of the need to teach to…

How Long is my Toilet Roll?--A Simple Exercise in Mathematical Modelling

ERIC Educational Resources Information Center

Johnston, Peter R.

2013-01-01

The simple question of how much paper is left on my toilet roll is studied from a mathematical modelling perspective. As is typical with applied mathematics, models of increasing complexity are introduced and solved. Solutions produced at each step are compared with the solution from the previous step. This process exposes students to the typical…

Designing PISA-Like Mathematics Tasks In Indonesia: Experiences and Challenges

NASA Astrophysics Data System (ADS)

Zulkardi, Z.; Kohar, A. W.

2018-01-01

The insignificant improvement of Indonesian students in PISA mathematics survey triggered researchers in Indonesia to develop PISA-like mathematics tasks. Some development studies have been conducted to produce valid and practical PISA-like problems that potentially effect on improving students’ mathematical literacy. This article describes the experiences of Indonesian task designers in developing PISA-like mathematics tasks as well as the potential future studies regarding to mathematical literacy as challenges for policy makers, researchers, and practitioners to improve students’ mathematical literacy in Indonesia. The results of this research indicate the task designers to consider domains of PISA like: context, mathematical content, and process as the first profiles of their missions. Our analysis shows that the designers mostly experienced difficulties regarding to the authenticity of context use and language structure. Interestingly, many of them used a variety of local wisdom in Indonesia as contexts for designing PISA-like tasks. In addition, the products developed were reported to be potentially effects on students’ interest and elicit students’ mathematical competencies as mentioned in PISA framework. Finally, this paper discusses future studies such as issues in bringing PISA task into an instructional practice.

Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills.

PubMed

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-09-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Relationships between school support, school facilities, ICT culture and mathematics teachers' attitudes towards ICT in teaching and learning

NASA Astrophysics Data System (ADS)

Ayub, Ahmad Fauzi Mohd; Bakar, Kamariah Abu; Ismail, Rohayati

2012-05-01

Information communication Technology (ICT) has been a major influence in the Malaysian Education System, especially in the teaching of mathematics. Since 2003, the Malaysian Ministry of Education has provided incentives to mathematics teacher to motivate them to use ICT using English as the medium of instruction, during the teaching and learning process. However, there are barriers that prevented mathematics teachers from using ICT in the classrooms. This study is to determine factors that influenced the attitudes of Malaysian Mathematic Teachers in integrating ICT in their teaching and learning. One hundred ninety one mathematics teachers were randomly selected for the purpose of this study. The three factors investigated were school support, school facilities and school culture which had been selected to be correlated with teachers' attitudes towards integrating ICT in the teaching and learning of mathematics. Findings showed that significant positive relationships existed between teachers' attitudes toward integrating ICT in the teaching and learning and school support, school facilities and ICT culture and This finding indicated that, in order to develop teachers' attitudes in using ICT during their teaching and learning process, they needed support from the school principals and also their colleagues. Apart from that, school facilities and also ICT culture were also found to be essential.

Mathematical Modeling of Thermofrictional Milling Process Using ANSYS WB Software

NASA Astrophysics Data System (ADS)

Sherov, K. T.; Sikhimbayev, M. R.; Sherov, A. K.; Donenbayev, B. S.; Rakishev, A. K.; Mazdubai, A. B.; Musayev, M. M.; Abeuova, A. M.

2017-06-01

This article presents ANSYS WB-based mathematical modelling of the thermofrictional milling process, which allowed studying the dynamics of thermal and physical processes occurring during the processing. The technique used also allows determination of the optimal cutting conditions of thermofrictional milling for processing various materials, in particular steel 40CN2MA, 30CGSA, 45, 3sp. In our study, from among a number of existing models of cutting fracture, we chose the criterion first proposed by prof. V. L. Kolmogorov. In order to increase the calculations performance, a mathematical model was proposed, that used only two objects: a parallelepiped-shaped workpiece and a cutting insert in the form of a pentagonal prism. In addition, the work takes into account the friction coefficient between a cutting insert and a workpiece taken equal to 0.4 mm. To determine the temperature in the subcontact layer of the workpiece, we introduced the coordinates of nine characteristic points with the same interval in the local coordinate system. As a result, the temperature values were obtained for different materials at the studied points during the cutter speed change. The research results showed the possibility of controlling thermal processes during processing by choosing the optimum cutting modes.

Choice of mathematical models for technological process of glass rod drawing

NASA Astrophysics Data System (ADS)

Alekseeva, L. B.

2017-10-01

The technological process of drawing glass rods (light guides) is considered. Automated control of the drawing process is reduced to the process of making decisions to ensure a given quality. The drawing process is considered as a control object, including the drawing device (control device) and the optical fiber forming zone (control object). To study the processes occurring in the formation zone, mathematical models are proposed, based on the continuum mechanics basics. To assess the influence of disturbances, a transfer function is obtained from the basis of the wave equation. Obtaining the regression equation also adequately describes the drawing process.

Investigating middle school students’ difficulties in mathematical literacy problems level 1 and 2

NASA Astrophysics Data System (ADS)

Setiawati, S.; Herman, T.; Jupri, A.

2017-11-01

The background of this study is the lack of mathematical literacy skills of students. The proficiency of students’ mathematical literacy skills based on the results of the PISA 2015 study shows that Indonesian students at the proficiency level 1. This fact gave rise to this study which aims to investigate middle school students’ difficulties in mathematical literacy problems level 1 and 2. Qualitative research was used in this study. An individual written test on mathematical literacy problems was administered, followed by interviews. The subjects of the study were 61 students grade VII in Bandung and 26 of them were interviewed afterward. Data analysis revealed that students’ error in performing arithmetic most frequently observed. Other observed difficulties concerned understanding about algebra concept, applying arithmetic operation in algebraic expressions, and interpreting symbols to represent the unknown. In solving mathematical literacy problems, students use their prior knowledge, although sometimes not relevant to the questions. Based on the results, we suggest that mathematics learning in contextual learning and which invites students to participate in the processes of understanding the concepts.

Comparative Study on the Senior Secondary School Mathematics Curricula Development in Ethiopia and Australia

ERIC Educational Resources Information Center

Meleta, Fufa E.; Zhang, Weizhong

2017-01-01

The main objective of this study is to compare the process of the senior secondary school mathematics curricula development in Ethiopia and Australia. The study was investigated qualitatively with document analysis and semi-structured interview research methods. The documents were collected from Federal Democratic Republic of Ethiopia Ministry of…

The Relationship between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties

ERIC Educational Resources Information Center

Swanson, H. Lee; Beebe-Frankenberger, Margaret

2004-01-01

This study identified cognitive processes that underlie individual differences in working memory (WM) and mathematical problem-solution accuracy in elementary school children at risk and not at risk for serious math difficulties (SMD). A battery of tests was administered that assessed problem solving, achievement, and cognitive processing in…

Pedagogical Affection in Didactics of Mathematics--Amazonas Region from the Phenomenology Perspective

ERIC Educational Resources Information Center

Zumaeta Arista, Segundo; Fuster Guillen, Doris; Ocaña Fernández, Yolvi

2018-01-01

This research work analyzed the experiences lived in the didactics of the mathematics by the teachers in the Amazonas region, whose emergent significance was the pedagogical affection in teaching understood as a process whereby two or more people interact socially, one of the passions of the mood. The study was conducted using the process of the…

Exploring Effects of High School Students' Mathematical Processing Skills and Conceptual Understanding of Chemical Concepts on Algorithmic Problem Solving

ERIC Educational Resources Information Center

Gultepe, Nejla; Yalcin Celik, Ayse; Kilic, Ziya

2013-01-01

The purpose of the study was to examine the effects of students' conceptual understanding of chemical concepts and mathematical processing skills on algorithmic problem-solving skills. The sample (N = 554) included grades 9, 10, and 11 students in Turkey. Data were collected using the instrument "MPC Test" and with interviews. The MPC…

Assessment of the Assessment Tool: Analysis of Items in a Non-MCQ Mathematics Exam

ERIC Educational Resources Information Center

Khoshaim, Heba Bakr; Rashid, Saima

2016-01-01

Assessment is one of the vital steps in the teaching and learning process. The reported action research examines the effectiveness of an assessment process and inspects the validity of exam questions used for the assessment purpose. The instructors of a college-level mathematics course studied questions used in the final exams during the academic…

How to build a course in mathematical-biological modeling: content and processes for knowledge and skill.

PubMed

Hoskinson, Anne-Marie

2010-01-01

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments.

Development and Evaluation of a Case-Based Digital Learning Tool about Children's Mathematical Thinking for Elementary School Teachers (L-TEST)

ERIC Educational Resources Information Center

Olkun, Sinan; Altun, Arif; Deryakulu, Deniz

2009-01-01

It is important for teachers of mathematics to know how pupils react to certain mathematical situations and what these reactions imply, in order to design more effective instructional environments based on their learning needs. This study reports the development processes of a digital learning tool (Learning Tool for Elementary School Teachers…

Listening to Early Career Teachers: How Can Elementary Mathematics Methods Courses Better Prepare Them to Utilize Standards-Based Practices in Their Classrooms?

ERIC Educational Resources Information Center

Coester, Lee Anne

2010-01-01

This study was designed to gather input from early career elementary teachers with the goal of finding ways to improve elementary mathematics methods courses. Multiple areas were explored including the degree to which respondents' elementary mathematics methods course focused on the NCTM Process Standards, the teachers' current standards-based…

Structure and Maintenance of a Mathematical Creative Lesson as a Mean of Pupils' Meta-Subject Results Achievement

ERIC Educational Resources Information Center

Gorev, Pavel M.; Aydar M. Kalimullin

2017-01-01

The purpose of the research is to study and change the structure of a mathematical lesson to improve quality of pupils' mathematical training and design mechanisms of inclusion the systems of open type tasks in educational process considering specifics of pupils' creative personality development. The leading method is modeling of a mathematical…

Using Mental Imagery Processes for Teaching and Research in Mathematics and Computer Science

ERIC Educational Resources Information Center

Arnoux, Pierre; Finkel, Alain

2010-01-01

The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We…

Teachers' Use of a Pedagogical Framework for Improvement in Mathematics Teaching: Case Studies from YuMi Deadly Maths

ERIC Educational Resources Information Center

Carter, Merilyn; Cooper, Tom; Anderson, Robyn

2016-01-01

This paper describes the pedagogical framework used by YuMi Deadly Maths, a school change process used to improve mathematics teaching and thus enhance employment and life chances for socially disadvantaged students. The framework, called the RAMR cycle, is capable of being used by mathematics teachers for planning and delivering lessons and units…

A Case Study Using CRA to Teach Students with Disabilities to Count Using Flexible Numbers: Applying Skip Counting to Multiplication

ERIC Educational Resources Information Center

Gibbs, Anna S.; Hinton, Vanessa M.; Flores, Margaret M.

2018-01-01

Children who struggle in mathematics have a limited understanding of the foundational processes of mathematics. A lack of conceptual understanding causes students to fall behind as they progress through the core curriculum. Children at high risk for developing mathematics disabilities fail to gain numeracy knowledge. The purpose of this case study…

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers.

PubMed

Cui, Jiaxin; Zhang, Yiyun; Cheng, Dazhi; Li, Dawei; Zhou, Xinlin

2017-01-01

Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation.

Middle School Mathematics Teachers' Reflection Activities in the Context of Lesson Study

ERIC Educational Resources Information Center

Bozkurt, Erhan; Yetkin-Özdemir, Iffet Elif

2018-01-01

The aim of this case study is to define reflection activities of a lesson study group that consisted of three middle school mathematics teachers in Usak, Turkey. In the process, the participants worked in collaboration for about 5 months to implement three study lesson practices. The data were collected through observations in the reflection…

A Case Study of Markdale High School's Implementation of Heterogeneously-Grouped Classes in English, Mathematics, Science, and Social Studies

ERIC Educational Resources Information Center

Pierre-Louis, Fred

2010-01-01

The purpose of this study was to describe Markdale High School's change from separate college preparatory and general level classes to heterogeneously-grouped classes in English, mathematics, science, and social studies, with particular emphasis on the principal's leadership style, change process, and teacher concerns (Hall & Hord, 2006)…

Nature and origins of mathematics difficulties in very preterm children: a different etiology than developmental dyscalculia.

PubMed

Simms, Victoria; Gilmore, Camilla; Cragg, Lucy; Clayton, Sarah; Marlow, Neil; Johnson, Samantha

2015-02-01

Children born very preterm (<32 wk) are at high risk for mathematics learning difficulties that are out of proportion to other academic and cognitive deficits. However, the etiology of mathematics difficulties in very preterm children is unknown. We sought to identify the nature and origins of preterm children's mathematics difficulties. One hundred and fifteen very preterm children aged 8-10 y were assessed in school with a control group of 77 term-born classmates. Achievement in mathematics, working memory, visuospatial processing, inhibition, and processing speed were assessed using standardized tests. Numerical representations and specific mathematics skills were assessed using experimental tests. Very preterm children had significantly poorer mathematics achievement, working memory, and visuospatial skills than term-born controls. Although preterm children had poorer performance in specific mathematics skills, there was no evidence of imprecise numerical representations. Difficulties in mathematics were associated with deficits in visuospatial processing and working memory. Mathematics difficulties in very preterm children are associated with deficits in working memory and visuospatial processing not numerical representations. Thus, very preterm children's mathematics difficulties are different in nature from those of children with developmental dyscalculia. Interventions targeting general cognitive problems, rather than numerical representations, may improve very preterm children's mathematics achievement.

Theoretical Framework of Researcher Knowledge Development in Mathematics Education

ERIC Educational Resources Information Center

Kontorovich, Igor'

2016-01-01

The goal of this paper is to present a framework of researcher knowledge development in conducting a study in mathematics education. The key components of the framework are: knowledge germane to conducting a particular study, processes of knowledge accumulation, and catalyzing filters that influence a researcher's decision making. The components…

Problem-Solving Studies in Mathematics. Monograph Series.

ERIC Educational Resources Information Center

Harvey, John G., Ed.; Romberg, Thomas A., Ed.

This monograph focuses on educational research on the processes and natures of problem-solving activities in mathematics. The first chapter presents an overview to both the field and the document itself. All of the studies reported reflect interrelated investigations carried out at the University of Madison-Wisconsin, as partial fulfillments of…

Correlates of Mathematics Anxiety.

ERIC Educational Resources Information Center

McCoy, Leah P.

Learning is a complex operation that involves a several factors. In studying the learning process, both the characteristics of the learner and the conditions of instruction must be considered. This study examined some of the factors that may influence the learning of mathematics. In particular, it sought to identify relationships among mathematics…

"Attrition Processes Out of Mathematics for Undergraduate Students." Attrition from Mathematics as a Social Process. Final Report.

ERIC Educational Resources Information Center

Maines, David R.; And Others

Investigated were those long-term processes which contribute to high rates of attrition for women out of mathematics. It is based on the contention that university students drop out of mathematics as a consequence of prior socialization, educational career contingencies, and goal commitment and career aspirations, with the mix of these factors…

Mathematics anxiety affects counting but not subitizing during visual enumeration.

PubMed

Maloney, Erin A; Risko, Evan F; Ansari, Daniel; Fugelsang, Jonathan

2010-02-01

Individuals with mathematics anxiety have been found to differ from their non-anxious peers on measures of higher-level mathematical processes, but not simple arithmetic. The current paper examines differences between mathematics anxious and non-mathematics anxious individuals in more basic numerical processing using a visual enumeration task. This task allows for the assessment of two systems of basic number processing: subitizing and counting. Mathematics anxious individuals, relative to non-mathematics anxious individuals, showed a deficit in the counting but not in the subitizing range. Furthermore, working memory was found to mediate this group difference. These findings demonstrate that the problems associated with mathematics anxiety exist at a level more basic than would be predicted from the extant literature. Copyright 2009 Elsevier B.V. All rights reserved.

Mastering algebra retrains the visual system to perceive hierarchical structure in equations.

PubMed

Marghetis, Tyler; Landy, David; Goldstone, Robert L

2016-01-01

Formal mathematics is a paragon of abstractness. It thus seems natural to assume that the mathematical expert should rely more on symbolic or conceptual processes, and less on perception and action. We argue instead that mathematical proficiency relies on perceptual systems that have been retrained to implement mathematical skills. Specifically, we investigated whether the visual system-in particular, object-based attention-is retrained so that parsing algebraic expressions and evaluating algebraic validity are accomplished by visual processing. Object-based attention occurs when the visual system organizes the world into discrete objects, which then guide the deployment of attention. One classic signature of object-based attention is better perceptual discrimination within, rather than between, visual objects. The current study reports that object-based attention occurs not only for simple shapes but also for symbolic mathematical elements within algebraic expressions-but only among individuals who have mastered the hierarchical syntax of algebra. Moreover, among these individuals, increased object-based attention within algebraic expressions is associated with a better ability to evaluate algebraic validity. These results suggest that, in mastering the rules of algebra, people retrain their visual system to represent and evaluate abstract mathematical structure. We thus argue that algebraic expertise involves the regimentation and reuse of evolutionarily ancient perceptual processes. Our findings implicate the visual system as central to learning and reasoning in mathematics, leading us to favor educational approaches to mathematics and related STEM fields that encourage students to adapt, not abandon, their use of perception.

Cognition in Children's Mathematical Processing: Bringing Psychology to the Classroom

ERIC Educational Resources Information Center

Witt, Marcus

2010-01-01

Introduction: The cognitive processes that underpin successful mathematical processing in children have been well researched by experimental psychologists, but are not widely understood among teachers of primary mathematics. This is a shame, as an understanding of these cognitive processes could be highly useful to practitioners. This paper…

Indicators that influence prospective mathematics teachers representational and reasoning abilities

NASA Astrophysics Data System (ADS)

Darta; Saputra, J.

2018-01-01

Representational and mathematical reasoning ability are very important ability as basic in mathematics learning process. The 2013 curriculum suggests that the use of a scientific approach emphasizes higher order thinking skills. Therefore, a scientific approach is required in mathematics learning to improve ability of representation and mathematical reasoning. The objectives of this research are: (1) to analyze representational and reasoning abilities, (2) to analyze indicators affecting the ability of representation and mathematical reasoning, (3) to analyze scientific approaches that can improve the ability of representation and mathematical reasoning. The subject of this research is the students of mathematics prospective teachers in the first semester at Private Higher Education of Bandung City. The research method of this research was descriptive analysis. The research data were collected using reasoning and representation tests on sixty-one students. Data processing was done by descriptive analysis specified based on the indicators of representation ability and mathematical reasoning that influenced it. The results of this first-year study showed that students still had many weaknesses in reasoning and mathematical representation that were influenced by the ability to understand the indicators of both capabilities. After observing the results of the first-year research, then in the second and third year, the development of teaching materials with a scientific approach in accordance with the needs of prospective students was planned.

The kinds of questions asked by novice teachers in learning mathematics

NASA Astrophysics Data System (ADS)

Zahra, L.; Kusmayadi, T. A.; Usodo, B.

2018-05-01

This study describes the kinds of questions asked by novice teachers during mathematics learning process in senior high school. This study used descriptive analysis. The subjects of this study were two novice teachers who teach mathematics in 10th grade. The result showed that the frequently asked questions by novice teachers based on the objective were compliance questions, rethorical questions and sometimes prompting questions and probing questions. The frequently questions asked by novice teacher based on the cognitive process dimension of Revised Bloom’s Taxonomy were questions of remembering, questions of understanding, questions of applying, questions of analyzing and questions of evaluating. The novice teachers asked the routine questions which had same thinking level. The question with the highest level of thinking did not asked by the novice teachers.

Oki-Doku: Number Puzzles

ERIC Educational Resources Information Center

Gomez, Cristina; Novak, Dani

2014-01-01

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) emphasize the Standards for Mathematical Practice (SMP) that describe processes and proficiencies included in the NCTM Process Standards (NCTM 2000) and in the Strands for Mathematical Proficiency (NRC 2001). The development of these mathematical practices should happen in…

The Mathematics Textbook at Tertiary Level as Curriculum Material--Exploring the Teacher's Decision-Making Process

ERIC Educational Resources Information Center

Randahl, Mira

2016-01-01

This paper reports on a study about how the mathematics textbook was perceived and used by the teacher in the context of a calculus part of a basic mathematics course for first-year engineering students. The focus was on the teacher's choices and the use of definitions, examples and exercises in a sequence of lectures introducing the derivative…

The Interactional Accomplishment of Not Knowing in Elementary School Science and Mathematics: Implications for Classroom Performance Assessment Practices

ERIC Educational Resources Information Center

Reis, Giuliano; Barwell, Richard

2013-01-01

The day-to-day business of being a science or mathematics teacher involves the continuous assessment of students. This, in turn, is an inherently discursive process. The aim of the present study is to examine some of the specific discursive practices through which science and mathematics knowing is jointly produced through classroom interaction.…

Developing Indicators of Classroom Practice to Evaluate the Impact of District Mathematics Reform Initiative: A Generalizability Analysis

ERIC Educational Resources Information Center

Newton, Xiaoxia A.

2010-01-01

This paper reported results from a generalizability study that examined the process of developing classroom practice indicators used to evaluate the impact of a school district's mathematics reform initiative. The study utilized classroom observational data from 32 second, fourth, eighth, and tenth grade teachers. The study addresses important…

Enhancing Parent Involvement in NC-CCSS for K-2 Mathematics

NASA Astrophysics Data System (ADS)

Johnson, D.

2014-12-01

Key Terms:Parent Involvement, Common Core State Standards, Homework, K - 2 Mathematics In this study, the 2014 REU math team developed and provided a workshop that assisted parents in understanding the North Carolina Common Core State Standards for K-2 Mathematics to assist with student homework assignments. Parent involvement is defined as parent participating in the educational processes and experiences of their children. A chi-square analysis was used to analyze data collected from the pre survey and the post survey administered to participants in the workshop. The study revealed all of the individual components of parent involvement were positively and significantly related to educational goals. The study identified various aspects of parent involvement that yielded statistically significant results in affirming that parent involvement attributed to urban student achievement. These findings were particularly helpful for indicating which kinds of parent involvement influenced academic success. Most notably, parent expectations and styles demonstrated a strong relationship with scholastic outcomes. Parent expectations and styles created an educationally oriented ambience that established an understanding of the certain level of support the child needed to succeed academically. The REU mathematics team focused on three essential questions in this study: (1) What practices will increase parent awareness of K-2 NC-CCSS for mathematics at P. W. Moore Elementary School? (2) What methods can be used to strengthen parent skills in assisting with mathematics homework assignments at P. W. Moore Elementary School? (3) What actions can be taken to motivate parent involvement in the school improvement process focusing on mathematics at P. W. Moore Elementary School?

Cognitive and Neural Correlates of Mathematical Giftedness in Adults and Children: A Review

PubMed Central

Myers, Timothy; Carey, Emma; Szűcs, Dénes

2017-01-01

Most mathematical cognition research has focused on understanding normal adult function and child development as well as mildly and moderately impaired mathematical skill, often labeled developmental dyscalculia and/or mathematical learning disability. In contrast, much less research is available on cognitive and neural correlates of gifted/excellent mathematical knowledge in adults and children. In order to facilitate further inquiry into this area, here we review 40 available studies, which examine the cognitive and neural basis of gifted mathematics. Studies associated a large number of cognitive factors with gifted mathematics, with spatial processing and working memory being the most frequently identified contributors. However, the current literature suffers from low statistical power, which most probably contributes to variability across findings. Other major shortcomings include failing to establish domain and stimulus specificity of findings, suggesting causation without sufficient evidence and the frequent use of invalid backward inference in neuro-imaging studies. Future studies must increase statistical power and neuro-imaging studies must rely on supporting behavioral data when interpreting findings. Studies should investigate the factors shown to correlate with math giftedness in a more specific manner and determine exactly how individual factors may contribute to gifted math ability. PMID:29118725

Mathematical modelling in developmental biology.

PubMed

Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

2013-06-01

In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

Intentional and automatic processing of numerical information in mathematical anxiety: testing the influence of emotional priming.

PubMed

Ashkenazi, Sarit

2018-02-05

Current theoretical approaches suggest that mathematical anxiety (MA) manifests itself as a weakness in quantity manipulations. This study is the first to examine automatic versus intentional processing of numerical information using the numerical Stroop paradigm in participants with high MA. To manipulate anxiety levels, we combined the numerical Stroop task with an affective priming paradigm. We took a group of college students with high MA and compared their performance to a group of participants with low MA. Under low anxiety conditions (neutral priming), participants with high MA showed relatively intact number processing abilities. However, under high anxiety conditions (mathematical priming), participants with high MA showed (1) higher processing of the non-numerical irrelevant information, which aligns with the theoretical view regarding deficits in selective attention in anxiety and (2) an abnormal numerical distance effect. These results demonstrate that abnormal, basic numerical processing in MA is context related.

MAESTRO: Mathematics and Earth Science Teachers' Resource Organization

NASA Astrophysics Data System (ADS)

Courtier, A. M.; Pyle, E. J.; Fichter, L.; Lucas, S.; Jackson, A.

2013-12-01

The Mathematics and Earth Science Teachers' Resource Organization (MAESTRO) partnership between James Madison University and Harrisonburg City and Page County Public Schools, funded through NSF-GEO. The partnership aims to transform mathematics and Earth science instruction in middle and high schools by developing an integrated mathematics and Earth systems science approach to instruction. This curricular integration is intended to enhance the mathematical skills and confidence of students through concrete, Earth systems-based examples, while increasing the relevance and rigor of Earth science instruction via quantification and mathematical modeling of Earth system phenomena. MAESTRO draws heavily from the Earth Science Literacy Initiative (2009) and is informed by criterion-level standardized test performance data in both mathematics and Earth science. The project has involved two summer professional development workshops, academic year Lesson Study (structured teacher observation and reflection), and will incorporate site-based case studies with direct student involvement. Participating teachers include Grade 6 Science and Mathematics teachers, and Grade 9 Earth Science and Algebra teachers. It is anticipated that the proposed integration across grade bands will first strengthen students' interests in mathematics and science (a problem in middle school) and subsequently reinforce the relevance of mathematics and other sciences (a problem in high school), both in support of Earth systems literacy. MAESTRO's approach to the integration of math and science focuses on using box models to emphasize the interconnections among the geo-, atmo-, bio-, and hydrospheres, and demonstrates the positive and negative feedback processes that connect their mutual evolution. Within this framework we explore specific relationships that can be described both qualitatively and mathematically, using mathematical operations appropriate for each grade level. Site-based case studies, developed in collaboration between teachers and JMU faculty members, provide a tangible, relevant setting in which students can apply and understand mathematical applications and scientific processes related to evolving Earth systems. Initial results from student questionnaires and teacher focus groups suggest that the anticipated impacts of MAESTRO on students are being realized, including increased valuing of mathematics and Earth science in society and transfer between mathematics and science courses. As a high percentage of students in the MAESTRO schools are of low socio-economic status, they also face the prospect of becoming first-generation college students, hopefully considering STEM academic pathways. MAESTRO will drive the development of challenging and engaging instruction designed to draw a larger pool of students into STEM career pathways.

Mathematics education for social justice

NASA Astrophysics Data System (ADS)

Suhendra

2016-02-01

Mathematics often perceived as a difficult subject with many students failing to understand why they learn mathematics. This situation has been further aggravated by the teaching and learning processes used, which is mechanistic without considering students' needs. The learning of mathematics tends to be just a compulsory subject, in which all students have to attend its classes. Social justice framework facilitates individuals or groups as a whole and provides equitable approaches to achieving equitable outcomes by recognising disadvantage. Applying social justice principles in educational context is related to how the teachers treat their students, dictates that all students the right to equal treatment regardless of their background and completed with applying social justice issues integrated with the content of the subject in order to internalise the principles of social justice simultaneously the concepts of the subject. The study examined the usefulness of implementing the social justice framework as a means of improving the quality of mathematics teaching in Indonesia involved four teacher-participants and their mathematics classes. The study used action research as the research methodology in which the teachers implemented and evaluated their use of social justice framework in their teaching. The data were collected using multiple research methods while analysis and interpretation of the data were carried out throughout the study. The findings of the study indicated that there were a number of challengesrelated to the implementation of the social justice framework. The findings also indicated that, the teachers were provided with a comprehensive guide that they could draw on to make decisions about how they could improve their lessons. The interactions among students and between the teachers and the students improved, they became more involved in teaching and learning process. Using social justice framework helped the teachers to make mathematics more relevant to students. This increased relevance led to increasing students' engagement in the teaching and learning process and becoming more accessible to all students. Additionally, the findings have the potential to make a contribution to those seeking to reform mathematics teaching in Indonesia. The results could inform policy makers and professional development providers about how social justice framework might contribute to the educational reform in Indonesia.

Investigation of the Bitumen Modification Process Regime Parameters Influence on Polymer-Bitumen Bonding Qualitative Indicators

NASA Astrophysics Data System (ADS)

Belyaev, P. S.; Mishchenko, S. V.; Belyaev, V. P.; Belousov, O. A.; Frolov, V. A.

2018-04-01

The objects of this study are petroleum road bitumen and polymeric bituminous binder for road surfaces obtained by polymer materials. The subject of the study is monitoring the polymer-bitumen binder quality changes as a result of varying the bitumen modification process. The purpose of the work is to identify the patterns of the modification process and build a mathematical model that provides the ability to calculate and select technological equipment. It is shown that the polymer-bitumen binder production with specified quality parameters can be ensured in apparatuses with agitators in turbulent mode without the colloidal mills use. Bitumen mix and modifying additives limiting indicators which can be used as restrictions in the form of mathematical model inequalities are defined. A mathematical model for the polymer-bitumen binder preparation has been developed and its adequacy has been confirmed.

Developing Fair Tests for Mathematics Curriculum Comparison Studies: The Role of Content Analyses

ERIC Educational Resources Information Center

Chavez, Oscar; Papick, Ira; Ross, Daniel J.; Grouws, Douglas A.

2011-01-01

This article describes the process of development of assessment instruments for a three-year longitudinal comparative study that focused on evaluating American high school students' mathematics learning from two distinct approaches to content organization: curriculum built around a sequence of three full-year courses (Algebra 1, Geometry, and…

Developing the Mathematics Learning Management Model for Improving Creative Thinking in Thailand

ERIC Educational Resources Information Center

Sriwongchai, Arunee; Jantharajit, Nirat; Chookhampaeng, Sumalee

2015-01-01

The study purposes were: 1) To study current states and problems of relevant secondary students in developing mathematics learning management model for improving creative thinking, 2) To evaluate the effectiveness of model about: a) efficiency of learning process, b) comparisons of pretest and posttest on creative thinking and achievement of…

Developing an Assessment Instrument to Measure Early Elementary Teachers' Mathematical Knowledge for Teaching

ERIC Educational Resources Information Center

Schoen, Robert C.; Bray, Wendy; Wolfe, Christopher; Tazaz, Amanda M.; Nielsen, Lynne

2017-01-01

This study reports on the development and field study of K-TEEM, a web-based assessment instrument designed to measure mathematical knowledge for teaching (MKT) at the early elementary level. The development process involved alignment with early elementary curriculum standards, expert review of items and scoring criteria, cognitive interviews with…

Evaluation of Turkish and Mathematics Curricula According to Value-Based Evaluation Model

ERIC Educational Resources Information Center

Duman, Serap Nur; Akbas, Oktay

2017-01-01

This study evaluated secondary school seventh-grade Turkish and mathematics programs using the Context-Input-Process-Product Evaluation Model based on student, teacher, and inspector views. The convergent parallel mixed method design was used in the study. Student values were identified using the scales for socio-level identification, traditional…

Accommodation in the Formal World of Mathematical Thinking

ERIC Educational Resources Information Center

Stewart, Sepideh; Schmidt, Ralf

2017-01-01

In this study, we examined a mathematician and one of his students' teaching journals and thought processes concurrently as the class was moving towards the proof of the Fundamental Theorem of Galois Theory. We employed Tall's framework of three worlds of mathematical thinking as well as Piaget's notion of accommodation to theoretically study the…

Designing a Bridging Discourse: Re-Mediation of a Mathematical Learning Disability

ERIC Educational Resources Information Center

Lewis, Katherine E.

2017-01-01

Students with disabilities present a unique instructional design challenge. These students often have qualitatively different ways of processing information, meaning that standard instructional approaches may not be effective. In this study I present a case study of a student with a mathematical learning disability for whom standard instruction on…

Friction-Stir Welding and Mathematical Modeling

NASA Technical Reports Server (NTRS)

Rostant, Victor D.

1999-01-01

The friction-stir welding process is a remarkable way for making butt and lap joints in aluminum alloys. This process operates by passing a rotating tool between two closely butted plates. Through this process it generates a lot of heat and heated material is stirred from both sides of the plates in which the outcome will one high quality weld. My research has been done to study the FSW through mathematical modeling, and using modeling to better understand what take place during the friction-stir weld.

Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test).

PubMed

Brankaer, Carmen; Ghesquière, Pol; De Smedt, Bert

2017-08-01

The ability to compare symbolic numerical magnitudes correlates with children's concurrent and future mathematics achievement. We developed and evaluated a quick timed paper-and-pencil measure that can easily be used, for example in large-scale research, in which children have to cross out the numerically larger of two Arabic one- and two-digit numbers (SYMP Test). We investigated performance on this test in 1,588 primary school children (Grades 1-6) and examined in each grade its associations with mathematics achievement. The SYMP Test had satisfactory test-retest reliability. The SYMP Test showed significant and stable correlations with mathematics achievement for both one-digit and two-digit comparison, across all grades. This replicates the previously observed association between symbolic numerical magnitude processing and mathematics achievement, but extends it by showing that the association is observed in all grades in primary education and occurs for single- as well as multi-digit processing. Children with mathematical learning difficulties performed significantly lower on one-digit comparison and two-digit comparison in all grades. This all suggests satisfactory construct and criterion-related validity of the SYMP Test, which can be used in research, when performing large-scale (intervention) studies, and by practitioners, as screening measure to identify children at risk for mathematical difficulties or dyscalculia.

Interactivity of Visual Mathematical Representations: Factors Affecting Learning and Cognitive Processes

ERIC Educational Resources Information Center

Sedig, Kamran; Liang, Hai-Ning

2006-01-01

Computer-based mathematical cognitive tools (MCTs) are a category of external aids intended to support and enhance learning and cognitive processes of learners. MCTs often contain interactive visual mathematical representations (VMRs), where VMRs are graphical representations that encode properties and relationships of mathematical concepts. In…

Third International Mathematics and Science Study 1999 Video Study Technical Report: Volume 2--Science. Technical Report. NCES 2011-049

ERIC Educational Resources Information Center

Garnier, Helen E.; Lemmens, Meike; Druker, Stephen L.; Roth, Kathleen J.

2011-01-01

This second volume of the Third International Mathematics and Science Study (TIMSS) 1999 Video Study Technical Report focuses on every aspect of the planning, implementation, processing, analysis, and reporting of the science components of the TIMSS 1999 Video Study. The report is intended to serve as a record of the actions and documentation of…

Mathematical disposition of junior high school students viewed from learning styles

NASA Astrophysics Data System (ADS)

Putra, Arief Karunia; Budiyono, Slamet, Isnandar

2017-08-01

The relevance of this study is the growth of character values for students in Indonesia. Mathematics is a subject that builds the character values for students. It can be seen from the students' confidence in answering mathematics problems, their persistent and resilience in mathematics task. In addition, students have a curiosity in mathematics and appreciate the usefulness of mathematics. In mathematics, it is called a mathematical disposition. One of the factors that can affect students' mathematical disposition is learning style. Each student has a dominant learning style. Three of the most popular ones are visual, auditory, and kinesthetic. The most important uses of learning styles is that it makes it easy for teachers to incorporate them into their teaching. The purpose of this study was to determine which one that gives better mathematical dispositions among students with learning styles of visual, auditory, or kinesthetic. The subjects were 150 students in Sleman regency. Data obtained through questionnaires. Based on data analysis that has been done with benchmark assessment method, it can be concluded that students with visual learning style has a mathematical disposition better than students with auditory and kinesthetic learning styles, while students with kinesthetic learning style has a mathematical disposition better than students with auditory learning style. These results can be used as a reference for students with individual learning styles to improve the mathematical positive disposition in the learning process of mathematics.

The motivation of lifelong mathematics learning

NASA Astrophysics Data System (ADS)

Hashim Ali, Siti Aishah

2013-04-01

As adults, we have always learned throughout our life, but this learning is informal. Now, more career-switchers and career-upgraders who are joining universities for further training are becoming the major group of adult learners. This current situation requires formal education in courses with controlled output. Hence, lifelong learning is seen as a necessity and an opportunity for these adult learners. One characteristic of adult education is that the learners tend to bring with them life experience from their past, especially when learning mathematics. Most of them associate mathematics with the school subjects and unable to recognize the mathematics in their daily practice as mathematics. They normally place a high value on learning mathematics because of its prominent role in their prospective careers, but their learning often requires overcoming personal experience and motivating themselves to learn mathematics again. This paper reports on the study conducted on a group of adult learners currently pursuing their study. The aim of this study is to explore (i) the motivation of the adult learners continuing their study; and (ii) the perception and motivation of these learners in learning mathematics. This paper will take this into account when we discuss learners' perception and motivation to learning mathematics, as interrelated phenomena. Finding from this study will provide helpful insights in understanding the learning process and adaption of adult learners to formal education.

Mathematical skills in Prader-Willi Syndrome.

PubMed

Bertella, L; Girelli, L; Grugni, G; Marchi, S; Molinari, E; Semenza, C

2005-02-01

This paper investigates mathematical skills in Prader-Willi Syndrome (PWS), a pathological condition because of congenital alterations of chromosome pair 15. The following questions were addressed: (1) Are mathematical skills in PWS relatively more impaired with respect to other cognitive functions (as has been repeatedly but anecdotally reported)?; and (2) What is the nature of the mathematical impairment? The first study employed the Wechsler Adult Intelligence Scale (WAIS) and an extensive battery of cognitive tasks for which norms are known. Both batteries include a mathematical section. The second study used a theoretically motivated series of mathematical tasks specifically designed to individually assess the different cognitive components underlying mathematical skills. Mathematical skills were found to be the most impaired cognitive abilities together with short-term memory capacity. No specific mathematical domain was seen to be unaffected in PWS participants. The clearest deficits observed concern 'syntactic' processes in number transcoding, multiplication, number facts retrieval and calculation procedures. Failure of mathematical skills is the most distinctive feature in the cognitive profile of PWS. However, to determine whether this is indeed a specific pattern of performance related to PWS, results must be compared with those obtained with patients manifesting other genetic disorders.

The (Mathematical) Modeling Process in Biosciences.

PubMed

Torres, Nestor V; Santos, Guido

2015-01-01

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

Integrating to Learn and Learning to Integrate: A Case Study of an Online Master's Program on Science-Mathematics Integration for Middle School Teachers

ERIC Educational Resources Information Center

Lee, Mimi Miyoung; Chauvot, Jennifer; Plankis, Brian; Vowell, Julie; Culpepper, Shea

2011-01-01

iSMART (Integration of Science, Mathematics, and Reflective Teaching) Program is an online science and mathematics integrated graduate program for middle school teachers across the state of Texas. As part of a large design-based research project, this paper describes the initial stages of the design process of the iSMART program for its first…

The Effectiveness of the Mathematics, Engineering, Science Achievement (MESA) Program's Administrative and Policy-Making Processes. A Report to the Legislature in Response to Assembly Bill 610 (1985). Commission Report 89-4.

ERIC Educational Resources Information Center

California State Postsecondary Education Commission, Sacramento.

The Mathematics, Engineering, Science Achievement (MESA) Program was established in 1970 to increase the number of minority students in college programs. This paper reports the MESA administrative operations and policy-making processes. Part 1 summarizes the background of this study. Part 2 describes MESA's administrative operations and provides…

A Graph Theoretical Approach to Study the Organization of the Cortical Networks during Different Mathematical Tasks

PubMed Central

Klados, Manousos A.; Kanatsouli, Kassia; Antoniou, Ioannis; Babiloni, Fabio; Tsirka, Vassiliki; Bamidis, Panagiotis D.; Micheloyannis, Sifis

2013-01-01

The two core systems of mathematical processing (subitizing and retrieval) as well as their functionality are already known and published. In this study we have used graph theory to compare the brain network organization of these two core systems in the cortical layer during difficult calculations. We have examined separately all the EEG frequency bands in healthy young individuals and we found that the network organization at rest, as well as during mathematical tasks has the characteristics of Small World Networks for all the bands, which is the optimum organization required for efficient information processing. The different mathematical stimuli provoked changes in the graph parameters of different frequency bands, especially the low frequency bands. More specific, in Delta band the induced network increases it’s local and global efficiency during the transition from subitizing to retrieval system, while results suggest that difficult mathematics provoke networks with higher cliquish organization due to more specific demands. The network of the Theta band follows the same pattern as before, having high nodal and remote organization during difficult mathematics. Also the spatial distribution of the network’s weights revealed more prominent connections in frontoparietal regions, revealing the working memory load due to the engagement of the retrieval system. The cortical networks of the alpha brainwaves were also more efficient, both locally and globally, during difficult mathematics, while the fact that alpha’s network was more dense on the frontparietal regions as well, reveals the engagement of the retrieval system again. Concluding, this study gives more evidences regarding the interaction of the two core systems, exploiting the produced functional networks of the cerebral cortex, especially for the difficult mathematics. PMID:23990992

A Graph theoretical approach to study the organization of the cortical networks during different mathematical tasks.

PubMed

Klados, Manousos A; Kanatsouli, Kassia; Antoniou, Ioannis; Babiloni, Fabio; Tsirka, Vassiliki; Bamidis, Panagiotis D; Micheloyannis, Sifis

2013-01-01

The two core systems of mathematical processing (subitizing and retrieval) as well as their functionality are already known and published. In this study we have used graph theory to compare the brain network organization of these two core systems in the cortical layer during difficult calculations. We have examined separately all the EEG frequency bands in healthy young individuals and we found that the network organization at rest, as well as during mathematical tasks has the characteristics of Small World Networks for all the bands, which is the optimum organization required for efficient information processing. The different mathematical stimuli provoked changes in the graph parameters of different frequency bands, especially the low frequency bands. More specific, in Delta band the induced network increases it's local and global efficiency during the transition from subitizing to retrieval system, while results suggest that difficult mathematics provoke networks with higher cliquish organization due to more specific demands. The network of the Theta band follows the same pattern as before, having high nodal and remote organization during difficult mathematics. Also the spatial distribution of the network's weights revealed more prominent connections in frontoparietal regions, revealing the working memory load due to the engagement of the retrieval system. The cortical networks of the alpha brainwaves were also more efficient, both locally and globally, during difficult mathematics, while the fact that alpha's network was more dense on the frontparietal regions as well, reveals the engagement of the retrieval system again. Concluding, this study gives more evidences regarding the interaction of the two core systems, exploiting the produced functional networks of the cerebral cortex, especially for the difficult mathematics.

Taguchi method for partial differential equations with application in tumor growth.

PubMed

Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena

2014-01-01

The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

The effect of using Indonesian realistic mathematics education (PMRI) approach on the mathematics achievement amongst primary school students

NASA Astrophysics Data System (ADS)

Zubainur, Cut Morina; Veloo, Arsaythamby; Khalid, Rozalina

2015-05-01

This study aims to determine the effects of the Indonesian Realistic Mathematics Education (PMRI) in Aceh primary schools, Indonesia. Although a plethora of research evidence highlights significant outcomes of the incorporation PMRI in mathematics, its use in the teaching and learning process is limited. Total of 50 standard five students from public primary school participated in this study; 25 students in the experimental group and 25 in the control group. The teaching approaches varied between the groups. While the experimental group experienced the PMRI approach, the control group encountered the conventional teaching approach of chalk and talk. Data was collected at two points namely the pre-test and post-test that lasted for five weeks. The results showed significant differences in mathematics achievement among primary students. In addition, PMRI also creates an active learning environment in solving exercises, and discussions among students and teachers. This study provides evidence that learning mathematics with PMRI benefits primary school students.

Adding Structure to the Transition Process to Advanced Mathematical Activity

ERIC Educational Resources Information Center

Engelbrecht, Johann

2010-01-01

The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical…

Promoting Students' Self-Directed Learning Ability through Teaching Mathematics for Social Justice

ERIC Educational Resources Information Center

Voss, Richard; Rickards, Tony

2016-01-01

Mathematics is a subject which is often taught using abstract methods and processes. These methods by their very nature may for students alienate the relationship between Mathematics and real life situations. Further, these abstract methods and processes may disenfranchise students from becoming self-directed learners of Mathematics. A solution to…

On Mathematical Proving

NASA Astrophysics Data System (ADS)

Stefaneas, Petros; Vandoulakis, Ioannis M.

2015-12-01

This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a "loose" semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.

Self and Peer Assessment of Mathematical Processes

ERIC Educational Resources Information Center

Onion, Alice; Javaheri, Elnaz

2011-01-01

This article explores using Bowland assessment tasks and Nuffield Applying Mathematical Processes (AMP) activities as part of a scheme of work. The Bowland tasks and Nuffield AMP activities are designed to develop students' mathematical thinking; they are focused on key processes. Unfamiliar demands are made on the students and they are challenged…

Students' Reflections on Mathematics Homework Feedback

ERIC Educational Resources Information Center

Landers, Mara; Reinholz, Daniel

2015-01-01

Homework is considered an important aspect of learning mathematics, but little research has considered how students utilize feedback as part of the homework process. This mixed methods, quasi-experimental study examines how community college students in a developmental intermediate algebra course participated in a feedback reflection activity…

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers

PubMed Central

Cui, Jiaxin; Zhang, Yiyun; Cheng, Dazhi; Li, Dawei; Zhou, Xinlin

2017-01-01

Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation. PMID:28824513

The system-resonance approach in modeling genetic structures.

PubMed

Petoukhov, Sergey V

2016-01-01

The founder of the theory of resonance in structural chemistry Linus Pauling established the importance of resonance patterns in organization of living systems. Any living organism is a great chorus of coordinated oscillatory processes. From the formal point of view, biological organism is an oscillatory system with a great number of degrees of freedom. Such systems are studied in the theory of oscillations using matrix mathematics of their resonance characteristics. This study is devoted to a new approach for modeling genetically inherited structures and processes in living organisms using mathematical tools of the theory of resonances. This approach reveals hidden relationships in a number of genetic phenomena and gives rise to a new class of bio-mathematical models, which contribute to a convergence of biology with physics and informatics. In addition some relationships of molecular-genetic ensembles with mathematics of noise-immunity coding of information in modern communications technology are shown. Perspectives of applications of the phenomena of vibrational mechanics for modeling in biology are discussed. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Obtaining mathematical models for assessing efficiency of dust collectors using integrated system of analysis and data management STATISTICA Design of Experiments

NASA Astrophysics Data System (ADS)

Azarov, A. V.; Zhukova, N. S.; Kozlovtseva, E. Yu; Dobrinsky, D. R.

2018-05-01

The article considers obtaining mathematical models to assess the efficiency of the dust collectors using an integrated system of analysis and data management STATISTICA Design of Experiments. The procedure for obtaining mathematical models and data processing is considered by the example of laboratory studies on a mounted installation containing a dust collector in counter-swirling flows (CSF) using gypsum dust of various fractions. Planning of experimental studies has been carried out in order to reduce the number of experiments and reduce the cost of experimental research. A second-order non-position plan (Box-Bencken plan) was used, which reduced the number of trials from 81 to 27. The order of statistical data research of Box-Benken plan using standard tools of integrated system for analysis and data management STATISTICA Design of Experiments is considered. Results of statistical data processing with significance estimation of coefficients and adequacy of mathematical models are presented.

The written mathematical communication profile of prospective math teacher in mathematical proving

NASA Astrophysics Data System (ADS)

Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.

2018-01-01

Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

A study of students' learning styles and mathematics anxiety amongst form four students in Kerian Perak

NASA Astrophysics Data System (ADS)

Esa, Suraya; Mohamed, Nurul Akmal

2017-05-01

This study aims to identify the relationship between students' learning styles and mathematics anxiety amongst Form Four students in Kerian, Perak. The study involves 175 Form Four students as respondents. The instrument which is used to assess the students' learning styles and mathematic anxiety is adapted from the Grasha's Learning Styles Inventory and the Mathematics Anxiety Scale (MAS) respectively. The types of learning styles used are independent, avoidant, collaborative, dependent, competitive and participant. The collected data is processed by SPSS (Statistical Packages for Social Sciences 16.0). The data is analysed by using descriptive statistics and inferential statistics that include t-test and Pearson correlation. The results show that majority of the students adopt collaborative learning style and the students have moderate level of mathematics anxiety. Moreover, it is found that there is significant difference between learning style avoidant, collaborative, dependent and participant based on gender. Amongst all students' learning style, there exists a weak but significant correlation between avoidant, independent and participant learning style and mathematics anxiety. It is very important for the teachers need to be concerned about the effects of learning styles on mathematics anxiety. Therefore, the teachers should understand mathematics anxiety and implement suitable learning strategies in order for the students to overcome their mathematics anxiety.

Working Memory, Attention, and Mathematical Problem Solving: A Longitudinal Study of Elementary School Children

ERIC Educational Resources Information Center

Swanson, H. Lee

2011-01-01

The role of working memory (WM) in children's growth in mathematical problem solving was examined in a longitudinal study of children (N = 127). A battery of tests was administered that assessed problem solving, achievement, WM, and cognitive processing (inhibition, speed, phonological coding) in Grade 1 children, with follow-up testing in Grades…

One Teacher, Two Lessons: The Lesson Study Process

ERIC Educational Resources Information Center

Robinson, Naomi; Leikin, Roza

2012-01-01

In this paper, we analyze 2 lessons by 1 teacher that took place during a lesson study (LS) cycle for a team of elementary mathematics teachers. We analyze the data on 2 levels: macro-level analysis, dealing with lesson structure and setting; and micro-level analysis, zooming in on mathematical tasks and the quality of whole-class discussion. We…

Project-Based Social Justice Mathematics: A Case Study of Five 6th Grade Students

ERIC Educational Resources Information Center

McHugh, Maighread L.

2015-01-01

The purpose of this qualitative multiple case study was to explore how five sixth grade female students navigated the process of project-based learning as they designed and implemented their own project centered on mathematics while using a social justice lens. The theoretical frameworks of Authentic Intellectual Work and Social Justice…

Developing an Assessment Instrument to Measure Early Elementary Teachers' Mathematical Knowledge for Teaching

ERIC Educational Resources Information Center

Schoen, Robert C.; Bray, Wendy; Wolfe, Christopher; Tazaz, Amanda M.; Nielsen, Lynne

2017-01-01

This study reports on the development and field study of K-TEEM, a web-based assessment instrument designed to measure mathematical knowledge for teaching (MKT) at the early elementary level. The development process involved alignment with early elementary curriculum standards, expert review of items and scoring criteria, cognitive interviews with…

The Increase of Critical Thinking Skills through Mathematical Investigation Approach

NASA Astrophysics Data System (ADS)

Sumarna, N.; Wahyudin; Herman, T.

2017-02-01

Some research findings on critical thinking skills of prospective elementary teachers, showed a response that is not optimal. On the other hand, critical thinking skills will lead a student in the process of analysis, evaluation and synthesis in solving a mathematical problem. This study attempts to perform an alternative solution with a focus on mathematics learning conditions that is held in the lecture room through mathematical investigation approach. This research method was Quasi-Experimental design with pre-test post-test design. Data analysis using a mixed method with Embedded design. Subjects were regular students enrolled in 2014 at the study program of education of primary school teachers. The number of research subjects were 111 students consisting of 56 students in the experimental group and 55 students in the control group. The results of the study showed that (1) there is a significant difference in the improvement of critical thinking ability of students who receive learning through mathematical investigation approach when compared with students studying through expository approach, and (2) there is no interaction effect between prior knowledge of mathematics and learning factors (mathematical investigation and expository) to increase of critical thinking skills of students.

Application of Learning Engineering Techniques Thinking Aloud Pair Problem Solving in Learning Mathematics Students Class VII SMPN 15 Padang

NASA Astrophysics Data System (ADS)

Widuri, S. Y. S.; Almash, L.; Zuzano, F.

2018-04-01

The students activity and responsible in studying mathematic is still lack. It gives an effect for the bad result in studying mathematic. There is one of learning technic to increase students activity in the classroom and the result of studying mathematic with applying a learning technic. It is “Thinking Aloud Pair Problem Solving (TAPPS)”. The purpose of this research is to recognize the developing of students activity in mathematic subject during applying that technic “TAPPS” in seven grade at SMPN 15 Padang and compare the students proportion in learning mathematic with TAPPS between learning process without it in seven grade at SMPN 15 Padang. Students activity for indicators 1, 2, 3, 4, 5, 6 at each meeting is likely to increase and students activity for indicator 7 at each meeting is likely to decrease. The finding of this research is χ 2 = 9,42 and the value of p is 0,0005 < p < 0,005. Therefore p < 0,05 has means H 0 was rejected and H 1 was accepted. Thus, it was concluded that the activities and result in studying mathematic increased after applying learning technic the TAPPS.

Development of an algorithm for improving quality and information processing capacity of MathSpeak synthetic speech renderings.

PubMed

Isaacson, M D; Srinivasan, S; Lloyd, L L

2010-01-01

MathSpeak is a set of rules for non speaking of mathematical expressions. These rules have been incorporated into a computerised module that translates printed mathematics into the non-ambiguous MathSpeak form for synthetic speech rendering. Differences between individual utterances produced with the translator module are difficult to discern because of insufficient pausing between utterances; hence, the purpose of this study was to develop an algorithm for improving the synthetic speech rendering of MathSpeak. To improve synthetic speech renderings, an algorithm for inserting pauses was developed based upon recordings of middle and high school math teachers speaking mathematic expressions. Efficacy testing of this algorithm was conducted with college students without disabilities and high school/college students with visual impairments. Parameters measured included reception accuracy, short-term memory retention, MathSpeak processing capacity and various rankings concerning the quality of synthetic speech renderings. All parameters measured showed statistically significant improvements when the algorithm was used. The algorithm improves the quality and information processing capacity of synthetic speech renderings of MathSpeak. This increases the capacity of individuals with print disabilities to perform mathematical activities and to successfully fulfill science, technology, engineering and mathematics academic and career objectives.

Mathematics Literacy of Secondary Students in Solving Simultanenous Linear Equations

NASA Astrophysics Data System (ADS)

Sitompul, R. S. I.; Budayasa, I. K.; Masriyah

2018-01-01

This study examines the profile of secondary students’ mathematical literacy in solving simultanenous linear equations problems in terms of cognitive style of visualizer and verbalizer. This research is a descriptive research with qualitative approach. The subjects in this research consist of one student with cognitive style of visualizer and one student with cognitive style of verbalizer. The main instrument in this research is the researcher herself and supporting instruments are cognitive style tests, mathematics skills tests, problem-solving tests and interview guidelines. Research was begun by determining the cognitive style test and mathematics skill test. The subjects chosen were given problem-solving test about simultaneous linear equations and continued with interview. To ensure the validity of the data, the researcher conducted data triangulation; the steps of data reduction, data presentation, data interpretation, and conclusion drawing. The results show that there is a similarity of visualizer and verbalizer-cognitive style in identifying and understanding the mathematical structure in the process of formulating. There are differences in how to represent problems in the process of implementing, there are differences in designing strategies and in the process of interpreting, and there are differences in explaining the logical reasons.

Mathematical support for automated geometry analysis of lathe machining of oblique peakless round-nose tools

NASA Astrophysics Data System (ADS)

Filippov, A. V.; Tarasov, S. Yu; Podgornyh, O. A.; Shamarin, N. N.; Filippova, E. O.

2017-01-01

Automatization of engineering processes requires developing relevant mathematical support and a computer software. Analysis of metal cutting kinematics and tool geometry is a necessary key task at the preproduction stage. This paper is focused on developing a procedure for determining the geometry of oblique peakless round-nose tool lathe machining with the use of vector/matrix transformations. Such an approach allows integration into modern mathematical software packages in distinction to the traditional analytic description. Such an advantage is very promising for developing automated control of the preproduction process. A kinematic criterion for the applicable tool geometry has been developed from the results of this study. The effect of tool blade inclination and curvature on the geometry-dependent process parameters was evaluated.

Editorial: Mathematical Methods and Modeling in Machine Fault Diagnosis

DOE PAGES

Yan, Ruqiang; Chen, Xuefeng; Li, Weihua; ...

2014-12-18

Modern mathematics has commonly been utilized as an effective tool to model mechanical equipment so that their dynamic characteristics can be studied analytically. This will help identify potential failures of mechanical equipment by observing change in the equipment’s dynamic parameters. On the other hand, dynamic signals are also important and provide reliable information about the equipment’s working status. Modern mathematics has also provided us with a systematic way to design and implement various signal processing methods, which are used to analyze these dynamic signals, and to enhance intrinsic signal components that are directly related to machine failures. This special issuemore » is aimed at stimulating not only new insights on mathematical methods for modeling but also recently developed signal processing methods, such as sparse decomposition with potential applications in machine fault diagnosis. Finally, the papers included in this special issue provide a glimpse into some of the research and applications in the field of machine fault diagnosis through applications of the modern mathematical methods.« less

Using mathematics to solve real world problems: the role of enablers

NASA Astrophysics Data System (ADS)

Geiger, Vincent; Stillman, Gloria; Brown, Jill; Galbriath, Peter; Niss, Mogens

2018-03-01

The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that "enable" year 10/11 students to successfully begin the modelling process, that is, formulate and mathematise a real world problem. The 3-year study will take a design research approach in working intensively with six schools across two educational jurisdictions. It is anticipated that this research will generate new theoretical and practical insights into the role of "enablers" within the process of mathematisation, leading to the development of principles for the design and implementation for tasks that support students' development as modellers.

On the Modeling of Vacuum Arc Remelting Process in Titanium Alloys

NASA Astrophysics Data System (ADS)

Patel, Ashish; Fiore, Daniel

2016-07-01

Mathematical modeling is routinely used in the process development and production of advanced aerospace alloys to gain greater insight into the effect of process parameters on final properties. This article describes the application of a 2-D mathematical VAR model presented at previous LMPC meetings. The impact of process parameters on melt pool geometry, solidification behavior, fluid-flow and chemistry in a Ti-6Al-4V ingot is discussed. Model predictions are validated against published data from a industrial size ingot, and results of a parametric study on particle dissolution are also discussed.

A Framework for Proofs and Refutations in School Mathematics: Increasing Content by Deductive Guessing

ERIC Educational Resources Information Center

Komatsu, Kotaro

2016-01-01

The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

An Interdisciplinary Approach to Designing Online Learning: Fostering Pre-Service Mathematics Teachers' Capabilities in Mathematical Modelling

ERIC Educational Resources Information Center

Geiger, Vince; Mulligan, Joanne; Date-Huxtable, Liz; Ahlip, Rehez; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian

2018-01-01

In this article we describe and evaluate processes utilized to develop an online learning module on mathematical modelling for pre-service teachers. The module development process involved a range of professionals working within the STEM disciplines including mathematics and science educators, mathematicians, scientists, in-service and pre-service…

Educational Triage and Ability-Grouping in Primary Mathematics: A Case-Study of the Impacts on Low-Attaining Pupils

ERIC Educational Resources Information Center

Marks, Rachel

2014-01-01

This case-study, drawing on an unanticipated theme arising from a wider study of ability-grouping in primary mathematics, documents some of the consequences of educational triage in the final year of one primary school. The paper discusses how a process of educational triage, as a response to accountability pressures, is justified by teachers on…

Thermomechanical Stresses Analysis of a Single Event Burnout Process

NASA Astrophysics Data System (ADS)

Tais, Carlos E.; Romero, Eduardo; Demarco, Gustavo L.

2009-06-01

This work analyzes the thermal and mechanical effects arising in a power Diffusion Metal Oxide Semiconductor (DMOS) during a Single Event Burnout (SEB) process. For studying these effects we propose a more detailed simulation structure than the previously used by other authors, solving the mathematical models by means of the Finite Element Method. We use a cylindrical heat generation region, with 5 W, 10 W, 50 W and 100 W for emulating the thermal phenomena occurring during SEB processes, avoiding the complexity of the mathematical treatment of the ion-semiconductor interaction.

Developing teaching process for enhancing students' mathematical problem solving in the 21st century through STEM education

NASA Astrophysics Data System (ADS)

Prawvichien, Sutthaporn; Siripun, Kulpatsorn; Yuenyong, Chokchai

2018-01-01

The STEM education could provide the context for students' learning in the 21st century. The Mathematical problem solving requires a context which simulates real life in order to give students experience of the power of mathematics in the world around them. This study aimed to develop the teaching process for enhancing students' mathematical problem solving in the 21st century through STEM education. The paper will clarify the STEM learning activities about graph theories regarding on the 6 steps of engineering design process. These include identify a challenge, exploring ideas, designing and planning, doing and developing, test and evaluate, and present the solution. The learning activities will start from the Identify a challenge stage which provides the northern part of Thailand flooding situation in order to set the students' tasks of develop the solutions of providing the routes of fastest moving people away from the flooding areas. The explore ideas stage will provide activities for enhance students to learn some knowledge based for designing the possible solutions. This knowledge based could focus on measuring, geometry, graph theory, and mathematical process. The design and plan stage will ask students to model the city based on the map and then provide the possible routes. The doing and development stage will ask students to develop the routes based on their possible model. The test and evaluating will ask students to clarify how to test and evaluate the possible routes, and then test it. The present solution stage will ask students to present the whole process of designing routes. Then, the paper will discuss how these learning activities could enhance students' mathematical problem solving. The paper may have implication for STEM education in school setting.

The beliefs of `Tomorrow's Teachers' about mathematics: precipitating change in beliefs as a result of participation in an Initial Teacher Education programme

NASA Astrophysics Data System (ADS)

Leavy, Aisling; Hourigan, Mairead

2018-07-01

Mathematics education research has given increasing attention to the role of affective factors in the learning process. While 'affect' is used to refer to a variety of aspects including feelings, emotions, beliefs, attitudes and conceptions, this paper focuses on 'beliefs' of elementary pre-service teachers. In particular, the study evaluates the effect of participation in a reform-based elementary pre-service teacher education (referred to as Initial Teacher Education (ITE)) programme on participants' 'beliefs about the nature of mathematics'. This was completed using two (sub)scales of the Aiken's Revised Mathematics Scale measuring Enjoyment of Mathematics (E) and belief in the Value of Mathematics (V). Both scales were administered before and after participants completed the mathematics education programme, which consisted of 5 compulsory and consecutive modules. This study reveals that entry-level pre-service teachers report generally positive beliefs about the value of and enjoyment in doing mathematics. The findings challenge previous research, which report the tendency of teachers' beliefs to be resistant to change while in teacher education and suggest that it is possible for ITE mathematics education programmes to stimulate improvement in beliefs and attitudes among participants. Particular programme features are identified as instrumental in this positive change in beliefs about mathematics.

Relation between Approximate Number System Acuity and Mathematical Achievement: The Influence of Fluency

PubMed Central

Wang, Li; Sun, Yuhua; Zhou, Xinlin

2016-01-01

Previous studies have observed inconsistent relations between the acuity of the Approximate Number System (ANS) and mathematical achievement. In this paper, we hypothesize that the relation between ANS acuity and mathematical achievement is influenced by fluency; that is, the mathematical achievement test covering a greater expanse of mathematical fluency may better reflect the relation between ANS acuity and mathematics skills. We explored three types of mathematical achievement tests utilized in this study: Subtraction, graded, and semester-final examination. The subtraction test was designed to measure the mathematical fluency. The graded test was more fluency-based than the semester-final examination, but both involved the same mathematical knowledge from the class curriculum. A total of 219 fifth graders from primary schools were asked to perform all three tests, then given a numerosity comparison task, a visual form perception task (figure matching), and a series of other tasks to assess general cognitive processes (mental rotation, non-verbal matrix reasoning, and choice reaction time). The findings were consistent with our expectations. The relation between ANS acuity and mathematical achievement was particularly clearly reflected in the participants’ performance on the visual form perception task, which supports the domain-general explanations for the underlying mechanisms of the relation between ANS acuity and math achievement. PMID:28066291

Mathematical Creative Process Wallas Model in Students Problem Posing with Lesson Study Approach

ERIC Educational Resources Information Center

Nuha, Muhammad 'Azmi; Waluya, S. B.; Junaedi, Iwan

2018-01-01

Creative thinking is very important in the modern era so that it should be improved by doing efforts such as making a lesson that train students to pose their own problems. The purposes of this research are (1) to give an initial description of students about mathematical creative thinking level in Problem Posing Model with Lesson Study approach…

Developing teachers' models for assessing students' competence in mathematical modelling through lesson study

NASA Astrophysics Data System (ADS)

Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Cakiroglu, Erdinc; Alacaci, Cengiz; Cetinkaya, Bulent

2017-08-01

Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage problems that arise in various stages of the modelling process. However, teachers' difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers' knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers' knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle.

Designing for Mathematical Abstraction

ERIC Educational Resources Information Center

Pratt, Dave; Noss, Richard

2010-01-01

Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as "designing for abstraction." In this paper, we draw on detailed design experiments from our research on children's understanding about chance and distribution to re-present this work as a case study in designing…

Thinking Process of Pseudo Construction in Mathematics Concepts

ERIC Educational Resources Information Center

Subanji; Nusantara, Toto

2016-01-01

This article aims at studying pseudo construction of student thinking in mathematical concepts, integer number operation, algebraic forms, area concepts, and triangle concepts. 391 junior high school students from four districts of East Java Province Indonesia were taken as the subjects. Data were collected by means of distributing the main…

Teachers' Perceptions of State Decision-Making Processes for Mathematics Curricula

ERIC Educational Resources Information Center

Bothwell, Brett

2012-01-01

The purpose of this qualitative case study was to explore teachers' knowledge and professional opinions concerning state policy changes for college and workplace preparation, state curricula requirements and standards, student tracking, graduation rates, and the implication these elements have in the mathematics classroom. A qualitative…

Writing in Math: A Disciplinary Literacy Approach

ERIC Educational Resources Information Center

Brozo, William G.; Crain, Sarah

2018-01-01

Mathematics teachers often resist generic literacy strategies because they do not seem relevant to math learning. Discipline-specific literacy practices that emerge directly from the math content and processes under study are more likely to be embraced by math teachers. Furthermore, national and state-level mathematics standards as well as Common…

Women Teachers' Experiences of Learning Mathematics

ERIC Educational Resources Information Center

Adams, Gill

2013-01-01

Continued concern over attainment and participation in secondary school mathematics has led to a focus on improving the quality of teaching and student outcomes through a variety of professional learning opportunities. A study of teacher professional identity serves to illuminate this learning; this constant process of sensemaking (Day and Kington…

The Influence of English-Korean Bilingualism in Solving Mathematics Word Problems.

ERIC Educational Resources Information Center

Whang, Woo-Hyung

1996-01-01

Purposeful sampling was used to select six English-Korean bilingual students to investigate language difficulties and cognitive processes in solving mathematics word problems. These six case studies revealed distinct patterns of difficulties in solving problems written in English and Korean, especially for students in transition stage. (Author/KMC)

Processes in the Development of Mathematics in Kindergarten Children from Title 1 Schools

ERIC Educational Resources Information Center

Foster, Matthew E.; Anthony, Jason L.; Clements, Doug H.; Sarama, Julie H.

2015-01-01

This study examined how well nonverbal IQ (or fluid intelligence), vocabulary, phonological awareness (PA), rapid autonomized naming (RAN), and phonological short-term memory (STM) predicted mathematics outcomes. The 208 participating kindergartners were administered tests of fluid intelligence, vocabulary, PA, RAN, STM, and numeracy in the fall…

Developmental gains in visuospatial memory predict gains in mathematics achievement.

PubMed

Li, Yaoran; Geary, David C

2013-01-01

Visuospatial competencies are related to performance in mathematical domains in adulthood, but are not consistently related to mathematics achievement in children. We confirmed the latter for first graders and demonstrated that children who show above average first-to-fifth grade gains in visuospatial memory have an advantage over other children in mathematics. The study involved the assessment of the mathematics and reading achievement of 177 children in kindergarten to fifth grade, inclusive, and their working memory capacity and processing speed in first and fifth grade. Intelligence was assessed in first grade and their second to fourth grade teachers reported on their in-class attentive behavior. Developmental gains in visuospatial memory span (d = 2.4) were larger than gains in the capacity of the central executive (d = 1.6) that in turn were larger than gains in phonological memory span (d = 1.1). First to fifth grade gains in visuospatial memory and in speed of numeral processing predicted end of fifth grade mathematics achievement, as did first grade central executive scores, intelligence, and in-class attentive behavior. The results suggest there are important individual differences in the rate of growth of visuospatial memory during childhood and that these differences become increasingly important for mathematics learning.

Mathematical modeling of a process the rolling delivery

NASA Astrophysics Data System (ADS)

Stepanov, Mikhail A.; Korolev, Andrey A.

2018-03-01

An adduced analysis of the scientific researches in a domain of the rolling equipments, also research of properties the working material. A one of perspective direction of scientific research this is mathematical modeling. That is broadly used in many scientific disciplines and especially at the technical, applied sciences. With the aid of mathematical modeling it can be study of physical properties of the researching objects and systems. A research of the rolling delivery and transporting devices realized with the aid of a construction of mathematical model of appropriate process. To be described the basic principles and conditions of a construction of mathematical models of the real objects. For example to be consider a construction of mathematical model the rolling delivery device. For a construction that is model used system of the equations, which consist of: Lagrange’s equation of a motion, describing of the law conservation of energy of a mechanical system, and the Navier - Stokes equations, which characterize of the flow of a continuous non-compressed fluid. A construction of mathematical model the rolling deliver to let determined of a total energy of device, and therefore to got the dependence upon the power of drive to a gap between of rolls. A corroborate the hypothesis about laminar the flow of a material into the rolling gap of deliver.

Developmental Gains in Visuospatial Memory Predict Gains in Mathematics Achievement

PubMed Central

Li, Yaoran; Geary, David C.

2013-01-01

Visuospatial competencies are related to performance in mathematical domains in adulthood, but are not consistently related to mathematics achievement in children. We confirmed the latter for first graders and demonstrated that children who show above average first-to-fifth grade gains in visuospatial memory have an advantage over other children in mathematics. The study involved the assessment of the mathematics and reading achievement of 177 children in kindergarten to fifth grade, inclusive, and their working memory capacity and processing speed in first and fifth grade. Intelligence was assessed in first grade and their second to fourth grade teachers reported on their in-class attentive behavior. Developmental gains in visuospatial memory span (d = 2.4) were larger than gains in the capacity of the central executive (d = 1.6) that in turn were larger than gains in phonological memory span (d = 1.1). First to fifth grade gains in visuospatial memory and in speed of numeral processing predicted end of fifth grade mathematics achievement, as did first grade central executive scores, intelligence, and in-class attentive behavior. The results suggest there are important individual differences in the rate of growth of visuospatial memory during childhood and that these differences become increasingly important for mathematics learning. PMID:23936154

Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

ERIC Educational Resources Information Center

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

Frequency of Home Numeracy Activities Is Differentially Related to Basic Number Processing and Calculation Skills in Kindergartners.

PubMed

Mutaf Yıldız, Belde; Sasanguie, Delphine; De Smedt, Bert; Reynvoet, Bert

2018-01-01

Home numeracy has been shown to play an important role in children's mathematical performance. However, findings are inconsistent as to which home numeracy activities are related to which mathematical skills. The present study disentangled between various mathematical abilities that were previously masked by the use of composite scores of mathematical achievement. Our aim was to shed light on the specific associations between home numeracy and various mathematical abilities. The relationships between kindergartners' home numeracy activities, their basic number processing and calculation skills were investigated. Participants were 128 kindergartners ( M age = 5.43 years, SD = 0.29, range: 4.88-6.02 years) and their parents. The children completed non-symbolic and symbolic comparison tasks, non-symbolic and symbolic number line estimation tasks, mapping tasks (enumeration and connecting), and two calculation tasks. Their parents completed a home numeracy questionnaire. Results indicated small but significant associations between formal home numeracy activities that involved more explicit teaching efforts (i.e., identifying numerals, counting) and children's enumeration skills. There was no correlation between formal home numeracy activities and non-symbolic number processing. Informal home numeracy activities that involved more implicit teaching attempts , such as "playing games" and "using numbers in daily life," were (weakly) correlated with calculation and symbolic number line estimation, respectively. The present findings suggest that disentangling between various basic number processing and calculation skills in children might unravel specific relations with both formal and informal home numeracy activities. This might explain earlier reported contradictory findings on the association between home numeracy and mathematical abilities.

Frequency of Home Numeracy Activities Is Differentially Related to Basic Number Processing and Calculation Skills in Kindergartners

PubMed Central

Mutaf Yıldız, Belde; Sasanguie, Delphine; De Smedt, Bert; Reynvoet, Bert

2018-01-01

Home numeracy has been shown to play an important role in children’s mathematical performance. However, findings are inconsistent as to which home numeracy activities are related to which mathematical skills. The present study disentangled between various mathematical abilities that were previously masked by the use of composite scores of mathematical achievement. Our aim was to shed light on the specific associations between home numeracy and various mathematical abilities. The relationships between kindergartners’ home numeracy activities, their basic number processing and calculation skills were investigated. Participants were 128 kindergartners (Mage = 5.43 years, SD = 0.29, range: 4.88–6.02 years) and their parents. The children completed non-symbolic and symbolic comparison tasks, non-symbolic and symbolic number line estimation tasks, mapping tasks (enumeration and connecting), and two calculation tasks. Their parents completed a home numeracy questionnaire. Results indicated small but significant associations between formal home numeracy activities that involved more explicit teaching efforts (i.e., identifying numerals, counting) and children’s enumeration skills. There was no correlation between formal home numeracy activities and non-symbolic number processing. Informal home numeracy activities that involved more implicit teaching attempts, such as “playing games” and “using numbers in daily life,” were (weakly) correlated with calculation and symbolic number line estimation, respectively. The present findings suggest that disentangling between various basic number processing and calculation skills in children might unravel specific relations with both formal and informal home numeracy activities. This might explain earlier reported contradictory findings on the association between home numeracy and mathematical abilities. PMID:29623055

Some remarks on quantum physics, stochastic processes, and nonlinear filtering theory

NASA Astrophysics Data System (ADS)

Balaji, Bhashyam

2016-05-01

The mathematical similarities between quantum mechanics and stochastic processes has been studied in the literature. Some of the major results are reviewed, such as the relationship between the Fokker-Planck equation and the Schrödinger equation. Also reviewed are more recent results that show the mathematical similarities between quantum many particle systems and concepts in other areas of applied science, such as stochastic Petri nets. Some connections to filtering theory are discussed.

Construction of the mathematical concept of pseudo thinking students

NASA Astrophysics Data System (ADS)

Anggraini, D.; Kusmayadi, T. A.; Pramudya, I.

2018-05-01

Thinking process is a process that begins with the acceptance of information, information processing and information calling in memory with structural changes that include concepts or knowledges. The concept or knowledge is individually constructed by each individual. While, students construct a mathematical concept, students may experience pseudo thinking. Pseudo thinking is a thinking process that results in an answer to a problem or construction to a concept “that is not true”. Pseudo thinking can be classified into two forms there are true pseudo and false pseudo. The construction of mathematical concepts in students of pseudo thinking should be immediately known because the error will have an impact on the next construction of mathematical concepts and to correct the errors it requires knowledge of the source of the error. Therefore, in this article will be discussed thinking process in constructing of mathematical concepts in students who experience pseudo thinking.

The Specific Features of design and process engineering in branch of industrial enterprise

NASA Astrophysics Data System (ADS)

Sosedko, V. V.; Yanishevskaya, A. G.

2017-06-01

Production output of industrial enterprise is organized in debugged working mechanisms at each stage of product’s life cycle from initial design documentation to product and finishing it with utilization. The topic of article is mathematical model of the system design and process engineering in branch of the industrial enterprise, statistical processing of estimated implementation results of developed mathematical model in branch, and demonstration of advantages at application at this enterprise. During the creation of model a data flow about driving of information, orders, details and modules in branch of enterprise groups of divisions were classified. Proceeding from the analysis of divisions activity, a data flow, details and documents the state graph of design and process engineering was constructed, transitions were described and coefficients are appropriated. To each condition of system of the constructed state graph the corresponding limiting state probabilities were defined, and also Kolmogorov’s equations are worked out. When integration of sets of equations of Kolmogorov the state probability of system activity the specified divisions and production as function of time in each instant is defined. On the basis of developed mathematical model of uniform system of designing and process engineering and manufacture, and a state graph by authors statistical processing the application of mathematical model results was carried out, and also advantage at application at this enterprise is shown. Researches on studying of loading services probability of branch and third-party contractors (the orders received from branch within a month) were conducted. The developed mathematical model of system design and process engineering and manufacture can be applied to definition of activity state probability of divisions and manufacture as function of time in each instant that will allow to keep account of loading of performance of work in branches of the enterprise.

The (Mathematical) Modeling Process in Biosciences

PubMed Central

Torres, Nestor V.; Santos, Guido

2015-01-01

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology. PMID:26734063

Students, Computers and Mathematics the Golden Trilogy in the Teaching-Learning Process

ERIC Educational Resources Information Center

García-Santillán, Arturo; Escalera-Chávez, Milka Elena; López-Morales, José Satsumi; Córdova Rangel, Arturo

2014-01-01

In this paper we examine the relationships between students' attitudes towards mathematics and technology, therefore, we take a Galbraith and Hines' scale (1998, 2000) about mathematics confidence, computer confidence, computer and mathematics interaction, mathematics motivation, computer motivation, and mathematics engagement. 164 questionnaires…

Modelling in Action. Examining How Students Approach Modelling Real Life Situations. Three Case Studies. Model of the Movement of an Elevator

ERIC Educational Resources Information Center

Rivas, Eugenia Marmolejo

2015-01-01

By means of three case studies, we will present two mathematical modelling activities that are suitable for students enrolled in senior high school and the first year of mathematics at university level. The activities have been designed to enrich the learning process and promote the formation of vital modelling skills. In case studies one and two,…

Differences in the acuity of the Approximate Number System in adults: the effect of mathematical ability.

PubMed

Guillaume, Mathieu; Nys, Julie; Mussolin, Christophe; Content, Alain

2013-11-01

It is largely admitted that processing numerosity relies on an innate Approximate Number System (ANS), and recent research consistently observed a relationship between ANS acuity and mathematical ability in childhood. However, studies assessing this relationship in adults led to contradictory results. In this study, adults with different levels of mathematical expertise performed two tasks on the same pairs of dot collections, based either on numerosity comparison or on cumulative area comparison. Number of dots and cumulative area were congruent in half of the stimuli, and incongruent in the other half. The results showed that adults with higher mathematical ability obtained lower Weber fractions in the numerical condition than participants with lower mathematical ability. Further, adults with lower mathematical ability were more affected by the interference of the continuous dimension in the numerical comparison task, whereas conversely higher-expertise adults showed stronger interference of the numerical dimension in the continuous comparison task. Finally, ANS acuity correlated with arithmetic performance. Taken together, the data suggest that individual differences in ANS acuity subsist in adulthood, and that they are related to mathematical ability. © 2013.

Persisting mathematics and science high school teachers: A Q-methodology study

NASA Astrophysics Data System (ADS)

Robbins-Lavicka, Michelle M.

There is a lack of qualified mathematics and science teachers at all levels of education in Arkansas. Lasting teaching initiative programs are needed to address retention so qualified teachers remain in the classroom. The dearth of studies regarding why mathematics and science teachers persist in the classroom beyond the traditional 5-year attrition period led this Q-methodological study to evaluate the subjective perceptions of persistent mathematics and science teachers to determine what makes them stay. This study sought to understand what factors persisting mathematics and science teachers used to explain their persistence in the classroom beyond 5 years and what educational factors contributed to persisting mathematics and science teachers. Q-methodology combines qualitative and quantitative techniques and provided a systematic means to investigate personal beliefs by collecting a concourse, developing a Q-sample and a person-sample, conducting a Q-sorting process, and analyzing the data. The results indicated that to encourage longevity within mathematics and science classrooms (a) teachers should remain cognizant of their ability to influence student attitudes toward teaching; (b) administrators should provide support for teachers and emphasize the role and importance of professional development; and (c) policy makers should focus their efforts and resources on developing recruitment plans, including mentorship programs, while providing and improving financial compensation. Significantly, the findings indicate that providing mentorship and role models at every level of mathematics and science education will likely encourage qualified teachers to remain in the mathematics and science classrooms, thus increasing the chance of positive social change.

Mathematical modelling of tissue formation in chondrocyte filter cultures.

PubMed

Catt, C J; Schuurman, W; Sengers, B G; van Weeren, P R; Dhert, W J A; Please, C P; Malda, J

2011-12-17

In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.

Orientations toward Mathematical Processes of Prospective Secondary Mathematics Teachers as Related to Work with Tasks

ERIC Educational Resources Information Center

Cannon, Tenille

2016-01-01

Mathematics can be conceptualized in different ways. Policy documents such as the National Council of Teachers of Mathematics (NCTM) (2000) and the Common Core State Standards Initiative (CCSSI) (2010), classify mathematics in terms of mathematical content (e.g., quadratic functions, Pythagorean theorem) and mathematical activity in the form of…

Individual Differences in Working Memory, Nonverbal IQ, and Mathematics Achievement and Brain Mechanisms Associated with Symbolic and Nonsymbolic Number Processing

ERIC Educational Resources Information Center

Gullick, Margaret M.; Sprute, Lisa A.; Temple, Elise

2011-01-01

Individual differences in mathematics performance may stem from domain-general factors like working memory and intelligence. Parietal and frontal brain areas have been implicated in number processing, but the influence of such cognitive factors on brain activity during mathematics processing is not known. The relationship between brain mechanisms…

Use of robotics kits for the enhancement of metacognitive skills of mathematics: a possible approach.

PubMed

La Paglia, Filippo; Rizzo, Rosalinda; La Barbera, Daniele

2011-01-01

The present study is aimed at analyzing the process of building and programming robots as a metacognitive tool of mathematics. Quantitative data from a study performed on a sample of students attending an Italian secondary school are described. Results showed that robotics activities may be used as a new metacognitive environment allowing students to improve their attitude towards mathematics, and to increase their attitude to reflect on themselves and on their own learning, and their higher-level control components, such as forecasting, planning, monitoring and evaluation exercises and problems related to implementation.

The Effect of Teaching Supported by Interactive Whiteboard on Students' Mathematical Achievements in Lower Secondary Education

ERIC Educational Resources Information Center

Tunaboylu, Ceren; Demir, Ergül

2017-01-01

The aim of this study is to investigate the effect of using the interactive whiteboard in mathematics teaching process on the 7th-grade students' achievement. This study was conducted as experimental design. Experimental and control groups were composed of 58 7th-grade students from one school in the 2015-2016 educational year in Ankara. As a…

Does It Matter Who Your Schoolmates Are? An Investigation of the Association between School Composition, School Processes and Mathematics Achievement in the Early Years of Primary Education

ERIC Educational Resources Information Center

Boonen, Tinneke; Speybroeck, Sara; de Bilde, Jerissa; Lamote, Carl; Van Damme, Jan; Onghena, Patrick

2014-01-01

Although many studies have focused on the importance of school composition for student achievement, there is still no consensus on "whether" school composition matters to student achievement, and, if so, "why". Therefore, the present study investigates the association between school composition and mathematics achievement at…

The Role of Intuition in the Process of Objectification of Mathematical Phenomena from a Husserlian Perspective: A Case Study

ERIC Educational Resources Information Center

Zagorianakos, Andonis; Shvarts, Anna

2015-01-01

The research is a study of the Husserlian approach to intuition, informed by Merleau-Ponty's theory of perception, in the case of a prospective teacher of mathematics. It explores the two major stages-categories of intuition, the essential relations between them, and their vital role in the emergence of empirical and abstract mathematical…

Integrating Physics and Math through Microcomputer-Based Laboratories (MBL): Effects on Discourse Type, Quality, and Mathematization

ERIC Educational Resources Information Center

BouJaoude, Saouma B.; Jurdak, Murad E.

2010-01-01

The purposes of this study were to understand the nature of discourse in terms of knowledge types and cognitive process, source of utterances (student or teacher), and time use in microcomputer-based labs (MBL) and verification type labs (VTL) and to gain an understanding of the role of MBL in promoting mathematization. The study was conducted in…

[Rational bases for cooperation between epidemiologists and mathematicians].

PubMed

Favorova, L A; Shatrov, I I

1977-10-01

The authors consider rational foundations underlying creatin of realistic models. The principal condition for the successful mathematical modelling is obtaining of the most full value primary materials on the course of the epidemic process. For this purpose the authors suggest definite principles of the methodical approach to the mathematical modelling. Possibilities of the use of mathematical methods for various groups of infections are consideder. Particular attention is paid to the works on the study of the infection risk in "small" collective bodies.

Investigating and Communicating Technology Mathematics Problem Solving Experience of Two Preservice Teachers

ERIC Educational Resources Information Center

Kuzle, Ana

2012-01-01

In this paper, I report on preservice teachers' reflections and perceptions on their problem-solving process in a technological context. The purpose of the study was to investigate how preservice teachers experience working individually in a dynamic geometry environment and how these experiences affect their own mathematical activity when…

Eleventh-Grade High School Students' Accounts of Mathematical Metacognitive Knowledge: Explicitness and Systematicity

ERIC Educational Resources Information Center

van Velzen, Joke H.

2016-01-01

Theoretically, it has been argued that a conscious understanding of metacognitive knowledge requires that this knowledge is explicit and systematic. The purpose of this descriptive study was to obtain a better understanding of explicitness and systematicity in knowledge of the mathematical problem-solving process. Eighteen 11th-grade…

A Living Metaphor of Differentiation: A Meta-Ethnography of Cognitively Guided Instruction in the Elementary Classroom

ERIC Educational Resources Information Center

Baker, Katherine; Harter, Meghan Evelynne

2015-01-01

This meta-ethnography explores qualitative studies around the Cognitively Guided Instruction (CGI) framework of mathematics and illustrates how CGI epitomizes differentiation. The meta-ethnographic process is used to synthesize CGI as differentiation, specifically within the elementary mathematics classroom. Thomas P. Carpenter is credited as one…

Statistics and Style. Mathematical Linguistics and Automatic Language Processing No. 6.

ERIC Educational Resources Information Center

Dolezel, Lubomir, Ed.; Bailey, Richard W., Ed.

This collection of 17 articles concerning the application of mathematical models and techniques to the study of literary style is an attempt to overcome the communication barriers that exist between scholars in the various fields that find their meeting ground in statistical stylistics. The articles selected were chosen to represent the best…

Exploration of Mathematics Problem Solving Process Based on the Thinking Level of Students in Junior High School

ERIC Educational Resources Information Center

Rahman, Abdul; Ahmar, Ansari Saleh

2016-01-01

Several studies suggest that most students are not in the same level of development (Slavin, 2008). From concrete operation level to formal operation level, students experience lateness in the transition phase. Consequently, students feel difficulty in solving mathematics problems. Method research is a qualitatively descriptive-explorative…

Relations among Brief Measures of Mathematics, Reading, and Processing Speed: A Construct Validity Study

ERIC Educational Resources Information Center

Maynard, Jennifer Leigh

2012-01-01

Emphasis on regular mathematics skill assessment, intervention, and progress monitoring under the RTI model has created a need for the development of assessment instruments that are psychometrically sound, reliable, universal, and brief. Important factors to consider when developing or selecting assessments for the school environment include what…

Revealing Layered Mathematical Learning Goals through an Examination of Mindset

ERIC Educational Resources Information Center

Willingham, James C.

2017-01-01

This exploratory case study investigated the role of mindset in the establishment of an elementary teacher's mathematical learning goals at different layers of her classroom and curriculum. Data from the critical case of a teacher displaying characteristics of the growth mindset and engaging in the processes of teaching change provided evidence…

Developmental Relations among Motor and Cognitive Processes and Mathematics Skills

ERIC Educational Resources Information Center

Kim, Helyn; Duran, Chelsea A. K.; Cameron, Claire E.; Grissmer, David

2018-01-01

This study explored transactional associations among visuomotor integration, attention, fine motor coordination, and mathematics skills in a diverse sample of one hundred thirty-five 5-year-olds (kindergarteners) and one hundred nineteen 6-year-olds (first graders) in the United States who were followed over the course of 2 school years.…

Working Memory Components as Predictors of Children's Mathematical Word Problem Solving

ERIC Educational Resources Information Center

Zheng, Xinhua; Swanson, H. Lee; Marcoulides, George A.

2011-01-01

This study determined the working memory (WM) components (executive, phonological loop, and visual-spatial sketchpad) that best predicted mathematical word problem-solving accuracy of elementary school children in Grades 2, 3, and 4 (N = 310). A battery of tests was administered to assess problem-solving accuracy, problem-solving processes, WM,…

Negotiating Meaning in Cross-National Studies of Mathematics Teaching: Kissing Frogs to Find Princes

ERIC Educational Resources Information Center

Andrews, Paul

2007-01-01

This paper outlines the iterative processes by which a multinational team of researchers developed a low-inference framework for the analysis of video recordings of mathematics lessons drawn from Flemish Belgium, England, Finland, Hungary and Spain. Located within a theoretical framework concerning learning as the negotiation of meaning, we…

Comparing Episodes of Mathematics Teaching for Higher Achievers in England and Germany

ERIC Educational Resources Information Center

Kelly, Peter; Kotthoff, Hans-Georg

2016-01-01

To illustrate similarities and differences in lower secondary level mathematics teaching with higher achievers and thereby explore privileging processes, we contrast a teaching episode in Baden-Württemberg, Germany with one in South West England. These have been selected from a larger study as typical within each region for higher achieving…

The Myths of Redesign in Developmental Mathematics

ERIC Educational Resources Information Center

Cafarella, Brian V.

2016-01-01

Due to poor student success rates in developmental mathematics, many institutions have implemented various forms of redesign into their developmental math curricula. Since the goal of redesign is to increase student success, it is salient to explore all aspects of the redesign process. Many studies have focused on the positive outcomes of redesign…

Experience and Educational Philosophies of Mathematics Teachers in an Urban Public High School

ERIC Educational Resources Information Center

Gaskin, Marjorie Elaine

2017-01-01

This qualitative research study identified the experiences and educational philosophies of mathematics teachers in an urban public high school framed by John Dewey's Theory of Experience and demonstrated by 21st century skills. To facilitate this process, the researcher used semi-structured interviews, direct observations, and collected lesson…

Mathematical modeling of the gas extraction from the gas hydrate deposit taking into account the replacement technology

NASA Astrophysics Data System (ADS)

Musakaev, N. G.; Khasanov, M. K.; Borodin, S. L.

2018-03-01

In the work on the basis of methods and equations of mechanics of multiphase systems the mathematical model of the process of carbon dioxide burial in the reservoir saturated with methane hydrate is proposed. Estimates are obtained that allow for this problem to neglect diffusion mixing of carbon dioxide and methane. The features of the process of methane displacement from CH4 hydrate by filling them with carbon dioxide are studied.

Automated method for the systematic interpretation of resonance peaks in spectrum data

DOEpatents

Damiano, B.; Wood, R.T.

1997-04-22

A method is described for spectral signature interpretation. The method includes the creation of a mathematical model of a system or process. A neural network training set is then developed based upon the mathematical model. The neural network training set is developed by using the mathematical model to generate measurable phenomena of the system or process based upon model input parameter that correspond to the physical condition of the system or process. The neural network training set is then used to adjust internal parameters of a neural network. The physical condition of an actual system or process represented by the mathematical model is then monitored by extracting spectral features from measured spectra of the actual process or system. The spectral features are then input into said neural network to determine the physical condition of the system or process represented by the mathematical model. More specifically, the neural network correlates the spectral features (i.e. measurable phenomena) of the actual process or system with the corresponding model input parameters. The model input parameters relate to specific components of the system or process, and, consequently, correspond to the physical condition of the process or system. 1 fig.

Automated method for the systematic interpretation of resonance peaks in spectrum data

DOEpatents

Damiano, Brian; Wood, Richard T.

1997-01-01

A method for spectral signature interpretation. The method includes the creation of a mathematical model of a system or process. A neural network training set is then developed based upon the mathematical model. The neural network training set is developed by using the mathematical model to generate measurable phenomena of the system or process based upon model input parameter that correspond to the physical condition of the system or process. The neural network training set is then used to adjust internal parameters of a neural network. The physical condition of an actual system or process represented by the mathematical model is then monitored by extracting spectral features from measured spectra of the actual process or system. The spectral features are then input into said neural network to determine the physical condition of the system or process represented by the mathematical. More specifically, the neural network correlates the spectral features (i.e. measurable phenomena) of the actual process or system with the corresponding model input parameters. The model input parameters relate to specific components of the system or process, and, consequently, correspond to the physical condition of the process or system.

Mathematical models of cell motility.

PubMed

Flaherty, Brendan; McGarry, J P; McHugh, P E

2007-01-01

Cell motility is an essential biological action in the creation, operation and maintenance of our bodies. Developing mathematical models elucidating cell motility will greatly advance our understanding of this fundamental biological process. With accurate models it is possible to explore many permutations of the same event and concisely investigate their outcome. While great advancements have been made in experimental studies of cell motility, it now has somewhat fallen on mathematical models to taking a leading role in future developments. The obvious reason for this is the complexity of cell motility. Employing the processing power of today's computers will give researches the ability to run complex biophysical and biochemical scenarios, without the inherent difficulty and time associated with in vitro investigations. Before any great advancement can be made, the basics of cell motility will have to be well-defined. Without this, complicated mathematical models will be hindered by their inherent conjecture. This review will look at current mathematical investigations of cell motility, explore the reasoning behind such work and conclude with how best to advance this interesting and challenging research area.

Cognitive Processes that Underlie Mathematical Precociousness in Young Children

ERIC Educational Resources Information Center

Swanson, H. Lee

2006-01-01

The working memory (WM) processes that underlie young children's (ages 6-8 years) mathematical precociousness were examined. A battery of tests that assessed components of WM (phonological loop, visual-spatial sketchpad, and central executive), naming speed, random generation, and fluency was administered to mathematically precocious and…

Mathematical Foresight: Thinking in the Future to Work in the Present

ERIC Educational Resources Information Center

Maciejewski, Wes; Barton, Bill

2016-01-01

Originating from interviews with mathematics colleagues, written accounts of mathematicians engaging with mathematics, and Wes's reflections on his own mathematical work, we describe a process that we call mathematical foresight: the imagining of a resolution to a mathematical situation and a path to that resolution. In a sense, mathematical…

Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

ERIC Educational Resources Information Center

Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe

2016-01-01

Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…

Problem solving of student with visual impairment related to mathematical literacy problem

NASA Astrophysics Data System (ADS)

Pratama, A. R.; Saputro, D. R. S.; Riyadi

2018-04-01

The student with visual impairment, total blind category depends on the sense of touch and hearing in obtaining information. In fact, the two senses can receive information less than 20%. Thus, students with visual impairment of the total blind categories in the learning process must have difficulty, including learning mathematics. This study aims to describe the problem-solving process of the student with visual impairment, total blind category on mathematical literacy issues based on Polya phase. This research using test method similar problems mathematical literacy in PISA and in-depth interviews. The subject of this study was a student with visual impairment, total blind category. Based on the result of the research, problem-solving related to mathematical literacy based on Polya phase is quite good. In the phase of understanding the problem, the student read about twice by brushing the text and assisted with information through hearing three times. The student with visual impairment in problem-solving based on the Polya phase, devising a plan by summoning knowledge and experience gained previously. At the phase of carrying out the plan, students with visual impairment implement the plan in accordance with pre-made. In the looking back phase, students with visual impairment need to check the answers three times but have not been able to find a way.

Analysis of mathematical literacy ability based on goal orientation in model eliciting activities learning with murder strategy

NASA Astrophysics Data System (ADS)

Wijayanti, R.; Waluya, S. B.; Masrukan

2018-03-01

The purpose of this research are (1) to analyze the learning quality of MEAs with MURDER strategy, (2) to analyze students’ mathematical literacy ability based on goal orientation in MEAs learning with MURDER strategy. This research is a mixed method research of concurrent embedded type where qualitative method as the primary method. The data were obtained using the methods of scale, observation, test and interviews. The results showed that (1) MEAs Learning with MURDER strategy on students' mathematical literacy ability is qualified, (2) Students who have mastery goal characteristics are able to master the seven components of mathematical literacy process although there are still two components that the solution is less than the maximum. Students who have performance goal characteristics have not mastered the components of mathematical literacy process with the maximum, they are only able to master the ability of using mathematics tool and the other components of mathematical literacy process is quite good.

Implementation of cooperative learning model type STAD with RME approach to understanding of mathematical concept student state junior high school in Pekanbaru

NASA Astrophysics Data System (ADS)

Nurhayati, Dian Mita; Hartono

2017-05-01

This study aims to determine whether there is a difference in the ability of understanding the concept of mathematics between students who use cooperative learning model Student Teams Achievement Division type with Realistic Mathematic Education approach and students who use regular learning in seventh grade SMPN 35 Pekanbaru. This study was quasi experiments with Posttest-only Control Design. The populations in this research were all the seventh grade students in one of state junior high school in Pekanbaru. The samples were a class that is used as the experimental class and one other as the control class. The process of sampling is using purposive sampling technique. Retrieval of data in this study using the documentation, observation sheets, and test. The test use t-test formula to determine whether there is a difference in student's understanding of mathematical concepts. Before the t-test, should be used to test the homogeneity and normality. Based in the analysis of these data with t0 = 2.9 there is a difference in student's understanding of mathematical concepts between experimental and control class. Percentage of students experimental class with score more than 65 was 76.9% and 56.4% of students control class. Thus be concluded, the ability of understanding mathematical concepts students who use the cooperative learning model type STAD with RME approach better than students using the regular learning. So that cooperative learning model type STAD with RME approach is well used in learning process.

Mathematical Modelling of Bacterial Populations in Bio-remediation Processes

NASA Astrophysics Data System (ADS)

Vasiliadou, Ioanna A.; Vayenas, Dimitris V.; Chrysikopoulos, Constantinos V.

2011-09-01

An understanding of bacterial behaviour concerns many field applications, such as the enhancement of water, wastewater and subsurface bio-remediation, the prevention of environmental pollution and the protection of human health. Numerous microorganisms have been identified to be able to degrade chemical pollutants, thus, a variety of bacteria are known that can be used in bio-remediation processes. In this study the development of mathematical models capable of describing bacterial behaviour considered in bio-augmentation plans, such as bacterial growth, consumption of nutrients, removal of pollutants, bacterial transport and attachment in porous media, is presented. The mathematical models may be used as a guide in designing and assessing the conditions under which areas contaminated with pollutants can be better remediated.

Advances in multi-scale modeling of solidification and casting processes

NASA Astrophysics Data System (ADS)

Liu, Baicheng; Xu, Qingyan; Jing, Tao; Shen, Houfa; Han, Zhiqiang

2011-04-01

The development of the aviation, energy and automobile industries requires an advanced integrated product/process R&D systems which could optimize the product and the process design as well. Integrated computational materials engineering (ICME) is a promising approach to fulfill this requirement and make the product and process development efficient, economic, and environmentally friendly. Advances in multi-scale modeling of solidification and casting processes, including mathematical models as well as engineering applications are presented in the paper. Dendrite morphology of magnesium and aluminum alloy of solidification process by using phase field and cellular automaton methods, mathematical models of segregation of large steel ingot, and microstructure models of unidirectionally solidified turbine blade casting are studied and discussed. In addition, some engineering case studies, including microstructure simulation of aluminum casting for automobile industry, segregation of large steel ingot for energy industry, and microstructure simulation of unidirectionally solidified turbine blade castings for aviation industry are discussed.

Cognitive and Emotional Factors in Children with Mathematical Learning Disabilities

ERIC Educational Resources Information Center

Passolunghi, Maria Chiara

2011-01-01

Emotional and cognitive factors were examined in 18 children with mathematical learning disabilities (MLD), compared with 18 normally achieving children, matched for chronological age, school level, gender and verbal IQ. Working memory, short-term memory, inhibitory processes, speed of processing and level of anxiety in mathematics were assessed…

Visual Processing in Generally Gifted and Mathematically Excelling Adolescents

ERIC Educational Resources Information Center

Paz-Baruch, Nurit; Leikin, Roza; Leikin, Mark

2016-01-01

Little empirical data are available concerning the cognitive abilities of gifted individuals in general and especially those who excel in mathematics. We examined visual processing abilities distinguishing between general giftedness (G) and excellence in mathematics (EM). The research population consisted of 190 students from four groups of 10th-…

Mathematical models used to inform study design or surveillance systems in infectious diseases: a systematic review.

PubMed

Herzog, Sereina A; Blaizot, Stéphanie; Hens, Niel

2017-12-18

Mathematical models offer the possibility to investigate the infectious disease dynamics over time and may help in informing design of studies. A systematic review was performed in order to determine to what extent mathematical models have been incorporated into the process of planning studies and hence inform study design for infectious diseases transmitted between humans and/or animals. We searched Ovid Medline and two trial registry platforms (Cochrane, WHO) using search terms related to infection, mathematical model, and study design from the earliest dates to October 2016. Eligible publications and registered trials included mathematical models (compartmental, individual-based, or Markov) which were described and used to inform the design of infectious disease studies. We extracted information about the investigated infection, population, model characteristics, and study design. We identified 28 unique publications but no registered trials. Focusing on compartmental and individual-based models we found 12 observational/surveillance studies and 11 clinical trials. Infections studied were equally animal and human infectious diseases for the observational/surveillance studies, while all but one between humans for clinical trials. The mathematical models were used to inform, amongst other things, the required sample size (n = 16), the statistical power (n = 9), the frequency at which samples should be taken (n = 6), and from whom (n = 6). Despite the fact that mathematical models have been advocated to be used at the planning stage of studies or surveillance systems, they are used scarcely. With only one exception, the publications described theoretical studies, hence, not being utilised in real studies.

Spatial Processing in Infancy Predicts Both Spatial and Mathematical Aptitude in Childhood.

PubMed

Lauer, Jillian E; Lourenco, Stella F

2016-10-01

Despite considerable interest in the role of spatial intelligence in science, technology, engineering, and mathematics (STEM) achievement, little is known about the ontogenetic origins of individual differences in spatial aptitude or their relation to later accomplishments in STEM disciplines. The current study provides evidence that spatial processes present in infancy predict interindividual variation in both spatial and mathematical competence later in development. Using a longitudinal design, we found that children's performance on a brief visuospatial change-detection task administered between 6 and 13 months of age was related to their spatial aptitude (i.e., mental-transformation skill) and mastery of symbolic-math concepts at 4 years of age, even when we controlled for general cognitive abilities and spatial memory. These results suggest that nascent spatial processes present in the first year of life not only act as precursors to later spatial intelligence but also predict math achievement during childhood.

The Role of Cognitive Processes, Foundational Math Skill, and Calculation Accuracy and Fluency in Word-Problem Solving versus Pre-Algebraic Knowledge

PubMed Central

Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.

2016-01-01

The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes. PMID:27786534

Mathematical models applied to the Cr(III) and Cr(VI) breakthrough curves.

PubMed

Ramirez C, Margarita; Pereira da Silva, Mônica; Ferreira L, Selma G; Vasco E, Oscar

2007-07-19

Trivalent and hexavalent chromium continuous biosorption was studied using residual brewer Saccharomyces cerevisiae immobilized in volcanic rock. The columns used in the process had a diameter of 4.5 cm and a length of 140 cm, working at an inlet flow rate of 15 mL/min. Breakthrough curves were used to study the yeast biosorption behavior in the process. The saturation time (ts) was 21 and 45 h for Cr(III) and Cr(VI), respectively, and a breakthrough time (tb) of 4 h for Cr(III) and 5 h for Cr(VI). The uptake capacity of the biosorbent for Cr(III) and Cr(VI) were 48 and 60 mg/g, respectively. Two non-diffusional mathematical models with parameters t0 and sigma were used to adjust the experimental data obtained. Microsoft Excel tools were used for the mathematical solution of the two parameters used.

An Evaluation Model Applied to a Mathematics-Methods Program Involving Three Characteristics of Teaching Style and Their Relationship to Pupil Achievement. Teacher Education Forum; Volume 3, Number 4.

ERIC Educational Resources Information Center

Dodd, Carol Ann

This study explores a technique for evaluating teacher education programs in terms of teaching competencies, as applied to the Indiana University Mathematics Methods Program (MMP). The evaluation procedures formulated for the study include a process product design in combination with a modification of Pophan's performance test paradigm and Gage's…

Are middle school mathematics teachers able to solve word problems without using variable?

NASA Astrophysics Data System (ADS)

Gökkurt Özdemir, Burçin; Erdem, Emrullah; Örnek, Tuğba; Soylu, Yasin

2018-01-01

Many people consider problem solving as a complex process in which variables such as x, y are used. Problems may not be solved by only using 'variable.' Problem solving can be rationalized and made easier using practical strategies. When especially the development of children at younger ages is considered, it is obvious that mathematics teachers should solve problems through concrete processes. In this context, middle school mathematics teachers' skills to solve word problems without using variables were examined in the current study. Through the case study method, this study was conducted with 60 middle school mathematics teachers who have different professional experiences in five provinces in Turkey. A test consisting of five open-ended word problems was used as the data collection tool. The content analysis technique was used to analyze the data. As a result of the analysis, it was seen that the most of the teachers used trial-and-error strategy or area model as the solution strategy. On the other hand, the teachers who solved the problems using variables such as x, a, n or symbols such as Δ, □, ○, * and who also felt into error by considering these solutions as without variable were also seen in the study.

The effect of mathematics anxiety on the processing of numerical magnitude.

PubMed

Maloney, Erin A; Ansari, Daniel; Fugelsang, Jonathan A

2011-01-01

In an effort to understand the origins of mathematics anxiety, we investigated the processing of symbolic magnitude by high mathematics-anxious (HMA) and low mathematics-anxious (LMA) individuals by examining their performance on two variants of the symbolic numerical comparison task. In two experiments, a numerical distance by mathematics anxiety (MA) interaction was obtained, demonstrating that the effect of numerical distance on response times was larger for HMA than for LMA individuals. These data support the claim that HMA individuals have less precise representations of numerical magnitude than their LMA peers, suggesting that MA is associated with low-level numerical deficits that compromise the development of higher level mathematical skills.

Student’s thinking process in solving word problems in geometry

NASA Astrophysics Data System (ADS)

Khasanah, V. N.; Usodo, B.; Subanti, S.

2018-05-01

This research aims to find out the thinking process of seventh grade of Junior High School in solve word problem solving of geometry. This research was descriptive qualitative research. The subject of the research was selected based on sex and differences in mathematical ability. Data collection was done based on student’s work test, interview, and observation. The result of the research showed that there was no difference of thinking process between male and female with high mathematical ability, and there were differences of thinking process between male and female with moderate and low mathematical ability. Also, it was found that male with moderate mathematical ability took a long time in the step of making problem solving plans. While female with moderate mathematical ability took a long time in the step of understanding the problems. The importance of knowing the thinking process of students in solving word problem solving were that the teacher knows the difficulties faced by students and to minimize the occurrence of the same error in problem solving. Teacher could prepare the right learning strategies which more appropriate with student’s thinking process.

Using a Brief Preschool Early Numeracy Skills Screener to Identify Young Children with Mathematics Difficulties

ERIC Educational Resources Information Center

Purpura, David J.; Reid, Erin E.; Eiland, Michael D.; Baroody, Arthur J.

2015-01-01

A critical component in enhancing academic success is identifying children at risk of later academic difficulties. Although significant efforts have been devoted to design effective assessment processes in elementary school, fewer efforts (particularly for mathematics) have been made for preschool. The focus of this study was to design and…

Exploring Teachers' Process of Change in Incorporating Problem Solving into the Mathematics Classroom

ERIC Educational Resources Information Center

Rutherford, Vanessa

2012-01-01

This study explores how a problem-solving based professional learning community (PLC) affects the beliefs, knowledge, and instructional practices of two sixth-grade mathematics teachers. An interview and two observations were conducted prior to beginning the year-long PLC in order to gather information about the participants' beliefs,…

Leisure Activities for the Development of Creative Intelligence in Mathematical Problem Solving

ERIC Educational Resources Information Center

Castro, Angélica Mercedes Tumbaco; Guerra, Galo Ernestro Cabanilla; Brito, Christian Antonio Pavón; Chávez, Tannia Gabriela Acosta

2018-01-01

The present work studies the influence of leisure activities on the creative intelligence of the students. An experimental pre- and post-test design was carried out with individuals selected in a sampling process. The design identifies the ease of students to place themselves in possible contexts and solve them mathematically through Polya's…

Challenges in Mathematics and Statistics Teaching Underpinned by Student-Lecturer Expectations

ERIC Educational Resources Information Center

Parashar, Deepak

2014-01-01

This study is motivated by the desire to address some of the enormous challenges faced by the students as well as the lecturer in fulfilling their respective expectations and duties demanded by the process of learning--teaching of mathematics and statistics within the framework of the constraining schedules laid down by the academic institutions…

Examples as an Instructional Tool in Mathematics and Science Classrooms: Teachers' Perceptions and Attitudes

ERIC Educational Resources Information Center

Huang, Xiaoxia; Cribbs, Jennifer

2017-01-01

This study examined mathematics and science teachers' perceptions and use of four types of examples, including typical textbook examples (standard worked examples) and erroneous worked examples in the written form as well as mastery modelling examples and peer modelling examples involving the verbalization of the problem-solving process. Data…

Pre-Service Secondary Mathematics Teachers' Metacognitive Awareness and Metacognitive Behaviours in Problem Solving Processes

ERIC Educational Resources Information Center

Bas, Fatih

2016-01-01

This study aims to observe the pre-service secondary mathematics teachers' metacognitive awareness in terms of the variables gender and class level and determine their metacognitive behaviours which showed in the non-routine problems. A partially mixed sequential dominant status design was carried out with a total of 287 participants. The data of…

Covariation between Variables in a Modelling Process: The ACODESA (Collaborative Learning, Scientific Debate and Self-Reflection) Method

ERIC Educational Resources Information Center

Hitt, Fernando; González-Martín, Alejandro S.

2015-01-01

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005,…

Professional Development School Triads Inquiring about Student Work in Elementary Mathematics

ERIC Educational Resources Information Center

Coon-Kitt, Mary Jayne; Nolan, James F.; Lloyd, Gwendolyn M.; Romig, Gail

2015-01-01

This article reports on a case of cross-role triads (mentor, intern, and supervisor) in a professional development school (PDS) setting engaged in the process of looking at student work in elementary mathematics over time. The study represents a significant effort to understand what inquiry-oriented behavior looks like in this context. By…

Deconstructing Building Blocks: Preschoolers' Spatial Assembly Performance Relates to Early Mathematical Skills

ERIC Educational Resources Information Center

Verdine, Brian N.; Golinkoff, Roberta M.; Hirsh-Pasek, Kathryn; Newcombe, Nora S.; Filipowicz, Andrew T.; Chang, Alicia

2014-01-01

This study focuses on three main goals: First, 3-year-olds' spatial assembly skills are probed using interlocking block constructions (N = 102). A detailed scoring scheme provides insight into early spatial processing and offers information beyond a basic accuracy score. Second, the relation of spatial assembly to early mathematical skills…

Quality Online Resources and Supports for Educators Teaching the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Walters, Kirk; Smith, Toni; Leinwand, Steve; Ford, Jennifer; Scheopner Torres, Aubrey

2015-01-01

This study was designed in response to a request from rural educators in the Northeast for support in identifying high-quality online resources to implement the Common Core State Standards for Mathematics (CCSSM). The process for identifying online resources included selecting resources that had an easily navigable CCSSM organizational structure…

Local Instruction Theory on Division in Mathematics GASING: The Case of Rural Area's Student in Indonesia

ERIC Educational Resources Information Center

Prahmana, Rully Charitas Indra; Suwasti, Petra

2014-01-01

Several studies on learning mathematics for rural area's student indicate that students have difficulty in understanding the concept of division operation. Students are more likely to be introduced by the use of the formula without involving the concept itself and learning division separate the concrete situation of learning process. This…

Mathematical modeling and Monte Carlo simulation of thermal inactivation of non-proteolytic Clostridium botulinum spores during continuous microwave-assisted pasteurization

USDA-ARS?s Scientific Manuscript database

The objective of this study is to develop a mathematical method to simulate the internal temperature history of products processed in a prototype microwave-assisted pasteurization system (MAPS) developed by Washington State University. Two products (10 oz. beef meatball trays and 16 oz. salmon fill...

Building Content and Communities: Developing a Shared Sense of Early Childhood Mathematics Pedagogy

ERIC Educational Resources Information Center

Linder, Sandra M.

2012-01-01

This article presents results from a case study analyzing the process of change for early childhood educators as they engage in a semester-long professional development (PD) experience focused on developing a teacher research agenda related to mathematics instruction. During this PD experience, 11 participants (5 second-grade and 6 third-grade…

Hiccups within Technology Mediated Lessons: A Catalyst for Mathematics Teachers' Epistemological Development

ERIC Educational Resources Information Center

Clark-Wilson, Alison; Noss, Richard

2015-01-01

The notion of the lesson "hiccup", defined as the perturbation experienced by a teacher during teaching that has been triggered by the use of mathematical technology, was first proposed in Clark-Wilson. Hiccups which are both unanticipated and unplanned, emerged from a study that sought to make sense of the process of secondary…

A Study on the Relationship between Six-Year-Old Children's Creativity and Mathematical Ability

ERIC Educational Resources Information Center

Baran, Gülen; Erdogan, Serap; Çakmak, Aygen

2011-01-01

Creativity is defined as a totality of processes and a way of attitude and behavior which exists in every child to a different extent. Every child is creative owing to their nature and their perspective on life. Offering children creative environments, especially during early childhood education, affects their mathematical abilities and supports…

A Framework for Problem-Based Learning: Teaching Mathematics with a Relational Problem-Based Pedagogy

ERIC Educational Resources Information Center

Schettino, Carmel

2016-01-01

One recommendation for encouraging young women and other underrepresented students in their mathematical studies is to find instructional methods, such as problem-based learning (PBL), that allow them to feel included in the learning process. Using a more relationally centered pedagogy along with more inclusive instructional methods may be a way…

First-Year Engineering Students' Use of Their Mathematics Textbook--Opportunities and Constraints

ERIC Educational Resources Information Center

Randahl, Mira

2012-01-01

The role of the mathematics textbook at tertiary level has received limited exposure in previous research although it is likely that students work individually and that some of this work depends on the use of the textbook. The aim of this study was to investigate the process of approaching the textbook from epistemological, cognitive, and…

Purchasing a Used Car Using Multiple Criteria Decision Making

ERIC Educational Resources Information Center

Edwards, Thomas G.; Chelst, Kenneth R.

2007-01-01

When studying mathematics, students often ask the age-old question, "When will I ever use this in my future?" The activities described in this article demonstrate for students a process that brings the power of mathematical reasoning to bear on a difficult decision involving multiple criteria that is sure to resonate with the interests of many of…

Developmental Mathematics in College: What the Research Is and Why There Isn't More.

ERIC Educational Resources Information Center

Schonberger, Ann K.

A review of the literature is presented on developmental mathematics courses in two- and four-year colleges and universities. The paper is organized within the categories of status studies, placement, program evaluation, class management, student characteristics, and thought processes. Highlights of the report include: (1) an average of 2.0…

Application of the Cluster Expansion to a Mathematical Model of the Long Memory Phenomenon in a Financial Market

NASA Astrophysics Data System (ADS)

Kuroda, Koji; Maskawa, Jun-ichi; Murai, Joshin

2013-08-01

Empirical studies of the high frequency data in stock markets show that the time series of trade signs or signed volumes has a long memory property. In this paper, we present a discrete time stochastic process for polymer model which describes trader's trading strategy, and show that a scale limit of the process converges to superposition of fractional Brownian motions with Hurst exponents and Brownian motion, provided that the index γ of the time scale about the trader's investment strategy coincides with the index δ of the interaction range in the discrete time process. The main tool for the investigation is the method of cluster expansion developed in the mathematical study of statistical mechanics.

Specialization of the Right Intraparietal Sulcus for Processing Mathematics During Development.

PubMed

Schel, Margot A; Klingberg, Torkel

2017-09-01

Mathematical ability, especially perception of numbers and performance of arithmetics, is known to rely on the activation of intraparietal sulcus (IPS). However, reasoning ability and working memory, 2 highly associated abilities also activate partly overlapping regions. Most studies aimed at localizing mathematical function have used group averages, where individual variability is averaged out, thus confounding the anatomical specificity when localizing cognitive functions. Here, we analyze the functional anatomy of the intraparietal cortex by using individual analysis of subregions of IPS based on how they are structurally connected to frontal, parietal, and occipital cortex. Analysis of cortical thickness showed that the right anterior IPS, defined by its connections to the frontal lobe, was associated with both visuospatial working memory, and mathematics in 6-year-old children. This region specialized during development to be specifically related to mathematics, but not visuospatial working memory in adolescents and adults. This could be an example of interactive specialization, where interacting with the environment in combination with interactions between cortical regions leads from a more general role of right anterior IPS in spatial processing, to a specialization of this region for mathematics. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

ERIC Educational Resources Information Center

Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

2016-01-01

This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

Helping Children Learn Mathematics through Multiple Intelligences and Standards for School Mathematics.

ERIC Educational Resources Information Center

Adams, Thomasenia Lott

2001-01-01

Focuses on the National Council of Teachers of Mathematics 2000 process-oriented standards of problem solving, reasoning and proof, communication, connections, and representation as providing a framework for using the multiple intelligences that children bring to mathematics learning. Presents ideas for mathematics lessons and activities to…

How Students Process Equations in Solving Quantitative Synthesis Problems? Role of Mathematical Complexity in Students' Mathematical Performance

ERIC Educational Resources Information Center

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-01-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking,…

Communication and Representation as Elements in Mathematical Literacy

ERIC Educational Resources Information Center

Thompson, Denisse R.; Chappell, Michaele F.

2007-01-01

The process standards of communication and representation in the "Principles and Standards for School Mathematics" are critical tools to help students develop mathematical literacy. In the mathematics classroom, students need to be encouraged to use speaking, listening, reading, and writing to communicate their understanding of mathematics words,…

Basic number processing in children with specific learning disorders: Comorbidity of reading and mathematics disorders.

PubMed

Moll, Kristina; Göbel, Silke M; Snowling, Margaret J

2015-01-01

As well as being the hallmark of mathematics disorders, deficits in number processing have also been reported for individuals with reading disorders. The aim of the present study was to investigate separately the components of numerical processing affected in reading and mathematical disorders within the framework of the Triple Code Model. Children with reading disorders (RD), mathematics disorders (MD), comorbid deficits (RD + MD), and typically developing children (TD) were tested on verbal, visual-verbal, and nonverbal number tasks. As expected, children with MD were impaired across a broad range of numerical tasks. In contrast, children with RD were impaired in (visual-)verbal number tasks but showed age-appropriate performance in nonverbal number skills, suggesting their impairments were domain specific and related to their reading difficulties. The comorbid group showed an additive profile of the impairments of the two single-deficit groups. Performance in speeded verbal number tasks was related to rapid automatized naming, a measure of visual-verbal access in the RD but not in the MD group. The results indicate that deficits in number skills are due to different underlying cognitive deficits in children with RD compared to children with MD: a phonological deficit in RD and a deficit in processing numerosities in MD.

An Investigation of the Engagement of Elementary Students in the NCTM Process Standards after One Year of Standards-Based Instruction

ERIC Educational Resources Information Center

Fillingim, Jennifer Gale

2010-01-01

Contemporary mathematics education reform has placed increased emphasis on K-12 mathematics curriculum. Reform-based curricula, often referred to as "Standards-based" due to philosophical alignment with the NCTM Process Standards, have generated controversy among families, educators, and researchers. The mathematics education research…

The Contributions of Domain-General and Numerical Factors to Third-Grade Arithmetic Skills and Mathematical Learning Disability

ERIC Educational Resources Information Center

Cowan, Richard; Powell, Daisy

2014-01-01

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed, and oral language) and numerical factors that include single-digit processing efficiency and multidigit skills…

How High Is the Tramping Track? Mathematising and Applying in a Calculus Model-Eliciting Activity

ERIC Educational Resources Information Center

Yoon, Caroline; Dreyfus, Tommy; Thomas, Michael O. J.

2010-01-01

Two complementary processes involved in mathematical modelling are mathematising a realistic situation and applying a mathematical technique to a given realistic situation. We present and analyse work from two undergraduate students and two secondary school teachers who engaged in both processes during a mathematical modelling task that required…

Developing and Piloting the Planning for Facilitating Mathematical Processes and Strategies for Preschool Learners

ERIC Educational Resources Information Center

Botha, M.; Maree, J. G.; de Witt, M. W.

2005-01-01

From an early age young children actively engage informally in acquiring fundamental concepts and process skills that form a basis for mathematical understanding. Quite logically, questions will arise during planning when young children first encounter a more formal learning environment: what strategy should one use to develop mathematical …

First-year engineering students' use of their mathematics textbook - opportunities and constraints

NASA Astrophysics Data System (ADS)

Randahl, Mira

2012-09-01

The role of the mathematics textbook at tertiary level has received limited exposure in previous research although it is likely that students work individually and that some of this work depends on the use of the textbook. The aim of this study was to investigate the process of approaching the textbook from epistemological, cognitive, and didactical perspectives. The focus was on identifying and discussing the opportunities and constraints in the process. The study was an explorative case study and the participants were first-year engineering students taking a basic calculus course. The data were collected through questionnaires, observations, and interviews. Results showed that the textbook was used to a very low degree and mainly perceived as a source of tasks. Different opportunities and constraints are pointed out and some didactical implications are suggested. The results and discussion indicate that a need for greater awareness about the use of mathematical textbooks in meaningful ways at tertiary level.

Analytic considerations and axiomatic approaches to the concept cell death and cell survival functions in biology and cancer treatment.

PubMed

Gkigkitzis, Ioannis; Haranas, Ioannis; Austerlitz, Carlos

2015-01-01

This study contains a discussion on the connection between current mathematical and biological modeling systems in response to the main research need for the development of a new mathematical theory for study of cell survival after medical treatment and cell biological behavior in general. This is a discussion of suggested future research directions and relations with interdisciplinary science. In an effort to establish the foundations for a possible framework that may be adopted to study and analyze the process of cell survival during treatment, we investigate the organic connection among an axiomatic system foundation, a predator-prey rate equation, and information theoretic signal processing. A new set theoretic approach is also introduced through the definition of cell survival units or cell survival units indicating the use of "proper classes" according to the Zermelo-Fraenkel set theory and the axiom of choice, as the mathematics appropriate for the development of biological theory of cell survival.

Data Collection Procedures and Descriptive Statistics for the Grade One Achievement Monitoring Tests (Baseline, S-1, S-2, and S-3), Coordinated Study No. 1. Working Paper 316. Report from the Project on Studies in Mathematics.

ERIC Educational Resources Information Center

Buchanan, Anne E.; Romberg, Thomas A.

As part of a 3-year study of arithmetic problem-solving skills in young children, pretests were administered to 180 middle class first grade students. Following each of three instructional units, another achievement test was administered. The three first grade units corresponded to the Developing Mathematical Processes curriculum and involved…

Blooms' separation of the final exam of Engineering Mathematics II: Item reliability using Rasch measurement model

NASA Astrophysics Data System (ADS)

Fuaad, Norain Farhana Ahmad; Nopiah, Zulkifli Mohd; Tawil, Norgainy Mohd; Othman, Haliza; Asshaari, Izamarlina; Osman, Mohd Hanif; Ismail, Nur Arzilah

2014-06-01

In engineering studies and researches, Mathematics is one of the main elements which express physical, chemical and engineering laws. Therefore, it is essential for engineering students to have a strong knowledge in the fundamental of mathematics in order to apply the knowledge to real life issues. However, based on the previous results of Mathematics Pre-Test, it shows that the engineering students lack the fundamental knowledge in certain topics in mathematics. Due to this, apart from making improvements in the methods of teaching and learning, studies on the construction of questions (items) should also be emphasized. The purpose of this study is to assist lecturers in the process of item development and to monitor the separation of items based on Blooms' Taxonomy and to measure the reliability of the items itself usingRasch Measurement Model as a tool. By using Rasch Measurement Model, the final exam questions of Engineering Mathematics II (Linear Algebra) for semester 2 sessions 2012/2013 were analysed and the results will provide the details onthe extent to which the content of the item providesuseful information about students' ability. This study reveals that the items used in Engineering Mathematics II (Linear Algebra) final exam are well constructed but the separation of the items raises concern as it is argued that it needs further attention, as there is abig gap between items at several levels of Blooms' cognitive skill.

Mathematics Learning Assisted Geogebra using Technologically Aligned Classroom (TAC) to Improve Communication Skills of Vocasional High School Student

NASA Astrophysics Data System (ADS)

Yuliardi, R.; Nurjanah

2017-09-01

The purpose of this study to analyze mathematical communication skill’s student to resolve geometry transformation problems through computer Assisted Geogebra using Technologically Aligned Classroom (TAC). The population in this study were students from one of Vocasional High School Student in West Java. Selection of sample by purposed random sampling, the experimental class is taught Technologically Aligned Classroom (TAC) with GeoGebra, while the control class is taught by conventional learning. This study was quasi-experimental with pretest and posttest control group design. Based on the results; (1) The enhancement of student mathematical communication skills through TAC was higher than the conventional learning; (2) based on gender, there were no differences of mathematical communication skilss student who exposed with TAC and conventional learning; (3) based on KAM test, there was significant enhancement of students’ communication skills among ability of high, middle, and low KAM. The differences occur between high KAM and middle KAM, and also between high KAM and low KAM. Based on this result, mathematics learning Assisted Geogebra using Technologically Aligned Classroom (TAC) can be applied in the process of Mathematics Learning in Vocasional High School.

Approximate numerical abilities and mathematics: Insight from correlational and experimental training studies.

PubMed

Hyde, D C; Berteletti, I; Mou, Y

2016-01-01

Humans have the ability to nonverbally represent the approximate numerosity of sets of objects. The cognitive system that supports this ability, often referred to as the approximate number system (ANS), is present in early infancy and continues to develop in precision over the life span. It has been proposed that the ANS forms a foundation for uniquely human symbolic number and mathematics learning. Recent work has brought two types of evidence to bear on the relationship between the ANS and human mathematics: correlational studies showing individual differences in approximate numerical abilities correlate with individual differences in mathematics achievement and experimental studies showing enhancing effects of nonsymbolic approximate numerical training on exact, symbolic mathematical abilities. From this work, at least two accounts can be derived from these empirical data. It may be the case that the ANS and mathematics are related because the cognitive and brain processes responsible for representing numerical quantity in each format overlap, the Representational Overlap Hypothesis, or because of commonalities in the cognitive operations involved in mentally manipulating the representations of each format, the Operational Overlap hypothesis. The two hypotheses make distinct predictions for future work to test. © 2016 Elsevier B.V. All rights reserved.

The relationships between spatial ability, logical thinking, mathematics performance and kinematics graph interpretation skills of 12th grade physics students

NASA Astrophysics Data System (ADS)

Bektasli, Behzat

Graphs have a broad use in science classrooms, especially in physics. In physics, kinematics is probably the topic for which graphs are most widely used. The participants in this study were from two different grade-12 physics classrooms, advanced placement and calculus-based physics. The main purpose of this study was to search for the relationships between student spatial ability, logical thinking, mathematical achievement, and kinematics graphs interpretation skills. The Purdue Spatial Visualization Test, the Middle Grades Integrated Process Skills Test (MIPT), and the Test of Understanding Graphs in Kinematics (TUG-K) were used for quantitative data collection. Classroom observations were made to acquire ideas about classroom environment and instructional techniques. Factor analysis, simple linear correlation, multiple linear regression, and descriptive statistics were used to analyze the quantitative data. Each instrument has two principal components. The selection and calculation of the slope and of the area were the two principal components of TUG-K. MIPT was composed of a component based upon processing text and a second component based upon processing symbolic information. The Purdue Spatial Visualization Test was composed of a component based upon one-step processing and a second component based upon two-step processing of information. Student ability to determine the slope in a kinematics graph was significantly correlated with spatial ability, logical thinking, and mathematics aptitude and achievement. However, student ability to determine the area in a kinematics graph was only significantly correlated with student pre-calculus semester 2 grades. Male students performed significantly better than female students on the slope items of TUG-K. Also, male students performed significantly better than female students on the PSAT mathematics assessment and spatial ability. This study found that students have different levels of spatial ability, logical thinking, and mathematics aptitude and achievement levels. These different levels were related to student learning of kinematics and they need to be considered when kinematics is being taught. It might be easier for students to understand the kinematics graphs if curriculum developers include more activities related to spatial ability and logical thinking.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, Ruqiang; Chen, Xuefeng; Li, Weihua

Modern mathematics has commonly been utilized as an effective tool to model mechanical equipment so that their dynamic characteristics can be studied analytically. This will help identify potential failures of mechanical equipment by observing change in the equipment’s dynamic parameters. On the other hand, dynamic signals are also important and provide reliable information about the equipment’s working status. Modern mathematics has also provided us with a systematic way to design and implement various signal processing methods, which are used to analyze these dynamic signals, and to enhance intrinsic signal components that are directly related to machine failures. This special issuemore » is aimed at stimulating not only new insights on mathematical methods for modeling but also recently developed signal processing methods, such as sparse decomposition with potential applications in machine fault diagnosis. Finally, the papers included in this special issue provide a glimpse into some of the research and applications in the field of machine fault diagnosis through applications of the modern mathematical methods.« less

How to Build a Course in Mathematical–Biological Modeling: Content and Processes for Knowledge and Skill

PubMed Central

2010-01-01

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical–biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments. PMID:20810966

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

DOE Office of Scientific and Technical Information (OSTI.GOV)

Plechac, Petr

2016-03-01

The overall objective of this project was to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics and developing rigorous mathematical techniques and computational algorithms to study such models. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals.

A comparison of mixed-integer linear programming models for workforce scheduling with position-dependent processing times

NASA Astrophysics Data System (ADS)

Moreno-Camacho, Carlos A.; Montoya-Torres, Jairo R.; Vélez-Gallego, Mario C.

2018-06-01

Only a few studies in the available scientific literature address the problem of having a group of workers that do not share identical levels of productivity during the planning horizon. This study considers a workforce scheduling problem in which the actual processing time is a function of the scheduling sequence to represent the decline in workers' performance, evaluating two classical performance measures separately: makespan and maximum tardiness. Several mathematical models are compared with each other to highlight the advantages of each approach. The mathematical models are tested with randomly generated instances available from a public e-library.

Data Processing Courses in High Schools?

ERIC Educational Resources Information Center

Reese, Don

1970-01-01

It is more important for students to have an understanding of basic fundamentals such as English, mathematics, social studies, and basic business understandings than a superficial understanding of data processing equipment and its operation. (Editor)

Brief Report: Preliminary Proposal of a Conceptual Model of a Digital Environment for Developing Mathematical Reasoning in Students with Autism Spectrum Disorders.

PubMed

Santos, Maria Isabel; Breda, Ana; Almeida, Ana Margarida

2015-08-01

There is clear evidence that in typically developing children reasoning and sense-making are essential in all mathematical learning and understanding processes. In children with autism spectrum disorders (ASD), however, these become much more significant, considering their importance to successful independent living. This paper presents a preliminary proposal of a digital environment, specifically targeted to promote the development of mathematical reasoning in students with ASD. Given the diversity of ASD, the prototyping of this environment requires the study of dynamic adaptation processes and the development of activities adjusted to each user's profile. We present the results obtained during the first phase of this ongoing research, describing a conceptual model of the proposed digital environment. Guidelines for future research are also discussed.

Research on Mathematics Teachers as Partners in Task Design

ERIC Educational Resources Information Center

Jones, Keith; Pepin, Birgit

2016-01-01

Mathematical tasks and tools, including tasks in the form of digital tools, are key resources in mathematics teaching and in mathematics teacher education. Even so, the "design" of mathematical tasks is perceived in different ways: sometimes seen as something distinct from the teaching and learning process, and sometimes as integral to…

Increasing Awareness of Practice through Interaction across Communities: The Lived Experiences of a Mathematician and Mathematics Teacher Educator

ERIC Educational Resources Information Center

Bleiler, Sarah K.

2015-01-01

Collaborations between mathematicians and mathematics teacher educators are increasingly being expected, and realized, within the context of mathematics teacher education. Most research related to collaborative efforts between members of the mathematics and mathematics education communities has focused on the products, rather than the process of…

Mathematical model of silicon smelting process basing on pelletized charge from technogenic raw materials

NASA Astrophysics Data System (ADS)

Nemchinova, N. V.; Tyutrin, A. A.; Salov, V. M.

2018-03-01

The silicon production process in the electric arc reduction furnaces (EAF) is studied using pelletized charge as an additive to the standard on the basis of the generated mathematical model. The results obtained due to the model will contribute to the analysis of the charge components behavior during melting with the achievement of optimum final parameters of the silicon production process. The authors proposed using technogenic waste as a raw material for the silicon production in a pelletized form using liquid glass and aluminum production dust from the electrostatic precipitators as a binder. The method of mathematical modeling with the help of the ‘Selector’ software package was used as a basis for the theoretical study. A model was simulated with the imitation of four furnace temperature zones and a crystalline silicon phase (25 °C). The main advantage of the created model is the ability to analyze the behavior of all burden materials (including pelletized charge) in the carbothermic process. The behavior analysis is based on the thermodynamic probability data of the burden materials interactions in the carbothermic process. The model accounts for 17 elements entering the furnace with raw materials, electrodes and air. The silicon melt, obtained by the modeling, contained 91.73 % wt. of the target product. The simulation results showed that in the use of the proposed combined charge, the recovery of silicon reached 69.248 %, which is in good agreement with practical data. The results of the crystalline silicon chemical composition modeling are compared with the real silicon samples of chemical analysis data, which showed the results of convergence. The efficiency of the mathematical modeling methods in the studying of the carbothermal silicon obtaining process with complex interphase transformations and the formation of numerous intermediate compounds using a pelletized charge as an additive to the traditional one is shown.

A Mathematical Experience Involving Defining Processes: In-Action Definitions and Zero-Definitions

ERIC Educational Resources Information Center

Ouvrier-Buffet, Cecile

2011-01-01

In this paper, a focus is made on defining processes at stake in an unfamiliar situation coming from discrete mathematics which brings surprising mathematical results. The epistemological framework of Lakatos is questioned and used for the design and the analysis of the situation. The cognitive background of Vergnaud's approach enriches the study…

UAH mathematical model of the variable polarity plasma ARC welding system calculation

NASA Technical Reports Server (NTRS)

Hung, R. J.

1994-01-01

Significant advantages of Variable Polarity Plasma Arc (VPPA) welding process include faster welding, fewer repairs, less joint preparation, reduced weldment distortion, and absence of porosity. A mathematical model is presented to analyze the VPPA welding process. Results of the mathematical model were compared with the experimental observation accomplished by the GDI team.

Objects, Signs, and Representations in the Semio-Cognitive Analysis of the Processes Involved in Teaching and Learning Mathematics: A Duvalian Perspective

ERIC Educational Resources Information Center

Iori, Maura

2017-01-01

In mathematical activities and in the analysis of mathematics teaching-learning processes, "objects," "signs", and "representations" are often mentioned, where the meaning assigned to those words is sometimes very broad, sometimes limited, other times intuitive, allusive, or not completely clear. On the other hand, as…

Predicting reading and mathematics from neural activity for feedback learning.

PubMed

Peters, Sabine; Van der Meulen, Mara; Zanolie, Kiki; Crone, Eveline A

2017-01-01

Although many studies use feedback learning paradigms to study the process of learning in laboratory settings, little is known about their relevance for real-world learning settings such as school. In a large developmental sample (N = 228, 8-25 years), we investigated whether performance and neural activity during a feedback learning task predicted reading and mathematics performance 2 years later. The results indicated that feedback learning performance predicted both reading and mathematics performance. Activity during feedback learning in left superior dorsolateral prefrontal cortex (DLPFC) predicted reading performance, whereas activity in presupplementary motor area/anterior cingulate cortex (pre-SMA/ACC) predicted mathematical performance. Moreover, left superior DLPFC and pre-SMA/ACC activity predicted unique variance in reading and mathematics ability over behavioral testing of feedback learning performance alone. These results provide valuable insights into the relationship between laboratory-based learning tasks and learning in school settings, and the value of neural assessments for prediction of school performance over behavioral testing alone. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Interplay of Determinism and Randomness: From Irreversibility to Chaos, Fractals, and Stochasticity

NASA Astrophysics Data System (ADS)

Tsonis, A.

2017-12-01

We will start our discussion into randomness by looking exclusively at our formal mathematical system to show that even in this pure and strictly logical system one cannot do away with randomness. By employing simple mathematical models, we will identify the three possible sources of randomness: randomness due to inability to find the rules (irreversibility), randomness due to inability to have infinite power (chaos), and randomness due to stochastic processes. Subsequently we will move from the mathematical system to our physical world to show that randomness, through the quantum mechanical character of small scales, through chaos, and because of the second law of thermodynamics, is an intrinsic property of nature as well. We will subsequently argue that the randomness in the physical world is consistent with the three sources of randomness suggested from the study of simple mathematical systems. Many examples ranging from purely mathematical to natural processes will be presented, which clearly demonstrate how the combination of rules and randomness produces the world we live in. Finally, the principle of least effort or the principle of minimum energy consumption will be suggested as the underlying principle behind this symbiosis between determinism and randomness.

On MTE-Model of Mathematics Teaching: Studying the Problems Related to a Plane Division Using the MTE-Model

ERIC Educational Resources Information Center

Bodroza-Pantic, O.; Matic-Kekic, Snezana; Jakovljev, Bogdanka; Markovic, Doko

2008-01-01

In this paper the didactically-methodological procedure named the MTE-model of mathematics teaching (Motivation test-Teaching-Examination test) is suggested and recommended when the teacher has subsequent lessons. This model is presented in detail through the processing of a nonstandard theme--the theme of decomposition of planes. Its efficiency…

The Growing Awareness Inventory: Building Capacity for Culturally Responsive Science and Mathematics with a Structured Observation Protocol

ERIC Educational Resources Information Center

Brown, Julie C.; Crippen, Kent J.

2016-01-01

This study represents a first iteration in the design process of the Growing Awareness Inventory (GAIn), a structured observation protocol for building the awareness of preservice teachers (PSTs) for resources in mathematics and science classrooms that can be used for culturally responsive pedagogy (CRP). The GAIn is designed to develop awareness…

Epistemological Beliefs of Prospective Preschool Teachers and Their Relation to Knowledge, Perception, and Planning Abilities in the Field of Mathematics: A Process Model

ERIC Educational Resources Information Center

Dunekacke, Simone; Jenßen, Lars; Eilerts, Katja; Blömeke, Sigrid

2016-01-01

Teacher competence is a multi-dimensional construct that includes beliefs as well as knowledge. The present study investigated the structure of prospective preschool teachers' mathematics-related beliefs and their relation to content knowledge and pedagogical content knowledge. In addition, prospective preschool teachers' perception and planning…

Tracing the Impact: A Case of a Professional Development Programme in Mathematical Literacy

ERIC Educational Resources Information Center

Bansilal, S.; Goba, B.; Webb, L.; James, A.; Khuzwayo, H.

2012-01-01

The introduction of the subject Mathematical Literacy (ML) as part of the education reform process, led to the development of many large scale in-service programmes designed to train practising teachers to teach the new subject. The purpose of the study is to examine the challenges associated with providing in-service training for teachers of ML,…

Environmental Studies: Mathematical, Computational and Statistical Analyses

DTIC Science & Technology

1993-03-03

mathematical analysis addresses the seasonally and longitudinally averaged circulation which is under the influence of a steady forcing located asymmetrically...employed, as has been suggested for some situations. A general discussion of how interfacial phenomena influence both the original contamination process...describing the large-scale advective and dispersive behaviour of contaminants transported by groundwater and the uncertainty associated with field-scale

Do Teachers Make Decisions Like Firefighters? Applying Naturalistic Decision-Making Methods to Teachers' In-Class Decision Making in Mathematics

ERIC Educational Resources Information Center

Jazby, Dan

2014-01-01

Research into human decision making (DM) processes from outside of education paint a different picture of DM than current DM models in education. This pilot study assesses the use of critical decision method (CDM)--developed from observations of firefighters' DM -- in the context of primary mathematics teachers' in-class DM. Preliminary results…

IEA's TIMSS 2003 International Report on Achievement in the Mathematics Cognitive Domains: Findings from a Developmental Project

ERIC Educational Resources Information Center

Mullis, Ina V. S.; Martin, Michael O.; Foy, Pierre

2005-01-01

This report documents the process undertaken to produce scales in three cognitive domains: knowing, applying, and reasoning. Included are the final scales showing differences among countries, as well as within countries. TIMSS 2003 is the third and most recently completed round of IEA's Trends in International Mathematics and Science Study, a…

Folding Back and the Dynamical Growth of Mathematical Understanding: Elaborating the Pirie-Kieren Theory

ERIC Educational Resources Information Center

Martin, Lyndon C.

2008-01-01

The study reported here extends the work of Pirie and Kieren on the nature and growth of mathematical understanding. The research examines in detail a key aspect of their theory, the process of 'folding back', and develops a theoretical framework of categories and sub-categories that more fully describe the phenomenon. This paper presents an…

The Effect of Game-Assisted Mathematics Education on Academic Achievement in Turkey: A Meta-Analysis Study

ERIC Educational Resources Information Center

Turgut, Sedat; Temur, Özlem Dogan

2017-01-01

In this research, the effects of using game in mathematics teaching process on academic achievement in Turkey were examined by metaanalysis method. For this purpose, the average effect size value and the average effect size values of the moderator variables (education level, the field of education, game type, implementation period and sample size)…

A preference for mathematical processing outweighs the selectivity for Arabic numbers in the inferior temporal gyrus.

PubMed

Grotheer, Mareike; Jeska, Brianna; Grill-Spector, Kalanit

2018-03-28

A region in the posterior inferior temporal gyrus (ITG), referred to as the number form area (NFA, here ITG-numbers) has been implicated in the visual processing of Arabic numbers. However, it is unknown if this region is specifically involved in the visual encoding of Arabic numbers per se or in mathematical processing more broadly. Using functional magnetic resonance imaging (fMRI) during experiments that systematically vary tasks and stimuli, we find that mathematical processing, not preference to Arabic numbers, consistently drives both mean and distributed responses in the posterior ITG. While we replicated findings of higher responses in ITG-numbers to numbers than other visual stimuli during a 1-back task, this preference to numbers was abolished when participants engaged in mathematical processing. In contrast, an ITG region (ITG-math) that showed higher responses during an adding task vs. other tasks maintained this preference for mathematical processing across a wide range of stimuli including numbers, number/letter morphs, hands, and dice. Analysis of distributed responses across an anatomically-defined posterior ITG expanse further revealed that mathematical task but not Arabic number form can be successfully and consistently decoded from these distributed responses. Together, our findings suggest that the function of neuronal regions in the posterior ITG goes beyond the specific visual processing of Arabic numbers. We hypothesize that they ascribe numerical content to the visual input, irrespective of the format of the stimulus. Copyright © 2018 Elsevier Inc. All rights reserved.

Studies on mathematical modeling of the leaching process in order to efficiently recover lead from the sulfate/oxide lead paste.

PubMed

Buzatu, Traian; Ghica, Gabriel Valeriu; Petrescu, Ionuţ Mircea; Iacob, Gheorghe; Buzatu, Mihai; Niculescu, Florentina

2017-02-01

Increasing global lead consumption has been mainly supported by the acid battery manufacturing industry. As the lead demand will continue to grow, to provide the necessary lead will require an efficient approach to recycling lead acid batteries. In this paper was performed a mathematical modeling of the process parameters for lead recovery from spent lead-acid batteries. The results of the mathematical modeling compare well with the experimental data. The experimental method applied consists in the solubilisation of the sulfate/oxide paste with sodium hydroxide solutions followed by electrolytic processing for lead recovery. The parameters taken into considerations were NaOH molarity (4M, 6M and 8M), solid/liquid ratio - S/L (1/10, 1/30 and 1/50) and temperature (40°C, 60°C and 80°C). The optimal conditions resulted by mathematical modeling of the electrolytic process of lead deposition from alkaline solutions have been established by using a second-order orthogonal program, in order to obtain a maximum efficiency of current without exceeding an imposed energy specific consumption. The optimum value for the leaching recovery efficiency, obtained through mathematical modeling, was 89.647%, with an error of δ y =3.623 which leads to a maximum recovery efficiency of 86.024%. The optimum values for each variable that ensure the lead extraction efficiency equal to 89.647% are the following: 3M - NaOH, 1/35 - S/L, 70°C - temperature. Copyright © 2016 Elsevier Ltd. All rights reserved.

The link between middle school mathematics course placement and achievement.

PubMed

Domina, Thurston

2014-01-01

The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students' mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth-grade algebra and geometry course placements are academically selective, but considerable between-school variation exists in students' odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness. © 2014 The Author. Child Development © 2014 Society for Research in Child Development, Inc.

Analysis of Undergraduate Students’ Mathematical Understanding Ability of the Limit of Function Based on APOS Theory Perspective

NASA Astrophysics Data System (ADS)

Afgani, M. W.; Suryadi, D.; Dahlan, J. A.

2017-09-01

The aim of this study was to know the level of undergraduate students’ mathematical understanding ability based on APOS theory perspective. The APOS theory provides an evaluation framework to describe the level of students’ understanding and mental structure about their conception to a mathematics concept. The levels of understanding in APOS theory are action, process, object, and schema conception. The subjects were 59 students of mathematics education whom had attended a class of the limit of function at a university in Palembang. The method was qualitative descriptive with 4 test items. The result showed that most of students were still at the level of action conception. They could calculate and use procedure precisely to the mathematics objects that was given, but could not reach the higher conception yet.

STEM Gives Meaning to Mathematics

ERIC Educational Resources Information Center

Hefty, Lukas J.

2015-01-01

The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…

Conservation Abilities, Visuospatial Skills, and Numerosity Processing Speed: Association With Math Achievement and Math Difficulties in Elementary School Children.

PubMed

Lambert, Katharina; Spinath, Birgit

The aim of the present study was to investigate the associations between elementary school children's mathematical achievement and their conservation abilities, visuospatial skills, and numerosity processing speed. We also assessed differences in these abilities between children with different types of learning problems. In Study 1 ( N = 229), we investigated second to fourth graders and in Study 2 ( N = 120), third and fourth graders. Analyses revealed significant contributions of numerosity processing speed and visuospatial skills to math achievement beyond IQ. Conservation abilities were predictive in Study 1 only. Children with math difficulties showed lower visuospatial skills and conservation abilities than children with typical achievement levels and children with reading and/or spelling difficulties, whereas children with combined difficulties explicitly showed low conservation abilities. These findings provide further evidence for the relations between children's math skills and their visuospatial skills, conservation abilities, and processing speed and contribute to the understanding of deficits that are specific to mathematical difficulties.

Exploring Yellowstone National Park with Mathematical Modeling

ERIC Educational Resources Information Center

Wickstrom, Megan H.; Carr, Ruth; Lackey, Dacia

2017-01-01

Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

An Analysis of Pre-Service Mathematics Teachers' Performance in Modelling Tasks in Terms of Spatial Visualisation Ability

ERIC Educational Resources Information Center

Tasova, Halil Ibrahim; Delice, Ali

2012-01-01

Mathematical modelling involves mathematical constructions chosen to represent some real world situations and the relationships among them; it is the process of expressing a real world situation mathematically. Visualisation can play a significant role in the development of thinking or understanding mathematical concepts, and also makes abstract…

Fourth-Grade Primary School Students' Thought Processes and Challenges Encountered during the Butter Beans Problem

ERIC Educational Resources Information Center

Sahin, Neslihan; Eraslan, Ali

2017-01-01

In parallel with mathematical modeling studies that have gradually drawn interest in recent years, the aim of this study is to investigate the thought processes of fourth-grade students in the Butter Beans Problem and to identify possible challenges in this process. For this purpose, a qualitative study was conducted at a university-foundation…

Tracking the Success of Pre-College Algebra Workshop Students in Subsequent College Mathematics Classes

ERIC Educational Resources Information Center

Fuller, Edgar; Deshler, Jessica M.; Kuhn, Betsy; Squire, Douglas

2014-01-01

In 2007 the Department of Mathematics at our institution began developing a placement process designed to identify at-risk students entering mathematics courses at the College Algebra and Calculus levels. Major changes in our placement testing process and the resulting interventions for at-risk students were put in place in Fall of 2008. At the…

Large-Scale Professional Development towards Emancipatory Mathematics: The Genesis of YuMi Deadly Maths

ERIC Educational Resources Information Center

Cooper, Tom; Carter, Merilyn

2016-01-01

This paper describes the genesis of YuMi Deadly Maths, a school change process that has been used in over 200 schools to develop mathematics teaching and learning to improve students' employment and life chances. The paper discusses the YuMi Deadly Maths approach to mathematics content and pedagogy, implemented through a process of PD and school…

The Use of Digital Technology in Finding Multiple Paths to Solve and Extend an Equilateral Triangle Task

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron

2016-01-01

Mathematical tasks are crucial elements for teachers to orient, foster and assess students' processes to comprehend and develop mathematical knowledge. During the process of working and solving a task, searching for or discussing multiple solution paths becomes a powerful strategy for students to engage in mathematical thinking. A simple task that…

Mathematics Education. Selected Papers from the Conference on Stochastic Processes and Their Applications. (15th, Nagoya, Japan, July 2-5, 1985).

ERIC Educational Resources Information Center

Hida, Takeyuki; Shimizu, Akinobu

This volume contains the papers and comments from the Workshop on Mathematics Education, a special session of the 15th Conference on Stochastic Processes and Their Applications, held in Nagoya, Japan, July 2-5, 1985. Topics covered include: (1) probability; (2) statistics; (3) deviation; (4) Japanese mathematics curriculum; (5) statistical…

Some aspects of mathematical and chemical modeling of complex chemical processes

NASA Technical Reports Server (NTRS)

Nemes, I.; Botar, L.; Danoczy, E.; Vidoczy, T.; Gal, D.

1983-01-01

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra.

Mathematics learning on geometry for children with autism

NASA Astrophysics Data System (ADS)

Widayati, F. E.; Usodo, B.; Pamudya, I.

2017-12-01

The purpose of this research is to describe: (1) the mathematics learning process in an inclusion class and (2) the obstacle during the process of mathematics learning in the inclusion class. This research is a descriptive qualitative research. The subjects were a mathematics teacher, children with autism, and a teacher assistant. Method of collecting data was observation and interview. Data validation technique is triangulation technique. The results of this research are : (1) There is a modification of lesson plan for children with autism. This modification such as the indicator of success, material, time, and assessment. Lesson plan for children with autism is arranged by mathematics teacher and teacher assistant. There is no special media for children with autism used by mathematics teacher. (2) The obstacle of children with autism is that they are difficult to understand mathematics concept. Besides, children with autism are easy to lose their focus.

The Dyslexic Student and Mathematics in Higher Education

ERIC Educational Resources Information Center

Perkin, Glynis; Croft, Tony

2007-01-01

Difficulties that are encountered by dyslexic undergraduates with their learning and understanding of mathematics are explored. Specific consideration is given to issues arising through mathematical content, its delivery, the procedures and processes of doing mathematics, and its assessment. Particular difficulties, which have emerged through…

Clinical Assessment in Mathematics: Learning the Craft.

ERIC Educational Resources Information Center

Hunting, Robert P.; Doig, Brian A.

1997-01-01

Discusses a professional development program called Clinical Approaches to Mathematics Assessment. Argues for the advanced training of mathematics teachers who understand knowledge construction processes of students; can use clinical tools for evaluating a student's unique mathematical "fingerprint"; and can create or adapt problems, tasks, or…

The role of cognitive processes, foundational math skill, and calculation accuracy and fluency in word-problem solving versus prealgebraic knowledge.

PubMed

Fuchs, Lynn S; Gilbert, Jennifer K; Powell, Sarah R; Cirino, Paul T; Fuchs, Douglas; Hamlett, Carol L; Seethaler, Pamela M; Tolar, Tammy D

2016-12-01

The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of Grade 2; calculation accuracy and calculation fluency at end of Grade 2; and prealgebraic knowledge and word-problem solving at end of Grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than prealgebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students' foundational mathematics skills or cognitive processes. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

The development of executive functions and early mathematics: a dynamic relationship.

PubMed

Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Boom, Jan; Leseman, Paul P M

2012-03-01

The relationship between executive functions and mathematical skills has been studied extensively, but results are inconclusive, and how this relationship evolves longitudinally is largely unknown. The aim was to investigate the factor structure of executive functions in inhibition, shifting, and updating; the longitudinal development of executive functions and mathematics; and the relation between them. A total of 211 children in grade 2 (7-8 years old) from 10 schools in the Netherlands. Children were followed in grade 1 and 2 of primary education. Executive functions and mathematics were measured four times. The test battery contained multiple tasks for each executive function: Animal stroop, local global, and Simon task for inhibition; Animal Shifting, Trail Making Test in Colours, and Sorting Task for shifting; and Digit Span Backwards, Odd One Out, and Keep Track for updating. The factor structure of executive functions was assessed and relations with mathematics were investigated using growth modelling. Confirmatory factor analysis (CFA) showed that inhibition and shifting could not be distinguished from each other. Updating was a separate factor, and its development was strongly related to mathematical development while inhibition and shifting did not predict mathematics in the presence of the updating factor. The strong relationship between updating and mathematics suggest that updating skills play a key role in the maths learning process. This makes updating a promising target for future intervention studies. ©2011 The British Psychological Society.

Adolescents' perceptions of socializers' beliefs, career-related conversations, and motivation in mathematics.

PubMed

Lazarides, Rebecca; Rubach, Charlott; Ittel, Angela

2017-03-01

Research based on the Eccles model of parent socialization demonstrated that parents are an important source of value and ability information for their children. Little is known, however, about the bidirectional effects between students' perceptions of their parents' beliefs and behaviors and the students' own domain-specific values. This study analyzed how students' perceptions of parents' beliefs and behaviors and students' mathematics values and mathematics-related career plans affect each other bidirectionally, and analyzed the role of students' gender as a moderator of these relations. Data from 475 students in 11th and 12th grade (girls: 50.3%; 31 classrooms; 12 schools), who participated in 2 waves of the study, were analyzed. Results of longitudinal structural equation models demonstrated that students' perceptions of their parents' mathematics value beliefs at Time 1 affected the students' own mathematics utility value at Time 2. Bidirectional effects were not shown in the full sample but were identified for boys. The paths within the tested model varied for boys and girls. For example, boys', not girls', mathematics intrinsic value predicted their reported conversations with their fathers about future occupational plans. Boys', not girls', perceived parents' mathematics value predicted the mathematics utility value. Findings are discussed in relation to their implications for parents and teachers, as well as in relation to gendered motivational processes. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Low performance on mathematical tasks in preschoolers: the importance of domain-general and domain-specific abilities.

PubMed

Costa, H M; Nicholson, B; Donlan, C; Van Herwegen, J

2018-04-01

Different domain-specific and domain-general cognitive precursors play a key role in the development of mathematical abilities. The contribution of these domains to mathematical ability changes during development. Primary school-aged children who show mathematical difficulties form a heterogeneous group, but it is not clear whether this also holds for preschool low achievers (LAs) and how domain-specific and domain-general abilities contribute to mathematical difficulties at a young age. The aim of this study was to explore the cognitive characteristics of a sample of preschool LAs and identify sub-types of LAs. 81 children were identified as LAs from 283 preschoolers aged 3 to 5 years old and were assessed on a number of domain-general and domain-specific tasks. Cluster analysis revealed four subgroups of LAs in mathematics: (1) a weak processing sub-type; (2) a general mathematical LAs sub-type; (3) a mixed abilities sub-type; and (4) a visuo-spatial deficit sub-type. Whilst two of the groups showed specific domain-general difficulties, none showed only domain-specific difficulties. Current findings suggest that preschool LAs constitute a heterogeneous group and stress the importance of domain-general factors for the development of mathematical abilities during the preschool years. © 2018 MENCAP and International Association of the Scientific Study of Intellectual and Developmental Disabilities and John Wiley & Sons Ltd.

The research of 4th grade mathematical curriculum electronic picture book construction and development in integrating indigenous culture

NASA Astrophysics Data System (ADS)

Chen, Yen Ting; Hsin Wang, Juei

2017-02-01

This research aimed at integrating Seediq culture and mathematical course design for fourth-grade elementary school, and then transforming this mathematical course into an electronic picture book. During the process of electronic book development, the researchers collected videos of six participants engaged in discussion, reflection minutes after the meeting written by the attendants, the researchers' observation and review journals, and conversations with the participants. Then, researchers utilized Content Analysis to explore, try, review and retry steps of electronic book making process. The main findings: There are four periods of electronic book making process, research occurrence period, curriculum design period, electronic book transformation period, and result evaluation period. The picture book included the White Stone Legend born from Seediq seniors, historical battle for hunting field between tribes, and concepts of approximation, angle, triangle, and quadrangle features. At last, with the research result, this article presents the corroboration of related works, and then proposes suggestions of electronic book teaching and follow-up studies.

Monitoring temperatures in coal conversion and combustion processes via ultrasound

NASA Astrophysics Data System (ADS)

Gopalsami, N.; Raptis, A. C.; Mulcahey, T. P.

1980-02-01

The state of the art of instrumentation for monitoring temperatures in coal conversion and combustion systems is examined. The instrumentation types studied include thermocouples, radiation pyrometers, and acoustical thermometers. The capabilities and limitations of each type are reviewed. A feasibility study of the ultrasonic thermometry is described. A mathematical model of a pulse-echo ultrasonic temperature measurement system is developed using linear system theory. The mathematical model lends itself to the adaptation of generalized correlation techniques for the estimation of propagation delays. Computer simulations are made to test the efficacy of the signal processing techniques for noise-free as well as noisy signals. Based on the theoretical study, acoustic techniques to measure temperature in reactors and combustors are feasible.

On the Reasonable and Unreasonable Effectiveness of Mathematics in Classical and Quantum Physics

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2011-03-01

The point of departure for this article is Werner Heisenberg's remark, made in 1929: "It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which seems entirely adequate for the treatment of atomic processes." The cost of this discovery, at least in Heisenberg's and related interpretations of quantum mechanics (such as that of Niels Bohr), is that, in contrast to classical mechanics, the mathematical scheme in question no longer offers a description, even an idealized one, of quantum objects and processes. This scheme only enables predictions, in general, probabilistic in character, of the outcomes of quantum experiments. As a result, a new type of the relationships between mathematics and physics is established, which, in the language of Eugene Wigner adopted in my title, indeed makes the effectiveness of mathematics unreasonable in quantum but, as I shall explain, not in classical physics. The article discusses these new relationships between mathematics and physics in quantum theory and their implications for theoretical physics—past, present, and future.

Recent Trends in Karst Geomorphology.

ERIC Educational Resources Information Center

Palmer, Arthur N.

1984-01-01

Recent trends related to the karst processes and the evolution of karst landscapes are discussed. The hydrochemical processes responsible for the origin of karst are expanded on to illustrate the present scope of karst studies. These geomorphological studies are combined with concepts and techniques from hydraulics, chemistry, and mathematics. (JN)

Mathematics authentic assessment on statistics learning: the case for student mini projects

NASA Astrophysics Data System (ADS)

Fauziah, D.; Mardiyana; Saputro, D. R. S.

2018-03-01

Mathematics authentic assessment is a form of meaningful measurement of student learning outcomes for the sphere of attitude, skill and knowledge in mathematics. The construction of attitude, skill and knowledge achieved through the fulfilment of tasks which involve active and creative role of the students. One type of authentic assessment is student mini projects, started from planning, data collecting, organizing, processing, analysing and presenting the data. The purpose of this research is to learn the process of using authentic assessments on statistics learning which is conducted by teachers and to discuss specifically the use of mini projects to improving students’ learning in the school of Surakarta. This research is an action research, where the data collected through the results of the assessments rubric of student mini projects. The result of data analysis shows that the average score of rubric of student mini projects result is 82 with 96% classical completeness. This study shows that the application of authentic assessment can improve students’ mathematics learning outcomes. Findings showed that teachers and students participate actively during teaching and learning process, both inside and outside of the school. Student mini projects also provide opportunities to interact with other people in the real context while collecting information and giving presentation to the community. Additionally, students are able to exceed more on the process of statistics learning using authentic assessment.

Empowering Mathematical Practices

ERIC Educational Resources Information Center

Coomes, Jacqueline; Lee, Hyung Sook

2017-01-01

Mathematics teachers want to empower students as mathematical thinkers and doers (NCTM 2000). Specific ways of thinking and doing mathematics were described in the Process Standards (NCTM 2000); they were further characterized as habits of mind (Mark, Goldenberg, and Sword 2010); and more recently, they were detailed in the Common Core's Standards…

Making the Most of Modeling Tasks

ERIC Educational Resources Information Center

Wernet, Jamie L.; Lawrence, Kevin A.; Gilbertson, Nicholas J.

2015-01-01

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

Research Mathematicians' Practices in Selecting Mathematical Problems

ERIC Educational Resources Information Center

Misfeldt, Morten; Johansen, Mikkel Willum

2015-01-01

Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how mathematicians select and pose problems and discuss to…

The Teaching of Mathematics in Secondary Schools as a Tool for Self-Reliance and Re-Branding Process in Nigeria

ERIC Educational Resources Information Center

Jonah, Tali D.; Caleb, Mbwas .L.; Stephen, Abe A.

2012-01-01

Mathematics teaching is an interaction between the teacher and the learners that leads to acquisition of desirable mathematical knowledge, ideas and skills necessary for applicability in our everyday life. This paper therefore looks at the concept of self-reliance, the concept of mathematics teaching, problems and prospects of mathematics teaching…

Problem Solving: How Do In-Service Secondary School Teachers of Mathematics Make Sense of a Non-Routine Problem Context?

ERIC Educational Resources Information Center

Mwei, Philip K.

2017-01-01

The concept of mathematical problem solving is an important mathematical process in mathematics curricula of education systems worldwide. These math curricula demand that learners are exposed to authentic problems that foster successful problem solving. To attain this very important goal, there must be mathematics teachers well versed in content…

From boring to scoring - a collaborative serious game for learning and practicing mathematical logic for computer science education

NASA Astrophysics Data System (ADS)

Schäfer, Andreas; Holz, Jan; Leonhardt, Thiemo; Schroeder, Ulrik; Brauner, Philipp; Ziefle, Martina

2013-06-01

In this study, we address the problem of low retention and high dropout rates of computer science university students in early semesters of the studies. Complex and high abstract mathematical learning materials have been identified as one reason for the dropout rate. In order to support the understanding and practicing of core mathematical concepts, we developed a game-based multitouch learning environment in which the need for a suitable learning environment for mathematical logic was combined with the ability to train cooperation and collaboration in a learning scenario. As application domain, the field of mathematical logic had been chosen. The development process was accomplished along three steps: First, ethnographic interviews were run with 12 students of computer science revealing typical problems with mathematical logic. Second, a multitouch learning environment was developed. The game consists of multiple learning and playing modes in which teams of students can collaborate or compete against each other. Finally, a twofold evaluation of the environment was carried out (user study and cognitive walk-through). Overall, the evaluation showed that the game environment was easy to use and rated as helpful: The chosen approach of a multiplayer game supporting competition, collaboration, and cooperation is perceived as motivating and "fun."

Introducing a Symbolic Interactionist Approach on Teaching Mathematics: The Case of Revoicing as an Interactional Strategy in the Teaching of Probability

ERIC Educational Resources Information Center

Eckert, Andreas; Nilsson, Per

2017-01-01

This study examines an interactional view on teaching mathematics, whereby meaning is co-produced with the students through a process of negotiation. Further, teaching is viewed from a symbolic interactionism perspective, allowing the analysis to focus on the teacher's role in the negotiation of meaning. Using methods inspired by grounded theory,…

Grasp of Consciousness and Performance in Mathematics Making Explicit the Ways of Thinking in Solving Cartesian Product Problems

ERIC Educational Resources Information Center

Soares, Maria Tereza Carneiro; Moro, Maria Lucia Faria; Spinillo, Alina Galvao

2012-01-01

This study examines the relationship between the grasp of consciousness of the reasoning process in Grades 5 and 8 pupils from a public and a private school, and their performance in mathematical problems of Cartesian product. Forty-two participants aged from 10 to 16 solved four problems in writing and explained their solution procedures by…

How Visual Imagery Contributed to College: A Case of How Visual Imagery Contributes to a College Algebra Student's Understanding of the Concept of Function in the United States

ERIC Educational Resources Information Center

Lane, Rebekah M.

2011-01-01

This investigation utilized the qualitative case study method. Seventy-one College Algebra students were given a mathematical processing instrument. This testing device measured a student's preference for visual thinking. Two students were purposefully selected using the instrument. The visual mathematical learner (VL) was discussed in this…

Using Blended Learning to Facilitate the Mathematical thought Processes of Primary School Learners in a Computer Laboratory: A Case Study in Calculating Simple Areas

ERIC Educational Resources Information Center

Naidoo, N.; Naidoo, R.

2007-01-01

Primary school learners' first encounters with mathematics in a traditional learning environment often create lifelong "math phobia."(Papert 1980) The situation in a country emerging from an oppressive education system designed to educationally disempower the majority of the population is much worse. The typical scenario in a previously…

Evaluating a technical university's placement test using the Rasch measurement model

NASA Astrophysics Data System (ADS)

Salleh, Tuan Salwani; Bakri, Norhayati; Zin, Zalhan Mohd

2016-10-01

This study discusses the process of validating a mathematics placement test at a technical university. The main objective is to produce a valid and reliable test to measure students' prerequisite knowledge to learn engineering technology mathematics. It is crucial to have a valid and reliable test as the results will be used in a critical decision making to assign students into different groups of Technical Mathematics 1. The placement test which consists of 50 mathematics questions were tested on 82 new diplomas in engineering technology students at a technical university. This study employed rasch measurement model to analyze the data through the Winsteps software. The results revealed that there are ten test questions lower than less able students' ability. Nevertheless, all the ten questions satisfied infit and outfit standard values. Thus, all the questions can be reused in the future placement test at the technical university.

Challenges in Math.

ERIC Educational Resources Information Center

Feng, Chengde

1992-01-01

Fourteen mathematics problems from the 1987 Chinese Primary School Mathematics Examination for fifth and sixth grade students are presented. The word problems, accompanied by answers, involve algebra, division, ratios, areas, and other mathematical processes. (JDD)

First-Grade Predictors of Mathematical Learning Disability: A Latent Class Trajectory Analysis

PubMed Central

Geary, David C.; Bailey, Drew H.; Littlefield, Andrew; Wood, Phillip; Hoard, Mary K.; Nugent, Lara

2009-01-01

Kindergarten to 3rd grade mathematics achievement scores from a prospective study of mathematical development were subjected to latent growth trajectory analyses (n = 306). The four corresponding classes included children with mathematical learning disability (MLD, 6% of sample), and low (LA, 50%), typically (TA, 39%) and high (HA, 5%) achieving children. The groups were administered a battery of intelligence (IQ), working memory, and mathematical-cognition measures in 1st grade. The children with MLD had general deficits in working memory and IQ, and potentially more specific deficits on measures of number sense. The LA children did not have working memory or IQ deficits, but showed moderate deficits on these number sense measures and for addition fact retrieval. The distinguishing features of the HA children were a strong visuospatial working memory, a strong number sense, and frequent use of memory-based processes to solve addition problems. Implications for the early identification of children at risk for poor mathematics achievement are discussed. PMID:20046817

Individual differences in mathematical competence predict parietal brain activation during mental calculation.

PubMed

Grabner, Roland H; Ansari, Daniel; Reishofer, Gernot; Stern, Elsbeth; Ebner, Franz; Neuper, Christa

2007-11-01

Functional neuroimaging studies have revealed that parietal brain circuits subserve arithmetic problem solving and that their recruitment dynamically changes as a function of training and development. The present study investigated whether the brain activation during mental calculation is also modulated by individual differences in mathematical competence. Twenty-five adult students were selected from a larger pool based on their performance on standardized tests of intelligence and arithmetic and divided into groups of individuals with relatively lower and higher mathematical competence. These groups did not differ in their non-numerical intelligence or age. In an fMRI block-design, participants had to verify the correctness of single-digit and multi-digit multiplication problems. Analyses revealed that the individuals with higher mathematical competence displayed stronger activation of the left angular gyrus while solving both types of arithmetic problems. Additional correlational analyses corroborated the association between individual differences in mathematical competence and angular gyrus activation, even when variability in task performance was controlled for. These findings demonstrate that the recruitment of the left angular gyrus during arithmetic problem solving underlies individual differences in mathematical ability and suggests a stronger reliance on automatic, language-mediated processes in more competent individuals.

Mathematical modeling of physiological systems: an essential tool for discovery.

PubMed

Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J

2014-08-28

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.

Brain stimulation, mathematical, and numerical training: Contribution of core and noncore skills.

PubMed

Looi, C Y; Cohen Kadosh, R

2016-01-01

Mathematical abilities that are correlated with various life outcomes vary across individuals. One approach to improve mathematical abilities is by understanding the underlying cognitive functions. Theoretical and experimental evidence suggest that mathematical abilities are subserved by "core" and "noncore" skills. Core skills are commonly regarded as the "innate" capacity to attend to and process numerical information, while noncore skills are those that are important for mathematical cognition, but are not exclusive to the mathematical domain such as executive functions, spatial skills, and attention. In recent years, mathematical training has been combined with the application of noninvasive brain stimulation to further enhance training outcomes. However, the development of more strategic training paradigms is hindered by the lack of understanding on the contributory nature of core and noncore skills and their neural underpinnings. In the current review, we will examine the effects of brain stimulation with focus on transcranial electrical stimulation on core and noncore skills, and its impact on mathematical and numerical training. We will conclude with a discussion on the theoretical and experimental implications of these studies and directions for further research. © 2016 Elsevier B.V. All rights reserved.

On the Relationships between (Relatively) Advanced Mathematical Knowledge and (Relatively) Advanced Problem-Solving Behaviours

ERIC Educational Resources Information Center

Koichu, Boris

2010-01-01

This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

Structurally Sound Statistics Instruction

ERIC Educational Resources Information Center

Casey, Stephanie A.; Bostic, Jonathan D.

2016-01-01

The Common Core's Standards for Mathematical Practice (SMP) call for all K-grade 12 students to develop expertise in the processes and proficiencies of doing mathematics. However, the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) as a whole addresses students' learning of not only mathematics but also statistics. This situation…

Harry Potter and the Coding of Secrets

ERIC Educational Resources Information Center

Chua, Boon Liang

2008-01-01

When students learn mathematics, they tend to understand and remember the mathematical processes that they find practical and relevant. It is not surprising then that "Principles and Standards for School Mathematics" (NCTM 2000) encourages teachers to help students discover the relevance of mathematics in their daily lives. To help young people…

Saussurian Linguistics Revisited: Can It Inform Our Interpretation of Mathematical Activity?.

ERIC Educational Resources Information Center

McNamara, O.

1995-01-01

Examines the basic notions of Ferdinand de Saussure and proposes that language is fundamental to the process of learning mathematics. Investigates possible mathematical perspectives upon Saussure's ideas and explores the contribution his work can offer to enhance and enrich the interpretive framework through which mathematical activity is observed…

Automatic Semantic Generation and Arabic Translation of Mathematical Expressions on the Web

ERIC Educational Resources Information Center

Doush, Iyad Abu; Al-Bdarneh, Sondos

2013-01-01

Automatic processing of mathematical information on the web imposes some difficulties. This paper presents a novel technique for automatic generation of mathematical equations semantic and Arabic translation on the web. The proposed system facilitates unambiguous representation of mathematical equations by correlating equations to their known…

Mathematical Communication in the Classroom: A Teacher Makes a Difference

ERIC Educational Resources Information Center

Cooke, Bessie Davis; Buchholz, Dilek

2005-01-01

The National Council of Teachers of Mathematics (NCTM) states that "Communication is an essential part of mathematics and mathematics education" (2000, p. 60). In fact, communication is one of the five process standards emphasized by NCTM. The communication standard highlights the importance of young children communicating their mathematical…

Thinking Conics

ERIC Educational Resources Information Center

Lewis, Richard

2008-01-01

For their course, mathematics students at Bath Spa University were asked to choose a topic and explore the mathematics. As well as learning some mathematics, the author hoped that the assignment would shed light on the process of mathematical investigation itself. Their course leader had suggested that the topic of conic sections was rich, and…

Inssues for Consideration by Mathematics Educators: Selected Papers.

ERIC Educational Resources Information Center

Denmark, Tom, Ed.

This set of papers, selected from presentations at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics, are of primary interest to mathematics educators. In the first paper, Romberg describes a model for diagnosing mathematical learning difficulties which extends the diagnostic process beyond…

Establishing Validity of the Thai Mathematics Teaching Efficacy Beliefs Instrument

ERIC Educational Resources Information Center

Matney, Gabriel; Jackson, Jack L., II.; Panarach, Yupadee

2016-01-01

This article presents our work in translating the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) from English to Thai and our resulting investigation of validity with Thai preservice teachers. The translation process occurred over several meetings between two U.S. mathematics educators and one Thai mathematics educator. To check for…

NCTM Principles and Standards for Mathematically Talented Students

ERIC Educational Resources Information Center

Deal, Linda J.; Wismer, Michael G.

2010-01-01

The "Principles and Standards for School Mathematics" published in 2000 by the National Council of Teachers of Mathematics (NCTM) created a vision of mathematical concepts and processes to establish core educational guidelines for instruction from grades K to 12. The overall plan does emphasize higher level thinking, problem solving, and…

Mathematics, Programming, and STEM

ERIC Educational Resources Information Center

Yeh, Andy; Chandra, Vinesh

2015-01-01

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10- week teaching experiment, mathematical meaning-making was enriched when primary…

Introduction to a special section on ecohydrology of semiarid environments: Confronting mathematical models with ecosystem complexity

NASA Astrophysics Data System (ADS)

Svoray, Tal; Assouline, Shmuel; Katul, Gabriel

2015-11-01

Current literature provides large number of publications about ecohydrological processes and their effect on the biota in drylands. Given the limited laboratory and field experiments in such systems, many of these publications are based on mathematical models of varying complexity. The underlying implicit assumption is that the data set used to evaluate these models covers the parameter space of conditions that characterize drylands and that the models represent the actual processes with acceptable certainty. However, a question raised is to what extent these mathematical models are valid when confronted with observed ecosystem complexity? This Introduction reviews the 16 papers that comprise the Special Section on Eco-hydrology of Semiarid Environments: Confronting Mathematical Models with Ecosystem Complexity. The subjects studied in these papers include rainfall regime, infiltration and preferential flow, evaporation and evapotranspiration, annual net primary production, dispersal and invasion, and vegetation greening. The findings in the papers published in this Special Section show that innovative mathematical modeling approaches can represent actual field measurements. Hence, there are strong grounds for suggesting that mathematical models can contribute to greater understanding of ecosystem complexity through characterization of space-time dynamics of biomass and water storage as well as their multiscale interactions. However, the generality of the models and their low-dimensional representation of many processes may also be a "curse" that results in failures when particulars of an ecosystem are required. It is envisaged that the search for a unifying "general" model, while seductive, may remain elusive in the foreseeable future. It is for this reason that improving the merger between experiments and models of various degrees of complexity continues to shape the future research agenda.

The analysis of mathematics literacy on PMRI learning with media schoology of junior high school students

NASA Astrophysics Data System (ADS)

Wardono; Mariani, S.

2018-03-01

Indonesia as a developing country in the future will have high competitiveness if its students have high mathematics literacy ability. The current reality from year to year rankings of PISA mathematics literacy Indonesian students are still not good. This research is motivated by the importance and low ability of the mathematics literacy. The purpose of this study is to: (1) analyze the effectiveness of PMRI learning with media Schoology, (2) describe the ability of students' mathematics literacy on PMRI learning with media Schoology which is reviewed based on seven components of mathematics literacy, namely communication, mathematizing, representation, reasoning, devising strategies, using symbols, and using mathematics tool. The method used in this research is the method of sequential design method mix. Techniques of data collection using observation, interviews, tests, and documentation. Data analysis techniques use proportion test, appellate test, and use descriptive analysis. Based on the data analysis, it can be concluded; (1) PMRI learning with media Schoology effectively improve the ability of mathematics literacy because of the achievement of classical completeness, students' mathematics literacy ability in PMRI learning with media Schoology is higher than expository learning, and there is increasing ability of mathematics literacy in PMRI learning with media Schoology of 30%. (2) Highly capable students attain excellent mathematics literacy skills, can work using broad thinking with appropriate resolution strategies. Students who are capable of achieving good mathematics literacy skills can summarize information, present problem-solving processes, and interpret solutions. low-ability students have reached the level of ability of mathematics literacy good enough that can solve the problem in a simple way.

Refractive Thinking Profile In Solving Mathematical Problem Reviewed from Students Math Capability

NASA Astrophysics Data System (ADS)

Maslukha, M.; Lukito, A.; Ekawati, R.

2018-01-01

Refraction is a mental activity experienced by a person to make a decision through reflective thinking and critical thinking. Differences in mathematical capability have an influence on the difference of student’s refractive thinking processes in solving math problems. This descriptive research aims to generate a picture of refractive thinking of students in solving mathematical problems in terms of students’ math skill. Subjects in this study consisted of three students, namely students with high, medium, and low math skills based on mathematics capability test. Data collection methods used are test-based methods and interviews. After collected data is analyzed through three stages that are, condensing and displaying data, data display, and drawing and verifying conclusion. Results showed refractive thinking profiles of three subjects is different. This difference occurs at the planning and execution stage of the problem. This difference is influenced by mathematical capability and experience of each subject.

Mathematical Disabilities in Children with Velo-Cardio-Facial Syndrome

ERIC Educational Resources Information Center

De Smedt, B.; Swillen, A.; Devriendt, K.; Fryns, J. P.; Verschaffel, L.; Ghesquiere, P.

2007-01-01

Current neurocognitive theories of number processing [Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. "Cognitive Neuropsychology," 20, 487-506] state that mathematical performance is made possible by two functionally and anatomically distinct subsystems of number processing: a verbal system…

Determination of thermophysical characteristics of vulcanizable rubber products by the mathematical modeling method

NASA Astrophysics Data System (ADS)

Tikhomirov, S. G.; Pyatakov, Y. V.; Karmanova, O. V.; Maslov, A. A.

2018-03-01

The studies of the vulcanization kinetics of elastomers were carried out using a Truck tyre tread rubber compound. The formal kinetic scheme of vulcanization of rubbers sulfur-accelerator curing system was used which generalizes the set of reactions occurring in the curing process. A mathematical model is developed for determining the thermal parameters vulcanizable mixture comprising algorithms for solving direct and inverse problems for system of equations of heat conduction and kinetics of the curing process. The performance of the model is confirmed by the results of numerical experiments on model examples.

Topics in geophysical fluid dynamics: Atmospheric dynamics, dynamo theory, and climate dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghil, M.; Childress, S.

1987-01-01

This text is the first study to apply systematically the successive bifurcations approach to complex time-dependent processes in large scale atmospheric dynamics, geomagnetism, and theoretical climate dynamics. The presentation of recent results on planetary-scale phenomena in the earth's atmosphere, ocean, cryosphere, mantle and core provides an integral account of mathematical theory and methods together with physical phenomena and processes. The authors address a number of problems in rapidly developing areas of geophysics, bringing into closer contact the modern tools of nonlinear mathematics and the novel problems of global change in the environment.

Computer-Based Mathematics Instructions for Engineering Students

NASA Technical Reports Server (NTRS)

Khan, Mustaq A.; Wall, Curtiss E.

1996-01-01

Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.

Analysis of mathematical problem-solving ability based on metacognition on problem-based learning

NASA Astrophysics Data System (ADS)

Mulyono; Hadiyanti, R.

2018-03-01

Problem-solving is the primary purpose of the mathematics curriculum. Problem-solving abilities influenced beliefs and metacognition. Metacognition as superordinate capabilities can direct, regulate cognition and motivation and then problem-solving processes. This study aims to (1) test and analyzes the quality of problem-based learning and (2) investigate the problem-solving capabilities based on metacognition. This research uses mixed method study with The subject research are class XI students of Mathematics and Science at High School Kesatrian 2 Semarang which divided into tacit use, aware use, strategic use and reflective use level. The collecting data using scale, interviews, and tests. The data processed with the proportion of test, t-test, and paired samples t-test. The result shows that the students with levels tacit use were able to complete the whole matter given, but do not understand what and why a strategy is used. Students with aware use level were able to solve the problem, be able to build new knowledge through problem-solving to the indicators, understand the problem, determine the strategies used, although not right. Students on the Strategic ladder Use can be applied and adopt a wide variety of appropriate strategies to solve the issues and achieved re-examine indicators of process and outcome. The student with reflective use level is not found in this study. Based on the results suggested that study about the identification of metacognition in problem-solving so that the characteristics of each level of metacognition more clearly in a more significant sampling. Teachers need to know in depth about the student metacognitive activity and its relationship with mathematical problem solving and another problem resolution.

Promoting Writing in Mathematics: Prospective Teachers' Experiences and Perspectives on the Process of Writing When Doing Mathematics as Problem Solving

ERIC Educational Resources Information Center

Kuzle, Ana

2013-01-01

Despite a great deal of research on the benefits of writing in mathematics, writing plays a minimal role, if any, in secondary and tertiary mathematics education. In order for teachers to use writing in their classrooms, they themselves have to experience writing mathematics within the teacher education programme. The present paper reports on a…

Novel mathematic models for quantitative transitivity of quality-markers in extraction process of the Buyanghuanwu decoction.

PubMed

Zhang, Yu-Tian; Xiao, Mei-Feng; Deng, Kai-Wen; Yang, Yan-Tao; Zhou, Yi-Qun; Zhou, Jin; He, Fu-Yuan; Liu, Wen-Long

2018-06-01

Nowadays, to research and formulate an efficiency extraction system for Chinese herbal medicine, scientists have always been facing a great challenge for quality management, so that the transitivity of Q-markers in quantitative analysis of TCM was proposed by Prof. Liu recently. In order to improve the quality of extraction from raw medicinal materials for clinical preparations, a series of integrated mathematic models for transitivity of Q-markers in quantitative analysis of TCM were established. Buyanghuanwu decoction (BYHWD) was a commonly TCMs prescription, which was used to prevent and treat the ischemic heart and brain diseases. In this paper, we selected BYHWD as an extraction experimental subject to study the quantitative transitivity of TCM. Based on theory of Fick's Rule and Noyes-Whitney equation, novel kinetic models were established for extraction of active components. Meanwhile, fitting out kinetic equations of extracted models and then calculating the inherent parameters in material piece and Q-marker quantitative transfer coefficients, which were considered as indexes to evaluate transitivity of Q-markers in quantitative analysis of the extraction process of BYHWD. HPLC was applied to screen and analyze the potential Q-markers in the extraction process. Fick's Rule and Noyes-Whitney equation were adopted for mathematically modeling extraction process. Kinetic parameters were fitted and calculated by the Statistical Program for Social Sciences 20.0 software. The transferable efficiency was described and evaluated by potential Q-markers transfer trajectory via transitivity availability AUC, extraction ratio P, and decomposition ratio D respectively. The Q-marker was identified with AUC, P, D. Astragaloside IV, laetrile, paeoniflorin, and ferulic acid were studied as potential Q-markers from BYHWD. The relative technologic parameters were presented by mathematic models, which could adequately illustrate the inherent properties of raw materials preparation and affection of Q-markers transitivity in equilibrium processing. AUC, P, D for potential Q-markers of AST-IV, laetrile, paeoniflorin, and FA were obtained, with the results of 289.9 mAu s, 46.24%, 22.35%; 1730 mAu s, 84.48%, 1.963%; 5600 mAu s, 70.22%, 0.4752%; 7810 mAu s, 24.29%, 4.235%, respectively. The results showed that the suitable Q-markers were laetrile and paeoniflorin in our study, which exhibited acceptable traceability and transitivity in the extraction process of TCMs. Therefore, these novel mathematic models might be developed as a new standard to control TCMs quality process from raw medicinal materials to product manufacturing. Copyright © 2018 Elsevier GmbH. All rights reserved.

GeoGebra Assist Discovery Learning Model for Problem Solving Ability and Attitude toward Mathematics

NASA Astrophysics Data System (ADS)

Murni, V.; Sariyasa, S.; Ardana, I. M.

2017-09-01

This study aims to describe the effet of GeoGebra utilization in the discovery learning model on mathematical problem solving ability and students’ attitude toward mathematics. This research was quasi experimental and post-test only control group design was used in this study. The population in this study was 181 of students. The sampling technique used was cluster random sampling, so the sample in this study was 120 students divided into 4 classes, 2 classes for the experimental class and 2 classes for the control class. Data were analyzed by using one way MANOVA. The results of data analysis showed that the utilization of GeoGebra in discovery learning can lead to solving problems and attitudes towards mathematics are better. This is because the presentation of problems using geogebra can assist students in identifying and solving problems and attracting students’ interest because geogebra provides an immediate response process to students. The results of the research are the utilization of geogebra in the discovery learning can be applied in learning and teaching wider subject matter, beside subject matter in this study.

Mathematics for understanding disease.

PubMed

Bies, R R; Gastonguay, M R; Schwartz, S L

2008-06-01

The application of mathematical models to reflect the organization and activity of biological systems can be viewed as a continuum of purpose. The far left of the continuum is solely the prediction of biological parameter values, wherein an understanding of the underlying biological processes is irrelevant to the purpose. At the far right of the continuum are mathematical models, the purposes of which are a precise understanding of those biological processes. No models in present use fall at either end of the continuum. Without question, however, the emphasis in regards to purpose has been on prediction, e.g., clinical trial simulation and empirical disease progression modeling. Clearly the model that ultimately incorporates a universal understanding of biological organization will also precisely predict biological events, giving the continuum the logical form of a tautology. Currently that goal lies at an immeasurable distance. Nonetheless, the motive here is to urge movement in the direction of that goal. The distance traveled toward understanding naturally depends upon the nature of the scientific question posed with respect to comprehending and/or predicting a particular disease process. A move toward mathematical models implies a move away from static empirical modeling and toward models that focus on systems biology, wherein modeling entails the systematic study of the complex pattern of organization inherent in biological systems.

Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement?

PubMed

Sasanguie, Delphine; Göbel, Silke M; Moll, Kristina; Smets, Karolien; Reynvoet, Bert

2013-03-01

In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities. Copyright © 2012 Elsevier Inc. All rights reserved.

Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient

NASA Astrophysics Data System (ADS)

Aryani, F.; Amin, S. M.; Sulaiman, R.

2018-01-01

Algebraic reasoning is a process in which students generalize mathematical ideas from a set of particular instances and express them in increasingly formal and age-appropriate ways. Using problem solving approach to develop algebraic reasoning of mathematics may enhace the long-term learning trajectory of the majority students. The purpose of this research was to describe the algebraic reasoning of quitter, camper, and climber junior high school students in solving mathematical problems. This research used qualitative descriptive method. Subjects were determined by purposive sampling. The technique of collecting data was done by task-based interviews.The results showed that the algebraic reasoning of three students in the process of pattern seeking by identifying the things that are known and asked in a similar way. But three students found the elements of pattern recognition in different ways or method. So, they are generalize the problem of pattern formation with different ways. The study of algebraic reasoning and problem solving can be a learning paradigm in the improve students’ knowledge and skills in algebra work. The goal is to help students’ improve academic competence, develop algebraic reasoning in problem solving.

The Effect of Dynamic and Interactive Mathematics Learning Environments (DIMLE), Supporting Multiple Representations, on Perceptions of Elementary Mathematics Pre-Service Teachers in Problem Solving Process

ERIC Educational Resources Information Center

Ozdemir, S.; Reis, Z. Ayvaz

2013-01-01

Mathematics is an important discipline, providing crucial tools, such as problem solving, to improve our cognitive abilities. In order to solve a problem, it is better to envision and represent through multiple means. Multiple representations can help a person to redefine a problem with his/her own words in that envisioning process. Dynamic and…

Gender: Its relation to Mathematical Creative Thinking Skill

NASA Astrophysics Data System (ADS)

Permatasari, H. R.; Wahyudin, W.

2017-09-01

Mathematical creative thinking skill is one of the most important capabilities in the present century, both for men and women. One of the current issues is about gender and how gender mainstreaming can be realized optimally. The purpose of this study is to determine the comparison of the mathematical creative thinking skill increasing between male and female students after the application of Team Games Tournament (TGT) learning. This research was conducted at 28 students in the 4th grade of an elementary school in Bandung City. The research method used is quasi experiment because it is aimed to test wether there are differences in mathematical creative thinking skill improving between male and female students after being treatment in the form of learnig with TGT. The result of this research is that there is no difference in mathematical creative thinking skill improving between male and female students after the application of TGT learning. It is influenced by some factors such as how the teacher treats male and female with the same treatment in learning process. Recommendation of this research that can be done further research about this topic more deeply. Beside that, the teacher especially in elementary school can use the TGT learning application to reduce the gap between male and female students during the learning process.

Who is afraid of math? Two sources of genetic variance for mathematical anxiety.

PubMed

Wang, Zhe; Hart, Sara Ann; Kovas, Yulia; Lukowski, Sarah; Soden, Brooke; Thompson, Lee A; Plomin, Robert; McLoughlin, Grainne; Bartlett, Christopher W; Lyons, Ian M; Petrill, Stephen A

2014-09-01

Emerging work suggests that academic achievement may be influenced by the management of affect as well as through efficient information processing of task demands. In particular, mathematical anxiety has attracted recent attention because of its damaging psychological effects and potential associations with mathematical problem solving and achievement. This study investigated the genetic and environmental factors contributing to the observed differences in the anxiety people feel when confronted with mathematical tasks. In addition, the genetic and environmental mechanisms that link mathematical anxiety with math cognition and general anxiety were also explored. Univariate and multivariate quantitative genetic models were conducted in a sample of 514 12-year-old twin siblings. Genetic factors accounted for roughly 40% of the variation in mathematical anxiety, with the remaining being accounted for by child-specific environmental factors. Multivariate genetic analyses suggested that mathematical anxiety was influenced by the genetic and nonfamilial environmental risk factors associated with general anxiety and additional independent genetic influences associated with math-based problem solving. The development of mathematical anxiety may involve not only exposure to negative experiences with mathematics, but also likely involves genetic risks related to both anxiety and math cognition. These results suggest that integrating cognitive and affective domains may be particularly important for mathematics and may extend to other areas of academic achievement. © 2014 The Authors. Journal of Child Psychology and Psychiatry. © 2014 Association for Child and Adolescent Mental Health.

Who’s Afraid of Math? Two Sources of Genetic Variance for Mathematical Anxiety

PubMed Central

Wang, Zhe; Hart, Sara Ann; Kovas, Yulia; Lukowski, Sarah; Soden, Brooke; Thompson, Lee A.; Plomin, Robert; McLoughlin, Grainne; Bartlett, Christopher W.; Lyons, Ian M.; Petrill, Stephen A.

2015-01-01

Background Emerging work suggests that academic achievement may be influenced by the management of affect as well as through efficient information processing of task demands. In particular, mathematical anxiety has attracted recent attention because of its damaging psychological effects and potential associations with mathematical problem-solving and achievement. The present study investigated the genetic and environmental factors contributing to the observed differences in the anxiety people feel when confronted with mathematical tasks. In addition, the genetic and environmental mechanisms that link mathematical anxiety with math cognition and general anxiety were also explored. Methods Univariate and multivariate quantitative genetic models were conducted in a sample of 514 12-year-old twin siblings. Results Genetic factors accounted for roughly 40% of the variation in mathematical anxiety, with the remaining being accounted for by child-specific environmental factors. Multivariate genetic analyses suggested that mathematical anxiety was influenced by the genetic and non-familial environmental risk factors associated with general anxiety and additional independent genetic influences associated with math-based problem solving. Conclusions The development of mathematical anxiety may involve not only exposure to negative experiences with mathematics, but also likely involves genetic risks related to both anxiety and math cognition. These results suggest that integrating cognitive and affective domains may be particularly important for mathematics, and may extend to other areas of academic achievement. PMID:24611799

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students' mathematical performance

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-12-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students' mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students' simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students' formulation and combination of equations. Several reasons may explain this difference, including the students' different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

Two-Dimensional Mathematical Modeling of the Pack Carburizing Process

NASA Astrophysics Data System (ADS)

Sarkar, S.; Gupta, G. S.

2008-10-01

Pack carburization is the oldest method among the case-hardening treatments, and sufficient attempts have not been made to understand this process in terms of heat and mass transfer, effect of alloying elements, dimensions of the sample, etc. Thus, a two-dimensional mathematical model in cylindrical coordinate is developed for simulating the pack carburization process for chromium-bearing steel in this study. Heat and mass balance equations are solved simultaneously, where the surface temperature of the sample varies with time, but the carbon potential at the surface during the process remains constant. The fully implicit finite volume technique is used to solve the governing equations. Good agreement has been found between the predicted and published data. The effect of temperature, carburizing time, dimensions of the sample, etc. on the pack carburizing process shows some interesting results. It is found that the two-dimensional model gives better insight into understanding the carburizing process.

Hydrogen Production via a High-Efficiency Low-Temperature Reformer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paul KT Liu; Theo T. Tsotsis

2006-05-31

Fuel cells are promoted by the US government as a viable alternative for clean and efficient energy generation. It is anticipated that the fuel cell market will rise if the key technical barriers can be overcome. One of them is certainly fuel processing and purification. Existing fuel reforming processes are energy intensive, extremely complicated and capital intensive; these disadvantages handicap the scale-down of existing reforming process, targeting distributed or on-board/stationary hydrogen production applications. Our project involves the bench-scale demonstration of a high-efficiency low-temperature steam reforming process. Hydrogen production can be operated at 350 to 400ºC with our invention, as opposedmore » to >800ºC of existing reforming. In addition, our proposed process improves the start-up deficiency of conventional reforming due to its low temperature operation. The objective of this project is to demonstrate the invented process concept via a bench scale unit and verify mathematical simulation for future process optimization study. Under this project, we have performed the experimental work to determine the adsorption isotherm, reaction kinetics, and membrane permeances required to perform the process simulation based upon the mathematical model developed by us. A ceramic membrane coated with palladium thin film fabricated by us was employed in this study. The adsorption isotherm for a selected hydrotalcite adsorbent was determined experimentally. Further, the capacity loss under cyclic adsorption/desorption was confirmed to be negligible. Finally a commercial steam reforming catalyst was used to produce the reaction kinetic parameters required for the proposed operating condition. With these input parameters, a mathematical simulation was performed to predict the performance of the invented process. According to our simulation, our invented hybrid process can deliver 35 to 55% methane conversion, in comparison with the 12 and 18-21% conversion of the packed bed and an adsorptive reactor respectively. In addition CO contamination with <10 to 120 ppm is predicted for the invented process depending upon the cycle time for the PSA type operation. In comparison, the adsorption reactor can also deliver a similar CO contaminant at the low end; however, its high end reaches as high as 300 ppm based upon the simulation of our proposed operating condition. Our experimental results for the packed bed and the membrane reactor deliver 12 and 18% conversion at 400°C, approaching the conversion by the mathematical simulation. Due to the time constraint, the experimental study on the conversion of the invented process has not been complete. However, our in-house study using a similar process concept for the water gas shift reaction has demonstrated the reliability of our mathematical simulation for the invented process. In summary, we are confident that the invented process can deliver efficiently high purity hydrogen at a low temperature (~400°C). According to our projection, the invented process can further achieve 5% energy savings and ~50% capital savings over conventional reforming for fuel cell applications. The pollution abatement potential associated with the implementation of fuel cells, including the elimination of nitrogen oxides and CO, and the reduction in volatile organics and CO2, can thus be realized with the implementation of this invented process. The projected total market size for equipment sale for the proposed process in US is $1.5 billion annually.« less

Is Mathematical Anxiety Always Bad for Math Learning: The Role of Math Motivation

PubMed Central

Wang, Zhe; Lukowski, Sarah L.; Hart, Sara Ann; Lyons, Ian M.; Thompson, Lee A.; Kovas, Yulia; Mazzocco, Michèle M.; Plomin, Robert; Petrill, Stephen A.

2015-01-01

The linear relations between math anxiety and math cognition have been frequently studied. However, the relations between anxiety and performance on complex cognitive tasks have been repeatedly demonstrated to follow a curvilinear fashion. Given the lack of attention to the possibility of such complex interplay between emotion and cognition in the math learning literature, the current study aimed to address this gap via exploring the relations between math anxiety, math motivation, and math cognition. The current study consisted of two samples. One sample included 262 pairs of young adolescent twins and the other included 237 adult college students. Participants self-reported their math anxiety and math motivation. Math cognition was assessed using a comprehensive battery of mathematics tasks. In both samples, results showed inverted-U relations between math anxiety and math performance in students with high intrinsic math motivation, and modest negative associations between math anxiety and math performance in students with low intrinsic math motivation. However, this pattern was not observed in tasks assessing student’s nonsymbolic and symbolic number estimation. These findings may help advance our understanding of mathematics learning processes and may provide important insights for treatment programs that target improving mathematics learning experiences and mathematical skills. PMID:26518438

Intersectional Analysis in Critical Mathematics Education Research: A Response to Figure Hiding

ERIC Educational Resources Information Center

Bullock, Erika C.

2018-01-01

In this chapter, I use figure hiding as a metaphor representing the processes of exclusion and suppression that critical mathematics education (CME) seeks to address. Figure hiding renders identities and modes of thought in mathematics education and mathematics education research invisible. CME has a commitment to addressing figure hiding by…

Understanding Understanding Mathematics. Artificial Intelligence Memo No. 488.

ERIC Educational Resources Information Center

Michener, Edwina Rissland

This document is concerned with the important extra-logical knowledge that is often outside of traditional discussions in mathematics, and looks at some of the ingredients and processes involved in the understanding of mathematics. The goal is to develop a conceptual framework in which to talk about mathematical knowledge and to understand the…

McDonald's vs Father Christmas

ERIC Educational Resources Information Center

Pratt, Dave; Simpson, Amanda

2004-01-01

Mathematics in textbooks and indeed in conventional classrooms is often presented as exercises or worksheets in which the mathematics itself has been processed into a form that is easily digested. This McDonald's version of mathematics ensures that the mathematical skill or technique is laid bare and typically the sole focus of attention. In this…

Mathematics and Its Other: (Dis)locating the Feminine

ERIC Educational Resources Information Center

de Freitas, Elizabeth

2008-01-01

In this article, the author examines how school mathematics maps itself onto the body, delineating the contours of a gendered learner. The author draws on Judith Butler to discuss the process by which school mathematics contributes to the stabilising/legitimating of a cultural arbitrary like gender, and how mathematics inscribes otherness onto the…

Use of Angle Model to Understand Addition and Subtraction of Fractions

ERIC Educational Resources Information Center

Mukwambo, Muzwangowenyu; Ngcoza, Kenneth; Ramasike, Lineo Florence

2018-01-01

Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and…

Mathematics and Economics: Connections for Life, 9-12.

ERIC Educational Resources Information Center

MacDonald, Rich; Breidenbach, Lisa; Doetschman, Evelyn L.

Bringing mathematics and economics together to connect them in students' minds gives students very important skills they can use in their lives. This book is intended for high school mathematics teachers, with lessons designed to reinforce the mathematics concepts and processes taught by using examples from economics. The book consists of 15…

Mission Mathematics: Linking Aerospace and the NCTM Standards, K-6.

ERIC Educational Resources Information Center

Hynes, Mary Ellen, Ed.

This book is designed to present mathematical problems and tasks that focus on the National Council of Teachers of Mathematics (NCTM) curriculum and evaluation standards in the context of aerospace activities. It aims at actively engaging students in NCTM's four process standards: (1) problem solving; (2) mathematical reasoning; (3) communicating…

How Do Mathematicians Learn Math?: Resources and Acts for Constructing and Understanding Mathematics

ERIC Educational Resources Information Center

Wilkerson-Jerde, Michelle H.; Wilensky, Uri J.

2011-01-01

In this paper, we present an analytic framework for investigating expert mathematical learning as the process of building a "network of mathematical resources" by establishing relationships between different components and properties of mathematical ideas. We then use this framework to analyze the reasoning of ten mathematicians and mathematics…

Emotion, Identity and Teacher Learning: Becoming a Primary Mathematics Teacher

ERIC Educational Resources Information Center

Hodgen, Jeremy; Askew, Mike

2007-01-01

Teacher change in mathematics education is recognised to be a difficult and at times painful process. This is particularly so in countries such as England where primary mathematics is taught by non-specialist teachers, who have often had negative experiences of their own school mathematics. In this paper we explore primary teachers' emotional…

Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process

ERIC Educational Resources Information Center

Bal, Aytgen Pinar; Doganay, Ahmet

2014-01-01

The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

Examining the Process of Developing a Research-Based Mathematics Curriculum and Its Policy Implications

ERIC Educational Resources Information Center

Superfine, Alison Castro; Kelso, Catherine Randall; Beal, Susan

2010-01-01

The implementation of "research-based" mathematics curricula is increasingly becoming a central element of mathematics education reform policies. Given the recent focus on grounding mathematics curriculum policies in research, it is important to understand precisely what it means for a curriculum to be research-based. Using the Curriculum Research…

Remedial Mathematics: Diagnostic and Prescriptive Approaches. Papers from the First National Conference on Remedial Mathematics.

ERIC Educational Resources Information Center

Higgins, Jon L., Ed.; Heddens, James W., Ed.

The papers in this publication were developed from speeches and reactions presented at the first National Conference on Remedial Mathematics held at Kent State University in 1974. Papers focus on identifying and describing the remedial mathematics student, classroom diagnosis, clinical diagnosis, the diagnostic process, and promising procedures…

Project-Based Learning and Design-Focused Projects to Motivate Secondary Mathematics Students

ERIC Educational Resources Information Center

Remijan, Kelly W.

2017-01-01

This article illustrates how mathematics teachers can develop design-focused projects, related to project-based learning, to motivate secondary mathematics students. With first-hand experience as a secondary mathematics teacher, I provide a series of steps related to the engineering design process, which are helpful to teachers in developing…

Identifying Systems of Interaction in Mathematical Engagement

ERIC Educational Resources Information Center

Brown, Bruce J. L.

2014-01-01

Mathematical engagement is a complex process of interaction between the person and the world. This interaction is strongly influenced by the concepts and structure of the mathematical field, by the practical and symbolic tools of mathematics and by the focus of investigation in the world. This paper reports on research that involves a detailed…

Fracking: Drilling into Math and Social Justice

ERIC Educational Resources Information Center

Hendrickson, Katie A.

2015-01-01

Mathematical modeling, a focus of the Common Core State Standards for School Mathematics (CCSSI 2010) and one of the Standards for Mathematical Practice, is generally considered to be the process of exploring a real-world situation and making sense of it using mathematics (Lesh and Zawojewski 2007). Teachers need to create opportunities for…

Research on Mathematical Literacy in Schools--Aim, Approach and Attention

ERIC Educational Resources Information Center

Haara, Frode Olav; Bolstad, Oda Heidi; Jenssen, Eirik S.

2017-01-01

The development of mathematical literacy in schools is of significant concern at the policy level, and research is an important source of information in this process. This review article focuses on areas of research interest identified in empirical projects on mathematical literacy, and how mathematical literacy in schools is approached by…

Mathematical Knowledge: Its Growth through Teaching. Mathematics Education Library, Volume 10.

ERIC Educational Resources Information Center

Bishop, Alan J., Ed.; And Others

This book presents issues concerning relationships between mathematical knowledge and the teaching and learning processes, focusing especially on the genesis of mathematical knowledge in the classroom. The chapter titles are: (1) The Fragility of Knowledge (Guy Brousseau and Michael Otte); (2) The Double Bind as a Didactical Trap (Stieg…

The Poisson Random Process. Applications of Probability Theory to Operations Research. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 340.

ERIC Educational Resources Information Center

Wilde, Carroll O.

The Poisson probability distribution is seen to provide a mathematical model from which useful information can be obtained in practical applications. The distribution and some situations to which it applies are studied, and ways to find answers to practical questions are noted. The unit includes exercises and a model exam, and provides answers to…

Mathematical Model of Bone Regeneration in a Porous Implant

NASA Astrophysics Data System (ADS)

Maslov, L. B.

2017-07-01

A mathematical model of the reparative regeneration of bone tissue governed by the law of cell differentiation and action of an external periodic mechanical loading is presented. The model allows one to study the recovery processes of injured human locomotor system elements under a dynamic loading and to theoretically substantiate the choice of an optimum periodic impact on the defective tissues for their fastest and steady healing.

Are Graphic Novels Always "Cool"? Parent and Student Perspectives on Elementary Mathematics and Science Graphic Novels: The Need for Action Research by School Leaders

ERIC Educational Resources Information Center

Nesmith, Suzanne; Cooper, Sandi; Schwarz, Gretchen; Walker, Amanda

2016-01-01

Often the stakeholders most affected by curriculum change are uninvolved in the change process, leading to curriculum reforms that fail. Thus, a group of university researchers conducted a small-scale study to explore the thoughts and opinions of parents and elementary students on the use of mathematics and science graphic novels to support the…

Mathematical tasks, study approaches, and course grades in undergraduate mathematics: a year-by-year analysis

NASA Astrophysics Data System (ADS)

Maciejewski, Wes; Merchant, Sandra

2016-04-01

Students approach learning in different ways, depending on the experienced learning situation. A deep approach is geared toward long-term retention and conceptual change while a surface approach focuses on quickly acquiring knowledge for immediate use. These approaches ultimately affect the students' academic outcomes. This study takes a cross-sectional look at the approaches to learning used by students from courses across all four years of undergraduate mathematics and analyses how these relate to the students' grades. We find that deep learning correlates with grade in the first year and not in the upper years. Surficial learning has no correlation with grades in the first year and a strong negative correlation with grades in the upper years. Using Bloom's taxonomy, we argue that the nature of the tasks given to students is fundamentally different in lower and upper year courses. We find that first-year courses emphasize tasks that require only low-level cognitive processes. Upper year courses require higher level processes but, surprisingly, have a simultaneous greater emphasis on recall and understanding. These observations explain the differences in correlations between approaches to learning and course grades. We conclude with some concerns about the disconnect between first year and upper year mathematics courses and the effect this may have on students.

Visual short term memory related brain activity predicts mathematical abilities.

PubMed

Boulet-Craig, Aubrée; Robaey, Philippe; Lacourse, Karine; Jerbi, Karim; Oswald, Victor; Krajinovic, Maja; Laverdière, Caroline; Sinnett, Daniel; Jolicoeur, Pierre; Lippé, Sarah

2017-07-01

Previous research suggests visual short-term memory (VSTM) capacity and mathematical abilities are significantly related. Moreover, both processes activate similar brain regions within the parietal cortex, in particular, the intraparietal sulcus; however, it is still unclear whether the neuronal underpinnings of VSTM directly correlate with mathematical operation and reasoning abilities. The main objective was to investigate the association between parieto-occipital brain activity during the retention period of a VSTM task and performance in mathematics. The authors measured mathematical abilities and VSTM capacity as well as brain activity during memory maintenance using magnetoencephalography (MEG) in 19 healthy adult participants. Event-related magnetic fields (ERFs) were computed on the MEG data. Linear regressions were used to estimate the strength of the relation between VSTM related brain activity and mathematical abilities. The amplitude of parieto-occipital cerebral activity during the retention of visual information was related to performance in 2 standardized mathematical tasks: mathematical reasoning and calculation fluency. The findings show that brain activity during retention period of a VSTM task is associated with mathematical abilities. Contributions of VSTM processes to numerical cognition should be considered in cognitive interventions. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Rigorous Mathematical Thinking Approach to Enhance Students’ Mathematical Creative and Critical Thinking Abilities

NASA Astrophysics Data System (ADS)

Hidayat, D.; Nurlaelah, E.; Dahlan, J. A.

2017-09-01

The ability of mathematical creative and critical thinking are two abilities that need to be developed in the learning of mathematics. Therefore, efforts need to be made in the design of learning that is capable of developing both capabilities. The purpose of this research is to examine the mathematical creative and critical thinking ability of students who get rigorous mathematical thinking (RMT) approach and students who get expository approach. This research was quasi experiment with control group pretest-posttest design. The population were all of students grade 11th in one of the senior high school in Bandung. The result showed that: the achievement of mathematical creative and critical thinking abilities of student who obtain RMT is better than students who obtain expository approach. The use of Psychological tools and mediation with criteria of intentionality, reciprocity, and mediated of meaning on RMT helps students in developing condition in critical and creative processes. This achievement contributes to the development of integrated learning design on students’ critical and creative thinking processes.

Heuristic and algorithmic processing in English, mathematics, and science education.

PubMed

Sharps, Matthew J; Hess, Adam B; Price-Sharps, Jana L; Teh, Jane

2008-01-01

Many college students experience difficulties in basic academic skills. Recent research suggests that much of this difficulty may lie in heuristic competency--the ability to use and successfully manage general cognitive strategies. In the present study, the authors evaluated this possibility. They compared participants' performance on a practice California Basic Educational Skills Test and on a series of questions in the natural sciences with heuristic and algorithmic performance on a series of mathematics and reading comprehension exercises. Heuristic competency in mathematics was associated with better scores in science and mathematics. Verbal and algorithmic skills were associated with better reading comprehension. These results indicate the importance of including heuristic training in educational contexts and highlight the importance of a relatively domain-specific approach to questions of cognition in higher education.

Early Foundations for Mathematics Learning and Their Relations to Learning Disabilities.

PubMed

Geary, David C

2013-02-01

Children's quantitative competencies upon entry into school can have lifelong consequences. Children who start behind generally stay behind, and mathematical skills at school completion influence employment prospects and wages in adulthood. I review the current debate over whether early quantitative learning is supported by (a) an inherent system for representing approximate magnitudes, (b) an attentional-control system that enables explicit processing of quantitative symbols, such as Arabic numerals, or (c) the logical problem-solving abilities that facilitate learning of the relations among numerals. Studies of children with mathematical learning disabilities and difficulties have suggested that each of these competencies may be involved, but to different degrees and at different points in the learning process. Clarifying how and when these competencies facilitate early quantitative learning and developing interventions to address their impact on children have the potential to yield substantial benefits for individuals and for society.

Two-dimensional coupled mathematical modeling of fluvial processes with intense sediment transport and rapid bed evolution

NASA Astrophysics Data System (ADS)

Yue, Zhiyuan; Cao, Zhixian; Li, Xin; Che, Tao

2008-09-01

Alluvial rivers may experience intense sediment transport and rapid bed evolution under a high flow regime, for which traditional decoupled mathematical river models based on simplified conservation equations are not applicable. A two-dimensional coupled mathematical model is presented, which is generally applicable to the fluvial processes with either intense or weak sediment transport. The governing equations of the model comprise the complete shallow water hydrodynamic equations closed with Manning roughness for boundary resistance and empirical relationships for sediment exchange with the erodible bed. The second-order Total-Variation-Diminishing version of the Weighted-Average-Flux method, along with the HLLC approximate Riemann Solver, is adapted to solve the governing equations, which can properly resolve shock waves and contact discontinuities. The model is applied to the pilot study of the flooding due to a sudden outburst of a real glacial-lake.

Mobile technologies in the service of students' learning of mathematics: the example of game application A.L.E.X. in the context of a primary school in Cyprus

NASA Astrophysics Data System (ADS)

Kyriakides, Andreas O.; Meletiou-Mavrotheris, Maria; Prodromou, Theodosia

2016-03-01

This article reports on the main experiences gained from a 2-year study which incorporated A.L.E.X., an educational puzzle game available on iPad or Android tablet devices, within the primary school mathematics curriculum. The study took place in a public primary school, located in a rural area of Cyprus. The majority of its students come from low socioeconomic status families. Among the school community, a group of 15 pupils (eight boys and seven girls), aged 10-11 years old, was randomly selected to comprise the sample. The same group of students was visited twice within a period of 2 years, and a teaching intervention was organized. In both interventions, the application A.L.E.X. accompanied by a student worksheet constituted the main means of instruction. The worksheets were designed to integrate a technology with core mathematical ideas embedded in the national mathematics curriculum. Findings gained from the teaching intervention suggest that game apps hold a lot of promise as a tool for reforming mathematics education. While working with A.L.E.X., the children identified and processed mathematical themes that emerged spontaneously. They experienced unique emotions of surprise and enthusiasm regarding the existence of games with mathematical content that led them to acknowledge the pedagogical role that tablet devices could play. This helped them to broaden their fundamentally narrow viewpoint of mathematics as being primarily computation and arithmetic.

Student-Perceived Mothers' and Fathers' Beliefs, Mathematics and English Motivations, and Career Choices.

PubMed

Lazarides, Rebecca; Watt, Helen M G

2017-12-01

According to Eccles and Jacobs' (1986) parent socialization model, parents' gendered ability and value beliefs influence girls' and boys' interpretations of those beliefs, and hence students' domain-specific valuing of tasks and competence beliefs and subsequent career plans. Studies have rarely analyzed how both student-perceived mothers' and fathers' beliefs affect girls' and boys' task values, success expectancies, and career plans across domains. This study analyzed survey data of 459 students (262 boys) assessed through Grades 9, 10, and 11 from three coeducational secondary schools in Sydney, Australia. Longitudinal structural equation models revealed gendered value transmission pathways for girls in mathematics. Although mathematics test scores did not vary statistically significantly, girls reported statistically significantly lower mothers' ability beliefs for them in mathematics than boys at Time 1, which led to their statistically significantly lower mathematics intrinsic value at Time 2 and mathematics-related career plans at Time 3. Such gendered pathways did not occur in English. Matched same-gender effects and gendered pathways in parent socialization processes were evident; perceived mothers' value beliefs were more strongly related to girls' than boys' importance values in English. Student-perceived fathers' ability beliefs positively predicted boys', not girls', importance value in mathematics. Implications for educational practice emphasize the need to target girls' and boys' interest when aiming to enhance their mathematical career motivations. © 2017 The Authors. Journal of Research on Adolescence © 2017 Society for Research on Adolescence.

Comparison of Science Process Skills with STEM Career Interests of Middle School Students

ERIC Educational Resources Information Center

Zorlu, Fulya; Zorlu, Yusuf

2017-01-01

This study was aimed to examine the relation between the STEM (Science, Technology, Engineering and Mathematics) career interests and science process skills of middle school seventh grade students. Method of this study was the relational survey method. The study was conducted on the basis of voluntariness and participants were 133 seventh grade…

Discrete Dynamical Modeling.

ERIC Educational Resources Information Center

Sandefur, James T.

1991-01-01

Discussed is the process of translating situations involving changing quantities into mathematical relationships. This process, called dynamical modeling, allows students to learn new mathematics while sharpening their algebraic skills. A description of dynamical systems, problem-solving methods, a graphical analysis, and available classroom…

[New trends in the evaluation of mathematics learning disabilities. The role of metacognition].

PubMed

Miranda-Casas, A; Acosta-Escareño, G; Tarraga-Minguez, R; Fernández, M I; Rosel-Remírez, J

2005-01-15

The current trends in the evaluation of mathematics learning disabilities (MLD), based on cognitive and empirical models, are oriented towards combining procedures involving the criteria and the evaluation of cognitive and metacognitive processes, associated to performance in mathematical tasks. The objective of this study is to analyse the metacognitive skills of prediction and evaluation in performing maths tasks and to compare metacognitive performance among pupils with MLD and younger pupils without MLD, who have the same level of mathematical performance. Likewise, we analyse these pupils' desire to learn. Subjects and methods. We compare a total of 44 pupils from the second cycle of primary education (8-10 years old) with and without mathematics learning disabilities. Significant differences are observed between pupils with and without mathematics learning disabilities in their capacity to predict and assess all of the tasks evaluated. As regards their 'desire to learn', no significant differences were found between pupils with and without MLD, which indicated that those with MLD assess their chances of successfully performing maths tasks in the same way as those without MLD. Finally, the findings reveal a similar metacognitive profile in pupils with MLD and the younger pupils with no mathematics learning disabilities. In future studies we consider it important to analyse the influence of the socio-affective belief system in the use of metacognitive skills.

Math Process Standards Series, Grades PreK-2 [with CD-ROMs

ERIC Educational Resources Information Center

O'Connell, Susan, Ed.

2007-01-01

The National Council of Teachers of Mathematics (NCTM)'s Process Standards support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every primary teacher the opportunity to explore each standard in depth. With language and examples that don't require…

Developing Mathematical Processes (DMP). Field Test Evaluation, 1972-1973.

ERIC Educational Resources Information Center

Schall, William E.; And Others

The field test of the Developing Mathematical Processes (DMP) program was conducted jointly by the Falconer Central School, St. Mary's Elementary School in Dunkirk, New York, and the Teacher Education Research Center at the State University College in Fredonia, New York. DMP is a research-based, innovative, process-oriented elementary mathematics…

Cognitive Components of a Mathematical Processing Network in 9-Year-Old Children

ERIC Educational Resources Information Center

Szucs, Dénes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2014-01-01

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are…

Study the Problem.

ERIC Educational Resources Information Center

Choate, Joyce S.

1990-01-01

The initial step of a strategic process for solving mathematical problems, "studying the question," is discussed. A lesson plan for teaching students to identify and revise arithmetic problems is presented, involving directed instruction and supervised practice. (JDD)

An Epidemiological Study of Number Processing and Mental Calculation in Greek Schoolchildren

ERIC Educational Resources Information Center

Koumoula, Anastasia; Tsironi, Vanda; Stamouli, Victoria; Bardani, Irini; Stavroula, Siapati; Graham, Annik; Kafantaris, Ignatios; Charalambidou, Irini; Dellatolas, Georges; von Aster, Michael

2004-01-01

The aim of this study was to validate and standardize an instrument for the diagnosis of developmental dyscalculia (mathematics disorder) in a Greek population and to obtain relevant epidemiological data. We used the "Neuropsychological Test Battery for Number Processing and Calculation in Children" (NUCALC) in a community sample of 240 students…

Integrating spatial and numerical structure in mathematical patterning

NASA Astrophysics Data System (ADS)

Ni’mah, K.; Purwanto; Irawan, E. B.; Hidayanto, E.

2018-03-01

This paper reports a study monitoring the integrating spatial and numerical structure in mathematical patterning skills of 30 students grade 7th of junior high school. The purpose of this research is to clarify the processes by which learners construct new knowledge in mathematical patterning. Findings indicate that: (1) students are unable to organize the structure of spatial and numerical, (2) students were only able to organize the spatial structure, but the numerical structure is still incorrect, (3) students were only able to organize numerical structure, but its spatial structure is still incorrect, (4) students were able to organize both of the spatial and numerical structure.

Growth Processes and Formal Logic. Comments on History and Mathematics Regarded as Combined Educational Tools

ERIC Educational Resources Information Center

Seltman, Muriel; Seltman, P. E. J.

1978-01-01

The authors stress the importance of bringing together the causal logic of history and the formal logic of mathematics in order to humanize mathematics and make it more accessible. An example of such treatment is given in a discussion of the centrality of Euclid and the Euclidean system to mathematics development. (MN)

Unraveling the Mystery of the Origin of Mathematical Problems: Using a Problem-Posing Framework with Prospective Mathematics Teachers

ERIC Educational Resources Information Center

Contreras, Jose

2007-01-01

In this article, I model how a problem-posing framework can be used to enhance our abilities to systematically generate mathematical problems by modifying the attributes of a given problem. The problem-posing model calls for the application of the following fundamental mathematical processes: proving, reversing, specializing, generalizing, and…

An Examination of the Statistical Problem-Solving Process as a Potential Means for Developing an Understanding of Argumentation

ERIC Educational Resources Information Center

Smith Baum, Brittany Deshae

2017-01-01

As part of the recent history of the mathematics curriculum, reasoning and argument have been emphasized throughout mathematics curriculum standards. Specifically, as part of the Common Core State Standards for Mathematics, the Standards for Mathematical Practice were presented, which included the expectation that students develop arguments and…

Pre-Service Teachers' Modelling Processes through Engagement with Model Eliciting Activities with a Technological Tool

ERIC Educational Resources Information Center

Daher, Wajeeh M.; Shahbari, Juhaina Awawdeh

2015-01-01

Engaging mathematics students with modelling activities helps them learn mathematics meaningfully. This engagement, in the case of model eliciting activities, helps the students elicit mathematical models by interpreting real-world situation in mathematical ways. This is especially true when the students utilize technology to build the models.…

Development and Application of a Chinese Version of the Short Attitudes toward Mathematics Inventory

ERIC Educational Resources Information Center

Lin, Shu-Hui; Huang, Yun-Chen

2016-01-01

Student attitudes toward mathematics play an important role in the teaching and learning processes of mathematics as positive attitudes correlate with higher student achievement. This paper aims to develop and explore the validity of a Chinese version of the short attitudes toward mathematics inventory (short ATMI) for Taiwanese undergraduates,…

Preliminary Evaluation Report on the Los Angeles City Schools SB 28 Demonstration Program in Mathematics. CSE Working Paper No. 1.

ERIC Educational Resources Information Center

Gordon, C. Wayne

The objectives of the Los Angeles Model Mathematics Project (LAMMP) are stated by the administration as improvement of mathematical skills and understanding of mathematical concepts; improvement of the pupils' self-image; identification of specific assets and limitations relating to the learning process; development and use of special…

Students' Differentiated Translation Processes

ERIC Educational Resources Information Center

Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla

2014-01-01

Understanding how students translate between mathematical representations is of both practical and theoretical importance. This study examined students' processes in their generation of symbolic and graphic representations of given polynomial functions. The purpose was to investigate how students perform these translations. The result of the study…

Early math matters: kindergarten number competence and later mathematics outcomes.

PubMed

Jordan, Nancy C; Kaplan, David; Ramineni, Chaitanya; Locuniak, Maria N

2009-05-01

Children's number competencies over 6 time points, from the beginning of kindergarten to the middle of 1st grade, were examined in relation to their mathematics achievement over 5 later time points, from the end of 1st grade to the end of 3rd grade. The relation between early number competence and mathematics achievement was strong and significant throughout the study period. A sequential process growth curve model showed that kindergarten number competence predicted rate of growth in mathematics achievement between 1st and 3rd grades as well as achievement level through 3rd grade. Further, rate of growth in early number competence predicted mathematics performance level in 3rd grade. Although low-income children performed more poorly than their middle-income counterparts in mathematics achievement and progressed at a slower rate, their performance and growth were mediated through relatively weak kindergarten number competence. Similarly, the better performance and faster growth of children who entered kindergarten at an older age were explained by kindergarten number competence. The findings show the importance of early number competence for setting children's learning trajectories in elementary school mathematics. Copyright 2009 APA, all rights reserved

Early Math Matters: Kindergarten Number Competence and Later Mathematics Outcomes

PubMed Central

Jordan, Nancy C.; Kaplan, David; Ramineni, Chaitanya; Locuniak, Maria N.

2009-01-01

Children’s number competencies over 6 time points, from the beginning of kindergarten to the middle of 1st grade, were examined in relation to their mathematics achievement over 5 later time points, from the end of 1st grade to the end of 3rd grade. The relation between early number competence and mathematics achievement was strong and significant throughout the study period. A sequential process growth curve model showed that kindergarten number competence predicted rate of growth in mathematics achievement between 1st and 3rd grades as well as achievement level through 3rd grade. Further, rate of growth in early number competence predicted mathematics performance level in 3rd grade. Although low-income children performed more poorly than their middle-income counterparts in mathematics achievement and progressed at a slower rate, their performance and growth were mediated through relatively weak kindergarten number competence. Similarly, the better performance and faster growth of children who entered kindergarten at an older age were explained by kindergarten number competence. The findings show the importance of early number competence for setting children’s learning trajectories in elementary school mathematics. PMID:19413436

PREDICTING SUBSURFACE CONTAMINANT TRANSPORT AND TRANSFORMATION: CONSIDERATIONS FOR MODEL SELECTION AND FIELD VALIDATION

EPA Science Inventory

Predicting subsurface contaminant transport and transformation requires mathematical models based on a variety of physical, chemical, and biological processes. The mathematical model is an attempt to quantitatively describe observed processes in order to permit systematic forecas...

Mathematical model and software for investigation of internal ballistic processes in high-speed projectile installations

NASA Astrophysics Data System (ADS)

Diachkovskii, A. S.; Zykova, A. I.; Ishchenko, A. N.; Kasimov, V. Z.; Rogaev, K. S.; Sidorov, A. D.

2017-11-01

This paper describes a software package that allows to explore the interior ballistics processes occurring in a shot scheme with bulk charges using propellant pasty substances at various loading schemes, etc. As a mathematical model, a model of a polydisperse mixture of non-deformable particles and a carrier gas phase is used in the quasi-one-dimensional approximation. Writing the equations of the mathematical model allows to use it to describe a broad class of interior ballistics processes. Features of the using approach are illustrated by calculating the ignition period for the charge of tubular propellant.