Visible Thinking in High School Mathematics

ERIC Educational Resources Information Center

Sliman, Emily

2013-01-01

If a teacher asked their students what thinking looks like, what would they say? Would they just look at the teacher quizzically? The question is challenging because thinking is largely an invisible endeavor, and developing thoughtful students can be a daunting task. However, the job of mathematics teachers is to develop students who think about…

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),…

Conversations about curriculum change: mathematical thinking and team-based learning in a discrete mathematics course

NASA Astrophysics Data System (ADS)

Paterson, Judy; Sneddon, Jamie

2011-10-01

This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused on what he calls the 'unspoken curriculum': mathematical thinking. We consider the ways in which the TBL model promoted and enabled this in the light of literature on mathematical thinking, sense-making and behaviours, and strongly suggest that this approach warrants more attention from the mathematics teaching community. We also discuss shifts in the mathematician's thinking about task construction as he refined the tasks to encourage students to think and behave like mathematicians.

Mathematical Teaching Strategies: Pathways to Critical Thinking and Metacognition

ERIC Educational Resources Information Center

Su, Hui Fang Huang; Ricci, Frederick A.; Mnatsakanian, Mamikon

2016-01-01

A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…

The Transition to Formal Thinking in Mathematics

ERIC Educational Resources Information Center

Tall, David

2008-01-01

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

Cognitive Psychology and Mathematical Thinking.

ERIC Educational Resources Information Center

Greer, Brian

1981-01-01

This review illustrates aspects of cognitive psychology relevant to the understanding of how people think mathematically. Developments in memory research, artificial intelligence, visually mediated processes, and problem-solving research are discussed. (MP)

Explicating mathematical thinking in differential equations using a computer algebra system

NASA Astrophysics Data System (ADS)

Zeynivandnezhad, Fereshteh; Bates, Rachel

2018-07-01

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance students' mathematical thinking by implementing a computer algebra system and active learning pedagogical approaches. students' mathematical thinking processes were analyzed while completing specific differential equations tasks based on posed prompts and questions and Instrumental Genesis. Data were collected from 37 engineering students in a public Malaysian university. This study used the descriptive and interpretive qualitative research design to investigate the students' perspectives of emerging mathematical understanding and approaches to learning mathematics in an undergraduate differential equations course. Results of this study concluded that students used a variety of mathematical thinking processes in a non-sequential manner. Additionally, the outcomes provide justification for continued use of technologies such as computer algebra systems in undergraduate mathematics courses and the need for further studies to uncover the various processes students utilize to complete specific mathematical tasks.

Inhibiting Intuitive Thinking in Mathematics Education

ERIC Educational Resources Information Center

Thomas, Michael O. J.

2015-01-01

The papers in this issue describe recent collaborative research into the role of inhibition of intuitive thinking in mathematics education. This commentary reflects on this research from a mathematics education perspective and draws attention to some of the challenges that arise in collaboration between research fields with different cultures,…

Students’ Mathematical Creative Thinking through Problem Posing Learning

NASA Astrophysics Data System (ADS)

Ulfah, U.; Prabawanto, S.; Jupri, A.

2017-09-01

The research aims to investigate the differences in enhancement of students’ mathematical creative thinking ability of those who received problem posing approach assisted by manipulative media and students who received problem posing approach without manipulative media. This study was a quasi experimental research with non-equivalent control group design. Population of this research was third-grade students of a primary school in Bandung city in 2016/2017 academic year. Sample of this research was two classes as experiment class and control class. The instrument used is a test of mathematical creative thinking ability. Based on the results of the research, it is known that the enhancement of the students’ mathematical creative thinking ability of those who received problem posing approach with manipulative media aid is higher than the ability of those who received problem posing approach without manipulative media aid. Students who get learning problem posing learning accustomed in arranging mathematical sentence become matter of story so it can facilitate students to comprehend about story

Helping Students Acquire Thinking Skills through Mathematics Instruction.

ERIC Educational Resources Information Center

Van Devender, Evelyn M.

1992-01-01

Describes three activities that the teacher can employ to help students develop thinking skills through mathematics instruction: (1) memorization using the technique of chunking; (2) higher order thinking with magic squares; and (3) predicting games. Identifies eight facets of the teacher's role in promoting thinking skills. (MDH)

Characteristic of critical and creative thinking of students of mathematics education study program

NASA Astrophysics Data System (ADS)

Rochmad; Agoestanto, A.; Kharis, M.

2018-03-01

Critical and creative thinking give important role in learning matematics for mathematics education students. This research to explored the characteristic of critical and creative thinking of students of mathematics study program in mathematics department. Critical thinking and creative thinking can be illustrated as two sides of a coin, which one is associated to the other. In elementary linear algebra courses, however, critical thinking can be seen as a foundation to build students’ creative thinking.

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.

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.

Analysis of creative mathematical thinking ability by using model eliciting activities (MEAs)

NASA Astrophysics Data System (ADS)

Winda, A.; Sufyani, P.; Elah, N.

2018-05-01

Lack of creative mathematical thinking ability can lead to not accustomed with open ended problem. Students’ creative mathematical thinking ability in the first grade at one of junior high school in Tangerang City is not fully developed. The reason of students’ creative mathematical thinking ability is not optimally developed is so related with learning process which has done by the mathematics teacher, maybe the learning design that teacher use is unsuitable for increasing students’ activity in the learning process. This research objective is to see the differences in students’ ways of answering the problems in terms of students’ creative mathematical thinking ability during the implementation of Model Eliciting Activities (MEAs). This research use post-test experimental class design. The indicators for creative mathematical thinking ability in this research arranged in three parts, as follow: (1) Fluency to answer the problems; (2) Flexibility to solve the problems; (3) Originality of answers. The result of this research found that by using the same learning model and same instrument from Model Eliciting Activities (MEAs) there are some differences in the way students answer the problems and Model Eliciting Activities (MEAs) can be one of approach used to increase students’ creative mathematical thinking ability.

Level of Student's Creative Thinking in Classroom Mathematics

ERIC Educational Resources Information Center

Siswono, Tatag Yuli Eko

2011-01-01

It is reasonable to assume that people are creative, but the degree of creativity is different. The Idea of the level of student's creative thinking has been expressed by experts, such as Gotoh (2004), and Krulik and Rudnick (1999). The perspective of the mathematics creative thinking refers to a combination of logical and divergent thinking which…

Advanced Numerical-Algebraic Thinking: Constructing the Concept of Covariation as a Prelude to the Concept of Function

ERIC Educational Resources Information Center

Hitt, Fernando; Morasse, Christian

2009-01-01

Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We…

Student’s rigorous mathematical thinking based on cognitive style

NASA Astrophysics Data System (ADS)

Fitriyani, H.; Khasanah, U.

2017-12-01

The purpose of this research was to determine the rigorous mathematical thinking (RMT) of mathematics education students in solving math problems in terms of reflective and impulsive cognitive styles. The research used descriptive qualitative approach. Subjects in this research were 4 students of the reflective and impulsive cognitive style which was each consisting male and female subjects. Data collection techniques used problem-solving test and interview. Analysis of research data used Miles and Huberman model that was reduction of data, presentation of data, and conclusion. The results showed that impulsive male subjects used three levels of the cognitive function required for RMT that were qualitative thinking, quantitative thinking with precision, and relational thinking completely while the other three subjects were only able to use cognitive function at qualitative thinking level of RMT. Therefore the subject of impulsive male has a better RMT ability than the other three research subjects.

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.

A preliminary study on the integral relationship between critical thinking and mathematical thinking among practicing civil engineers

NASA Astrophysics Data System (ADS)

Osman, Sharifah; Mohammad, Shahrin; Abu, Mohd Salleh

2015-05-01

Mathematics and engineering are inexorably and significantly linked and essentially required in analyzing and accessing thought to make good judgment when dealing in complex and varied engineering problems. A study in the current engineering education curriculum to explore how the critical thinking and mathematical thinking relates to one another, is therefore timely crucial. Unfortunately, there is not much information available explicating about the link. This paper aims to report findings of a critical review as well as to provide brief description of an on-going research aimed to investigate the dispositions of critical thinking and the relationship and integration between critical thinking and mathematical thinking during the execution of civil engineering tasks. The first part of the paper reports an in-depth review on these matters based on rather limited resources. The review showed a considerable form of congruency between these two perspectives of thinking, with some prevalent trends of engineering workplace tasks, problems and challenges. The second part describes an on-going research to be conducted by the researcher to investigate rigorously the relationship and integration between these two types of thinking within the perspective of civil engineering tasks. A reasonably close non-participant observations and semi-structured interviews will be executed for the pilot and main stages of the study. The data will be analyzed using constant comparative analysis in which the grounded theory methodology will be adopted. The findings will serve as a useful grounding for constructing a substantive theory revealing the integral relationship between critical thinking and mathematical thinking in the real civil engineering practice context. The substantive theory, from an angle of view, is expected to contribute some additional useful information to the engineering program outcomes and engineering education instructions, aligns with the expectations of

A Mathematical Mystery Tour: Higher-Thinking Math Tasks.

ERIC Educational Resources Information Center

Wahl, Mark

This book contains mathematics activities based upon the concepts of Fibonacci numbers and the Golden Ratio. The activities include higher order thinking skills, calculation practice, integration with different subject areas, mathematics history, extensions and home tasks, teaching notes, and questions for thought and comprehension. A visual map…

Defining Computational Thinking for Mathematics and Science Classrooms

ERIC Educational Resources Information Center

Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri

2016-01-01

Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new…

Screencasts: Formative Assessment for Mathematical Thinking

ERIC Educational Resources Information Center

Soto, Melissa; Ambrose, Rebecca

2016-01-01

Increased attention to reasoning and justification in mathematics classrooms requires the use of more authentic assessment methods. Particularly important are tools that allow teachers and students opportunities to engage in formative assessment practices such as gathering data, interpreting understanding, and revising thinking or instruction.…

An Analysis of Mathematics Teacher Candidates' Critical Thinking Dispositions and Their Logical Thinking Skills

ERIC Educational Resources Information Center

Incikabi, Lutfi; Tuna, Abdulkadir; Biber, Abdullah Cagri

2013-01-01

This study aimed to investigate the existence of the relationship between mathematics teacher candidates' critical thinking skills and their logical thinking dispositions in terms of the variables of grade level in college, high school type, and gender. The current study utilized relational survey model and included a total of 99 mathematics…

The Effect of Concept Attainment Model on Mathematically Critical Thinking Ability of The University Students

NASA Astrophysics Data System (ADS)

Angraini, L. M.; Kartasasmita, B.; Dasari, D.

2017-02-01

This study examined the university students’ mathematically critical thinking ability through Concept Attainment Model learning. The Kolmogorov-Smirnov test, Levene test, t test, ANOVA one and two ways were used to analyse the data. The results of this study showed that (1) there is no difference grade on the student’s mathematical critical thinking ability between experimental group and conventional group as a whole, (2) there is no difference on the students’ mathematical critical thinking ability of experimental classes based on their mathematical early ability (3) there is no interaction between the learning that is used with the students’ mathematical early ability on the students’ mathematical critical thinking ability.

Profile of male-field dependent (FD) prospective teacher's reflective thinking in solving contextual mathematical problem

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student's curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student's reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers' reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher's activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.

Students' Thinking and the Depth of the Mathematics Curriculum

ERIC Educational Resources Information Center

Kent, Laura B.

2014-01-01

This article explores the impact of students' thinking centered professional development on mathematics teaching and learning. Purposeful pedagogy and problem posing are examined as mechanisms by which teachers can potentially deepen students' understanding of mathematics. A classroom example comparing student generated strategies versus…

Leveling Students' Creative Thinking in Solving and Posing Mathematical Problem

ERIC Educational Resources Information Center

Siswono, Tatag Yuli Eko

2010-01-01

Many researchers assume that people are creative, but their degree of creativity is different. The notion of creative thinking level has been discussed .by experts. The perspective of mathematics creative thinking refers to a combination of logical and divergent thinking which is based on intuition but has a conscious aim. The divergent thinking…

Student teachers’ mathematical questioning and courage in metaphorical thinking learning

NASA Astrophysics Data System (ADS)

Hendriana, H.; Hidayat, W.; Ristiana, M. G.

2018-01-01

This study was designed in the form of experiments with control group design and post-test only which aimed to examine the role of metaphorical thinking learning in the mathematical questioning ability of student teachers based on the level of mathematical courage. The population of this study was student teachers of mathematics education study program in West Java Province, while the sample of this study was 152 student teachers which were set purposively and then randomly to be included in the experimental class and control class. Based on the results and discussion, it was concluded that: (a) the mathematical questioning ability of student teachers who received Metaphorical Thinking learning was better than those who received conventional learning seen from mathematical courage level; (b) learning and mathematical courage level factors affected the achievement of student teachers’ mathematical questioning ability. In addition, there was no interaction effect between learning and mathematical courage level (high, medium, and low) simultaneously in developing student teachers’ mathematical questioning ability; (c) achievement of mastering mathematical questioning ability of student teacher was still not well achieved on indicator of problem posing in the form of non-routine question and open question.

Mathematics Teachers' Knowledge of Student Thinking and Its Evidences in Their Instruction

ERIC Educational Resources Information Center

Çelik, Aytug Özaltun; Güzel, Esra Bukova

2017-01-01

The aim of this case study is to examine mathematics teachers' knowledge of students' thinking and its evidences in their teaching. The participants were three secondary mathematics teachers. Data were gathered from interviews and observations. While analyzing the data, the framework about teachers' knowledge of students' thinking was used. The…

Leveling of Critical Thinking Abilities of Students of Mathematics Education in Mathematical Problem Solving

ERIC Educational Resources Information Center

Rasiman

2015-01-01

This research aims to determine the leveling of critical thinking abilities of students of mathematics education in mathematical problem solving. It includes qualitative-explorative study that was conducted at University of PGRI Semarang. The generated data in the form of information obtained problem solving question and interview guides. The…

Explicating Mathematical Thinking in Differential Equations Using a Computer Algebra System

ERIC Educational Resources Information Center

Zeynivandnezhad, Fereshteh; Bates, Rachel

2018-01-01

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance…

A Research on Mathematical Thinking Skills: Mathematical Thinking Skills of Athletes in Individual and Team Sports

ERIC Educational Resources Information Center

Onal, Halil; Inan, Mehmet; Bozkurt, Sinan

2017-01-01

The aim of this research is to examine the mathematical thinking skills of licensed athletes engaged in individual and team sports. The research is designed as a survey model. The sample of the research is composed of 59 female and 170 male licensed athletes (n = 229) and (aged 14 to 52) licensed who do the sports of shooting, billiards, archery,…

Students' Exploratory Thinking about a Nonroutine Calculus Task

ERIC Educational Resources Information Center

Nabb, Keith

2013-01-01

In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect.…

A study of rural preschool practitioners' views on young children's mathematical thinking

NASA Astrophysics Data System (ADS)

Hunting, Robert P.; Mousley, Judith A.; Perry, Bob

2012-03-01

The project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian states. The questions focused on five broad themes: children's mathematics learning, support for mathematics teaching, technology and computers, attitudes and feelings, and assessment and record keeping. We review results from the interview data for each of these themes, discuss their importance, and outline recommendations related to teacher education as well as resource development and research.

Discovery learning model with geogebra assisted for improvement mathematical visual thinking ability

NASA Astrophysics Data System (ADS)

Juandi, D.; Priatna, N.

2018-05-01

The main goal of this study is to improve the mathematical visual thinking ability of high school student through implementation the Discovery Learning Model with Geogebra Assisted. This objective can be achieved through study used quasi-experimental method, with non-random pretest-posttest control design. The sample subject of this research consist of 62 senior school student grade XI in one of school in Bandung district. The required data will be collected through documentation, observation, written tests, interviews, daily journals, and student worksheets. The results of this study are: 1) Improvement students Mathematical Visual Thinking Ability who obtain learning with applied the Discovery Learning Model with Geogebra assisted is significantly higher than students who obtain conventional learning; 2) There is a difference in the improvement of students’ Mathematical Visual Thinking ability between groups based on prior knowledge mathematical abilities (high, medium, and low) who obtained the treatment. 3) The Mathematical Visual Thinking Ability improvement of the high group is significantly higher than in the medium and low groups. 4) The quality of improvement ability of high and low prior knowledge is moderate category, in while the quality of improvement ability in the high category achieved by student with medium prior knowledge.

Listening to and Learning from Student Thinking

ERIC Educational Resources Information Center

Kazemi, Elham; Gibbons, Lynsey K.; Lomax, Kendra; Franke, Megan L.

2016-01-01

Eliciting, responding to, and advancing students' mathematical thinking all lie at the heart of great teaching. In this article, the authors describe a formative assessment approach that teachers can use to learn more about their students' mathematical thinking and inform their instructional decisions. This assessment approach draws on a widely…

Developing Contextual Mathematical Thinking Learning Model to Enhance Higher-Order Thinking Ability for Middle School Students

ERIC Educational Resources Information Center

Samo, Damianus D.; Darhim; Kartasasmita, Bana

2017-01-01

The purpose of this research is to develop contextual mathematical thinking learning model which is valid, practical and effective based on the theoretical reviews and its support to enhance higher-order thinking ability. This study is a research and development (R & D) with three main phases: investigation, development, and implementation.…

Children's Mathematical Reasoning: Opportunities for Developing Understanding and Creative Thinking

ERIC Educational Resources Information Center

Vale, Colleen; Bragg, Leicha A.; Widjaja, Wanty; Herbert, Sandra; Loong, Esther Yook-Kin

2017-01-01

Reasoning underpins students' mathematical understanding and promotes creative thinking. It is regarded as a key mathematical proficiency. This article discusses the reasoning actions that primary children employed and teachers noticed for the "What else belongs?" task focused on forming and testing conjectures.

Upgrading geometry conceptual understanding and strategic competence through implementing rigorous mathematical thinking (RMT)

NASA Astrophysics Data System (ADS)

Nugraheni, Z.; Budiyono, B.; Slamet, I.

2018-03-01

To reach higher order thinking skill, needed to be mastered the conceptual understanding and strategic competence as they are two basic parts of high order thinking skill (HOTS). RMT is a unique realization of the cognitive conceptual construction approach based on Feurstein with his theory of Mediated Learning Experience (MLE) and Vygotsky’s sociocultural theory. This was quasi-experimental research which compared the experimental class that was given Rigorous Mathematical Thinking (RMT) as learning method and the control class that was given Direct Learning (DL) as the conventional learning activity. This study examined whether there was different effect of two learning model toward conceptual understanding and strategic competence of Junior High School Students. The data was analyzed by using Multivariate Analysis of Variance (MANOVA) and obtained a significant difference between experimental and control class when considered jointly on the mathematics conceptual understanding and strategic competence (shown by Wilk’s Λ = 0.84). Further, by independent t-test is known that there was significant difference between two classes both on mathematical conceptual understanding and strategic competence. By this result is known that Rigorous Mathematical Thinking (RMT) had positive impact toward Mathematics conceptual understanding and strategic competence.

The Influence of Building Block Play on Mathematics Achievement and Logical and Divergent Thinking in Italian Primary School Mathematics Classes

ERIC Educational Resources Information Center

Pirrone, Concetta; Tienken, Christopher H.; Pagano, Tatiana; Di Nuovo, Santo

2018-01-01

In an experimental study to explain the effect of structured Building Block Play with LEGO™ bricks on 6-year-old student mathematics achievement and in the areas of logical thinking, divergent thinking, nonverbal reasoning, and mental imagery, students in the experimental group scored significantly higher (p = 0.05) in mathematics achievement and…

Racial Differences in Mathematics Test Scores for Advanced Mathematics Students

ERIC Educational Resources Information Center

Minor, Elizabeth Covay

2016-01-01

Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…

Promoting middle school students’ mathematical creative thinking ability using scientific approach

NASA Astrophysics Data System (ADS)

Istiqomah, A.; Perbowo, K. S.; Purwanto, S. E.

2018-01-01

This research aims to identify the strength of scientific approach in order to develop mathematical creative thinking in junior high school. Descriptive qualitative method is used in this research. 34 students in 7th grade are chosen using purposive sampling. For collecting data, this research uses test, observation, and interview. The test consists of 6 items which have been tested for their validity and reliability and used in pre-test and post-test. The pre-test shows that students average score in mathematical creative thinking is 43 (low), while in post-test it is 69 (middle). The N-gain in mathematical creative thinking point is 0.461, which is classified in the middle grade. Furthermore, the N-gain for each indicator, they score 0.438 for fluency; 0.568 for flexibility; and 0.382 for novelty. The N-gain for those indicators falls under middle grade. The research shows that scientific approach develops more flexibility, and, on the other hand, it develops less novelty.

Connecting Advanced and Secondary Mathematics

ERIC Educational Resources Information Center

Murray, Eileen; Baldinger, Erin; Wasserman, Nicholas; Broderick, Shawn; White, Diana

2017-01-01

There is an ongoing debate among scholars in understanding what mathematical knowledge secondary teachers should have in order to provide effective instruction. We explore connections between advanced and secondary mathematics as an entry point into this debate. In many cases, advanced mathematics is considered relevant for secondary teachers…

Artificial Intelligence, Computational Thinking, and Mathematics Education

ERIC Educational Resources Information Center

Gadanidis, George

2017-01-01

Purpose: The purpose of this paper is to examine the intersection of artificial intelligence (AI), computational thinking (CT), and mathematics education (ME) for young students (K-8). Specifically, it focuses on three key elements that are common to AI, CT and ME: agency, modeling of phenomena and abstracting concepts beyond specific instances.…

Advanced Mathematical Study and the Development of Conditional Reasoning Skills

PubMed Central

Attridge, Nina; Inglis, Matthew

2013-01-01

Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general ‘thinking skills’. Today, this argument, known as the ‘Theory of Formal Discipline’ is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought. PMID:23869241

Preparing Beginning Teachers to Elicit and Interpret Students' Mathematical Thinking

ERIC Educational Resources Information Center

Sleep, Laurie; Boerst, Timothy A.

2012-01-01

This study investigated how teacher education assignments can be designed to support beginning teachers in learning to do the work of teaching. We examined beginners' formative assessment practices--in particular, their eliciting and interpreting of students' mathematical thinking--in the context of an elementary mathematics methods assignment,…

Support of mathematical thinking through embodied cognition: Nondigital and digital approaches.

PubMed

Tran, Cathy; Smith, Brandon; Buschkuehl, Martin

2017-01-01

Research on mathematics education has shown that learners' actions can influence how they think and vice versa. Much of this work has been rooted in the use of manipulatives, gestures, and body movements. Our article dissects the mechanisms that underscore the impact of embodied activities and applies this lens to explore how to harness the affordances of new technology to enhance mathematical thinking. This is especially crucial given the increasing accessibility of technology-such as digital touch devices, 3D printers, and location sensors-for constructing embodied experiences. Providing guidance for incorporating those tools, we focus on the role that embodied cognition can play in communicating mathematical concepts as well as in allowing learners to experiment and evolve their ideas. To inspire future integration of theory in the development of technologically enhanced embodied mathematics experiences, we provide examples of how this can be done. Finally, we outline future directions in the areas of design, implementation, and assessment of embodied learning of mathematics.

Analysis of Mathematics Critical Thinking Students in Junior High School Based on Cognitive Style

NASA Astrophysics Data System (ADS)

Agoestanto, A.; Sukestiyarno, YL; Rochmad

2017-04-01

The purpose of this research was to determine the critical thinking ability of mathematics from junior high school students based on FI and FD cognitive style. Data of this research were taken from students grade VIII at SMPN 2 Ambarawa. The research method used a descriptive qualitative approach. Data was taken with a testing method; the critical thinking was measured with WGCTA which is modified with mathematical problems, the cognitive style was measured with GEFT. The student’s test result was analysed, then four students were selected, the two of them are FI cognitive style, and the others are FD cognitive style, for qualitative analysis. The result showed that the ability of mathematics critical thinking students with FI cognitive style is better than FD cognitive style on the ability of inference, assumption, deduction, and interpretation. While on the aspect of argument evaluation, mathematics critical thinking ability of students with FD cognitive style is a little better than students with FI cognitive style.

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…

Advanced Mathematical Thinking and Students' Mathematical Learning: Reflection from Students' Problem-Solving in Mathematics Classroom

ERIC Educational Resources Information Center

Sangpom, Wasukree; Suthisung, Nisara; Kongthip, Yanin; Inprasitha, Maitree

2016-01-01

Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students' inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In…

Connecting Research to Teaching: Lenses for Examining Students' Mathematical Thinking

ERIC Educational Resources Information Center

Linsenmeier, Katherine A.; Sherin, Miriam; Walkoe, Janet; Mulligan, Martha

2014-01-01

The authors present three strategies for making sense of students' mathematical thinking. These lenses make the abstract idea of "making sense of student thinking" more manageable and concrete. We start by taking an initial look at a student's idea, going deeper, and finally looking across several ideas.

Metaphorical Thinking Learning and Junior High School Teachers' Mathematical Questioning Ability

ERIC Educational Resources Information Center

Hendriana, Heris; Rohaeti, Euis Eti; Hidayat, Wahyu

2017-01-01

This control-group posttest-only experimental design study aims to investigate the role of learning that teaches metaphorical thinking in mathematical questioning ability of junior high school teachers. The population of this study was mathematics junior high school teachers in West Java province. The samples were 82 mathematics junior high school…

The Impact of Chess Instruction on the Critical Thinking Ability and Mathematical Achievement of Developmental Mathematics Students

ERIC Educational Resources Information Center

Berkley, Darrin K.

2012-01-01

This sequential explanatory mixed-methods study determined whether the game of chess can be used as an educational tool to improve critical thinking skills of developmental mathematics students and improve mathematics achievement for these students. Five research questions were investigated. These questions were as follows: (a) Is there a…

Cognitive correlates of performance in advanced mathematics.

PubMed

Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

2012-03-01

Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.

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…

What Secondary Teachers Think and Do about Student Engagement in Mathematics

ERIC Educational Resources Information Center

Skilling, Karen; Bobis, Janette; Martin, Andrew J.; Anderson, Judy; Way, Jennifer

2016-01-01

What teachers' think about student engagement influences the teaching practices they adopt, their responses to students and the efforts they make in the classroom. Interviews were conducted with 31 mathematics teachers from ten high schools to investigate their perceptions and beliefs about student engagement in mathematics. Teachers also reported…

Developing Instructional Design to Improve Mathematical Higher Order Thinking Skills of Students

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Apino, E.; Retnawati, H.

2017-02-01

This study aimed to describe the instructional design to improve the Higher Order Thinking Skills (HOTS) of students in learning mathematics. This research is design research involving teachers and students of class X MIPA 1 MAN Yigyakarta III, Special Region of Yogyakarta, Indonesia. Data collected through focus group discussions and tests. Data analyzed by quantitative descriptive. The results showed that the instructional design developed is effective to improving students’ HOTS in learning mathematics. Instructional design developed generally include three main components: (1) involve students in the activities non-routine problem solving; (2) facilitating students to develop the ability to analyze and evaluate (critical thinking) and the ability to create (creative thinking); and (3) encourage students to construct their own knowledge.

The Role of Technology in Supporting Students' Mathematical Thinking: Extending the Metaphors of Amplifier and Reorganizer

ERIC Educational Resources Information Center

Sherman, Milan

2014-01-01

The use of instructional technology in secondary mathematics education has proliferated in the last decade, and students' mathematical thinking and reasoning has received more attention during this time as well. However, few studies have investigated the role of instructional technology in supporting students' mathematical thinking. In…

Issues in Designing Assessments of Historical Thinking

ERIC Educational Resources Information Center

Ercikan, Kadriye; Seixas, Peter

2015-01-01

Similar to educators in mathematics, science, and reading, history educators around the world have mobilized curricular reform movements toward including complex thinking in history education, advancing historical thinking, developing historical consciousness, and teaching competence in historical sense making. These reform movements, including…

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…

Improving Student Higher-Order Thinking Skills in Mathematics.

ERIC Educational Resources Information Center

Butkowski, Jean; And Others

This report describes a program for improving higher-order thinking skills in mathematics of (n=17) third-, (n=27) fifth-, and (n=27) sixth-grade students in a middle class community. Three interventions were chosen: (1) cooperative learning to develop student self-confidence and to improve student achievement, (2) the instruction of students in…

Open-Ended Approach: An Effort in Cultivating Students' Mathematical Creative Thinking Ability and Self-Esteem in Mathematics

ERIC Educational Resources Information Center

Fatah, Abdul; Suryadi, Didi; Sabandar, Jozua; Turmudi

2016-01-01

The present study aims at examining the use of open-ended approach in cultivating senior high school students' mathematical creative thinking ability (MCTA) and self-esteem (SE) in mathematics viewed from school category. The subjects of this research were the students grade XI at three schools; high, middle and low category in Kota Serang, Banten…

Gender differences in algebraic thinking ability to solve mathematics problems

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Kusumaningsih, W.; Darhim; Herman, T.; Turmudi

2018-05-01

This study aimed to conduct a gender study on students' algebraic thinking ability in solving a mathematics problem, polyhedron concept, for grade VIII. This research used a qualitative method. The data was collected using: test and interview methods. The subjects in this study were eight male and female students with different level of abilities. It was found that the algebraic thinking skills of male students reached high group of five categories. They were superior in terms of reasoning and quick understanding in solving problems. Algebraic thinking ability of high-achieving group of female students also met five categories of algebraic thinking indicators. They were more diligent, tenacious and thorough in solving problems. Algebraic thinking ability of male students in medium category only satisfied three categories of algebraic thinking indicators. They were sufficient in terms of reasoning and understanding in solving problems. Algebraic thinking ability group of female students in medium group also satisfied three categories of algebraic thinking indicators. They were fairly diligent, tenacious and meticulous on working on the problems.

Creative Thinking Ability to Increase Student Mathematical of Junior High School by Applying Models Numbered Heads Together

ERIC Educational Resources Information Center

Lince, Ranak

2016-01-01

Mathematical ability of students creative thinking is a component that must be mastered by the student. Mathematical creative thinking plays an important role, both in solving the problem and well, even in high school students. Therefore, efforts are needed to convey ideas in mathematics. But the reality is not yet developed the ability to…

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…

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…

Critical Thinking Skills of Students through Mathematics Learning with ASSURE Model Assisted by Software Autograph

NASA Astrophysics Data System (ADS)

Kristianti, Y.; Prabawanto, S.; Suhendra, S.

2017-09-01

This study aims to examine the ability of critical thinking and students who attain learning mathematics with learning model ASSURE assisted Autograph software. The design of this study was experimental group with pre-test and post-test control group. The experimental group obtained a mathematics learning with ASSURE-assisted model Autograph software and the control group acquired the mathematics learning with the conventional model. The data are obtained from the research results through critical thinking skills tests. This research was conducted at junior high school level with research population in one of junior high school student in Subang Regency of Lesson Year 2016/2017 and research sample of class VIII student in one of junior high school in Subang Regency for 2 classes. Analysis of research data is administered quantitatively. Quantitative data analysis was performed on the normalized gain level between the two sample groups using a one-way anova test. The results show that mathematics learning with ASSURE assisted model Autograph software can improve the critical thinking ability of junior high school students. Mathematical learning using ASSURE-assisted model Autograph software is significantly better in improving the critical thinking skills of junior high school students compared with conventional models.

Attributes of Instances of Student Mathematical Thinking That Are Worth Building on in Whole-Class Discussion

ERIC Educational Resources Information Center

Van Zoest, Laura R.; Stockero, Shari L.; Leatham, Keith R.; Peterson, Blake E.; Atanga, Napthalin A.; Ochieng, Mary A.

2017-01-01

This study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners' understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative…

Teachers' Considerations of Students' Thinking during Mathematics Lesson Design

ERIC Educational Resources Information Center

Amador, Julie M.

2016-01-01

Teachers' abilities to design mathematics lessons are related to their capability to mobilize resources to meeting intended learning goals based on their noticing. In this process, knowing how teachers consider Students' thinking is important for understanding how they are making decisions to promote student learning. While teaching, what teachers…

Analysis of creative mathematic thinking ability in problem based learning model based on self-regulation learning

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Munahefi, D. N.; Waluya, S. B.; Rochmad

2018-03-01

The purpose of this research identified the effectiveness of Problem Based Learning (PBL) models based on Self Regulation Leaning (SRL) on the ability of mathematical creative thinking and analyzed the ability of mathematical creative thinking of high school students in solving mathematical problems. The population of this study was students of grade X SMA N 3 Klaten. The research method used in this research was sequential explanatory. Quantitative stages with simple random sampling technique, where two classes were selected randomly as experimental class was taught with the PBL model based on SRL and control class was taught with expository model. The selection of samples at the qualitative stage was non-probability sampling technique in which each selected 3 students were high, medium, and low academic levels. PBL model with SRL approach effectived to students’ mathematical creative thinking ability. The ability of mathematical creative thinking of low academic level students with PBL model approach of SRL were achieving the aspect of fluency and flexibility. Students of academic level were achieving fluency and flexibility aspects well. But the originality of students at the academic level was not yet well structured. Students of high academic level could reach the aspect of originality.

Making Connections in Practice: How Prospective Elementary Teachers Connect to Children's Mathematical Thinking and Community Funds of Knowledge in Mathematics Instruction

ERIC Educational Resources Information Center

Aguirre, Julia M.; Turner, Erin E.; Bartell, Tonya Gau; Kalinec-Craig, Crystal; Foote, Mary Q.; Roth McDuffie, Amy; Drake, Corey

2013-01-01

This study examines the ways prospective elementary teachers (PSTs) made connections to children's mathematical thinking and children's community funds of knowledge in mathematics lesson plans. We analyzed the work of 70 PSTs from across three university sites associated with an instructional module for elementary mathematics methods courses that…

Cultivating Computational Thinking Practices and Mathematical Habits of Mind in Lattice Land

ERIC Educational Resources Information Center

Pei, Christina; Weintrop, David; Wilensky, Uri

2018-01-01

There is a great deal of overlap between the set of practices collected under the term "computational thinking" and the mathematical habits of mind that are the focus of much mathematics instruction. Despite this overlap, the links between these two desirable educational outcomes are rarely made explicit, either in classrooms or in the…

Interference thinking in constructing students’ knowledge to solve mathematical problems

NASA Astrophysics Data System (ADS)

Jayanti, W. E.; Usodo, B.; Subanti, S.

2018-04-01

This research aims to describe interference thinking in constructing students’ knowledge to solve mathematical problems. Interference thinking in solving problems occurs when students have two concepts that interfere with each other’s concept. Construction of problem-solving can be traced using Piaget’s assimilation and accommodation framework, helping to know the students’ thinking structures in solving the problems. The method of this research was a qualitative method with case research strategy. The data in this research involving problem-solving result and transcripts of interviews about students’ errors in solving the problem. The results of this research focus only on the student who experience proactive interference, where student in solving a problem using old information to interfere with the ability to recall new information. The student who experience interference thinking in constructing their knowledge occurs when the students’ thinking structures in the assimilation and accommodation process are incomplete. However, after being given reflection to the student, then the students’ thinking process has reached equilibrium condition even though the result obtained remains wrong.

The Construction of a Square through Multiple Approaches to Foster Learners' Mathematical Thinking

ERIC Educational Resources Information Center

Reyes-Rodriguez, Aaron; Santos-Trigo, Manuel; Barrera-Mora, Fernando

2017-01-01

The task of constructing a square is used to argue that looking for and pursuing several solution routes is a powerful principle to identify and analyse properties of mathematical objects, to understand problem statements and to engage in mathematical thinking activities. Developing mathematical understanding requires that students delve into…

Developing Student-Centered Learning Model to Improve High Order Mathematical Thinking Ability

ERIC Educational Resources Information Center

Saragih, Sahat; Napitupulu, Elvis

2015-01-01

The purpose of this research was to develop student-centered learning model aiming to improve high order mathematical thinking ability of junior high school students of based on curriculum 2013 in North Sumatera, Indonesia. The special purpose of this research was to analyze and to formulate the purpose of mathematics lesson in high order…

Exploring Prospective Secondary Mathematics Teachers' Interpretation of Student Thinking through Analysing Students' Work in Modelling

ERIC Educational Resources Information Center

Didis, Makbule Gozde; Erbas, Ayhan Kursat; Cetinkaya, Bulent; Cakiroglu, Erdinc; Alacaci, Cengiz

2016-01-01

Researchers point out the importance of teachers' knowledge of student thinking and the role of examining student work in various contexts to develop a knowledge base regarding students' ways of thinking. This study investigated prospective secondary mathematics teachers' interpretations of students' thinking as manifested in students' work that…

"This Is the First Time I've Done This": Exploring Secondary Prospective Mathematics Teachers' Noticing of Students' Mathematical Thinking

ERIC Educational Resources Information Center

Simpson, Amber; Haltiwanger, Leigh

2017-01-01

This mixed methods study investigates the ways in which secondary mathematics prospective teachers acquire skills needed to attend to, interpret, and respond to students' mathematical thinking and the ways in which their perceived strengths and weaknesses influence their skills when this type of formalized training is not part of their program.…

Designing and Developing Assessments of Complex Thinking in Mathematics for the Middle Grades

ERIC Educational Resources Information Center

Graf, Edith Aurora; Arieli-Attali, Meirav

2015-01-01

Designing an assessment system for complex thinking in mathematics involves decisions at every stage, from how to represent the target competencies to how to interpret evidence from student performances. Beyond learning to solve particular problems in a particular area, learning mathematics with understanding involves comprehending connections…

The impact of rigorous mathematical thinking as learning method toward geometry understanding

NASA Astrophysics Data System (ADS)

Nugraheni, Z.; Budiyono, B.; Slamet, I.

2018-05-01

To reach higher order thinking skill, needed to be mastered the conceptual understanding. RMT is a unique realization of the cognitive conceptual construction approach based on Mediated Learning Experience (MLE) theory by Feurstein and Vygotsky’s sociocultural theory. This was quasi experimental research which was comparing the experimental class that was given Rigorous Mathematical Thinking (RMT) as learning method and control class that was given Direct Learning (DL) as the conventional learning activity. This study examined whether there was different effect of two learning method toward conceptual understanding of Junior High School students. The data was analyzed by using Independent t-test and obtained a significant difference of mean value between experimental and control class on geometry conceptual understanding. Further, by semi-structure interview known that students taught by RMT had deeper conceptual understanding than students who were taught by conventional way. By these result known that Rigorous Mathematical Thinking (RMT) as learning method have positive impact toward Geometry conceptual understanding.

Investigating and analyzing prospective teacher's reflective thinking in solving mathematical problem: A case study of female-field dependent (FD) prospective teacher

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-05-01

In the last few years, reflective thinking becomes very popular term in the world of education, especially in professional education of teachers. One of goals of the educational personnel and teacher institutions create responsible prospective teachers and they are able reflective thinking. Reflective thinking is a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. Reflective thinking can be applied in mathematics becauseby reflective thinking, students can improve theircuriosity to solve mathematical problem. In solving mathematical problem is assumed that cognitive style has an impact on prospective teacher's mental activity. As a consequence, reflective thinking and cognitive style are important things in solving mathematical problem. The subject, in this research paper, isa female-prospective teacher who has fielddependent cognitive style. The purpose of this research paperis to investigate the ability of prospective teachers' reflective thinking in solving mathematical problem. This research paper is a descriptive by using qualitativeapproach. To analyze the data related to prospectiveteacher's reflective thinking in solving contextual mathematicalproblem, the researchers focus in four main categories which describe prospective teacher's activities in using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.

Students' Critical Mathematical Thinking Skills and Character: Experiments for Junior High School Students through Realistic Mathematics Education Culture-Based

ERIC Educational Resources Information Center

Palinussa, Anderson L.

2013-01-01

This paper presents the findings of a quasi-experimental with pre-test-post-test design and control group that aims to assess students' critical mathematical thinking skills and character through realistic mathematics education (RME) culture-based. Subjects of this study were 106 junior high school students from two low and medium schools level in…

Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Afthina, H.; Mardiyana; Pramudya, I.

2017-09-01

This research aims to determine the impact of mathematics learning applying Think Pair Share (TPS) using Realistic Mathematics Education (RME) viewed from mathematical-logical intelligence in geometry learning. Method that used in this research is quasi experimental research The result of this research shows that (1) mathematics achievement applying TPS using RME approach gives a better result than those applying direct learning model; (2) students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low one, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one; (3) there is no interaction between learning model and the level of students’ mathematical-logical intelligence in giving a mathematics achievement. The impact of this research is that TPS model using RME approach can be applied in mathematics learning so that students can learn more actively and understand the material more, and mathematics learning become more meaningful. On the other hand, internal factors of students must become a consideration toward the success of students’ mathematical achievement particularly in geometry material.

Teachers' Perceptions of Examining Students' Thinking: Changing Mathematics Instructional Practice

ERIC Educational Resources Information Center

Anderson-Pence, Katie L.

2015-01-01

This paper seeks to illuminate teachers' perceptions of the challenges and benefits of systematically examining students' thinking as part of a professional development program in elementary mathematics education. Using a framework of models of conceptual change and principles of discomfort, three elementary teachers' perceptions of their…

Developing Mathematical Thinking in the Primary Classroom: Liberating Students and Teachers as Learners of Mathematics

ERIC Educational Resources Information Center

Hudson, Brian; Henderson, Sheila; Hudson, Alison

2015-01-01

This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011-2012. The teachers were all participants in a newly developed Masters course that had been designed with the aim of promoting the development of mathematical thinking in the primary classroom as part of…

Factors Considered by Elementary Teachers When Developing and Modifying Mathematical Tasks to Support Children's Mathematical Thinking

NASA Astrophysics Data System (ADS)

Fredenberg, Michael Duane

The idea that problems and tasks play a pivotal role in a mathematics lesson has a long standing in mathematics education research. Recent calls for teaching reform appeal for training teachers to better understand how students learn mathematics and to employ students' mathematical thinking as the basis for pedagogy (CCSSM, 2010; NCTM, 2000; NRC 1999). The teaching practices of (a) developing a task for a mathematics lesson and, (b) modifying the task for students while enacting the lesson fit within the scope of supporting students' mathematical thinking. Surprisingly, an extensive search of the literature did not yield any research aimed to identify and refine the constituent parts of the aforementioned teaching practices in the manner called for by Grossman and xiii colleagues (2009). Consequently, my research addresses the two questions: (a) what factors do exemplary elementary teachers consider when developing a task for a mathematics lesson? (b) what factors do they consider when they modify a task for a student when enacting a lesson? I conducted a multiple case study involving three elementary teachers, each with extensive training in the area of Cognitively Guided Instruction (CGI), as well as several years experience teaching mathematics following the principles of CGI (Carpenter et al., 1999). I recorded video of three mathematics lessons with each participant and after each lesson I conducted a semi-structured stimulated recall interview. A subsequent follow-up clinical interview was conducted soon thereafter to further explore the teacher's thoughts (Ginsberg, 1997). In addition, my methodology included interjecting myself at select times during a lesson to ask the teacher to explain her reasoning. Qualitative analysis led to a framework that identified four categories of influencing factors and seven categories of supporting objectives for the development of a task. Subsets of these factors and objectives emerged as particularly relevant when the

Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

ERIC Educational Resources Information Center

Mairing, Jackson Pasini

2017-01-01

Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…

Hybrid Task Design: Connecting Learning Opportunities Related to Critical Thinking and Statistical Thinking

ERIC Educational Resources Information Center

Kuntze, Sebastian; Aizikovitsh-Udi, Einav; Clarke, David

2017-01-01

Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and…

Development of Mathematics Learning Strategy Module, Based on Higher Order Thinking Skill (Hots) To Improve Mathematic Communication And Self Efficacy On Students Mathematics Department

NASA Astrophysics Data System (ADS)

Andriani, Ade; Dewi, Izwita; Halomoan, Budi

2018-03-01

In general, this research is conducted to improve the quality of lectures on mathematics learning strategy in Mathematics Department. The specific objective of this research is to develop learning instrument of mathematics learning strategy based on Higher Order Thinking Skill (HOTS) that can be used to improve mathematical communication and self efficacy of mathematics education students. The type of research is development research (Research & Development), where this research aims to develop a new product or improve the product that has been made. This development research refers to the four-D Model, which consists of four stages: defining, designing, developing, and disseminating. The instrument of this research is the validation sheet and the student response sheet of the instrument.

An initial framework for the language of higher-order thinking mathematics practices

NASA Astrophysics Data System (ADS)

Staples, Megan E.; Truxaw, Mary P.

2012-09-01

This article presents an examination of the language demands of cognitively demanding tasks and proposes an initial framework for the language demands of higher-order mathematics thinking practices. We articulate four categories for this framework: language of generalisation, language of comparison, language of proportional reasoning, and language of analysing impact. These categories were developed out of our collaborative work to design and implement higher-order thinking tasks with a group of Grade 9 (14- and 15-year-olds) teachers teaching in a linguistically diverse setting; analyses of student work samples on these tasks; and our knowledge of the literature. We describe each type of language demand and then analyse student work in each category to reveal linguistic challenges facing students as they engage these mathematical tasks. Implications for teaching and professional development are discussed.

Critical Thinking Skills of an Eighth Grade Male Student with High Mathematical Ability in Solving Problem

NASA Astrophysics Data System (ADS)

Ismail

2018-01-01

This study aims to describe student’s critical thinking skill of grade VIII in solving mathematical problem. A qualitative research was conducted to a male student with high mathematical ability. Student’s critical thinking skill was obtained from a depth task-based interview. The result show that male student’s critical thinking skill of the student as follows. In understanding the problem, the student did categorization, significance decoding, and meaning clarification. In devising a plan he examined his ideas, detected his argument, analyzed his argument and evaluated his argument. During the implementation phase, the skill that appeared were analyzing of the argument and inference skill such as drawing conclusion, deliver alternative thinking, and problem solving skills. At last, in rechecking all the measures, they did self-correcting and self-examination.

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

Five Affordances of Computational Thinking to Support Elementary Mathematics Education

ERIC Educational Resources Information Center

Gadanidis, George

2017-01-01

With the increased focus on computational thinking (CT) in education, it is important to investigate the affordances that CT may offer to support teaching and learning. This paper outlines five affordances of CT that may support elementary mathematics education, whose conceptualization was refined in a year-long study involving eight Grades 3-4…

The Role of Visualisation in Developing Critical Thinking in Mathematics

ERIC Educational Resources Information Center

Makina, A.

2010-01-01

Research has been conducted on the role and importance of visualisation in many fields, including psychology, but very little has been done to extend its role to mathematics education in particular. Furthermore, much research has been done on the importance of critical thinking. However, to date not much has been done to clarify the fact that…

The Stakes of Movement: A Dynamic Approach to Mathematical Thinking

ERIC Educational Resources Information Center

Roth, Wolff-Michael; Maheux, Jean-François

2015-01-01

Standard approaches to thinking in the mathematics curriculum depict it as the result of some stable constructions in the mind of the person, constructions that are the results of individual efforts in the mind of subjects or of collective efforts that are then appropriated by and into the mind of individuals. Such work does not appreciate what…

Cognitive Correlates of Performance in Advanced Mathematics

ERIC Educational Resources Information Center

Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

2012-01-01

Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…

Middle School Mathematics: 2006-07 to 2008-09. Impact Evaluation. E&R Report No. 10.11

ERIC Educational Resources Information Center

Paeplow, Colleen

2010-01-01

In 2006-07, seven Wake County Public School System (WCPSS) middle schools piloted Algebraic Thinking as an alternate approach to teaching middle school mathematics. Algebraic Thinking was developed to help students in grade 6 reach higher mathematics courses by combining the regular and advanced middle school mathematics courses into one…

Analysis of critical thinking ability of VII grade students based on the mathematical anxiety level through learning cycle 7E model

NASA Astrophysics Data System (ADS)

Widyaningsih, E.; Waluya, S. B.; Kurniasih, A. W.

2018-03-01

This study aims to know mastery learning of students’ critical thinking ability with learning cycle 7E, determine whether the critical thinking ability of the students with learning cycle 7E is better than students’ critical thinking ability with expository model, and describe the students’ critical thinking phases based on the mathematical anxiety level. The method is mixed method with concurrent embedded. The population is VII grade students of SMP Negeri 3 Kebumen academic year 2016/2017. Subjects are determined by purposive sampling, selected two students from each level of mathematical anxiety. Data collection techniques include test, questionnaire, interview, and documentation. Quantitative data analysis techniques include mean test, proportion test, difference test of two means, difference test of two proportions and for qualitative data used Miles and Huberman model. The results show that: (1) students’ critical thinking ability with learning cycle 7E achieve mastery learning; (2) students’ critical thinking ability with learning cycle 7E is better than students’ critical thinking ability with expository model; (3) description of students’ critical thinking phases based on the mathematical anxiety level that is the lower the mathematical anxiety level, the subjects have been able to fulfil all of the indicators of clarification, assessment, inference, and strategies phases.

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…

Reflective Learning and Prospective Teachers' Conceptual Understanding, Critical Thinking, Problem Solving, and Mathematical Communication Skills

ERIC Educational Resources Information Center

Junsay, Merle L.

2016-01-01

This is a quasi-experimental study that explored the effects of reflective learning on prospective teachers' conceptual understanding, critical thinking, problem solving, and mathematical communication skills and the relationship of these variables. It involved 60 prospective teachers from two basic mathematics classes of an institution of higher…

The Relationship between Higher Order Thinking Skills and Academic Performance of Student in Mathematics Instruction

ERIC Educational Resources Information Center

Tanujaya, Benidiktus; Mumu, Jeinne; Margono, Gaguk

2017-01-01

Higher order thinking skills (HOTS) is one of important aspects in education. Students with high level of higher order thinking skills tend to be more successful. However, do this phenomenon also happen in the learning of Mathematics? To answer this question, this research aims to study the relationship between HOTS and students' academic…

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).…

Critical Thinking Skills Of Junior High School Female Students With High Mathematical Skills In Solving Contextual And Formal Mathematical Problems

NASA Astrophysics Data System (ADS)

Ismail; Suwarsono, St.; Lukito, A.

2018-01-01

Critical thinking is one of the most important skills of the 21st century in addition to other learning skills such as creative thinking, communication skills and collaborative skills. This is what makes researchers feel the need to conduct research on critical thinking skills in junior high school students. The purpose of this study is to describe the critical thinking skills of junior high school female students with high mathematical skills in solving contextual and formal mathematical problems. To achieve this is used qualitative research. The subject of the study was a female student of eight grade junior high school. The students’ critical thinking skills are derived from in-depth problem-based interviews using interview guidelines. Interviews conducted in this study are problem-based interviews, which are done by the subject given a written assignment and given time to complete. The results show that critical thinking skills of female high school students with high math skills are as follows: In solving the problem at the stage of understanding the problem used interpretation skills with sub-indicators: categorization, decode, and clarify meaning. At the planning stage of the problem-solving strategy is used analytical skills with sub-indicators: idea checking, argument identification and argument analysis and evaluation skills with sub indicators: assessing the argument. In the implementation phase of problem solving, inference skills are used with subindicators: drawing conclusions, and problem solving and explanatory skills with sub-indicators: problem presentation, justification procedures, and argument articulation. At the re-checking stage all steps have been employed self-regulatory skills with sub-indicators: self-correction and selfstudy.

What secondary teachers think and do about student engagement in mathematics

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Skilling, Karen; Bobis, Janette; Martin, Andrew J.; Anderson, Judy; Way, Jennifer

2016-12-01

What teachers' think about student engagement influences the teaching practices they adopt, their responses to students and the efforts they make in the classroom. Interviews were conducted with 31 mathematics teachers from ten high schools to investigate their perceptions and beliefs about student engagement in mathematics. Teachers also reported the practices they used to engage their students during mathematics lessons. Teacher perceptions of student engagement were categorised according to recognised `types' (behavioural, emotional and cognitive) and `levels' (ranging from disengaged to engaged). The teachers' reports emphasised immediate attention being paid to students' behaviours and overt emotions towards mathematics with fewer and less extensive reports made about students' cognitive engagement. Teachers' abilities to implement practices considered supportive of student engagement were linked to a number of elements, including their self-efficacy. Perceptions of being powerless to engage their students resulted in many teachers limiting their efforts to attempt some form of intervention.

Exploring the Possibilities of Using Tic-Tac-Toe to Think and Communicate about Mathematics

ERIC Educational Resources Information Center

Clarkson, Philip C.

2008-01-01

Doing mathematics, and thinking about how you are doing it at the same time, are not the easiest things to do. It is even more difficult if students are not aware that they should be attempting both processes at the same time. They are likely to concentrate on the immediate task of "doing" the mathematics, rather than trying to access the deeper…

Convergent and Divergent Thinking in Task Modification: A Case of Korean Prospective Mathematics Teachers' Exploration

ERIC Educational Resources Information Center

Lee, Kyeong-Hwa

2017-01-01

This study investigated how 38 secondary mathematics prospective teachers modified textbook tasks for convergent and divergent thinking while learning to teach mathematics during university coursework. The coursework focused prospective teachers' attention on their analyses of textbook tasks in terms of potential affordances and constraints for…

Accommodation in the formal world of mathematical thinking

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Stewart, Sepideh; Schmidt, Ralf

2017-11-01

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 narratives. This paper reveals the pedagogical challenges of proving an elegant theory as the events unfolded. Although the mathematician was conscious of the students' abilities as he carefully made the path accessible, the disparity between the mind of the mathematician and the student became apparent.

Characterizing a Highly Accomplished Teacher's Noticing of Third-Grade Students' Mathematical Thinking

ERIC Educational Resources Information Center

Taylan, Rukiye Didem

2017-01-01

This study investigated a highly accomplished third-grade teacher's noticing of students' mathematical thinking as she taught multiplication and division. Through an innovative method, which allowed for documenting in-the-moment teacher noticing, the author was able to explore teacher noticing and reflective practices in the context of classroom…

Cognitive Technologies for Mathematics Education. Technical Report No. 37.

ERIC Educational Resources Information Center

Pea, Roy D.

This paper provides an historical perspective on the possible roles of cognitive technologies in thinking as "reorganizers" of the mind. It suggests that by understanding the transformational roles of advanced technologies for mathematical thinking, positive contributions can be made to research and practice on the use of computers in…

Lower-Order Mathematical Thinking Skills in Finance, from the Viewpoint of Financial Employees in the Iranian Bank of Industry and Mine

ERIC Educational Resources Information Center

Kumleh, Seyedeh Zahra Aboalhasani; Roodposhti, Fereydon Rahnamay; Shahvarani, Ahmad; Lotfi, Farhad Hosseinzadeh

2017-01-01

In this paper, lower-order mathematical thinking skills within finance were studied from the viewpoint of financial employees in the Iranian Bank of Industry and Mine. To conduct this research, a questionnaire was developed after reviewing lower-order mathematical thinking skills in finance. In accordance with the revised Bloom's taxonomy, the…

The Enhancement of Mathematical Critical Thinking Ability of Aliyah Madrasas Student Model Using Gorontalo by Interactive Learning Setting Cooperative Model

ERIC Educational Resources Information Center

Husnaeni

2016-01-01

Critical thinking ability of students' mathematical is a component that must be mastered by the student. Learn to think critically means using mental processes, such as attention, categorize, selection, and rate/decide. Critical thinking ability in giving proper guidance in thinking and working, and assist in determining the relationship between…

The Impact of Problem-Based Learning Approach to Senior High School Students' Mathematics Critical Thinking Ability

ERIC Educational Resources Information Center

Widyatiningtyas, Reviandari; Kusumah, Yaya S.; Sumarmo, Utari; Sabandar, Jozua

2015-01-01

The study reported the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students' prior mathematical ability to student's mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from…

Why Do Students Drop Advanced Mathematics?

ERIC Educational Resources Information Center

Horn, Ilana

2004-01-01

Students, especially black, Latino and Native American youth and students of low socio-economic status drop out of advanced mathematics. Teachers must coordinate their expectations, their knowledge of students and their teaching practices in order to stop struggling students from dropping out of advanced math classes.

The Effectiveness of Local Culture-Based Mathematical Heuristic-KR Learning towards Enhancing Student's Creative Thinking Skill

ERIC Educational Resources Information Center

Tandiseru, Selvi Rajuaty

2015-01-01

The problem in this research is the lack of creative thinking skills of students. One of the learning models that is expected to enhance student's creative thinking skill is the local culture-based mathematical heuristic-KR learning model (LC-BMHLM). Heuristic-KR is a learning model which was introduced by Krulik and Rudnick (1995) that is the…

Educational interventions to advance children's scientific thinking.

PubMed

Klahr, David; Zimmerman, Corinne; Jirout, Jamie

2011-08-19

The goal of science education interventions is to nurture, enrich, and sustain children's natural and spontaneous interest in scientific knowledge and procedures. We present taxonomy for classifying different types of research on scientific thinking from the perspective of cognitive development and associated attempts to teach science. We summarize the literature on the early--unschooled--development of scientific thinking, and then focus on recent research on how best to teach science to children from preschool to middle school. We summarize some of the current disagreements in the field of science education and offer some suggestions on ways to continue to advance the science of science instruction.

A Framework for Mathematical Thinking: The Case of Linear Algebra

ERIC Educational Resources Information Center

Stewart, Sepideh; Thomas, Michael O. J.

2009-01-01

Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…

On Embodiment, Artifacts, and Signs: A Semiotic-Cultural Perspective on Mathematical Thinking

ERIC Educational Resources Information Center

Radford, Luis; Bardini, Caroline; Sabena, Cristina; Diallo, Pounthioun; Simbagoye, Athanase

2005-01-01

The cognitive significance of the body has become one of the major topics in current psychology. However, it is our contention that claims about the embodied nature of thinking must come to terms with the problem of the relationship between the body as a locus for the constitution of students' subjective mathematical meanings and the historical…

Efforts to Improve Mathematics Teacher Competency Through Training Program on Design Olympiad Mathematics Problems Based on Higher Order Thinking Skills in The Junior High School

NASA Astrophysics Data System (ADS)

Arnellis, A.; Jamaan, E. Z.; Amalita, N.

2018-04-01

The goal to analyse a improvement of teacher competence after being trained in preparing high-order math olympicad based on high order thinking skills in junior high school teachers in Pesisir Selatan Regency. The sample of these activities are teachers at the MGMP junior high school in Pesisir Selatan District. Evaluation of the implementation is done by giving a pre test and post test, which will measure the success rate of the implementation of this activities. The existence of the devotion activities is expected to understand the enrichment of mathematics olympiad material and training in the preparation of math olympiad questions for the teachers of South Pesisir district junior high school, motivating and raising the interest of the participants in order to follow the mathematics olympiad with the enrichment of mathematics materials and the training of problem solving about mathematics olympiad for junior high school teachers, the participants gain experience and gain insight, as well as the ins and outs of junior mathematics olympiad and implement to teachers and students in olympic competitions. The result of that the post-test is better than the result of pretest in the training of mathematics teacher competence improvement in composing the mathematics olympiad problem based on high order thinking skills of junior high school (SMP) in Pesisir Selatan District, West Sumatra, Indonesia.

The Impact of Critical Thinking and Logico-Mathematical Intelligence on Algorithmic Design Skills

ERIC Educational Resources Information Center

Korkmaz, Ozgen

2012-01-01

The present study aims to reveal the impact of students' critical thinking and logico-mathematical intelligence levels of students on their algorithm design skills. This research was a descriptive study and carried out by survey methods. The sample consisted of 45 first-year educational faculty undergraduate students. The data was collected by…

Leveraging Cognitive Technology Tools to Expand Opportunities for Critical Thinking in Elementary Mathematics

ERIC Educational Resources Information Center

Suh, Jennifer

2010-01-01

The following study describes design research in an elementary school near the metropolitan D.C. area with a diverse student population. The goal of the project was to design tasks that leveraged technology and enhance the access to critical thinking in specific mathematical concepts: data analysis and probability. It highlights the opportunities…

Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication

ERIC Educational Resources Information Center

Kaya, Defne; Aydin, Hasan

2016-01-01

Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…

Learning to teach upper primary school algebra: changes to teachers' mathematical knowledge for teaching functional thinking

NASA Astrophysics Data System (ADS)

Wilkie, Karina J.

2016-06-01

A key aspect of learning algebra in the middle years of schooling is exploring the functional relationship between two variables: noticing and generalising the relationship, and expressing it mathematically. This article describes research on the professional learning of upper primary school teachers for developing their students' functional thinking through pattern generalisation. This aspect of algebra learning has been explicitly brought to the attention of upper primary teachers in the recently introduced Australian curriculum. Ten practising teachers participated over 1 year in a design-based research project involving a sequence of geometric pattern generalisation lessons with their classes. Initial and final survey responses and teachers' interactions in regular meetings and lessons were analysed from cognitive and situated perspectives on professional learning, using a theoretical model for the different types of knowledge needed for teaching mathematics. The teachers demonstrated an increase in certain aspects of their mathematical knowledge for teaching algebra as well as some residual issues. Implications for the professional learning of practising and pre-service teachers to develop their mathematics knowledge for teaching functional thinking, and challenges with operationalising knowledge categories for field-based research are presented.

Growing of the mathematical thinking imaginative to students in designing of the teaching aids for CWD towards to joyful learning

NASA Astrophysics Data System (ADS)

Sugiman; Sugiharti, E.; Kurniawati, N. F.

2018-03-01

Government and the private parties had also organized of Special School (SS) and Inclusive School. SS requires of math teachers who were professional in the material, but also master the needs of Children with Disabilities (CwD) in teaching-learning process. The problem: How to design the Teaching Aids for CwD through Extra-Curriculum Training (ECT) activities to Joyful Learning? The purposes of this research: (1) To find new ways how to grow the imaginative in mathematical thinking for students of Mathematics Education. (2) To find a Teaching Aids Design that suitable for CwD who studying in SS. (3) In order to create a Teaching Aids for CwD through activities based on ECT to Joyful Learning. The research method was done by qualitative approach. The research subjects were 6 students of Mathematics Education Study Program of FMIPA UNNES who were interested in attending of the training activities based on ECT. The results: (1) ECT can be a place to grow an Imaginative in Mathematical Thinking of students, (2) created the design of the teaching aids for CwD through activities based on ECT to Joyful Learning as a mirror of the imaginative growth in mathematical thinking for students.

Teacher Leaders: Advancing Mathematics Learning

ERIC Educational Resources Information Center

Kinzer, Cathy J.; Rincón, Mari; Ward, Jana; Rincón, Ricardo; Gomez, Lesli

2014-01-01

Four elementary school instructors offer insights into their classrooms, their unique professional roles, and their leadership approaches as they reflect on their journey to advance teacher and student mathematics learning. They note a "teacher leader" serves as an example to other educators and strives to impact student learning;…

Responding to Children's Mathematical Thinking in the Moment: An Emerging Framework of Teaching Moves

ERIC Educational Resources Information Center

Jacobs, Victoria R.; Empson, Susan B.

2016-01-01

This case study contributes to efforts to characterize teaching that is responsive to children's mathematical thinking. We conceptualize "responsive teaching" as a type of teaching in which teachers' instructional decisions about what to pursue and how to pursue it are continually adjusted during instruction in response to children's…

The Implementation of Open-Inquiry Approach to Improve Students' Learning Activities, Responses, and Mathematical Creative Thinking Skills

ERIC Educational Resources Information Center

Kadir; Lucyana; Satriawati, Gusni

2017-01-01

This study aims to reveal the improvement of the students' learning activities, responses, and mathematical creative thinking skills (MCTS) through open-inquiry approach (OIA). Other relevant studies in mathematics learning tend to focus on guided inquiry, and especially in Indonesia, OIA is still less applied. This study is conducted at State…

Undergraduate Mathematics Majors' Writing Performance Producing Proofs and Counterexamples about Continuous Functions

ERIC Educational Resources Information Center

Ko, Yi-Yin; Knuth, Eric

2009-01-01

In advanced mathematical thinking, proving and refuting are crucial abilities to demonstrate whether and why a proposition is true or false. Learning proofs and counterexamples within the domain of continuous functions is important because students encounter continuous functions in many mathematics courses. Recently, a growing number of studies…

Preschoolers' Thinking during Block Play

ERIC Educational Resources Information Center

Piccolo, Diana L.; Test, Joan

2010-01-01

Children build foundations for mathematical thinking in early play and exploration. During the preschool years, children enjoy exploring mathematical concepts--such as patterns, shape, spatial relationships, and measurement--leading them to spontaneously engage in mathematical thinking during play. Block play is one common example that engages…

Teacher Questioning and Invitations to Participate in Advanced Mathematics Lectures

ERIC Educational Resources Information Center

Paoletti, Teo; Krupnik, Victoria; Papadopoulos, Dimitrios; Olsen, Joseph; Fukawa-Connelly, Tim; Weber, Keith

2018-01-01

We were interested in exploring the extent to which advanced mathematics lecturers provide students with opportunities to play a role in considering or generating course content. To do this, we examined the questioning practices of 11 lecturers who taught advanced mathematics courses at the university level. Because we are unaware of other studies…

Intuitive vs Analytical Thinking: Four Perspectives

ERIC Educational Resources Information Center

Leron, Uri; Hazzan, Orit

2009-01-01

This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives--mathematics, mathematics education, cognitive psychology, and evolutionary psychology--each offering a different view on mathematical thinking and learning and, in particular, on the…

Relationship between Professional Values and Critical Thinking Disposition of Science-Technology and Mathematics Teachers

ERIC Educational Resources Information Center

Sahin, Senar Alkin; Tunca, Nihal; Altinkurt, Yahya; Yilmaz, Kürsad

2016-01-01

The purpose of this study is to determine the relationship between the professional values and critical thinking disposition of science-technology and mathematics teachers working in middle schools. The survey research method was employed in the study. The sample of the study is comprised of 193 teachers (90 science-technology and 103 mathematics…

Development and evaluation of form three mathematics i-Think module (Mi-T3) on algebraic formulae topic

NASA Astrophysics Data System (ADS)

Sam, Sazilah; Abdullah, Mohd Faizal Nizam Lee

2017-05-01

This article introduces the Form Three Mathematics i-Think Module (Mi-T3). The main objective of this Mi-T3 is to assist form three students develop their higher order thinking skills (HOTS). The Sidek Module Development Model (SMDM) and eight innovative thinking maps (i-Think) were applied as a guideline in developing Mi-T3. A validation stage was carried out by eight experts, and content validation achievement more than 90% obtained. A group of form three students and teachers was piloted to check the module's reliability through one to one and small group evaluation and Cronbach Alpha more than 0.90 was obtained. Implications of the study are discussed in this article.

Scientific thinking in young children: theoretical advances, empirical research, and policy implications.

PubMed

Gopnik, Alison

2012-09-28

New theoretical ideas and empirical research show that very young children's learning and thinking are strikingly similar to much learning and thinking in science. Preschoolers test hypotheses against data and make causal inferences; they learn from statistics and informal experimentation, and from watching and listening to others. The mathematical framework of probabilistic models and Bayesian inference can describe this learning in precise ways. These discoveries have implications for early childhood education and policy. In particular, they suggest both that early childhood experience is extremely important and that the trend toward more structured and academic early childhood programs is misguided.

Development of “OQALE” Based Reference Module for School Geometry Subject and Analysis of Mathematical Creative Thinking Skills

NASA Astrophysics Data System (ADS)

Wulandari, N. A. D.; Sukestiyarno, Y. L.

2017-04-01

This research aims to develop an OQALE based reference module for school geometry subject that meets the criteria of a valid and practical. OQALE approach is learning by of O = observation, Q = question, A = Analyze, L = Logic, E = Express. Geometry subject presented in the module are a triangle, the Pythagorean theorem, and rectangular. Mathematical skills of creative thinking shown from four aspects: fluency, flexibility, originality and elaboration. Research procedures in the development of reference module using a strategy of the investigation and development described by [2], which is limited to the sixth stage is leading field testing. The focus of this research is to develop a reference module that is valid, practical and able to increase the mathematical creative thinking skills of students. The testing is limited to three teachers, nine students and two mathematic readers using purposive sampling technique. The data validity, practicality, and creative thinking skills upgrading collected through questionnaires, observations, and interviews and analysed with a valid test, practical test, gain test and qualitative descriptive. The results were obtained (1) the validity of the module = 4.52, which is 4.20 ≤ Vm< 5.00 included in the category of very valid; (2) the results of the questionnaire responses of teachers = 4.53, which is 4.20 ≤ Rg< 5.00 included in the category of very good; (3) the results of the survey responses of students = 3.13, which is 2.80 ≤ Rpd< 3.40 included in the category of good with an average percentage of 78%; and (4) increasing skills of creative thinking mathematically nine students through the test of the gain included in the high and medium category. The conclusions of this research are the generated OQALE based reference module for school geometry subjectis valid and practical.

Promoting middle school students’ abstract-thinking ability through cognitive apprenticeship instruction in mathematics learning

NASA Astrophysics Data System (ADS)

Yusepa, B. G. P.; Kusumah, Y. S.; Kartasasmita, B. G.

2018-01-01

The aim of this study is to get an in-depth understanding of students’ abstract-thinking ability in mathematics learning. This study was an experimental research with pre-test and post-test control group design. The subject of this study was eighth-grade students from two junior high schools in Bandung. In each schools, two parallel groups were selected and assigned into control and experimental groups. The experimental group was exposed to Cognitive Apprenticeship Instruction (CAI) treatment, whereas the control group was exposed to conventional learning. The results showed that abstract-thinking ability of students in experimental group was better than that of those in control group in which it could be observed from the overall and school level. It could be concluded that CAI could be a good alternative learning model to enhance students’ abstract-thinking ability.

Reassessing the Economic Value of Advanced Level Mathematics

ERIC Educational Resources Information Center

Adkins, Michael; Noyes, Andrew

2016-01-01

In the late 1990s, the economic return to Advanced level (A-level) mathematics was examined. The analysis was based upon a series of log-linear models of earnings in the 1958 National Child Development Survey (NCDS) and the National Survey of 1980 Graduates and Diplomates. The core finding was that A-level mathematics had a unique earnings premium…

Mathematical Critical Thinking and Curiosity Attitude in Problem Based Learning and Cognitive Conflict Strategy: A Study in Number Theory Course

ERIC Educational Resources Information Center

Zetriuslita; Wahyudin; Jarnawi

2017-01-01

This research aims to describe and analyze result of applying Problem-Based Learning and Cognitive Conflict Strategy (PBLCCS) in increasing students' Mathematical Critical Thinking (MCT) ability and Mathematical Curiosity Attitude (MCA). Adopting a quasi-experimental method with pretest-posttest control group design and using mixed method with…

Assessing Children's Multiplicative Thinking

ERIC Educational Resources Information Center

Hurst, Chris; Hurrell, Derek

2016-01-01

Multiplicative thinking is a "big idea" of mathematics that underpins much of the mathematics learned beyond the early primary school years. This paper reports on a current study that utilises an interview tool and a written quiz to gather data about children's multiplicative thinking. The development of the tools and some of the…

The Development of Learning Devices Based Guided Discovery Model to Improve Understanding Concept and Critical Thinking Mathematically Ability of Students at Islamic Junior High School of Medan

ERIC Educational Resources Information Center

Yuliani, Kiki; Saragih, Sahat

2015-01-01

The purpose of this research was to: 1) development of learning devices based guided discovery model in improving of understanding concept and critical thinking mathematically ability of students at Islamic Junior High School; 2) describe improvement understanding concept and critical thinking mathematically ability of students at MTs by using…

Developing Learning Model Based on Local Culture and Instrument for Mathematical Higher Order Thinking Ability

ERIC Educational Resources Information Center

Saragih, Sahat; Napitupulu, E. Elvis; Fauzi, Amin

2017-01-01

This research aims to develop a student-centered learning model based on local culture and instrument of mathematical higher order thinking of junior high school students in the frame of the 2013-Curriculum in North Sumatra, Indonesia. The subjects of the research are seventh graders which are taken proportionally random consisted of three public…

Secondary School Advanced Mathematics, Chapter 3, Formal Geometry. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the second of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered…

Secondary School Advanced Mathematics, Chapter 3, Formal Geometry. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the second of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This volume is devoted to a rigorous development of theorems in plane geometry from 22…

Mathematical thinking and origami

NASA Astrophysics Data System (ADS)

Wares, Arsalan

2016-01-01

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.

Development of an Instrument to Measure Higher Order Thinking Skills in Senior High School Mathematics Instruction

ERIC Educational Resources Information Center

Tanujaya, Benidiktus

2016-01-01

The purpose of this research was to develop an instrument that can be used to measure higher-order thinking skills (HOTS) in mathematics instruction of high school students. This research was conducted using a standard procedure of instrument development, from the development of conceptual definitions, development of operational definitions,…

VStops: A Thinking Strategy and Visual Representation Approach in Mathematical Word Problem Solving toward Enhancing STEM Literacy

ERIC Educational Resources Information Center

Abdullah, Nasarudin; Halim, Lilia; Zakaria, Effandi

2014-01-01

This study aimed to determine the impact of strategic thinking and visual representation approaches (VStops) on the achievement, conceptual knowledge, metacognitive awareness, awareness of problem-solving strategies, and student attitudes toward mathematical word problem solving among primary school students. The experimental group (N = 96)…

Examining the Relationship between Thinking Styles and Technological Pedagogical Content Knowledge of the Candidate Mathematics Teachers

ERIC Educational Resources Information Center

Canbolat, Nuran; Erdogan, Ahmet; Yazlik, Derya Ozlem

2016-01-01

The aim of this research is measuring the technological pedagogical content knowledge of the candidate elementary mathematics teachers, identifying the thinking styles of the same candidates and finding out that whether there is a correlation or not. The research has the characteristics of a basic research to add new information to the scientific…

Thinking is believing.

PubMed

Kasturirangan, Rajesh

2008-01-01

Philosophers as well lay people often think of beliefs as psychological states with dubious epistemic properties. Beliefs are conceptualized as unregulated conceptual structures, for the most part hypothetical and often fanciful or deluded. Thinking and reasoning on the other hand are seen as rational activities regulated by rules and governed by norms. Computational modeling of the mind has focused on rule-governed behavior, ultimately trying to reduce them to rules of logic. What if thinking is less like reasoning and more like believing? I argue that the classical model of thought as rational is mistaken and that thinking is fundamentally constituted by believing. This new approach forces us to re-evaluate classical epistemic concepts like "truth", "justification" etc. Furthermore, if thinking is believing, then it is not clear how thoughts can be modeled computationally. We need new mathematical ideas to model thought, ideas that are quite different from traditional logic-based mathematical structures.

The materiality of mathematics: presenting mathematics at the blackboard.

PubMed

Greiffenhagen, Christian

2014-09-01

Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.

Mathematics Teachers' Level of Knowledge and Practice on the Implementation of Higher-Order Thinking Skills (HOTS)

ERIC Educational Resources Information Center

Abdullah, Abdul Halim; Mokhtar, Mahani; Halim, Noor Dayana Abd; Ali, Dayana Farzeeha; Tahir, Lokman Mohd; Kohar, Umar Haiyat Abdul

2017-01-01

This study aims to identify the level of knowledge and practice on the implementation of higher-order thinking skills (HOTS) among mathematics teachers at a secondary school in the district of Terengganu. The study focused on the aspects of curriculum, pedagogy and assessment and compared them with demographic factors of the respondents. It used…

Advanced Analytic Cognition: Thinking Dispositions

DTIC Science & Technology

2013-09-01

on this instrument showed no significant differences between the experimental and control groups . Further, posttest means were not significantly...different from pretest means in either group ( Pretest : Experimental M = 296, Control M = 297; Posttest : Experimental M = 298, Control M = 302). It...for critical thinking in nursing also addressed thinking dispositions.  The planning group on critical thinking at Frostburg State University

Mathematics/Arithmetic Knowledge-Based Way of Thinking and Its Maintenance Needed for Engineers

NASA Astrophysics Data System (ADS)

Harada, Shoji

Examining curriculum among universities revealed that no significant difference in math class or related subjects can be seen. However, amount and depth of those studies, in general, differed depending on content of curriculum and the level of achievement at entrance to individual university. Universalization of higher education shows that students have many problems in learning higher level of traditional math and that the memory of math they learned quickly fades away after passing in exam. It means that further development of higher math knowledgebased engineer after graduation from universities. Under these circumstances, the present author, as one of fun of math, propose how to maintain way of thinking generated by math knowledge. What necessary for engineer is to pay attention to common books, dealing with elementary mathematics or arithmetic- related matters. This surely leads engineer to nourish math/arithmetic knowledge-based way of thinking.

Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the last of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…

Avoiding Misinterpretations of Piaget and Vygotsky: Mathematical Teaching without Learning, Learning without Teaching, or Helpful Learning-Path Teaching?

ERIC Educational Resources Information Center

Fuson, Karen C.

2009-01-01

This article provides an overview of some perspectives about special issues in classroom mathematical teaching and learning that have stemmed from the huge explosion of research in children's mathematical thinking stimulated by Piaget. It concentrates on issues that are particularly important for less-advanced learners and for those who might be…

What Is Happening in the Use of ICT Mathematics to Support Young Adolescent Learners? A New Zealand Experience

ERIC Educational Resources Information Center

Nicholas, Karen; Fletcher, Jo

2017-01-01

Advances in learning approaches can enhance deeper levels of mathematical thinking and engagement through the use of new digital environments and technologies. The growing utilisation of portable digital devices in schools has meant there are enhanced tools to support mathematical learning and understandings. This article focused on those who work…

Improving students’ mathematical critical thinking through rigorous teaching and learning model with informal argument

NASA Astrophysics Data System (ADS)

Hamid, H.

2018-01-01

The purpose of this study is to analyze an improvement of students’ mathematical critical thinking (CT) ability in Real Analysis course by using Rigorous Teaching and Learning (RTL) model with informal argument. In addition, this research also attempted to understand students’ CT on their initial mathematical ability (IMA). This study was conducted at a private university in academic year 2015/2016. The study employed the quasi-experimental method with pretest-posttest control group design. The participants of the study were 83 students in which 43 students were in the experimental group and 40 students were in the control group. The finding of the study showed that students in experimental group outperformed students in control group on mathematical CT ability based on their IMA (high, medium, low) in learning Real Analysis. In addition, based on medium IMA the improvement of mathematical CT ability of students who were exposed to RTL model with informal argument was greater than that of students who were exposed to CI (conventional instruction). There was also no effect of interaction between RTL model and CI model with both (high, medium, and low) IMA increased mathematical CT ability. Finally, based on (high, medium, and low) IMA there was a significant improvement in the achievement of all indicators of mathematical CT ability of students who were exposed to RTL model with informal argument than that of students who were exposed to CI.

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…

The Impact of Advanced Curriculum on the Achievement of Mathematically Promising Elementary Students

ERIC Educational Resources Information Center

Gavin, M. Katherine; Casa, Tutita M.; Adelson, Jill L.; Carroll, Susan R.; Sheffield, Linda Jensen

2009-01-01

The primary aim of Project M[superscript 3]: Mentoring Mathematical Minds was to develop and field test advanced units for mathematically promising elementary students based on exemplary practices in gifted and mathematics education. This article describes the development of the units and reports on mathematics achievement results for students in…

Ways of Thinking Associated with Mathematics Teachers' Problem Posing in the Context of Division of Fractions

ERIC Educational Resources Information Center

Koichu, Boris; Harel, Guershon; Manaster, Alfred

2013-01-01

Twenty-four mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and…

Hybrid Tasks: Promoting Statistical Thinking and Critical Thinking through the Same Mathematical Activities

ERIC Educational Resources Information Center

Aizikovitsh-Udi, Einav; Clarke, David; Kuntze, Sebastian

2014-01-01

Even though statistical thinking and critical thinking appear to have strong links from a theoretical point of view, empirical research into the intersections and potential interrelatedness of these aspects of competence is scarce. Our research suggests that thinking skills in both areas may be interdependent. Given this interconnection, it should…

Profile of mathematical reasoning ability of 8th grade students seen from communicational ability, basic skills, connection, and logical thinking

NASA Astrophysics Data System (ADS)

Sumarsih; Budiyono; Indriati, D.

2018-04-01

This research aims to understand the students’ weaknesses in mathematical reasoning ability in junior secondary school. A set of multiple choice tests were used to measure this ability involve components mathematical communication, basic skills, connection, and logical thinking. A total of 259 respondents were determined by stratified cluster random sampling. Data were analyzed using one-way Anova test with Fobs = 109.5760 and F = 3.0000. The results show that students’ ability from schools with high National Exam in mathematics category was the best and followed by medium and low category. Mathematical connection is the most difficult component performed by students. In addition, most students also have difficulty in expressing ideas and developing logical arguments.

The development of form two mathematics i-Think module (Mi-T2)

NASA Astrophysics Data System (ADS)

Yao, Foo Jing; Abdullah, Mohd Faizal Nizam Lee; Tien, Lee Tien

2017-05-01

This study aims to develop a training module i-THINK Mathematics Form Two (Mi-T2) to increase the higher-order thinking skills of students. The Mi-T2 training module was built based on the Sidek Module Development Model (2001). Constructivist learning theory, cognitive learning theory, i-THINK map and higher order thinking skills were the building blocks of the module development. In this study, researcher determined the validity and reliability of Mi-T2 module. The design being used in this study was descriptive study. To determine the needs of Mi-T2 module, questionnaires and literature review were used to collect data. When the need of the module was determined, the module was built and a pilot study was conducted to test the reliability of the Mi-T2 module. The pilot study was conducted at a secondary school in North Kinta, Perak. A Form Two class was selected to be the sample study through clustered random sampling. The pilot study was conducted for two months and one topic had been studied. The Mi-T2 module was evaluated by five expert panels to determine the content validity of the module. The instruments being used in the study were questionnaires about the necessity of the Mi-T2 module for guidance, questionnaires about the validity of the module and questionnaires concerning the reliability of the module. Statistical analysis was conducted to determine the validity and reliability coefficients of the Mi-T2 module. The content validity of Mi-T2 module was determined by Cohen's Kappa's (1968) agreement coefficient and the reliability of Mi-T2 module was determined by Cronbach Alpha's value scale. The content validity of Mi-T2 module was 0.89 and the Cronbach Alpha's value of Mi-T2 module was 0.911.

Bingo! Select Games for Mathematical Thinking

ERIC Educational Resources Information Center

Jackson, Christa; Taylor, Cynthia; Buchheister, Kelley

2013-01-01

Games can both generate excitement among students and motivate them to participate in mathematics. Although games have been used primarily to "review" mathematical concepts at the middle school level, games should, and often do, have other instructional purposes. When teachers use mathematical games as an instructional strategy, they are…

Teaching by Open-Approach Method in Japanese Mathematics Classroom.

ERIC Educational Resources Information Center

Nohda, Nobuhiko

Mathematics educators in Japan have traditionally emphasized mathematical perspectives in research and practice. This paper features an account of changes in mathematics education in Japan that focus on the possibilities of individual students as well as their mathematical ways of thinking. Students' mathematical thinking, mathematical…

Thinking Like a Mathematician

ERIC Educational Resources Information Center

Weiss, Michael K.; Moore-Russo, Deborah

2012-01-01

What does it mean to think like a mathematician? One of the great paradoxes of mathematics education is that, although mathematics teachers are immersed in mathematical work every day of their professional lives, most of them nevertheless have little experience with the kind of work that research mathematicians do. Their ideas of what doing…

Students’ thinking preferences in solving mathematics problems based on learning styles: a comparison of paper-pencil and geogebra

NASA Astrophysics Data System (ADS)

Farihah, Umi

2018-04-01

The purpose of this study was to analyze students’ thinking preferences in solving mathematics problems using paper pencil comparing to geogebra based on their learning styles. This research employed a qualitative descriptive study. The subjects of this research was six of eighth grade students of Madrasah Tsanawiyah Negeri 2 Trenggalek, East Java Indonesia academic year 2015-2016 with their difference learning styles; two visual students, two auditory students, and two kinesthetic students.. During the interview, the students presented the Paper and Pencil-based Task (PBTs) and the Geogebra-based Task (GBTs). By investigating students’ solution methods and the representation in solving the problems, the researcher compared their visual and non-visual thinking preferences in solving mathematics problems while they were using Geogebra and without Geogebra. Based on the result of research analysis, it was shown that the comparison between students’ PBTs and GBTs solution either visual, auditory, or kinesthetic represented how Geogebra can influence their solution method. By using Geogebra, they prefer using visual method while presenting GBTs to using non-visual method.

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…

Advanced Mathematics 305--Optional Half Credit. Interim Guide.

ERIC Educational Resources Information Center

Manitoba Dept. of Education, Winnipeg.

This manual outlines an advanced mathematics course for secondary school students in Manitoba (Canada). Included are eight different topics for a total of ten modules, with each module accounting for 18 40-minute periods. Teachers, or teachers and students cooperatively, should select the equivalent of five modules from the eight topics covered.…

Advanced mathematics communication beyond modality of\\xA0sight

NASA Astrophysics Data System (ADS)

Sedaghatjou, Mina

2018-01-01

This study illustrates how mathematical communication and learning are inherently multimodal and embodied; hence, sight-disabled students are also able to conceptualize visuospatial information and mathematical concepts through tactile and auditory activities. Adapting a perceptuomotor integration approach, the study shows that the lack of access to visual fields in an advanced mathematics course does not obstruct a blind student's ability to visualize, but transforms it. The goal of this study is not to compare the visually impaired student with non-visually impaired students to address the 'differences' in understanding; instead, I discuss the challenges that a blind student, named Anthony, has encountered and the ways that we tackled those problems. I also demonstrate how the proper and precisely crafted tactile materials empowered Anthony to learn mathematical functions.

Analyzing Preservice Mathematics Teachers' Professional Noticing

ERIC Educational Resources Information Center

Amador, Julie M.; Carter, Ingrid; Hudson, Rick A.

2016-01-01

Recent research in mathematics education has highlighted the importance of teachers' abilities to professionally notice students' thinking. This study examined what preservice teachers professionally notice during lesson study to further describe their attention to students' mathematical thinking, their interpretations about students' reasoning,…

Teaching Mathematics: Challenging the Sacred Cow of Mathematical Certainty.

ERIC Educational Resources Information Center

Borba, Marcelo C.

1992-01-01

Challenges the concept of mathematical certainty and questions whether it is a useful concept for elementary and secondary mathematics curriculum. Encourages teachers to bring this issue into the classroom and ask students to think about it critically. (HB)

Mathematics and Engineering in Real Life through Mathematical Competitions

ERIC Educational Resources Information Center

More, M.

2018-01-01

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build…

Visual Thinking and Gender Differences in High School Calculus

ERIC Educational Resources Information Center

Haciomeroglu, Erhan Selcuk; Chicken, Eric

2012-01-01

This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…

The Effect of Using a Proposed Teaching Strategy Based on the Selective Thinking on Students' Acquisition Concepts in Mathematics

ERIC Educational Resources Information Center

Qudah, Ahmad Hassan

2016-01-01

This study aimed at identify the effect of using a proposed teaching strategy based on the selective thinking in acquire mathematical concepts by Classroom Teacher Students at Al- al- Bayt University, The sample of the study consisted of (74) students, equally distributed into a control group and an experimental group. The selective thinking…

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.

Examination of the Computational Thinking Skills of Students

ERIC Educational Resources Information Center

Korucu, Agah Tugrul; Gencturk, Abdullah Tarik; Gundogdu, Mustafa Mucahit

2017-01-01

Computational thinking is generally considered as a kind of analytical way of thinking. According to Wings (2008) it shares with mathematical thinking, engineering thinking and scientific thinking in the general ways in which we may use for solving a problem, designing and evaluating complex systems or understanding computability and intelligence…

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

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.

Origins of the brain networks for advanced mathematics in expert mathematicians

PubMed Central

Amalric, Marie; Dehaene, Stanislas

2016-01-01

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124

Origins of the brain networks for advanced mathematics in expert mathematicians.

PubMed

Amalric, Marie; Dehaene, Stanislas

2016-05-03

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.

Reflective Journaling for Critical Thinking Development in Advanced Practice Registered Nurse Students.

PubMed

Raterink, Ginger

2016-02-01

Critical thinking, clinical decision making, and critical reflection have been identified as skills required of nurses in every clinical situation. The Educating Nurses: A Call for Radical Transformation report suggested that critical reflection is a key to improving the educational process. Reflective journaling is a tool that helps develop such skills. This article presents the tool of reflective journaling and the use of this process by educators working with students. It describes the use of reflective journaling in graduate nursing education, as well as a scoring process to evaluate the reflection and provide feedback. Students and faculty found the journaling to be helpful for reflection of a clinical situation focused on critical thinking skill development. The rubric scoring tool provided faculty with a method for feedback. Reflective journaling is a tool that faculty and students can use to develop critical thinking skills for the role of the advanced practice RN. A rubric scoring system offers a consistent format for feedback. Copyright 2016, SLACK Incorporated.

How Syntactic Reasoners Can Develop Understanding, Evaluate Conjectures, and Generate Counterexamples in Advanced Mathematics

ERIC Educational Resources Information Center

Weber, Keith

2009-01-01

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…

Support with Caveats: Advocates' Views of the Theory of Formal Discipline as a Reason for the Study of Advanced Mathematics

ERIC Educational Resources Information Center

Wainwright, Elaine; Attridge, Nina; Wainwright, David; Alcock, Lara; Inglis, Matthew

2017-01-01

The Theory of Formal Discipline (TFD) suggests that studying mathematics improves general thinking skills. Empirical evidence for the TFD is sparse, yet it is cited in policy reports as a justification for the importance of mathematics in school curricula. The study reported in this article investigated the extent to which influential UK advocates…

The Only Absolute Truth in Mathematics is the Myth of Mathematics as Universal

ERIC Educational Resources Information Center

Kantner, M. Joanne

2008-01-01

Culture and national origin can affect thinking about mathematics and mathematics learning. The myth that mathematics is objective and culture free becomes a barrier to adults learning mathematics. Adult educators must reflect upon culture's influence on learning and recognize the implications of universality myths on students' learning in…

Children thinking mathematically beyond authoritative identities

NASA Astrophysics Data System (ADS)

MacMillan, Agnes

1995-10-01

A study into the mathematics-related interactions and developing attitudes of young children during the transition period between pre-school and school is reported. Transcripts of interactions during a six-week observation period in one of two preschool sites are coded according to the classifications defined within a theoretical framework. Two separate episodes of construction play were analysed and one of these is used to examine the mathematical nature of the children's interactions within an emerging model of autonomous learning. The results of the analysis indicate that access to self-regulatory social relations is very closely linked to the accessibility of mathematical meanings.

Some observations on the interdigitation of advances in medical science and mathematics.

PubMed

Glamore, Michael James; West, James L; O'leary, James Patrick

2013-12-01

The immense advancement of our understanding of disease processes has not been a uniform progression related to the passage of time. Advances have been made in "lurches" and "catches" since the advent of the written word. There has been a remarkable interdependency between such advances in medicine and advances in mathematics that has proved beneficial to both. This work explores some of these critical relationships and documents how the individuals involved contributed to advances in each.

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).

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…

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.

Multiplicative Thinking: Much More than Knowing Multiplication Facts and Procedures

ERIC Educational Resources Information Center

Hurst, Chris; Hurrell, Derek

2016-01-01

Multiplicative thinking is accepted as a "big idea" of mathematics that underpins important mathematical concepts such as fraction understanding, proportional reasoning, and algebraic thinking. It is characterised by understandings such as the multiplicative relationship between places in the number system, basic and extended number…

Investigating Children's Multiplicative Thinking: Implications for Teaching

ERIC Educational Resources Information Center

Hurst, Chris; Hurrell, Derek

2016-01-01

Multiplicative thinking is a "big idea" of mathematics that underpins much of the mathematics learned beyond the early primary school years. This article reports on a recent study that utilised an interview tool and a written quiz to gather data about children's multiplicative thinking. Our research has so far revealed that many primary…

Analysis of mathematical literacy ability based on self-efficacy in model eliciting activities using metaphorical thinking approach

NASA Astrophysics Data System (ADS)

Setiani, C.; Waluya, S. B.; Wardono

2018-03-01

The purposes of this research are: (1) to identify learning quality in Model Eliciting Activities (MEAs) using a Metaphorical Thinking (MT) approach regarding qualitative and quantitative; (2) to analyze mathematical literacy of students based on Self-Efficacy (SE). This research is mixed method concurrent embedded design with qualitative research as the primary method. The quantitative research used quasi-experimental with non-equivalent control group design. The population is VIII grade students of SMP Negeri 3 Semarang Indonesia. Quantitative data is examined by conducting completeness mean test, standard completeness test, mean differentiation test and proportional differentiation test. Qualitative data is analyzed descriptively. The result of this research shows that MEAs learning using MT approach accomplishes good criteria both quantitatively and qualitatively. Students with low self-efficacy can identify problems, but they are lack ability to arrange problem-solving strategy on mathematical literacy questions. Students with medium self-efficacy can identify information provided in issues, but they find difficulties to use math symbols in making a representation. Students with high self-efficacy are excellent to represent problems into mathematical models as well as figures by using appropriate symbols and tools, so they can arrange strategy easily to solve mathematical literacy questions.

Who Can Know Mathematics?

ERIC Educational Resources Information Center

Walshaw, Margaret

2014-01-01

This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…

Developing a Learning Progression for Curriculum, Instruction, and Student Learning: An Example from Mathematics Education

ERIC Educational Resources Information Center

Fonger, Nicole L.; Stephens, Ana; Blanton, Maria; Isler, Isil; Knuth, Eric; Gardiner, Angela Murphy

2018-01-01

Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked…

Gender Differences in the Use and Benefit of Advanced Learning Technologies for Mathematics

ERIC Educational Resources Information Center

Arroyo, Ivon; Burleson, Winslow; Tai, Minghui; Muldner, Kasia; Woolf, Beverly Park

2013-01-01

We provide evidence of persistent gender effects for students using advanced adaptive technology while learning mathematics. This technology improves each gender's learning and affective predispositions toward mathematics, but specific features in the software help either female or male students. Gender differences were seen in the students' style…

Advancing our thinking in presence-only and used-available analysis.

PubMed

Warton, David; Aarts, Geert

2013-11-01

1. The problems of analysing used-available data and presence-only data are equivalent, and this paper uses this equivalence as a platform for exploring opportunities for advancing analysis methodology. 2. We suggest some potential methodological advances in used-available analysis, made possible via lessons learnt in the presence-only literature, for example, using modern methods to improve predictive performance. We also consider the converse - potential advances in presence-only analysis inspired by used-available methodology. 3. Notwithstanding these potential advances in methodology, perhaps a greater opportunity is in advancing our thinking about how to apply a given method to a particular data set. 4. It is shown by example that strikingly different results can be achieved for a single data set by applying a given method of analysis in different ways - hence having chosen a method of analysis, the next step of working out how to apply it is critical to performance. 5. We review some key issues to consider in deciding how to apply an analysis method: apply the method in a manner that reflects the study design; consider data properties; and use diagnostic tools to assess how reasonable a given analysis is for the data at hand. © 2013 The Authors. Journal of Animal Ecology © 2013 British Ecological Society.

Sliding into Multiplicative Thinking: The Power of the "Marvellous Multiplier"

ERIC Educational Resources Information Center

Hurst, Chris; Hurrell, Derek

2016-01-01

Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…

Innovations in Science and Mathematics Education: Advanced Designs for Technologies of Learning.

ERIC Educational Resources Information Center

Jacobson, Michael J., Ed.; Kozma, Robert B., Ed.

This collection of essays consists of current work that addresses the challenge not just to put the newest technologies in schools, but to identify advanced ways to design and use these new technologies to advance learning. These essays are intended for science and mathematics educators, educational and cognitive researchers, instructional…

A Cognition Analysis of QUASAR's Mathematics Performance Assessment Tasks and Their Sensitivity to Measuring Changes in Middle School Students' Thinking and Reasoning.

ERIC Educational Resources Information Center

Cai, Jinfa, And Others

1996-01-01

Presents a conceptual framework for analyzing students' mathematical understanding, reasoning, problem solving, and communication. Analyses of student responses indicated that the tasks appear to measure the complex thinking and reasoning processes that they were designed to assess. Concludes that the QUASAR assessment tasks can capture changes in…

Computational thinking and thinking about computing

PubMed Central

Wing, Jeannette M.

2008-01-01

Computational thinking will influence everyone in every field of endeavour. This vision poses a new educational challenge for our society, especially for our children. In thinking about computing, we need to be attuned to the three drivers of our field: science, technology and society. Accelerating technological advances and monumental societal demands force us to revisit the most basic scientific questions of computing. PMID:18672462

PREFACE: International Conference on Advancement in Science and Technology 2012 (iCAST): Contemporary Mathematics, Mathematical Physics and their Applications

NASA Astrophysics Data System (ADS)

Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Hee, Pah Chin

2013-04-01

The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences. We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support . This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products. Guest Editors Nasir Ganikhodjaev, Farrukh Mukhamedov and Pah Chin Hee The PDF contains the committee lists, board list and biographies of the plenary speakers.

Mathematics in the Early Years.

ERIC Educational Resources Information Center

Copley, Juanita V., Ed.

Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining…

Business Mathematics Curriculum.

ERIC Educational Resources Information Center

EASTCONN Regional Educational Services Center, North Windham, CT.

This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…

Fostering Instructor Knowledge of Student Thinking Using the Flipped Classroom

ERIC Educational Resources Information Center

Strayer, Jeremy F.; Hart, James B.; Bleiler, Sarah K.

2015-01-01

In this article, we share a model of flipped instruction that allowed us to gain a window into our students' mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be…

Advanced Algebra and Calculus. High School Mathematics Curricula. Instructor's Guide.

ERIC Educational Resources Information Center

Natour, Denise M.

This manual is an instructor's guide for the utilization of the "CCA High School Mathematics Curricula: Advanced Algebra and Calculus" courseware developed by the Computer-based Education Research Laboratory (CERL). The curriculum comprises 34 algebra lessons within 12 units and 15 calculus lessons that are computer-based and require…

Computational Thinking Concepts for Grade School

ERIC Educational Resources Information Center

Sanford, John F.; Naidu, Jaideep T.

2016-01-01

Early education has classically introduced reading, writing, and mathematics. Recent literature discusses the importance of adding "computational thinking" as a core ability that every child must learn. The goal is to develop students by making them equally comfortable with computational thinking as they are with other core areas of…

Children Have the Capacity to Think Multiplicatively, as Long as …

ERIC Educational Resources Information Center

Hurst, Chris

2017-01-01

Multiplicative thinking has been widely accepted as a critically important "big idea" of mathematics and one which underpins much mathematical understanding beyond the primary years of schooling. It is therefore of importance to consider the capacity of children to think multiplicatively but also to consider the capacity of their…

Recommendations to Support Computational Thinking in the Elementary Classroom

ERIC Educational Resources Information Center

Estapa, Anne; Hutchison, Amy; Nadolny, Larysa

2018-01-01

Computational thinking is an important and necessary way of thinking for computer programmers and other professionals in science, technology, engineering, and mathematics (STEM). Research on emerging practices around computational thinking that is developed through coding initiatives in schools reports that elementary children typically learn how…

Developing geogebra-assisted reciprocal teaching strategy to improve junior high school students’ abstraction ability, lateral thinking and mathematical persistence

NASA Astrophysics Data System (ADS)

Priatna, N.; Martadiputra, B. A. P.; Wibisono, Y.

2018-05-01

The development of science and technology requires reform in the utilization of various resources for mathematics teaching and learning process. One of the efforts that can be made is the implementation of GeoGebra-assisted Reciprocal Teaching strategy in mathematics instruction as an effective strategy in improving students’ cognitive, affective, and psychomotor abilities. This research is intended to implement GeoGebra-assisted Reciprocal Teaching strategy in improving abstraction ability, lateral thinking, and mathematical persistence of junior high school students. It employed quasi-experimental method with non-random pre-test and post-test control design. More specifically, it used the 2x3 factorial design, namely the learning factors that included GeoGebra-assisted Reciprocal Teaching and conventional teaching learning, and levels of early mathematical ability (high, middle, and low). The subjects in this research were the eighth grade students of junior high school, taken with purposive sampling. The results of this research show: Abstraction and lateral abilities of students who were taught with GeoGebra-assisted Reciprocal Teaching strategy were significantly higher than those of students who received conventional learning. Mathematical persistence of students taught with GeoGebra-assisted Reciprocal Teaching strategy was also significantly higher than of those taught with conventional learning.

Analysis of students’ creative thinking level in problem solving based on national council of teachers of mathematics

NASA Astrophysics Data System (ADS)

Hobri; Suharto; Rifqi Naja, Ahmad

2018-04-01

This research aims to determine students’ creative thinking level in problem solving based on NCTM in function subject. The research type is descriptive with qualitative approach. Data collection methods which were used are test and interview. Creative thinking level in problem solving based on NCTM indicators consists of (1) Make mathematical model from a contextual problem and solve the problem, (2) Solve problem using various possible alternatives, (3) Find new alternative(s) to solve the problem, (4) Determine the most efficient and effective alternative for that problem, (5) Review and correct mistake(s) on the process of problem solving. Result of the research showed that 10 students categorized in very satisfying level, 23 students categorized in satisfying level and 1 students categorized in less satisfying level. Students in very satisfying level meet all indicators, students in satisfying level meet first, second, fourth, and fifth indicator, while students in less satisfying level only meet first and fifth indicator.

Mathematics through Experience

ERIC Educational Resources Information Center

Hristozova, Nedyalka

2016-01-01

The author shares some examples from her Bulgarian project, "Mathematics Through Experience", which approaches mathematics from a practical, real-life perspective in order to develop creative thinking: just like science! What was most important to her was to motivate her students to study maths and science by giving them a taste of how…

Using Questioning to Stimulate Mathematical Thinking

ERIC Educational Resources Information Center

Way, Jenni

2008-01-01

Good questioning techniques have long been regarded as a fundamental tool of effective teachers and research has found that "differences in students' thinking and reasoning could be attributed to the type of questions that teachers asked" (Wood, 2002). Past research shows that 93% of teacher questions were "lower order" knowledge-based questions…

La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

NASA Astrophysics Data System (ADS)

Cable, John

2014-01-01

This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.

Preparing and Supporting Black Students to Enroll and Achieve in Advanced Mathematics Classes in Middle School: A Case Study

ERIC Educational Resources Information Center

Cobbs, Joyce Bernice

2014-01-01

The literature on minority student achievement indicates that Black students are underrepresented in advanced mathematics courses. Advanced mathematics courses offer students the opportunity to engage with challenging curricula, experience rigorous instruction, and interact with quality teachers. The middle school years are particularly…

Computational Thinking in Mathematics Teacher Education

ERIC Educational Resources Information Center

Gadanidis, George; Cendros, Rosa; Floyd, Lisa; Namukasa, Immaculate

2017-01-01

As computational thinking (CT) is increasing in focus in K-12 education, it is important to consider how teacher education programs may better prepare teacher candidates (TCs). Previous studies have found that TCs do not always have a firm understanding of what CT involves, and they might not have clear ideas about how to develop CT in their…

Financial Mathematical Tasks in a Middle School Mathematics Textbook Series: A Content Analysis

ERIC Educational Resources Information Center

Hamburg, Maryanna P.

2009-01-01

This content analysis examined the distribution of financial mathematical tasks (FMTs), mathematical tasks that contain financial terminology and require financially related solutions, across the National Standards in K-12 Personal Finance Education categories (JumpStart Coalition, 2007), the thinking skills as identified by "A Taxonomy for…

Lectures in Advanced Mathematics: Why Students Might Not Understand What the Mathematics Professor Is Trying to Convey

ERIC Educational Resources Information Center

Lew, Kristen; Fukawa-Connelly, Timothy Patrick; Mejía-Ramos , Juan Pablo; Weber, Keith

2016-01-01

We describe a case study in which we investigate the effectiveness of a lecture in advanced mathematics. We first videorecorded a lecture delivered by an experienced professor who had a reputation for being an outstanding instructor. Using video recall, we then interviewed the professor to determine the ideas that he intended to convey and how he…

Advancement via Individual Determination: A Model for Equity in Secondary Mathematics

ERIC Educational Resources Information Center

Hodges, Cynthia D.

2013-01-01

This study examined the impact of Advancement Via Individual Determination (AVID) methodologies on the mathematics achievement of African American, European American, and Hispanic students as measured by the State of Texas Assessment of Academic Readiness (STAAR) End of Course (EOC) for Algebra I. This quantitative nonexperimental ex post facto…

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…

ABCs of Early Mathematics Experiences

ERIC Educational Resources Information Center

Hensen, Laurie E.

2005-01-01

Children begin to develop mathematical thinking before they enter school. Art, baking, playing with blocks, counting numbers, games, puzzles, singing, playing with pretend money, water play all these early mathematical experiences help the children to learn in the elementary school years.

How Middle Grade Teachers Think about Algebraic Reasoning

ERIC Educational Resources Information Center

Glassmeyer, David; Edwards, Belinda

2016-01-01

Algebraic reasoning is an essential habit of mind for building conceptual knowledge in K-12 mathematics, yet little is known about how middle school mathematics teachers think about algebraic reasoning. In this article we describe a research project examining how algebraic reasoning was considered by grades 6, 7, or 8 mathematics teachers in a…

Which Advanced Mathematics Courses Influence ACT Score? A State Level Analysis of the Iowa Class of 2012

ERIC Educational Resources Information Center

Grinstead, Mary L.

2013-01-01

This study explores the relationship between specific advanced mathematics courses and college readiness (as determined by ACT score). The ACT organization has found a consistent relationship between taking a minimum core number of mathematics courses and higher ACT scores (mathematics and composite) (ACT, Inc., 2012c). However, the extent to…

Science and Mathematics Advanced Placement Exams: Growth and Achievement over Time

ERIC Educational Resources Information Center

Judson, Eugene

2017-01-01

Rapid growth of Advanced Placement (AP) exams in the last 2 decades has been paralleled by national enthusiasm to promote availability and rigor of science, technology, engineering, and mathematics (STEM). Trends were examined in STEM AP to evaluate and compare growth and achievement. Analysis included individual STEM subjects and disaggregation…

Entering into dialogue about the mathematical value of contextual mathematising tasks

NASA Astrophysics Data System (ADS)

Yoon, Caroline; Chin, Sze Looi; Moala, John Griffith; Choy, Ban Heng

2018-03-01

Our project seeks to draw attention to the rich mathematical thinking that is generated when students work on contextual mathematising tasks. We use a design-based research approach to create ways of reporting that raise the visibility of this rich mathematical thinking while retaining and respecting its complexity. These reports will be aimed for three classroom stakeholders: (1) students, who wish to reflect on and enhance their mathematical learning; (2) teachers, who wish to integrate contextual mathematising tasks into their teaching practice and (3) researchers, who seek rich tasks for generating observable instances of mathematical thinking and learning. We anticipate that these reports and the underlying theoretical framework for creating them will contribute to greater awareness of and appreciation for the mathematical value of contextual mathematising tasks in learning, teaching and research.

Mathematics and engineering in real life through mathematical competitions

NASA Astrophysics Data System (ADS)

More, M.

2018-02-01

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

Incentivizing Advanced Mathematics Study at Upper Secondary Level: The Case of Bonus Points in Ireland

ERIC Educational Resources Information Center

Treacy, Páraic Thomas

2018-01-01

Secondary level mathematics education in Ireland has recently experienced a period of significant change with the introduction of new curricula and the addition of an incentive to study upper secondary mathematics at the most advanced level (Higher Level). This incentive, typically referred to as 'bonus points', appears to have aided a significant…

Secondary School Advanced Mathematics, Chapter 4, Equations, Inequalities, and Radicals, Chapter 5, Circles and Spheres. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the third of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

Changes in Elementary Mathematics Teachers' Understanding of Cognitive Demand: When Adapting, Creating, and Using Mathematical Performance Tasks

ERIC Educational Resources Information Center

Jamieson, Thad Spencer

2015-01-01

The use of mathematics performance tasks can provide a window into how a student is applying mathematics to various situations, how they are reasoning mathematically and how they are applying conceptual knowledge through problem solving and critical thinking. The purpose of this study was to investigate, according to the elementary mathematics…

A New Start for Mathematics Curriculum.

ERIC Educational Resources Information Center

Tucker, Alan

Arguing that a major re-thinking of the mathematics curriculum is needed, this paper urges two-year colleges to take the lead in curriculum revision. Section I suggests that the pre-calculus orientation of high school mathematics may be inappropriate, viewing mathematics related to computers and dependent on computers for computation as more…

Secondary School Advanced Mathematics, Chapter 4, Equations, Inequalities, and Radicals, Chapter 5, Circles and Spheres. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the third of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first of the two chapters in this text deals with equations, inequalities and radicals.…

Problem-Based Approach to Teaching Advanced Chemistry Laboratories and Developing Students' Critical Thinking Skills

ERIC Educational Resources Information Center

Quattrucci, Joseph G.

2018-01-01

A new method for teaching advanced laboratories at the undergraduate level is presented. The intent of this approach is to get students more engaged in the lab experience and apply critical thinking skills to solve problems. The structure of the lab is problem-based and provides students with a research-like experience. Students read the current…

Increasing Early Opportunities in Engineering for Advanced Learners in Elementary Classrooms: A Review of Recent Literature

ERIC Educational Resources Information Center

Dailey, Debbie; Cotabish, Alicia; Jackson, Nykela

2018-01-01

Present and future challenges in our society demand a solid science, technology, engineering, and mathematics (STEM) knowledge base, innovative thinking, and the ability to ask the right questions to generate multiple solutions. To prepare innovators to meet these challenges, we must recognize and develop their talents. This advancement and growth…

Exploring Wind Power: Improving Mathematical Thinking through Digital Fabrication

ERIC Educational Resources Information Center

Tillman, Daniel A.; An, Song A.; Cohen, Jonathan D.; Kjellstrom, William; Boren, Rachel L.

2014-01-01

This mixed methods study examined the impacts of digital fabrication activities that were integrated into contextualized mathematics education. The study investigated the students' mathematics content knowledge and attitudes. Data analysis yielded two key findings regarding our intervention combined with the other mathematics activities resulted…

Math Thinking Motivators. A Good Apple Math Activity Book for Grades 2-7.

ERIC Educational Resources Information Center

Bernstein, Bob

In this booklet are 43 mathematical games and activities to stimulate creative thinking in grades 2-7. The goal of teaching divergent thinking is stressed, as well as the need to encourage positive self-image, motivation, and creativity. For each activity, the mathematical skills addressed in the activity are listed; topics span the elementary…

Two Meanings of Algorithmic Mathematics.

ERIC Educational Resources Information Center

Maurer, Stephen B.

1984-01-01

Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…

Explanatory Unification by Proofs in School Mathematics

ERIC Educational Resources Information Center

Komatsu, Kotaro; Fujita, Taro; Jones, Keith; Naoki, Sue

2018-01-01

Kitcher's idea of 'explanatory unification', while originally proposed in the philosophy of science, may also be relevant to mathematics education, as a way of enhancing student thinking and achieving classroom activity that is closer to authentic mathematical practice. There is, however, no mathematics education research treating explanatory…

Integrating Mathematics across the Curriculum. NCTM-Aligned Activities.

ERIC Educational Resources Information Center

Martin, Hope

An effective curriculum gives students the opportunity to perceive relationships among different topics in mathematics, use mathematics in their everyday lives, and apply mathematical thinking and problem solving to other curriculum areas. This book contains fun and creative ways to integrate mathematics across the curriculum with a diversity of…

Neurally and mathematically motivated architecture for language and thought.

PubMed

Perlovsky, L I; Ilin, R

2010-01-01

Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt's "firmness" of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined.

Neurally and Mathematically Motivated Architecture for Language and Thought

PubMed Central

Perlovsky, L.I; Ilin, R

2010-01-01

Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt’s “firmness” of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined. PMID:21673788

What's Working: Program Factors Influencing California Community College Basic Skills Mathematics Students' Advancement to Transfer Level

ERIC Educational Resources Information Center

Fiero, Diane M.

2013-01-01

Purpose: The purpose of this study was to determine which basic skills program factors were exhibited by successful basic skills programs that helped students advance to transfer-level mathematics. This study specifically examined California community college basic skills programs that assist students who place in mathematics courses 2 levels…

Language Guidelines for a Mathematics Task Centre.

ERIC Educational Resources Information Center

Padula, Janice; Nin, Lucy

1999-01-01

Describes some of the thinking associated with the improvement of tasks, suggesting some guidelines for others to consider in producing written mathematics materials for young students. Provides examples of written mathematics materials. (ASK)

The Process of Thinking among Junior High School Students in Solving HOTS Question

ERIC Educational Resources Information Center

Bakry, Md Nor Bin Bakar

2015-01-01

Higher order thinking skills (HOTS) is one of the important aspect of teaching and learning mathematics. By using HOTS, student will be able to acquire a deep understand of mathematical concepts and can be applied in real life. Students ability to develop the capacity of the HOTS is closely related with thinking processes while solving mathematics…

A Constructive Response to "Where Mathematics Comes From."

ERIC Educational Resources Information Center

Schiralli, Martin; Sinclair, Nathalie

2003-01-01

Reviews the Lakoff and Nunez's book, "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (2000)," which provided many mathematics education researchers with a novel and startling perspective on mathematical thinking. Suggests that several of the book's flaws can be addressed through a more rigorous establishment of…

Think3d!: Improving Mathematics Learning through Embodied Spatial Training

ERIC Educational Resources Information Center

Burte, Heather; Gardony, Aaron L.; Hutton, Allyson; Taylor, Holly A.

2017-01-01

Spatial thinking skills positively relate to Science, Technology, Engineering, and Math (STEM) outcomes, but spatial training is largely absent in elementary school. Elementary school is a time when children develop foundational cognitive skills that will support STEM learning throughout their education. Spatial thinking should be considered a…

Mathematics Laboratories--More than Fun

ERIC Educational Resources Information Center

Vance, James H.; Kieren, Thomas E.

1972-01-01

The study assessed the effectiveness of methematical laboratories as compared with the regular mathematics teaching program. A control group, mathematical laboratory group, and a third group called a Class Discovery Group were formed for making comparisons. Gains were higher on cumulative achievement, transfer, and divergent thinking measures for…

Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

ERIC Educational Resources Information Center

Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

2016-01-01

Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

Secondary School Advanced Mathematics, Chapter 1, Organizing Geometric Knowledge, Chapter 2, Concepts and Skills in Algebra. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the first of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first chapter, devoted to organizing geometric knowledge, deals with the distinction…

Investigating Mathematics through Digital Media: Cognitive Visual Perturbations

ERIC Educational Resources Information Center

Calder, Nigel

2011-01-01

How might investigating mathematical tasks through digital media influence students' learning trajectories, and hence their mathematical thinking? This article reports on elements of an ongoing study that examines how engaging mathematical phenomena through digital pedagogical media might influence understanding. As the students sought…

Reflective thinking in solving an algebra problem: a case study of field independent-prospective teacher

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Yuli Eko Siswono, Tatag

2017-10-01

Nowadays, reflective thinking is one of the important things which become a concern in learning mathematics, especially in solving a mathematical problem. The purpose of this paper is to describe how the student used reflective thinking when solved an algebra problem. The subject of this research is one female student who has field independent cognitive style. This research is a descriptive exploratory study with data analysis using qualitative approach to describe in depth reflective thinking of prospective teacher in solving an algebra problem. Four main categories are used to analyse the reflective thinking in solving an algebra problem: (1) formulation and synthesis of experience, (2) orderliness of experience, (3) evaluating the experience and (4) testing the selected solution based on the experience. The results showed that the subject described the problem by using another word and the subject also found the difficulties in making mathematical modelling. The subject analysed two concepts used in solving problem. For instance, geometry related to point and line while algebra is related to algebra arithmetic operation. The subject stated that solution must have four aspect to get effective solution, specifically the ability to (a) understand the meaning of every words; (b) make mathematical modelling; (c) calculate mathematically; (d) interpret solution obtained logically. To test the internal consistency or error in solution, the subject checked and looked back related procedures and operations used. Moreover, the subject tried to resolve the problem in a different way to compare the answers which had been obtained before. The findings supported the assertion that reflective thinking provides an opportunity for the students in improving their weakness in mathematical problem solving. It can make a grow accuracy and concentration in solving a mathematical problem. Consequently, the students will get the right and logic answer by reflective thinking.

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…

Reading the News: The Statistical Preparation of Pre-Service Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Chesler, Joshua

2015-01-01

Undergraduate mathematics programs must prepare teachers for the challenges of teaching statistical thinking as advocated in standards documents and statistics education literature. This study investigates the statistical thinking of pre-service secondary mathematics teachers at the end of their undergraduate educations. Although all had completed…

Using Portfolio Assignments to Assess Students' Mathematical Thinking

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy; Buck, Stephen

2010-01-01

Writing in mathematics can improve procedural knowledge and communication skills and may also help students better understand and then remember problems. The majority of mathematics teachers know that they ought to include some writing assignments in their instructional plans, but the challenge of covering the curriculum and the time required to…

Secondary School Advanced Mathematics, Chapter 1, Organizing Geometric Knowledge, Chapter 2, Concepts and Skills in Algebra. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the first of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

Factors Contributing to Rural High School Students' Participation in Advanced Mathematics Courses. Working Paper No. 34

ERIC Educational Resources Information Center

Anderson, Rick

2006-01-01

The focus of this paper is a group of rural high school students and the factors that contributed to their participation in mathematics classes beyond those minimally required for high school graduation. The author follows Gutierrez (2002) in referring to participation as course taking, particularly in elective and advanced mathematics classes.…

The Effect of Scratch- and Lego Mindstorms Ev3-Based Programming Activities on Academic Achievement, Problem-Solving Skills and Logical-Mathematical Thinking Skills of Students

ERIC Educational Resources Information Center

Korkmaz, Özgen

2016-01-01

The aim of this study was to investigate the effect of the Scratch and Lego Mindstorms Ev3 programming activities on academic achievement with respect to computer programming, and on the problem-solving and logical-mathematical thinking skills of students. This study was a semi-experimental, pretest-posttest study with two experimental groups and…

Transfer of Algebraic and Graphical Thinking between Mathematics and Chemistry

ERIC Educational Resources Information Center

Potgieter, Marietjie; Harding, Ansie; Engelbrecht, Johann

2008-01-01

Students in undergraduate chemistry courses find, as a rule, topics with a strong mathematical basis difficult to master. In this study we investigate whether such mathematically related problems are due to deficiencies in their mathematics foundation or due to the complexity introduced by transfer of mathematics to a new scientific domain. In the…

Mathematical literacy skills of students' in term of gender differences

NASA Astrophysics Data System (ADS)

Lailiyah, Siti

2017-08-01

Good mathematical literacy skills will hopefully help maximize the tasks and role of the prospective teacher in activities. Mathematical literacy focus on students' ability to analyze, justify, and communicate ideas effectively, formulate, solve and interpret mathematical problems in a variety of forms and situations. The purpose of this study is to describe the mathematical literacy skills of the prospective teacher in term of gender differences. This research used a qualitative approach with a case study. Subjects of this study were taken from two male students and two female students of the mathematics education prospective teacher who have followed Community Service Program (CSP) in literacy. Data were collected through methods think a loud and interviews. Four prospective teachers were asked to fill mathematical literacy test and video taken during solving this test. Students are required to convey loud what he was thinking when solving problems. After students get the solution, researchers grouped the students' answers and results think aloud. Furthermore, the data are grouped and analyzed according to indicators of mathematical literacy skills. Male students have good of each indicator in mathematical literacy skills (the first indicator to the sixth indicator). Female students have good of mathematical literacy skills (the first indicator, the second indicator, the third indicator, the fourth indicator and the sixth indicator), except for the fifth indicators that are enough.

Incentivizing advanced mathematics study at upper secondary level: the case of bonus points in Ireland

NASA Astrophysics Data System (ADS)

Treacy, Páraic Thomas

2018-04-01

Secondary level mathematics education in Ireland has recently experienced a period of significant change with the introduction of new curricula and the addition of an incentive to study upper secondary mathematics at the most advanced level (Higher Level). This incentive, typically referred to as 'bonus points', appears to have aided a significant increase in the number of students studying upper secondary mathematics at Higher Level. However, thematic analysis of interviews with experienced upper secondary mathematics examiners and exploration of mathematics diagnostic test data outlined in this paper suggest that the difficulty of the Higher Level upper secondary mathematics final examination in Ireland has reduced since the introduction of the bonus points initiative. The sharp increase in students attempting this examination coupled with a policy of maintaining a consistent proportion of students achieving passing grades was identified as a key reason for this possible reduction in standards.

Students’ Relational Thinking of Impulsive and Reflective in Solving Mathematical Problem

NASA Astrophysics Data System (ADS)

Satriawan, M. A.; Budiarto, M. T.; Siswono, T. Y. E.

2018-01-01

This is a descriptive research which qualitatively investigates students’ relational thinking of impulsive and reflective cognitive style in solving mathematical problem. The method used in this research are test and interview. The data analyzed by reducing, presenting and concluding the data. The results of research show that the students’ reflective cognitive style can possibly help to find out important elements in understanding a problem. Reading more than one is useful to identify what is being questioned and write the information which is known, building relation in every element and connecting information with arithmetic operation, connecting between what is being questioned with known information, making equation model to find out the value by using substitution, and building a connection on re-checking, re-reading, and re-counting. The impulsive students’ cognitive style supports important elements in understanding problems, building a connection in every element, connecting information with arithmetic operation, building a relation about a problem comprehensively by connecting between what is being questioned with known information, finding out the unknown value by using arithmetic operation without making any equation model. The result of re-checking problem solving, impulsive student was only reading at glance without re-counting the result of problem solving.

Mathematics Underground

ERIC Educational Resources Information Center

Luther, Kenneth H.

2012-01-01

Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

Contradictions between and within School and University Activity Systems Helping to Explain Students' Difficulty with Advanced Mathematics

ERIC Educational Resources Information Center

Jooganah, Kamila; Williams, Julian S.

2016-01-01

This article explores how contradictions, as framed by activity theory (Engeström, 1987), can explain first-year undergraduate students' experiences of learning advanced mathematics. Analysing qualitative interview and observational data of students and lecturers based in one university mathematics department, we argue that contradictions between…

Entering into Dialogue about the Mathematical Value of Contextual Mathematising Tasks

ERIC Educational Resources Information Center

Yoon, Caroline; Chin, Sze Looi; Moala, John Griffith; Choy, Ban Heng

2018-01-01

Our project seeks to draw attention to the rich mathematical thinking that is generated when students work on contextual mathematising tasks. We use a design-based research approach to create ways of reporting that raise the visibility of this rich mathematical thinking while retaining and respecting its complexity. These reports will be aimed for…

Promoting Access to Common Core Mathematics for Students with Severe Disabilities through Mathematical Problem Solving

ERIC Educational Resources Information Center

Spooner, Fred; Saunders, Alicia; Root, Jenny; Brosh, Chelsi

2017-01-01

There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…

An Inside Track: Fostering Mathematical Practices

ERIC Educational Resources Information Center

Buchheister, Kelley; Jackson, Christa; Taylor, Cynthia

2015-01-01

Classroom teachers may not initially consider games as opportunities for students to engage in deep mathematical thinking. However, this article reveals how a second grade veteran teacher used Attribute Trains, a game adapted from NCTM Illuminations, to foster his students' thinking related to key ideas within the Standards for Mathematical…

Inversion in Mathematical Thinking and Learning

ERIC Educational Resources Information Center

Greer, Brian

2012-01-01

Inversion is a fundamental relational building block both within mathematics as the study of structures and within people's physical and social experience, linked to many other key elements such as equilibrium, invariance, reversal, compensation, symmetry, and balance. Within purely formal arithmetic, the inverse relationships between addition and…

Our Prospective Mathematic Teachers Are Not Critical Thinkers Yet

ERIC Educational Resources Information Center

As'ari, Abdur Rahman; Mahmudi, Ali; Nuerlaelah, Elah

2017-01-01

In order to help students develop their critical thinking skills, teachers need to model the critical thinking skills and dispositions in front of their students. Unfortunately, very rare studies investigating prospective teachers' readiness in critical thinking dispositions are available in the field of mathematics education. This study was…

National Center for Mathematics and Science - what we do

Science.gov Websites

. teachers need more substantive professional development about student thinking and subject matter student thinking is a cornerstone of professional development. In our work with teachers, we have observed the ways that teachers examined student thinking about important mathematics and science ideas, and

Effectiveness of higher order thinking skills (HOTS) based i-Think map concept towards primary students

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Ping, Owi Wei; Ahmad, Azhar; Adnan, Mazlini; Hua, Ang Kean

2017-05-01

Higher Order Thinking Skills (HOTS) is a new concept of education reform based on the Taxonomies Bloom. The concept concentrate on student understanding in learning process based on their own methods. Through the HOTS questions are able to train students to think creatively, critic and innovative. The aim of this study was to identify the student's proficiency in solving HOTS Mathematics question by using i-Think map. This research takes place in Sabak Bernam, Selangor. The method applied is quantitative approach that involves approximately all of the standard five students. Pra-posttest was conduct before and after the intervention using i-Think map in solving the HOTS questions. The result indicates significant improvement for post-test, which prove that applying i-Think map enhance the students ability to solve HOTS question. Survey's analysis showed 90% of the students agree having i-Thinking map in analysis the question carefully and using keywords in the map to solve the questions. As conclusion, this process benefits students to minimize in making the mistake when solving the questions. Therefore, teachers are necessarily to guide students in applying the eligible i-Think map and methods in analyzing the question through finding the keywords.

Ancient Paradoxes Can Extend Mathematical Thinking

ERIC Educational Resources Information Center

Czocher, Jennifer A.; Moss, Diana L.

2017-01-01

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

Mathematical Problem Solving Ability of Eleventh Standard Students

ERIC Educational Resources Information Center

Priya, J. Johnsi

2017-01-01

There is a general assertion among mathematics instructors that learners need to acquire problem solving expertise, figure out how to communicate using mathematics knowledge and aptitude, create numerical reasoning and thinking, to see the interconnectedness amongst mathematics and other subjects. Based on this perspective, the present study aims…

Hot Ideas. A Mathematical Response to a Piece of Text

ERIC Educational Resources Information Center

Grey, Melinda

2005-01-01

Children's literature can enhance mathematics lessons by providing a meaningful context, demonstrating that mathematics develops from human experiences and contributes an aesthetic dimension to learning mathematics. Written as a series of real life inspired snapshots of mathematical thinking, "Counting on Frank" (Rod Clement, 1990)…

Advanced Analytic Cognition: Critical Thinking

DTIC Science & Technology

2013-09-01

showed no significant differences between the experimental and control groups . Further, posttest means were not significantly different from pretest ...means in either group ( Pretest : Experimental M = 296, Control M = 297; Posttest : Experimental M = 298, Control M = 302). It appears that taking a...Delphi group - this was the largest dissident group on any topic - supported the view expressed in this chapter, that critical thinking should be

Evaluating the Effects of Lesson Study as a Way to Help Student Teachers Learn How to Use Student Thinking when Planning and Revising Mathematics Lesson Plans

ERIC Educational Resources Information Center

Sisofo, Eric Joseph

2010-01-01

The use of student thinking in teaching has been linked to improved instruction and learning. It is reasonable to assume that the University of Delaware's undergraduate program might be interested in figuring out ways to develop this skill in its mathematics specialist pre-service teachers. Currently, the student teaching experience at the…

The reality of Mathematics

NASA Astrophysics Data System (ADS)

Ligomenides, Panos A.

2009-05-01

The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.

The effect of Think Pair Share (TPS) using scientific approach on students’ self-confidence and mathematical problem-solving

NASA Astrophysics Data System (ADS)

Rifa’i, A.; Lestari, H. P.

2018-03-01

This study was designed to know the effects of Think Pair Share using Scientific Approach on students' self-confidence and mathematical problem-solving. Quasi-experimental with pre-test post-test non-equivalent group method was used as a basis for design this study. Self-confidence questionnaire and problem-solving test have been used for measurement of the two variables. Two classes of the first grade in religious senior high school (MAN) in Indonesia were randomly selected for this study. Teaching sequence and series from mathematics book at control group in the traditional way and at experiment group has been in TPS using scientific approach learning method. For data analysis regarding students’ problem-solving skill and self-confidence, One-Sample t-Test, Independent Sample t-Test, and Multivariate of Variance (MANOVA) were used. The results showed that (1) TPS using a scientific approach and traditional learning had positive effects (2) TPS using scientific approach learning in comparative with traditional learning had a more significant effect on students’ self-confidence and problem-solving skill.

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…

Enhancing students’ critical thinking skills through critical thinking assessment in calculus course

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Zulfaneti; Edriati, S.; Mukhni

2018-01-01

This study aims to determine the development of students’ critical thinking skills through the implementation of critical thinking instruments in Calculus lectures. The instruments consist of observation sheets, critical thinking test, self-assessment, peer assessment and portfolio. The research was a qualitative research; with the participants were 53 first-year students who take Integral Calculus in Mathematics Education Department STKIP PGRI Sumatera Barat representing high-ability students, medium and low. The data in this study were collected by tests, interviews, observations and field notes. Data were analyzed descriptively; data reduction, data presentation, and conclusions. For testing the validity of data, it was used credibility test data by increasing persistence and triangulation. The results showed that in high-level students there is a change of ability from Critical enough to be Very Critical, in the students with moderate and low ability there is a change of ability from Uncritical to Critical. So it can be concluded that the assessment instruments have a good contribution and can improve the ability of critical thinking.

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…

Global Perspectives: Developing Media Literacy Skills to Advance Critical Thinking

ERIC Educational Resources Information Center

Radeloff, Cheryl L.; Bergman, Barbara J.

2009-01-01

Women's studies and feminist curricula have been lauded for the development and application of critical thinking skills for social and political change in its students (Fisher; Kellner and Share; Mayberry). Critical thinking can be defined as the ability to identify and challenge assumptions, to search for alternative ways of thinking, and to…

Blurring Boundaries within Mathematics Education: Prospective K-8 Teachers Interrogating Intersectional Identities, Narratives, and Positionings in Out-of-School Contexts

ERIC Educational Resources Information Center

Guzman, Lynette DeAun

2017-01-01

Mathematics teacher noticing as a pedagogical practice--attending to, interpreting, and responding to children's mathematical thinking--is growing within mathematics education communities. Much of the research literature primarily focuses on supporting teacher noticing of children's mathematical thinking within classroom contexts, such as…

Functional Thinking Profile of Junior High School Student in Solving Mathematical Problem Observed by Differences of Sex

NASA Astrophysics Data System (ADS)

Siregar, A. P.; Juniati, D.; Sulaiman, R.

2018-01-01

This study involving 2 grade VIII students was taken place in SMPK Anak Bangsa Surabaya. Subjects were selected using equal mathematics ability criteria. Data was collected using provision of problem-solving tasks and followed by a task-based interview. Obtained data was analysed through the following steps, which are data reduction, data presentation, and conclusions. Meanwhile, to obtain a valid data, in this study, researchers used data triangulation. The results indicated that in the problem number 1 about identifying patterns, the subjects of male and female show a tendency of similarities in stating what is known and asked the question. However, the male students provided a more specific answer in explaining the magnitude of the difference between the first quantity and the increased differences in the other quantities. Related the activities in determining the relationship between two quantities, male subjects and women subject tended to have similarities in the sense of using trial and error on existing mathematical operations. It can be concluded that the functional way of thinking both subjects is relatively identic. Nevertheless, the male subject showed the more specific answer in finding the difference between the two quantities and finding the correspondence relationship between the quantities.

Effects of Advance Organiser Strategy during Instruction on Secondary School Students' Mathematics Achievement in Kenya's Nakuru District

ERIC Educational Resources Information Center

Githua, Bernard N.; Nyabwa, Rachel Angela

2008-01-01

Students have continued to perform poorly in KCSE examinations in certain mathematics topics taught in secondary schools in Kenya. One such topic is commercial arithmetic. Successful teaching of mathematics depends partly on correct use of teaching methods in classroom settings. This study sought to examine how the use of advance organisers during…

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…

Development of Analytical Thinking Ability and Attitudes towards Science Learning of Grade-11 Students through Science Technology Engineering and Mathematics (STEM Education) in the Study of Stoichiometry

ERIC Educational Resources Information Center

Chonkaew, Patcharee; Sukhummek, Boonnak; Faikhamta, Chatree

2016-01-01

The purpose of this study was to investigate the analytical thinking abilities and attitudes towards science learning of grade-11 students through science, technology, engineering, and mathematics (STEM) education integrated with a problem-based learning in the study of stoichiometry. The research tools consisted of a pre- and post-analytical…

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…

What Students Say about Their Mathematical Thinking When They Listen

ERIC Educational Resources Information Center

Kosko, Karl W.

2014-01-01

Mathematical listening is an important aspect of mathematical communication. Yet there are relatively few examinations of this phenomenon. Further, existing studies of students' mathematical listening come from observational data, lacking the student perspective. This study examined student replies to an open-response question regarding what…

Mathematics Teacher TPACK Standards and Development Model

ERIC Educational Resources Information Center

Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis

2009-01-01

What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…

Synopses for Modern Secondary School Mathematics.

ERIC Educational Resources Information Center

Organisation for Economic Cooperation and Development, Paris (France). Directorate for Scientific Affairs.

The 1959 Royaumont seminar "New Thinking in School Mathematics," having agreed on the need for modernization, recommended that a second group of experts work out detailed synopses of the entire subject matter of secondary school mathematics. This book is the report of the second seminar and contains the Dubrovnik Program which stimulated…

Discussion from a Mathematics Education Perspective

ERIC Educational Resources Information Center

Clements, Douglas; Sarama, Julie

2015-01-01

In a review of the special issue, we conclude that the articles are research gems in the domain of preschool mathematics education. Most share several features, such as their perspective on research methodology and their view of mathematics thinking and learning. They address the cognitive architecture and processes and the developmental levels…

Motivating Prospective Elementary School Teachers to Learn Mathematics by Focusing upon Children's Mathematical Thinking

ERIC Educational Resources Information Center

Philipp, Randolph A.

2008-01-01

Elementary school children in the United States are not developing acceptable levels of mathematical proficiency (National Center for Education Statistics, 1999), and a major concern of teacher educators is that teachers lack the depth and flexibility of mathematical understanding and the corresponding beliefs they need to teach for proficiency…

New Thinking about College Mathematics: Implications for High School Teaching

ERIC Educational Resources Information Center

Marcus, Robin; Fukawa-Connelly, Tim; Conklin, Michael; Fey, James T.

2007-01-01

This article describes recommendations made by participants in a large project of the Mathematical Association of America (MAA), in which representatives of "partner disciplines" shared what they would like students to learn in the first two years of college mathematics. The article further suggests implications for high school mathematics.…

Learning with Touchscreen Devices: Game Strategies to Improve Geometric Thinking

ERIC Educational Resources Information Center

Soldano, Carlotta; Arzarello, Ferdinando

2016-01-01

The aim of this paper is to reflect on the importance of the students' game-strategic thinking during the development of mathematical activities. In particular, we hypothesise that this type of thinking helps students in the construction of logical links between concepts during the "argumentation phase" of the proving process. The…

Introductory science and mathematics education for 21st-Century biologists.

PubMed

Bialek, William; Botstein, David

2004-02-06

Galileo wrote that "the book of nature is written in the language of mathematics"; his quantitative approach to understanding the natural world arguably marks the beginning of modern science. Nearly 400 years later, the fragmented teaching of science in our universities still leaves biology outside the quantitative and mathematical culture that has come to define the physical sciences and engineering. This strikes us as particularly inopportune at a time when opportunities for quantitative thinking about biological systems are exploding. We propose that a way out of this dilemma is a unified introductory science curriculum that fully incorporates mathematics and quantitative thinking.

Symbols and the Bifurcation between Procedural and Conceptual Thinking.

ERIC Educational Resources Information Center

Tall, David; Gray, Eddie; Bin Ali, Maselan; Crowley, Lillie; DeMarois, Phil; McGowen, Mercedes; Pitta, Demetra; Pinto, Marcia; Thomas, Michael; Yusof, Yudariah

Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this presentation, the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and…

Provisional Approaches to Goals for School Mathematics; Cambridge Conference on School Mathematics Feasibility Study No. 37.

ERIC Educational Resources Information Center

Cambridge Conference on School Mathematics, Newton, MA.

These materials were written with the aim of reflecting the thinking of Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics K-6. In view of the experiences of other curriculum groups and of the general discussions since 1963, the present report initiates the next step in evolving the "Goals".…

A Model of Historical Thinking

ERIC Educational Resources Information Center

Seixas, Peter

2017-01-01

"Historical thinking" has a central role in the theory and practice of history education. At a minimum, history educators must work with a model of historical thinking if they are to formulate potential progression in students' advance through a school history curriculum, test that progression empirically, and shape instructional…

Increasing Critical Thinking Skills To Improve Problem-Solving Ability in Mathematics.

ERIC Educational Resources Information Center

Jackson, Louise

This report investigated to what extent a curriculum designed to actively teach critical thinking skills resulted in students utilizing higher-order thinking skills (e.g., analysis, synthesis and evaluation). An intervention strategy was designed for a sixth grade class located in a diverse suburban community in northern Illinois. The intervention…

Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education. Studies in Mathematical Thinking and Learning Series

ERIC Educational Resources Information Center

Clements, Douglas H., Ed.; DiBiase, Ann-Marie, Ed.; Sarama, Julie, Ed.

2004-01-01

This book brings together the combined wisdom of a diverse group of experts involved with early childhood mathematics. The book originates from the landmark 2000 Conference on Standards for Pre-kindergarten and Kindergarten Mathematics Education, attended by representatives from almost every state developing standards for young children's…

Literacy in Language and Mathematics: More in Common Than You Think

ERIC Educational Resources Information Center

Thompson, Denisse R.; Rubenstein, Rheta N.

2014-01-01

This paper shares perspectives on literacy in mathematics, particularly highlighting commonalities with literacy in language arts. We discuss levels of language development appropriate for the mathematics classroom, issues related to mathematical definitions, implied meanings in many mathematics concepts, and the importance of justification. We…

Puzzle-based learning in engineering mathematics: students' attitudes

NASA Astrophysics Data System (ADS)

Klymchuk, Sergiy

2017-11-01

The article reports on the results of two case studies on the impact of the regular use of puzzles as a pedagogical strategy in the teaching and learning of engineering mathematics. The intention of using puzzles is to engage students' emotions, creativity and curiosity and also to enhance their generic thinking skills and lateral thinking 'outside the box'. Students' attitudes towards this pedagogical strategy are evaluated via short questionnaires with two groups of university students taking a second-year engineering mathematics course. Students' responses to the questionnaire are presented and analyzed in the paper.

Mathematical Lens: Roller Coasters and Railways

ERIC Educational Resources Information Center

Daire, Sandra Arguelles

2009-01-01

This article uses photographs as a springboard for mathematical inquiry to encourage readers to see patterns and relationships that they can think about and extend in a mathematically playful way. Herein, two photographs are presented along with a discussion of the meaning of slopes and their relationship to gradient and pitch. (Contains 6…

Young Children's Mathematics References during Free Play in Family Childcare Settings

ERIC Educational Resources Information Center

Hendershot, Shawnee M.; Berghout Austin, Ann M.; Blevins-Knabe, Belinda; Ota, Carrie

2016-01-01

Very little is known about children's discussion of mathematics topics during unstructured play. Ginsburg, Lin, Ness, and Seo [2003. Young American and Chinese children's everyday mathematical activity. Mathematical Thinking and Learning, 5(4), 235-258. Retrieved from…

Effects of Experiential Learning Approach on Students' Mathematical Creativity among Secondary School Students of Kericho East Sub-County, Kenya

ERIC Educational Resources Information Center

Chesimet, M. C.; Githua, B. N.; Ng'eno, J. K.

2016-01-01

Mathematics is a subject which seeks to understand patterns that permeate both the world around us and the mind within us. There are many ways of thinking and the kind of thinking one learns in mathematics is an ability to handle abstraction and solve problems that require knowledge of mathematics. Mathematical creativity is essential for…

Advancing K-8 Teachers' STEM Education for Teaching Interdisciplinary Science and Mathematics with Technologies

ERIC Educational Resources Information Center

Niess, Margaret; Gillow-Wiles, Henry

2013-01-01

This primarily online Master's degree program focused on advancing K-8 teachers' interdisciplinary mathematical and science content knowledge while integrating appropriate digital technologies as learning and teaching tools. The mixed-method, interpretive study examined in-service teachers' technological, pedagogical, and content knowledge (TPACK)…

The Thinking-about-Derivative Test for Undergraduate Students: Development and Validation

ERIC Educational Resources Information Center

Aydin, Utkun; Ubuz, Behiye

2015-01-01

Two studies were conducted for the development and validation of a multidimensional test to assess undergraduate students' mathematical thinking about derivative. The first study involved two phases: question generation and refinement of the Thinking-about-Derivative Test (TDT). The second study included four phases as follows: test…

What We Think We Know About Maya Mathematics and Astronomy

NASA Astrophysics Data System (ADS)

Van Stone, M.

2016-01-01

In most cultures, mathematics and astronomy are obscure and arcane. Not so to the ancient Maya. Despite what we consider technological “deficiencies”—they lacked both metal tools and the wheel—their public inscriptions paid uniquely sophisticated attention to these sciences. At any given monument, fully half the text is devoted to situating events in time, particularly specifying the precise number of days between events, whether historical or mythological. Often these intervals have numerological significance, and many are precise multiples of the periodicities of heavenly bodies. The Maya apparently were fully aware of the exact length of the tropical year, the sidereal year, the cycles of Venus, and eclipses; and there is evidence that they even celebrated events reflecting the 26,000-year precession cycle. However, Maya illuminati had an agenda quite alien to our way of thinking. Clues to their knowledge are arcane, rare, and often difficult for us to recognize with eyes clouded by our modern worldview. The body of work left to us consists of just a few tantalizing sherds of a once-rich and diverse astromythological tradition. Moreover, there was no single pan-Mayan mythos. An astronomical alignment seen repeatedly in one city will be completely absent in others. Each city-state emphasized specific and often unique features, and they often contradict one another. But we soldier on. The diversity we find so frustrating is simply the fine structure of their worldview. Intellectual historians have for too long been, like Procrustes, trying to force all Maya science and religion into a single universal straitjacket.

Developing Mathematical Thinking: Changing Teachers' Knowledge and Instruction

ERIC Educational Resources Information Center

Brendefur, Jonathan L.; Thiede, Keith; Strother, Sam; Bunning, Kim; Peck, Duane

2013-01-01

In the present research, we evaluated the effectiveness of a multi-year professional development program in mathematics for elementary teachers. Each year the program focused on a different domain of mathematics. We found the program increased teachers' knowledge of (a) number and operations, (b) measurement and geometry, and (c) probability and…

Indicators of Multiplicative Reasoning among Fourth Grade Students

ERIC Educational Resources Information Center

Carrier, James A.

2010-01-01

Many students encounter difficulty in their transition to advanced mathematical thinking. Such difficulty may be explained by a lack of understanding of many concepts taught in early school years, especially multiplicative reasoning. Advanced mathematical thinking depends on the development of multiplicative reasoning. The purpose of this study…

School Mathematics as a Creative Enterprise

ERIC Educational Resources Information Center

Sternberg, Robert J.

2017-01-01

In this article, I discuss how teaching of mathematics can develop and encourage creative thinking, not only in mathematics, but also in general. I begin by discussing creativity as a habit that teachers can help students develop. Then I briefly present the investment theory of creativity. The basic idea of the investment theory is that creative…

The Layering of Mathematical Interpretations through Digital Media

ERIC Educational Resources Information Center

Calder, Nigel

2012-01-01

How might understanding emerge when learners engage mathematical phenomena through digital technologies? This paper considers the ways children's mathematical thinking was influenced by their interpretations through various pedagogical discourses and how understanding emerged through those various filters. Current research into using digital…

What is the Role of Mathematics Education in the Computer Age?

ERIC Educational Resources Information Center

Popp, Jerome A.

1986-01-01

Proposes that the role of mathematics education be re-examined in terms of an increased emphasis on mathematical knowledge rather than attainment of calculational speed. Offers perspectives on the reform movement in mathematics education and advocates the teaching of the history, logic, and method of mathematical thinking. (ML)

Learning to Leverage Children's Multiple Mathematical Knowledge Bases in Mathematics Instruction

ERIC Educational Resources Information Center

Turner, Erin E.; Foote, Mary Q.; Stoehr, Kathleen Jablon; McDuffie, Amy Roth; Aguirre, Julia Maria; Bartell, Tonya Gau; Drake, Corey

2016-01-01

In this article, the authors explore prospective elementary teachers' engagement with and reflection on activities they conducted to learn about a single child from their practicum classroom. Through these activities, prospective teachers learned about their child's mathematical thinking and the interests, competencies, and resources she or he…

The Equity Education. Fostering the Advancement of Women in the Sciences, Mathematics, and Engineering.

ERIC Educational Resources Information Center

Davis, Cinda-Sue; And Others

This volume includes 10 reports that present findings and recommendations for advancing women in science, mathematics and engineering. Critical issues facing women in these disciplines are addressed, including demographic myths and realities at various educational levels; the educational pipeline for girls and women; involvement in education and…

Putting Research into Practice in the Elementary Grades: Readings from Journals of the National Council of Teachers of Mathematics.

ERIC Educational Resources Information Center

Chambers, Donald L., Ed.

This book describes children's mathematical thinking to guide and support teachers in their reflection upon student thinking and teaching and learning. It is organized into five parts: (1) reasoning, student thinking, and invented strategies independent of the mathematics content domain which addresses the role of discourse in helping students…

Algebraic Procedures and Creative Thinking

ERIC Educational Resources Information Center

Tabach, Michal; Friedlander, Alex

2017-01-01

Simplifying symbolic expressions is usually perceived in middle school algebra as an algorithmic activity, achieved by performing sequences of short drill-and-practice tasks, which have little to do with conceptual learning or with creative mathematical thinking. The aim of this study is to explore possible ways by which ninth-grade students can…

The Multicultural Mathematics Classroom: Culturally Aware Teaching through Cooperative Learning & Multiple Representations

ERIC Educational Resources Information Center

Jao, Limin

2012-01-01

The National Council of Teachers of Mathematics (NCTM, 2000) has created a set of standards to reform mathematics teaching procedures to ensure that all students understand mathematics and learn to think mathematically. The standards also require teachers to use strategies that allow all students to reason and communicate mathematically and…

Mathematics Teachers "Telling It Like It Is"

ERIC Educational Resources Information Center

Espedido, Rosei; Du Toit, Wilhelmina

2017-01-01

The authors of this article strongly advocate for a change to the current Australian model of primary education in order to, among other things, establish the concrete practicalities of systematic mathematics thinking thereby limiting the "re-teaching" time required of secondary school mathematics teachers; bring a clear focus to the…

Mathematics and Administration: Tools, Metaphors and Styles of Thinking.

ERIC Educational Resources Information Center

Hanson, Marjorie K.

This essay provides commentary on the place of mathematics in the study and practice of educational administration. The incidence of mathematical topics in the writing of the field is explored, and their isolation from each other and from the body of literature is pointed out. Possible areas of synthesis are sought from the traditional use of…

Corresponding Habits of Mind and Mathematical Ability

NASA Astrophysics Data System (ADS)

Dwirahayu, G.; Kustiawati, D.; Bidari, I.

2017-09-01

Objective of learning process regarding system of Indonesia government should be consist of knowledge, attitudes, and skills, or in general we call cognitive, affective and psychomotor. These objective are apply to mathematics education also. Attitude in mathematics known as habits of mind. The teacher should create a learning objective which including all, cognitive, affective and psychomotor. In general, math teachers in Indonesia pay attention to aspects of knowledge, and they ignore other aspects. Habits of mind is term which means the tendency to behave intellectually or intelligently when faced with problems which is immediately known solution. This article examines the math teacher’s attention to students’ habits of mind. The research done by survey method to 38 students at Islamic School 32 Jakarta academic year 2015/2016 from April to May 2016. Habits of mind are observed in this research restricted to persisting, thinking about thinking, thinking flexible and applying past knowledge to new situation. Based on survey, conclude that teacher, without realizing, they have to improve students’ habits of mind, as long as teaching and learning only persisting and thinking about thinking are already well developed, while flexible thinking and applying past knowledge to new situation has not well developed. We hope, math teacher can pay attention not only cognitive aspect but habits of mind also.

Catalyzing Genetic Thinking in Undergraduate Mathematics Education

ERIC Educational Resources Information Center

King, Samuel Olugbenga

2016-01-01

In undergraduate mathematics education, atypical problem solving approaches are usually discouraged because they are not adaptive to systematic deduction on which undergraduate instructional systems are predicated. I present preliminary qualitative research evidence that indicates that these atypical approaches, such as genetic guessing, which…

Spatial Thinking in Astronomy Education Research

ERIC Educational Resources Information Center

Cole, Merryn; Cohen, Cheryl; Wilhelm, Jennifer; Lindell, Rebecca

2018-01-01

[This paper is part of the Focused Collection on Astronomy Education Research.] Multiple studies show that spatial thinking skills contribute to students' performance in science, technology, engineering, and mathematics disciplines. The study of astronomy is no different with the understanding of many astronomical phenomena requiring spatial…

Guide to Mathematics Released Items: Understanding Scoring

ERIC Educational Resources Information Center

Partnership for Assessment of Readiness for College and Careers, 2017

2017-01-01

The Partnership for Assessment of Readiness for College and Careers (PARCC) mathematics items measure critical thinking, mathematical reasoning, and the ability to apply skills and knowledge to real-world problems. Students are asked to solve problems involving the key knowledge and skills for their grade level as identified by the Common Core…

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…

The Etiology of Mathematical Self-Evaluation and Mathematics Achievement: Understanding the Relationship Using a Cross-Lagged Twin Study from Ages 9 to 12

ERIC Educational Resources Information Center

Luo, Yu L. L.; Kovas, Yulia; Haworth, Claire M. A.; Plomin, Robert

2011-01-01

The genetic and environmental origins of individual differences in mathematical self-evaluation over time and its association with later mathematics achievement were investigated in a UK sample of 2138 twin pairs at ages 9 and 12. Self-evaluation indexed how good children think they are at mathematical activities and how much they like those…

Can goal-free problems facilitating students' flexible thinking?

NASA Astrophysics Data System (ADS)

Maulidya, Sity Rahmy; Hasanah, Rusi Ulfa; Retnowati, Endah

2017-08-01

Problem solving is the key of doing and also learning mathematics. It takes also the fundamental role of developing mathematical knowledge. Responding to the current reform movement in mathematics, students are expected to learn to be a flexible thinker. The ability to think flexible is challenged by the globalisation, hence influence mathematics education. A flexible thinking includes ability to apply knowledge in different contexts rather than simply use it in similar context when it is studied. Arguably problem solving activities can contribute to the development of the ability to apply skills to unfamiliar situations. Accordingly, an appropriate classroom instructional strategy must be developed. A cognitive load theory suggests that by reducing extraneous cognitive load during learning could enhance transfer learning. A goal-free problem strategy that is developed based in cognitive load theory have been showed to be effective for transfer learning. This strategy enables students to learn a large numbers of problem solving moves from a mathematics problem. The instruction in a goal-free problem directs students to `calculate as many solution as you can' rather than to calculate a single given goal. Many experiment research evident goal-free problem enhance learning. This literature review will discuss evidence goal-free problem facilitate students to solve problems flexibly and thus enhance their problem solving skills, including how its implication in the classroom.

The Development of Learning Model Based on Problem Solving to Construct High-Order Thinking Skill on the Learning Mathematics of 11th Grade in SMA/MA

ERIC Educational Resources Information Center

Syahputra, Edi; Surya, Edy

2017-01-01

This paper is a summary study of team Postgraduate on 11th grade. The objective of this study is to develop a learning model based on problem solving which can construct high-order thinking on the learning mathematics in SMA/MA. The subject of dissemination consists of Students of 11th grade in SMA/MA in 3 kabupaten/kota in North Sumatera, namely:…

Investigating Preservice Mathematics Teachers' Manipulative Material Design Processes

ERIC Educational Resources Information Center

Sandir, Hakan

2016-01-01

Students use concrete manipulatives to form an imperative affiliation between conceptual and procedural knowledge (Balka, 1993). Hence, it is necessary to design specific mathematics manipulatives that focus on different mathematical concepts. Preservice teachers need to know how to make and use manipulatives that stimulate students' thinking as…

Research on Mathematical Animation Using Pascal Animation as an Example

ERIC Educational Resources Information Center

Weng, Ting-Sheng; Yang, Der-Ching

2017-01-01

Most students thinking mathematics is a difficult subject. This study aims to enhance students' motivation and efficiency in learning mathematics. This study developed 3D animation on the binomial theorem with historical stories of mathematics as the plot. It also examined the effect of animation on students' learning willingness and…

Provocative Mathematics Questions: Drawing Attention to a Lack of Attention

ERIC Educational Resources Information Center

Klymchuk, Sergiy

2015-01-01

The article investigates the role of attention in the reflective thinking of school mathematics teachers. It analyses teachers' ability to pay attention to detail and "use" their mathematical knowledge. The vast majority of teachers can be expected to have an excellent knowledge of mathematical techniques. The question examined here is…

Mathematical Connections and Their Relationship to Mathematics Knowledge for Teaching Geometry

ERIC Educational Resources Information Center

Eli, Jennifer A.; Mohr-Schroeder, Margaret J.; Lee, Carl W.

2013-01-01

Effective competition in a rapidly growing global economy places demands on a society to produce individuals capable of higher-order critical thinking, creative problem solving, connection making, and innovation. We must look to our teacher education programs to help prospective middle grades teachers build the mathematical habits of mind that…

Algebraic Thinking through Koch Snowflake Constructions

ERIC Educational Resources Information Center

Ghosh, Jonaki B.

2016-01-01

Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…

Developing Multiplicative Thinking from Additive Reasoning

ERIC Educational Resources Information Center

Tobias, Jennifer M.; Andreasen, Janet B.

2013-01-01

As students progress through elementary school, they encounter mathematics concepts that shift from additive to multiplicative situations (NCTM 2000). When they encounter fraction problems that require multiplicative thinking, they tend to incorrectly extend additive properties from whole numbers (Post et al. 1985). As a result, topics such as …

Gesture Supports Spatial Thinking in STEM

ERIC Educational Resources Information Center

Stieff, Mike; Lira, Matthew E.; Scopelitis, Stephanie A.

2016-01-01

The present article describes two studies that examine the impact of teaching students to use gesture to support spatial thinking in the Science, Technology, Engineering, and Mathematics (STEM) discipline of chemistry. In Study 1 we compared the effectiveness of instruction that involved either watching gesture, reproducing gesture, or reading…

Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

The DREME Network: Research and Interventions in Early Childhood Mathematics.

PubMed

Day-Hess, Crystal; Clements, Douglas H

2017-01-01

The DREME Network was created to advance the field of early mathematics research and improves the opportunities to develop math competencies offered to children birth through age 8 years, with an emphasis on the preschool years. All four main Network projects will have implications for interventions. Section 1 introduces the Network and its four projects. The remainder of the chapter focuses on one of these four projects, Making More of Math (MMM), in depth. MMM is directly developing an intervention for children, based on selecting high-quality instructional activities culled from the burgeoning curriculum resources. We first report a review of 457 activities from 6 research-based curricula, which describes the number of activities by content focus, type (nature), and setting of each activity. Given the interest in higher-order thinking skills and self-regulation, we then identified activities that had the potential to, develop both mathematics and executive function (EF) proficiencies. We rated these, selecting the top 10 for extensive coding by mathematics content and EF processes addressed. We find a wide divergence across curricula in all these categories and provide comprehensive reports for those interested in selecting, using, or developing early mathematics curricula. © 2017 Elsevier Inc. All rights reserved.

Neuroscientific Studies of Mathematical Thinking and Learning: A Critical Look from a Mathematics Education Viewpoint

ERIC Educational Resources Information Center

Verschaffel, Lieven; Lehtinen, Erno; Van Dooren, Wim

2016-01-01

In this commentary we take a critical look at the various studies being reported in this issue about the relationship between cognitive neuroscience and mathematics, from a mathematics education viewpoint. After a discussion of the individual contributions, which we have grouped into three categories--namely neuroscientific studies of (a)…

Celebrate Mathematical Curiosity

ERIC Educational Resources Information Center

Redford, Christine

2011-01-01

Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…

Mathematical Pattern Hunters

ERIC Educational Resources Information Center

Whitin, Phyllis; Whitin, David J.

2011-01-01

The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…

Conversations about Curriculum Change: Mathematical Thinking and Team-Based Learning in a Discrete Mathematics Course

ERIC Educational Resources Information Center

Paterson, Judy; Sneddon, Jamie

2011-01-01

This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…

Does the cognitive reflection test measure cognitive reflection? A mathematical modeling approach.

PubMed

Campitelli, Guillermo; Gerrans, Paul

2014-04-01

We used a mathematical modeling approach, based on a sample of 2,019 participants, to better understand what the cognitive reflection test (CRT; Frederick In Journal of Economic Perspectives, 19, 25-42, 2005) measures. This test, which is typically completed in less than 10 min, contains three problems and aims to measure the ability or disposition to resist reporting the response that first comes to mind. However, since the test contains three mathematically based problems, it is possible that the test only measures mathematical abilities, and not cognitive reflection. We found that the models that included an inhibition parameter (i.e., the probability of inhibiting an intuitive response), as well as a mathematical parameter (i.e., the probability of using an adequate mathematical procedure), fitted the data better than a model that only included a mathematical parameter. We also found that the inhibition parameter in males is best explained by both rational thinking ability and the disposition toward actively open-minded thinking, whereas in females this parameter was better explained by rational thinking only. With these findings, this study contributes to the understanding of the processes involved in solving the CRT, and will be particularly useful for researchers who are considering using this test in their research.

Developing the Young Gifted Child's Mathematical Mind

ERIC Educational Resources Information Center

Fisher, Carol

2016-01-01

Schools seem firmly rooted in the emphasis on computational mastery, and seldom seem to have time to develop other areas of mathematical thinking, such as real-world problem solving and the application of mathematical concepts. All too often, children seem to do well in math in the early grades because they easily memorize the facts and the…

Making Mathematics Relevant for Students in Bali

ERIC Educational Resources Information Center

Sema, Pryde Nubea

2008-01-01

The reactions of students towards mathematics in Bali (in the NW Province of Cameroon) are appalling. This is due to a misconception regarding its uses. The author thinks that these problems derive partly from the influence that the Western curriculum has had in Bali--mathematical contexts are based around train times in Liverpool instead of from…

SMP That Help Foster Algebraic Thinking

ERIC Educational Resources Information Center

Billings, Esther M. H.

2017-01-01

Arithmetic is a major mathematical focus in elementary school curriculum, and researchers such as Mason (2008) claim that "algebraic thinking is required in order to make sense of arithmetic" (p. 58). When adding, subtracting, multiplying, and dividing, learners must rely on a small set of fundamental properties also important for the…

CASMI: Virtual Learning Collaborative Environment for Mathematical Enrichment

ERIC Educational Resources Information Center

Freiman, Viktor; Manuel, Dominic; Lirette-Pitre, Nicole

2007-01-01

Challenging problems can make mathematics more attractive to all learners, including the gifted. Application problems that one still finds in regular textbooks often can be resolved by applying a single mathematical concept, operation, or formula. These problems do not require a higher order of thinking. They are, therefore, less cognitively and…

Nurturing Mathematical Thinkers from Birth: The Why, What, and How

ERIC Educational Resources Information Center

Chen, Jie-Qi; Hynes-Berry, Mary; Abel, Barbara; Sims, Colleen; Ginet, Lisa

2017-01-01

In this article, the authors examine the mathematical thinking and experiences that are unique to infants, toddlers, and 2-year-olds. They identify the four precursor mathematical concepts of attribute, comparison, pattern, and change and explore them in terms of why it is so important to attend to them, what makes them inherently mathematical and…

Textbook and Course Materials for 21-127 "Concepts of Mathematics"

ERIC Educational Resources Information Center

Sullivan, Brendan W.

2013-01-01

Concepts of Mathematics (21-127 at CMU) is a course designed to introduce students to the world of abstract mathematics, guiding them from more calculation-based math (that one learns in high school) to higher mathematics, which focuses more on abstract thinking, problem solving, and writing "proofs." This transition tends to be a shock:…

The Effects of an Educational Video Game on Mathematical Engagement

ERIC Educational Resources Information Center

Chang, Mido; Evans, Michael A.; Kim, Sunha; Norton, Anderson; Deater-Deckard, Kirby; Samur, Yavuz

2016-01-01

In an effort to maximizing success in mathematics, our research team implemented an educational video game in fifth grade mathematics classrooms in five schools in the Eastern US. The educational game was developed by our multi-disciplinary research team to achieve a hypothetical learning trajectory of mathematical thinking of 5th grade students.…

Learning to Think Spatially: What Do Students "See" in Numeracy Test Items?

ERIC Educational Resources Information Center

Diezmann, Carmel M.; Lowrie, Tom

2012-01-01

Learning to think spatially in mathematics involves developing proficiency with graphics. This paper reports on 2 investigations of spatial thinking and graphics. The first investigation explored the importance of graphics as 1 of 3 communication systems (i.e. text, symbols, graphics) used to provide information in numeracy test items. The results…

The analysis of student’s critical thinking ability on discovery learning by using hand on activity based on the curiosity

NASA Astrophysics Data System (ADS)

Sulistiani, E.; Waluya, S. B.; Masrukan

2018-03-01

This study aims to determine (1) the effectiveness of Discovery Learning model by using Hand on Activity toward critical thinking abilities, and (2) to describe students’ critical thinking abilities in Discovery Learning by Hand on Activity based on curiosity. This study is mixed method research with concurrent embedded design. Sample of this study are students of VII A and VII B of SMP Daarul Qur’an Ungaran. While the subject in this study is based on the curiosity of the students groups are classified Epistemic Curiosity (EC) and Perceptual Curiosity (PC). The results showed that the learning of Discovery Learning by using Hand on Activity is effective toward mathematics critical thinking abilities. Students of the EC type are able to complete six indicators of mathematics critical thinking abilities, although there are still two indicators that the result is less than the maximum. While students of PC type have not fully been able to complete the indicator of mathematics critical thinking abilities. They are only strong on indicators formulating questions, while on the other five indicators they are still weak. The critical thinking abilities of EC’s students is better than the critical thinking abilities of the PC’s students.

The analysis of probability task completion; Taxonomy of probabilistic thinking-based across gender in elementary school students

NASA Astrophysics Data System (ADS)

Sari, Dwi Ivayana; Budayasa, I. Ketut; Juniati, Dwi

2017-08-01

Formulation of mathematical learning goals now is not only oriented on cognitive product, but also leads to cognitive process, which is probabilistic thinking. Probabilistic thinking is needed by students to make a decision. Elementary school students are required to develop probabilistic thinking as foundation to learn probability at higher level. A framework of probabilistic thinking of students had been developed by using SOLO taxonomy, which consists of prestructural probabilistic thinking, unistructural probabilistic thinking, multistructural probabilistic thinking and relational probabilistic thinking. This study aimed to analyze of probability task completion based on taxonomy of probabilistic thinking. The subjects were two students of fifth grade; boy and girl. Subjects were selected by giving test of mathematical ability and then based on high math ability. Subjects were given probability tasks consisting of sample space, probability of an event and probability comparison. The data analysis consisted of categorization, reduction, interpretation and conclusion. Credibility of data used time triangulation. The results was level of boy's probabilistic thinking in completing probability tasks indicated multistructural probabilistic thinking, while level of girl's probabilistic thinking in completing probability tasks indicated unistructural probabilistic thinking. The results indicated that level of boy's probabilistic thinking was higher than level of girl's probabilistic thinking. The results could contribute to curriculum developer in developing probability learning goals for elementary school students. Indeed, teachers could teach probability with regarding gender difference.

Critical thinking level in geometry based on self-regulated learning

NASA Astrophysics Data System (ADS)

Bayuningsih, A. S.; Usodo, B.; Subanti, S.

2018-03-01

Critical thinking ability of mathematics students affected by the student’s ability in solving a specific problem. This research aims to determine the level of critical thinking (LCT) students in solving problems of geometry regarding self-regulated learning (SRL) students. This is a qualitative descriptive study with the purpose to analyze the level of Junior High School student’s critical thinking in the Regency of Banyumas. The subject is taken one student from each category SRL (high, medium and low). Data collection is given problem-solving tests to find out the level of critical thinking student, questionnaire, interview and documentation. The result of the research shows that student with SRL high is at the level of critical thinking 2, then a student with SRL medium is at the level of critical thinking 1 and student with SRL low is at the level of critical thinking 0. So students with SRL high, medium or low can solve math problems based on the critical thinking level of each student.

Characterizing and Facilitating Prospective Teachers' Engagement with Student Thinking about Fractions

ERIC Educational Resources Information Center

Baker, Katherine

2017-01-01

Reform-based mathematics instruction emphasizes that mathematics is learned through reasoning and sense-making rather than strict memorization and is taught through facilitation rather than telling (NCTM, 1989, 1991, 1995, 2000). Teachers' engagement with student thinking to inform instruction is central to such teaching. Engagement with student…

Using Prediction to Promote Mathematical Understanding and Reasoning

ERIC Educational Resources Information Center

Kasmer, Lisa; Kim, Ok-Kyeong

2011-01-01

Research has shown that prediction has the potential to promote the teaching and learning of mathematics because it can be used to enhance students' thinking and reasoning at all grade levels in various topics. This article addresses the effectiveness of using prediction on students' understanding and reasoning of mathematical concepts in a middle…

Prospective and current secondary mathematics teachers' criteria for evaluating mathematical cognitive technologies

NASA Astrophysics Data System (ADS)

Smith, Ryan C.; Shin, Dongjo; Kim, Somin

2017-07-01

As technology becomes more ubiquitous in the mathematics classroom, teachers are being asked to incorporate it into their lessons more than ever before. The amount of resources available online is staggering and teachers need to be able to analyse and identify resources that would be most appropriate and effective with their students. This study examines the criteria prospective and current secondary mathematics teachers use and value most when evaluating mathematical cognitive technologies (MCTs). Results indicate all groups of participants developed criteria focused on how well an MCT represents the mathematics, student interaction and engagement with the MCT, and whether the MCT was user-friendly. However, none of their criteria focused on how well an MCT would reflect students' solution strategies or illuminate their thinking. In addition, there were some differences between the criteria created by participants with and without teaching experience, specifically the types of supports available in an MCT. Implications for mathematics teacher educators are discussed.

Understanding Mathematics and Science Matters. Studies in Mathematical Thinking and Learning Series

ERIC Educational Resources Information Center

Romberg, Thomas A., Ed.; Carpenter, Thomas P., Ed.; Dremock, Fae, Ed.

2005-01-01

The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics…

Conceptualizing Mathematics as Discourse in Different Educational Settings

ERIC Educational Resources Information Center

Güçler, Beste; Wang, Sasha; Kim, Dong-Joong

2015-01-01

In this work, we focus on a relatively new theory in mathematics education research, which views thinking as communication and characterizes mathematics as a form of discourse. We discuss how this framework can be utilized in different educational settings by giving examples from our own research to highlight the insights it provides in the…

Thinking in Patterns to Solve Multiplication, Division, and Fraction Problems in Second Grade

ERIC Educational Resources Information Center

Stokes, Patricia D.

2016-01-01

Experts think in patterns and structures using the specific "language" of their domains. For mathematicians, these patterns and structures are represented by numbers, symbols and their relationships (Stokes, 2014a). To determine whether elementary students in the United States could learn to think in mathematical patterns to solve…

Geometry Report; Cambridge Conference on School Mathematics Feasibility Study No. 39.

ERIC Educational Resources Information Center

Stolzenberg, Gabriel

These materials were written with the aim of reflecting the thinking of the Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics. This report deals with some seventh grade mathematical concepts taught at Cambridge Friends' School. The discovery approach was utilized by the teacher in order to…

Inquiry-Based Learning and the Art of Mathematical Discourse

ERIC Educational Resources Information Center

von Renesse, Christine; Ecke, Volker

2015-01-01

Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate…

Technologies That Facilitate the Study of Advanced Mathematics by Students Who Are Blind: Teachers' Perspectives

ERIC Educational Resources Information Center

DePountis, Vicki M.; Pogrund, Rona L.; Griffin-Shirley, Nora; Lan, William Y.

2015-01-01

This research examined the perspectives of teachers of students with visual impairments (TVIs) regarding the use and effectiveness of electronic assistive technology (EAT) purported to assist students who are blind in advanced mathematics subjects. The data for this study were collected via an online survey distributed to a convenience sample of…

How Talented Rural Students Experience School Mathematics. Working Paper No. 29

ERIC Educational Resources Information Center

Howley, Aimee; Gholson, Melissa; Pendarvis, Edwina

2006-01-01

The purpose of this paper is to examine how mathematically talented children in a disadvantaged rural community experience mathematics, both as a discipline and as a school subject. The aim is to find answers to questions such as: "What do these children think mathematics is?" "What value do they attach to the study of…

Teaching Writing and Communication in a Mathematical Modeling Course

ERIC Educational Resources Information Center

Linhart, Jean Marie

2014-01-01

Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…

Career Advancement Outcomes in Academic Science, Technology, Engineering and Mathematics (STEM): Gender, Mentoring Resources, and Homophily

ERIC Educational Resources Information Center

Lee, Sang Eun

2017-01-01

This dissertation examines gender differences in career advancement outcomes among academic science, technology, engineering and mathematics (STEM) scientists. In particular, this research examines effects of gender, PhD advisors and postdoctoral supervisors mentoring resources and gender homophily in the mentoring dyads on the career advancement…

In-Situ Assays Using a New Advanced Mathematical Algorithm - 12400

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

Oginni, B.M.; Bronson, F.L.; Field, M.B.

2012-07-01

Current mathematical efficiency modeling software for in-situ counting, such as the commercially available In-Situ Object Calibration Software (ISOCS), typically allows the description of measurement geometries via a list of well-defined templates which describe regular objects, such as boxes, cylinder, or spheres. While for many situations, these regular objects are sufficient to describe the measurement conditions, there are occasions in which a more detailed model is desired. We have developed a new all-purpose geometry template that can extend the flexibility of current ISOCS templates. This new template still utilizes the same advanced mathematical algorithms as current templates, but allows the extensionmore » to a multitude of shapes and objects that can be placed at any location and even combined. In addition, detectors can be placed anywhere and aimed at any location within the measurement scene. Several applications of this algorithm to in-situ waste assay measurements, as well as, validations of this template using Monte Carlo calculations and experimental measurements are studied. Presented in this paper is a new template of the mathematical algorithms for evaluating efficiencies. This new template combines all the advantages of the ISOCS and it allows the use of very complex geometries, it also allows stacking of geometries on one another in the same measurement scene and it allows the detector to be placed anywhere in the measurement scene and pointing in any direction. We have shown that the template compares well with the previous ISOCS software within the limit of convergence of the code, and also compare well with the MCNPX and measured data within the joint uncertainties for the code and the data. The new template agrees with ISOCS to within 1.5% at all energies. It agrees with the MCNPX to within 10% at all energies and it agrees with most geometries within 5%. It finally agrees with measured data to within 10%. This mathematical algorithm can

Credit Card Mathematics

ERIC Educational Resources Information Center

Wood, Eric

2004-01-01

The history of mathematics is full of rich examples that can help students to see the place of the discipline within our cultural heritage. Valuable as this can be, it also has the unfortunate side-effect of making students think that all the math has already been done and they do not get a sense that the subject is dynamic and growing.…

Developing Mathematical Thinking and Self-Regulated Learning: A Teaching Experiment in a Seventh-Grade Mathematics Classroom

ERIC Educational Resources Information Center

Pape, S. J.; Bell, C. V.; Yetkin, IE.

2003-01-01

Mathematics educators have found sociocultural models of teaching and learning to be powerful in their ability to describe and support the pursuit of instruction based on recent standards documents (e.g., National Council of Teachers of Mathematics [NCTM], 1989, 2000). These models of instruction, however, have been criticized for their lack of…

A Mathematical Private Eye

ERIC Educational Resources Information Center

Lee, Ji-Eun; Kim, Kyoung-Tae

2007-01-01

This article proposes an instructional idea where students can figure out an individual's secret personal information using the power of mathematics, particularly the power of algebraic thinking. The proposed examples in this article start with a personalized context that other people do not know and end up with generalized patterns of solutions.…

Growth in Mathematical Understanding While Learning How To Teach: A Theoretical Perspective.

ERIC Educational Resources Information Center

Cavey, Laurie O.

This theoretical paper outlines a conceptual framework for examining growth in prospective teachers' mathematical understanding as they engage in thinking about and planning for the mathematical learning of others. The framework is based on the Pirie-Kieren (1994) Dynamical Theory for the Growth of Mathematical Understanding and extends into the…

Is There a Relationship between Creativity and Mathematical Creativity?

ERIC Educational Resources Information Center

Arikan, Elif Esra

2017-01-01

The aim of this study is to examine the mathematical creativity of individuals who think they have creative thinking skills. Forty-four teachers who work in private schools participated in this study and they have their pedagogical formation training from a public university in order to be a public teacher. Also participants have at least one year…

What Makes Critical Thinking Critical for Adult ESL Students

ERIC Educational Resources Information Center

Miekley, Joshua P.

2014-01-01

Critical-thinking skills help to prepare adult education students for a successful transition to college degree programs and for job advancement. Yet fostering critical thinking poses a challenge to ESL instructors. Brookfield (2012) provides a way forward for adult educators when he explains that the crux of critical thinking is to discover one's…

Computational Thinking in K-12: A Review of the State of the Field

ERIC Educational Resources Information Center

Grover, Shuchi; Pea, Roy

2013-01-01

Jeannette Wing's influential article on computational thinking 6 years ago argued for adding this new competency to every child's analytical ability as a vital ingredient of science, technology, engineering, and mathematics (STEM) learning. What is computational thinking? Why did this article resonate with so many and serve as a rallying cry for…

Analogy, higher order thinking, and education.

PubMed

Richland, Lindsey Engle; Simms, Nina

2015-01-01

Analogical reasoning, the ability to understand phenomena as systems of structured relationships that can be aligned, compared, and mapped together, plays a fundamental role in the technology rich, increasingly globalized educational climate of the 21st century. Flexible, conceptual thinking is prioritized in this view of education, and schools are emphasizing 'higher order thinking', rather than memorization of a cannon of key topics. The lack of a cognitively grounded definition for higher order thinking, however, has led to a field of research and practice with little coherence across domains or connection to the large body of cognitive science research on thinking. We review literature on analogy and disciplinary higher order thinking to propose that relational reasoning can be productively considered the cognitive underpinning of higher order thinking. We highlight the utility of this framework for developing insights into practice through a review of mathematics, science, and history educational contexts. In these disciplines, analogy is essential to developing expert-like disciplinary knowledge in which concepts are understood to be systems of relationships that can be connected and flexibly manipulated. At the same time, analogies in education require explicit support to ensure that learners notice the relevance of relational thinking, have adequate processing resources available to mentally hold and manipulate relations, and are able to recognize both the similarities and differences when drawing analogies between systems of relationships. © 2015 John Wiley & Sons, Ltd.

A Tree at Bedtime Investigation: Connecting Mathematics, Science, and Literature

ERIC Educational Resources Information Center

Kieff, Judith

2006-01-01

Activities that promote "active thinking" help children learn mathematics and science by allowing them to work at forming relationships, making connections, and integrating concepts and procedures. Dynamic and exciting children's books invite and motivate children to learn mathematics and science by responding to stories, characters, and their…

Everyday Pedagogical Practices in Mathematical Play Situations in German "Kindergarten"

ERIC Educational Resources Information Center

Brandt, Birgit

2013-01-01

This study describes situations in German daycare facilities (Kindergarten) in which the development of mathematical thinking in children is specifically encouraged through examination of common play objects. Using micro-sociological methods of analysis, the mathematical potential of such interactions between teacher and child is elaborated within…

A Dynamic Theory of Mathematical Understanding: Some Features and Implications.

ERIC Educational Resources Information Center

Pirie, Susan; Kieren, Thomas

Given the current and widespread practical interest in mathematical understanding, particularly with respect to higher order thinking skills, curriculum reform advocates in many countries cite the need for teaching mathematics with understanding. However, the characterization of understanding in ways that highlight its growth, as well as the…

Equations and Inequalities: Making Mathematics Accessible to All. PISA

ERIC Educational Resources Information Center

Piacentini, Mario; Monticone, Chiara

2016-01-01

More than ever, students need to engage with mathematics concepts, think quantitatively and analytically, and communicate using mathematics. All these skills are central to a young person's preparedness to tackle problems that arise at work and in life beyond the classroom. But the reality is that many students are not familiar with basic…

Dialogue on Early Childhood Science, Mathematics, and Technology Education.

ERIC Educational Resources Information Center

American Association for the Advancement of Science, Washington, DC.

Educators, scholars, and researchers in the United States convened at the Forum on Early Childhood Science, Mathematics, and Technology Education to discuss how, when, and even if science, mathematics, and technology should be taught to pre-kindergarten children. The product of that forum, this book summarizes some of the latest thinking about…

Integration of Technology, Curriculum, and Professional Development for Advancing Middle School Mathematics: Three Large-Scale Studies

ERIC Educational Resources Information Center

Roschelle, Jeremy; Shechtman, Nicole; Tatar, Deborah; Hegedus, Stephen; Hopkins, Bill; Empson, Susan; Knudsen, Jennifer; Gallagher, Lawrence P.

2010-01-01

The authors present three studies (two randomized controlled experiments and one embedded quasi-experiment) designed to evaluate the impact of replacement units targeting student learning of advanced middle school mathematics. The studies evaluated the SimCalc approach, which integrates an interactive representational technology, paper curriculum,…

The Psychophysics of Algebra Expertise: Mathematics Perceptual Learning Interventions Produce Durable Encoding Changes

ERIC Educational Resources Information Center

Bufford, Carolyn A.; Mettler, Everett; Geller, Emma H.; Kellman, Philip J.

2014-01-01

Mathematics requires thinking but also pattern recognition. Recent research indicates that perceptual learning (PL) interventions facilitate discovery of structure and recognition of patterns in mathematical domains, as assessed by tests of mathematical competence. Here we sought direct evidence that a brief perceptual learning module (PLM)…

Investigating students' perceptions of graduate learning outcomes in mathematics

NASA Astrophysics Data System (ADS)

King, Deborah; Varsavsky, Cristina; Belward, Shaun; Matthews, Kelly

2017-11-01

The purpose of this study is to explore the perceptions mathematics students have of the knowledge and skills they develop throughout their programme of study. It addresses current concerns about the employability of mathematics graduates by contributing much needed insight into how degree programmes are developing broader learning outcomes for students majoring in mathematics. Specifically, the study asked students who were close to completing a mathematics major (n = 144) to indicate the extent to which opportunities to develop mathematical knowledge along with more transferable skills (communication to experts and non-experts, writing, working in teams and thinking ethically) were included and assessed in their major. Their perceptions were compared to the importance they assign to each of these outcomes, their own assessment of improvement during the programme and their confidence in applying these outcomes. Overall, the findings reveal a pattern of high levels of students' agreement that these outcomes are important, but evidence a startling gap when compared to students' perceptions of the extent to which many of these - communication, writing, teamwork and ethical thinking - are actually included and assessed in the curriculum, and their confidence in using such learning.

Developing group investigation-based book on numerical analysis to increase critical thinking student’s ability

NASA Astrophysics Data System (ADS)

Maharani, S.; Suprapto, E.

2018-03-01

Critical thinking is very important in Mathematics; it can make student more understanding mathematics concept. Critical thinking is also needed in numerical analysis. The Numerical analysis's book is not yet including critical thinking in them. This research aims to develop group investigation-based book on numerical analysis to increase critical thinking student’s ability, to know the quality of the group investigation-based book on numerical analysis is valid, practical, and effective. The research method is Research and Development (R&D) with the subject are 30 student college department of Mathematics education at Universitas PGRI Madiun. The development model used is 4-D modified to 3-D until the stage development. The type of data used is descriptive qualitative data. Instruments used are sheets of validation, test, and questionnaire. Development results indicate that group investigation-based book on numerical analysis in the category of valid a value 84.25%. Students response to the books very positive, so group investigation-based book on numerical analysis category practical, i.e., 86.00%. The use of group investigation-based book on numerical analysis has been meeting the completeness criteria classical learning that is 84.32 %. Based on research result of this study concluded that group investigation-based book on numerical analysis is feasible because it meets the criteria valid, practical, and effective. So, the book can be used by every mathematics academician. The next research can be observed that book based group investigation in other subjects.

Think tank (3) - Present activities of other representative organizations

NASA Astrophysics Data System (ADS)

Obara, Michio

There were some think tank businesses in Japan before the war. South Manchuria Railway Company established its Research Department for the purpose of getting power to control Manchuria as a colony, and got the good results. Think tank business was flourishing three times after the war. This business attracts much attention when the social and economic paradigm is going to change. Among the key large-scale think tanks in Japan, Nomura Research Institute, Ltd. (NRI) was the first to enhance the system functions by the merger, and posted think tank function up in the SI business. Mitsubishi Research Institute, Inc. (MRI) intends to be an orthodox think tank, and established an advanced research institute and the laboratory for R&D. Daiwa Institute of Research, Ltd. (DIR) focuses on economic forecast by using system. Fuji Research Institute, Corp. (FUJI RIC) focuses on survey and policy proposing in macro-economics, and analyzing technology. The Japan Research Institute, Ltd. (JRI) focuses on regional development, and R&D in advanced technology.

Tracing the Construction of Mathematical Activity with an Advanced Graphing Calculator to Understand the Roles of Technology Developers, Teachers and Students

ERIC Educational Resources Information Center

Hillman, Thomas

2014-01-01

This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…

Creative Construction of Mathematics and Science Concepts in Early Childhood.

ERIC Educational Resources Information Center

Gallenstein, Nancy L.

Noting that effective teaching models that emphasize critical thinking in mathematics and science are used less often in early childhood classrooms than in those for older students, this book provides early childhood educators with an explanation of teaching models that promote 3- to 8-year-olds critical thinking, problem solving, decision making,…

On three forms of thinking: magical thinking, dream thinking, and transformative thinking.

PubMed

Ogden, Thomas H

2010-04-01

The author believes that contemporary psychoanalysis has shifted its emphasis from the understanding of the symbolic meaning of dreams, play, and associations to the exploration of the processes of thinking, dreaming, and playing. In this paper, he discusses his understanding of three forms of thinking-magical thinking, dream thinking, and transformative thinking-and provides clinical illustrations in which each of these forms of thinking figures prominently. The author views magical thinking as a form of thinking that subverts genuine thinking and psychological growth by substituting invented psychic reality for disturbing external reality. By contrast, dream thinking--our most profound form of thinking-involves viewing an emotional experience from multiple perspectives simultaneously: for example, the perspectives of primary process and secondary process thinking. In transformative thinking, one creates a new way of ordering experience that allows one to generate types of feeling, forms of object relatedness, and qualities of aliveness that had previously been unimaginable.

A Mathematics Software Database Update.

ERIC Educational Resources Information Center

Cunningham, R. S.; Smith, David A.

1987-01-01

Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)

Challenging a Teacher's Perceptions of Mathematical Smartness through Reflections on Students' Thinking

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2015-01-01

Creating equitable opportunities so all students can learn and succeed mathematically has been a key focus of mathematics education across several decades. Central to student achievement are students' mathematical identity and their feelings of success during instruction. Researchers (e.g., Boaler & Staples, 2008) have shown that teachers can…

Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom

NASA Astrophysics Data System (ADS)

Hitt, Fernando

2011-09-01

Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (i.e. cell phone). What about teachers' opinions? Mathematics teachers can be divided into three categories: those with a boundless overflow (enthusiasm) who want to use the technology without worrying much about the construction of mathematical concepts, those who reject outright the use of technology because they think that their use inhibits the development of mathematical skills and others that reflect on the balance that must exist between paper-pencil activities and use of technology. The mathematics teacher, by not having clear examples that support this last option about the balance of paper-pencil activities and technology, opt for one of the extreme positions outlined above. In this article, we show the results of research on a methodology based on collaborative learning (ACODESA) in the training of mathematics teachers in secondary schools and implementation of activities in an environment of paper-pencil and CAS in the mathematics classroom. We also note that with the development of technology on the use of electronic tablets and interactive whiteboards, these activities will take on greater momentum in the near future.

Building a Case for Blocks as Kindergarten Mathematics Learning Tools

ERIC Educational Resources Information Center

Kinzer, Cathy; Gerhardt, Kacie; Coca, Nicole

2016-01-01

Kindergarteners need access to blocks as thinking tools to develop, model, test, and articulate their mathematical ideas. In the current educational landscape, resources such as blocks are being pushed to the side and being replaced by procedural worksheets and academic "seat time" in order to address standards. Mathematics research…

La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

ERIC Educational Resources Information Center

Cable, John

2014-01-01

This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which…

Learning to Think Spatially in an Undergraduate Interdisciplinary Computational Design Context: A Case Study

ERIC Educational Resources Information Center

Ben Youssef, Belgacem; Berry, Barbara

2012-01-01

Spatial thinking skills are vital for success in everyday living and work, not to mention the centrality of spatial reasoning in scientific discoveries, design-based disciplines, medicine, geosciences and mathematics to name a few. This case study describes a course in spatial thinking and communicating designed and delivered by an…

Developing Mathematical Habits of Mind

ERIC Educational Resources Information Center

Mark, June; Cuoco, Al; Goldenberg, E. Paul; Sword, Sarah

2010-01-01

"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…

Towards a Dialogical Pedagogy: Some Characteristics of a Community of Mathematical Inquiry

ERIC Educational Resources Information Center

Kennedy, Nadia Stoyanova

2009-01-01

This paper discusses a teaching model called community of mathematical inquiry (CMI), characterized by dialogical and inquiry-driven communication and a dynamic structure of intertwined cognitive processes including distributed thinking, mathematical argumentation, integrated reasoning, conceptual transformation, internalization of critical…

Examining Mathematics Classroom Interactions: Elevating Student Roles in Teaching and Learning

ERIC Educational Resources Information Center

Kent, Laura

2017-01-01

This article introduces a model entitled, "Responsive Teaching through Problem Posing" or RTPP, that addresses a type of reform oriented mathematics teaching based on posing relevant problems, positioning students as experts of mathematics, and facilitating discourse. RTPP incorporates decades of research on students' thinking in…

Predicting change in epistemological beliefs, reflective thinking and learning styles: a longitudinal study.

PubMed

Phan, Huy P

2008-03-01

Although extensive research has examined epistemological beliefs, reflective thinking and learning approaches, very few studies have looked at these three theoretical frameworks in their totality. This research tested two separate structural models of epistemological beliefs, learning approaches, reflective thinking and academic performance among tertiary students over a period of 12 months. Participants were first-year Arts (N=616; 271 females, 345 males) and second-year Mathematics (N=581; 241 females, 341 males) university students. Students' epistemological beliefs were measured with the Schommer epistemological questionnaire (EQ, Schommer, 1990). Reflective thinking was measured with the reflective thinking questionnaire (RTQ, Kember et al., 2000). Student learning approaches were measured with the revised study process questionnaire (R-SPQ-2F, Biggs, Kember, & Leung, 2001). LISREL 8 was used to test two structural equation models - the cross-lag model and the causal-mediating model. In the cross-lag model involving Arts students, structural equation modelling showed that epistemological beliefs influenced student learning approaches rather than the contrary. In the causal-mediating model involving Mathematics students, the results indicate that both epistemological beliefs and learning approaches predicted reflective thinking and academic performance. Furthermore, learning approaches mediated the effect of epistemological beliefs on reflective thinking and academic performance. Results of this study are significant as they integrated the three theoretical frameworks within the one study.

Group Theory, Computational Thinking, and Young Mathematicians

ERIC Educational Resources Information Center

Gadanidis, George; Clements, Erin; Yiu, Chris

2018-01-01

In this article, we investigate the artistic puzzle of designing mathematics experiences (MEs) to engage young children with ideas of group theory, using a combination of hands-on and computational thinking (CT) tools. We elaborate on: (1) group theory and why we chose it as a context for young mathematicians' experiences with symmetry and…

The I Hate Mathematics! Book. A Brown Paper School Book.

ERIC Educational Resources Information Center

Burns, Marilyn

This 1975 book is written for children who do not like mathematics and presents activities which may help them to begin understanding mathematics. Activities are organized under the following headings: "Street Math"; "Maybe Grownups Aren't as Smart as You Think"; "Things to Do When You Have the Flu"; "A…

Beyond the Given: Stretching Mathematical Thinking through Journaling

ERIC Educational Resources Information Center

Hamdan, May

2017-01-01

This paper reflects on a teaching experiment and presents details of a pedagogical technique where students periodically write down their clearest interpretation of the conditions imposed on various discrete mathematical subjects they are learning in class. Through iterations, students generate a more complete understanding of the material, one…

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the fourth of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This text begins with a brief discussion of quadratic equations which motivates the…

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the fourth of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered…

Enhancing Thinking Skills in the Sciences and Mathematics.

ERIC Educational Resources Information Center

Halpern, Diane F., Ed.

The need to provide an improved science and mathematics curriculum is imperative. Over recent years cognitive psychologists and educators have responded to this need by designing instructional programs that are more compatible with our knowledge of how people acquire, use, and retain knowledge. This book contains many of the guiding principles…

Encouraging Young Women to Stay in the Mathematics Pipeline: Mathematics Camps for Young Women

ERIC Educational Resources Information Center

Chacon, Paul; Soto-Johnson, Hortensia

2003-01-01

For two summers, week-long residential mathematics programs were held for high school women, with the primary goal of encouraging them to continue their study of mathematics. The activities were designed to rekindle their excitement about mathematics and to support the idea that women should learn advanced mathematics. This paper reports the…

TIMSS Advanced 2008 Assessment Frameworks

ERIC Educational Resources Information Center

Garden, Robert A.; Lie, Svein; Robitaille, David F.; Angell, Carl; Martin, Michael O.; Mullis, Ina V.S.; Foy, Pierre; Arora, Alka

2006-01-01

Developing the Trends in International Mathematics and Science Study (TIMSS) Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008--one for advanced mathematics and one for physics. It also contains…

Analysis of Secondary School Students’ Algebraic Thinking and Math-Talk Learning Community to Help Students Learn

NASA Astrophysics Data System (ADS)

Nurhayati, D. M.; Herman, T.; Suhendra, S.

2017-09-01

This study aims to determine the difficulties of algebraic thinking ability of students in one of secondary school on quadrilateral subject and to describe Math-Talk Learning Community as the alternative way that can be done to overcome the difficulties of the students’ algebraic thinking ability. Research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and twenty three students as the sample that was chosen by purposive sampling technique. Data of algebraic thinking were collected through essay test. The results showed the percentage of achievement of students’ algebraic thinking’s indicators on three aspects: a) algebra as generalized arithmetic with the indicators (conceptually based computational strategies and estimation); b) algebra as the language of mathematics (meaning of variables, variable expressions and meaning of solution); c) algebra as a tool for functions and mathematical modelling (representing mathematical ideas using equations, tables, or words and generalizing patterns and rules in real-world contexts) is still low. It is predicted that because the secondary school students was not familiar with the abstract problem and they are still at a semi-concrete stage where the stage of cognitive development is between concrete and abstract. Based on the percentage achievement of each indicators, it can be concluded that the level of achievement of student’s mathematical communication using conventional learning is still low, so students’ algebraic thinking ability need to be improved.

MONTO: A Machine-Readable Ontology for Teaching Word Problems in Mathematics

ERIC Educational Resources Information Center

Lalingkar, Aparna; Ramnathan, Chandrashekar; Ramani, Srinivasan

2015-01-01

The Indian National Curriculum Framework has as one of its objectives the development of mathematical thinking and problem solving ability. However, recent studies conducted in Indian metros have expressed concern about students' mathematics learning. Except in some private coaching academies, regular classroom teaching does not include problem…

Connecting Social and Mathematical Thinking: The Use of "Real Life" Contexts

ERIC Educational Resources Information Center

Sawatzki, Carly

2014-01-01

This paper reports the findings of research into an educational intervention featuring open-ended mathematical problems situated in "real life" contexts and associated pedagogies. "Money and financial mathematics" is the topic in focus, with tasks termed "financial dilemmas" being trialled by 35 teachers in 16…

[Probability, Cambridge Conference on School Mathematics Feasibility Study No. 7.

ERIC Educational Resources Information Center

Davis, R.

These materials were written with the aim of reflecting the thinking of the Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics. They represent a practical response to a proposal by CCSM that some elements of probability be introduced in the elementary grades. These materials provide children…

The Progressive Development of Early Embodied Algebraic Thinking

NASA Astrophysics Data System (ADS)

Radford, Luis

2014-06-01

In this article I present some results from a 5-year longitudinal investigation with young students about the genesis of embodied, non-symbolic algebraic thinking and its progressive transition to culturally evolved forms of symbolic thinking. The investigation draws on a cultural-historical theory of teaching and learning—the theory of objectification. Within this theory, thinking is conceived of as a form of reflection and action that is simultaneously material and ideal: It includes inner and outer speech, sensuous forms of imagination and visualisation, gestures, rhythm, and their intertwinement with material culture (symbols, artifacts, etc.). The theory articulates a cultural view of development as an unfolding dialectic process between culturally and historically constituted forms of mathematical knowing and semiotically mediated classroom activity. Looking at the experimental data through these theoretical lenses reveals a developmental path where embodied forms of thinking are sublated or subsumed into more sophisticated ones through the mediation of properly designed classroom activity.

Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction. Studies in Mathematical Thinking and Learning Series

ERIC Educational Resources Information Center

Remillard, Janine T., Ed.; Herbel-Eisenmann, Beth A., Ed.; Lloyd, Gwendolyn M., Ed.

2011-01-01

This book compiles and synthesizes existing research on teachers' use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on--but not restricted to--those materials developed in the 1990s in response to the NCTM's Principles and Standards for School Mathematics. Despite…

Advanced High School Biology in an Era of Rapid Change: A Summary of the Biology Panel Report from the NRC Committee on Programs for Advanced Study of Mathematics and Science in American High Schools

ERIC Educational Resources Information Center

Wood, William B.

2002-01-01

A recently released National Research Council (NRC) report, "Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools", evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study,…

Elementary Teachers' Thinking about a Good Mathematics Lesson

ERIC Educational Resources Information Center

Li, Yeping

2011-01-01

In an effort to gain a better understanding of Chinese classroom teaching culture, this study aimed to examine elementary teachers' views about a good mathematics lesson in China. Through analyzing 57 teachers' essays collected from 7 elementary schools in 2 provinces, it is found that Chinese teachers emphasized the most about students and their…

Interfacing theories of program with theories of evaluation for advancing evaluation practice: Reductionism, systems thinking, and pragmatic synthesis.

PubMed

Chen, Huey T

2016-12-01

Theories of program and theories of evaluation form the foundation of program evaluation theories. Theories of program reflect assumptions on how to conceptualize an intervention program for evaluation purposes, while theories of evaluation reflect assumptions on how to design useful evaluation. These two types of theories are related, but often discussed separately. This paper attempts to use three theoretical perspectives (reductionism, systems thinking, and pragmatic synthesis) to interface them and discuss the implications for evaluation practice. Reductionism proposes that an intervention program can be broken into crucial components for rigorous analyses; systems thinking view an intervention program as dynamic and complex, requiring a holistic examination. In spite of their contributions, reductionism and systems thinking represent the extreme ends of a theoretical spectrum; many real-world programs, however, may fall in the middle. Pragmatic synthesis is being developed to serve these moderate- complexity programs. These three theoretical perspectives have their own strengths and challenges. Knowledge on these three perspectives and their evaluation implications can provide a better guide for designing fruitful evaluations, improving the quality of evaluation practice, informing potential areas for developing cutting-edge evaluation approaches, and contributing to advancing program evaluation toward a mature applied science. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

Student Strategies Suggesting Emergence of Mental Structures Supporting Logical and Abstract Thinking: Multiplicative Reasoning

ERIC Educational Resources Information Center

Carrier, Jim

2014-01-01

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

The Nature of Scaffolding in Undergraduate Students' Transition to Mathematical Proof

ERIC Educational Resources Information Center

Blanton, Maria L.; Stylianou, Despina A.; David, Maria Manuela

2003-01-01

This paper explores the role of instructional scaffolding in the development of undergraduate students' understanding of mathematical proof during a one-year discrete mathematics course. We describe here the framework adapted for the analysis of whole-class discussion and examine how the teacher scaffolded students' thinking. Results suggest that…

Practise What You Preach: The Interactive Whiteboard in Preschool Mathematics Education

ERIC Educational Resources Information Center

Bourbour, Maryam; Masoumi, Davoud

2017-01-01

The Interactive Whiteboard (IWB) is now a common technological artefact in Swedish preschools and schools. This study examines preschool teachers' thinking behind the embedding of IWB in the early years' mathematics classroom and how preschool teachers structure their mathematical activities when using IWB. Two complementary empirical studies,…

Governing Equality: Mathematics for All?

ERIC Educational Resources Information Center

Diaz, Jennifer D.

2013-01-01

With the notion of governmentality, this article considers how the equal sign (=) in the U.S. math curriculum organizes knowledge of equality and inscribes cultural rules for thinking, acting, and seeing in the world. Situating the discussion within contemporary math reforms aimed at teaching mathematics for all, I draw attention to how the…

Everyday Maths through Everyday Provision: Developing Opportunities for Mathematics in the Early Years

ERIC Educational Resources Information Center

Bennett, Elaine; Weidner, Jenny

2011-01-01

Children are born naturally mathematical, so why is it sometimes so difficult to observe children being mathematical? Why do so many of us think we are "bad" at maths and how does this subconsciously affect the provision, experiences and opportunities we provide for young children who are starting their mathematical learning journey? This easily…

An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service

PubMed Central

Al-hetar, Abdulaziz M.

2016-01-01

Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum. PMID:27855216

An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service.

PubMed

Shamsan, Zaid Ahmed; Al-Hetar, Abdulaziz M

2016-01-01

Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum.

Does an Ability to Pattern Indicate That Our Thinking Is Mathematical?

ERIC Educational Resources Information Center

McCluskey, Catherine; Mitchelmore, Michael; Mulligan, Joanne

2013-01-01

Research affirms that pattern and structure underlie the development of a broad range of mathematical concepts. However, the concept of pattern also occurs in other fields. This theoretical paper explores pattern recognition, a neurological construct based on the world of Goldberg (2005), and pattern as defined in the field of mathematics to…

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…

Influence of Demographic Factors on Students' Beliefs in Learning Mathematics

ERIC Educational Resources Information Center

Tahir, Izah Mohd; Bakar, Nor Mazlina Abu

2009-01-01

Learning mathematics has been recognized by many as important. It does not only develop students' ability to think in quantitative terms but can also enhance skills such as analytical and problem solving skills. However, to enable us to tell our students how important mathematics is we have to understand students' beliefs in learning mathematics…

Focus group discussion in mathematical physics learning

NASA Astrophysics Data System (ADS)

Ellianawati; Rudiana, D.; Sabandar, J.; Subali, B.

2018-03-01

The Focus Group Discussion (FGD) activity in Mathematical Physics learning has helped students perform the stages of problem solving reflectively. The FGD implementation was conducted to explore the problems and find the right strategy to improve the students' ability to solve the problem accurately which is one of reflective thinking component that has been difficult to improve. The research method used is descriptive qualitative by using single subject response in Physics student. During the FGD process, one student was observed of her reflective thinking development in solving the physics problem. The strategy chosen in the discussion activity was the Cognitive Apprenticeship-Instruction (CA-I) syntax. Based on the results of this study, it is obtained the information that after going through a series of stages of discussion, the students' reflective thinking skills is increased significantly. The scaffolding stage in the CA-I model plays an important role in the process of solving physics problems accurately. Students are able to recognize and formulate problems by describing problem sketches, identifying the variables involved, applying mathematical equations that accord to physics concepts, executing accurately, and applying evaluation by explaining the solution to various contexts.

Mathematics for Young Learners: 60 Games & Activities for Ages 3 through 7.

ERIC Educational Resources Information Center

Ellerby, Richard S.

By studying and practicing metacognition, teachers and parents are instilling positive attitudes toward learning by teaching how-to-learn skills that prepare children for assessing their own thinking about learning as they become more and more developmentally prepared. This book stresses the strategies for thinking in mathematical terms without…

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…

Mathematical Making in Teacher Preparation: What Knowledge Is Brought to Bear?

ERIC Educational Resources Information Center

Greenstein, Steven; Seventko, Justin

2017-01-01

In this paper, we describe an experience within mathematics teacher preparation that engages preservice teachers (PSTs) in Making and design practices that we hypothesized would inform their conceptual and pedagogical thinking. With a focus on the design of new tools to support mathematics teaching and learning, this Learning by Design experience…

Decentering: A Construct to Analyze and Explain Teacher Actions as They Relate to Student Thinking

ERIC Educational Resources Information Center

Teuscher, Dawn; Moore, Kevin C.; Carlson, Marilyn P.

2016-01-01

Mathematics educators and writers of mathematics education policy documents continue to emphasize the importance of teachers focusing on and using student thinking to inform their instructional decisions and interactions with students. In this paper, we characterize the interactions between a teacher and student(s) that exhibit this focus.…

A Descriptive Study Examining the Impact of Digital Writing Environments on Communication and Mathematical Reasoning for Students with Learning Disabilities

ERIC Educational Resources Information Center

Huscroft-D'Angelo, Jacqueline; Higgins, Kristina N.; Crawford, Lindy L.

2014-01-01

Proficiency in mathematics, including mathematical reasoning skills, requires students to communicate their mathematical thinking. Mathematical reasoning involves making sense of mathematical concepts in a logical way to form conclusions or judgments, and is often underdeveloped in students with learning disabilities. Technology-based environments…

Effects of a Mathematics Cognitive Acceleration Program on Student Achievement and Motivation

ERIC Educational Resources Information Center

Finau, Teukava; Treagust, David F.; Won, Mihye; Chandrasegaran, A. L.

2018-01-01

This paper presents the effects of a cognitive acceleration program in mathematics classes on Tongan students' achievements, motivation and self-regulation. Cognitive Acceleration in Mathematics Education (CAME) is a program developed at King's College and implemented worldwide with the aim of improving students' thinking skills, mathematics…

Mexican high school students' social representations of mathematics, its teaching and learning

NASA Astrophysics Data System (ADS)

Martínez-Sierra, Gustavo; Miranda-Tirado, Marisa

2015-07-01

This paper reports a qualitative research that identifies Mexican high school students' social representations of mathematics. For this purpose, the social representations of 'mathematics', 'learning mathematics' and 'teaching mathematics' were identified in a group of 50 students. Focus group interviews were carried out in order to obtain the data. The constant comparative style was the strategy used for the data analysis because it allowed the categories to emerge from the data. The students' social representations are: (A) Mathematics is…(1) important for daily life, (2) important for careers and for life, (3) important because it is in everything that surrounds us, (4) a way to solve problems of daily life, (5) calculations and operations with numbers, (6) complex and difficult, (7) exact and (6) a subject that develops thinking skills; (B) To learn mathematics is…(1) to possess knowledge to solve problems, (2) to be able to solve everyday problems, (3) to be able to make calculations and operations, and (4) to think logically to be able to solve problems; and (C) To teach mathematics is…(1) to transmit knowledge, (2) to know to share it, (3) to transmit the reasoning ability, and (4) to show how to solve problems.

Integrating Computational Thinking into Technology and Engineering Education

ERIC Educational Resources Information Center

Hacker, Michael

2018-01-01

Computational Thinking (CT) is being promoted as "a fundamental skill used by everyone in the world by the middle of the 21st Century" (Wing, 2006). CT has been effectively integrated into history, ELA, mathematics, art, and science courses (Settle, et al., 2012). However, there has been no analogous effort to integrate CT into…

Pre-Service Teachers' Opinions on Teaching Thinking Skills

ERIC Educational Resources Information Center

Akinoglu, Orhan; Karsantik, Yasemin

2016-01-01

The purpose of the present study is to determine pre-service teachers' opinions on teaching thinking skills. 134 senior pre-service pre-school, English and mathematics teachers studying at a state university in Istanbul participated in the study which is designed based on survey model. A questionnaire which was developed by the researchers was…

The Factors Affecting Techno-Pedagogical Competencies and Critical Thinking Skills of Preservice Mathematics Teachers

ERIC Educational Resources Information Center

Yildiz, Avni

2017-01-01

Students' high-level thinking skills, like critical thinking, have been developed thanks to the use of technology. When the previous researches in the literature are analyzed, it will be understood that this research is original by providing significant contributions to the literature. This research aims to investigate whether techno-pedagogical…

Designing Spaces for Creativity and Divergent Thinking: Pre-Service Teachers Creating Stop Motion Animation on Tablets

ERIC Educational Resources Information Center

O'Byrne, W. Ian; Radakovic, Nenad; Hunter-Doniger, Tracey; Fox, Madison; Kern, Reggie; Parnell, Stephanie

2018-01-01

In recent years, tablets have been shown to serve as incredible teaching tools in classrooms around the world. In mathematics education, divergent thinking, creativity, and play may play a key role in formation of adaptive thinking and math achievement. This qualitative, participatory action research investigated the use of an instructional model…

Driven by History: Mathematics Education Reform

ERIC Educational Resources Information Center

Permuth, Steve; Dalzell, Nicole

2013-01-01

The advancement of modern societies is fueled by mathematics, and mathematics education provides the foundation upon which future scientists and engineers will build. Society dictates how mathematics will be taught through the development and implementation of mathematics standards. When examining the progression of these standards, it is…

Strategic Alliance to Advanced Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level

ERIC Educational Resources Information Center

Scarborough, Jule Dee

2004-01-01

This document (book) reports on the Strategic Alliance to Advance Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level, funded by National Science Foundation. It was a collaborative partnership involving the Rockford Public Schools, Rock Valley College, and Northern Illinois…

Introducing Computational Thinking through Hands-on Projects Using R with Applications to Calculus, Probability and Data Analysis

ERIC Educational Resources Information Center

Benakli, Nadia; Kostadinov, Boyan; Satyanarayana, Ashwin; Singh, Satyanand

2017-01-01

The goal of this paper is to promote computational thinking among mathematics, engineering, science and technology students, through hands-on computer experiments. These activities have the potential to empower students to learn, create and invent with technology, and they engage computational thinking through simulations, visualizations and data…

Diversifying Our Perspectives on Mathematics about Space and Geometry: An Ecocultural Approach

ERIC Educational Resources Information Center

Owens, Kay

2014-01-01

School mathematics tends to have developed from the major cultures of Asia, the Mediterranean and Europe. However, indigenous cultures in particular may have distinctly different systematic ways of referring to space and thinking mathematically about spatial activity. Their approaches are based on the close link between the environment and…

Cognitive Activities in Solving Mathematical Tasks: The Role of a Cognitive Obstacle

ERIC Educational Resources Information Center

Antonijevic, Radovan

2016-01-01

In the process of learning mathematics, students practice various forms of thinking activities aimed to substantially contribute to the development of their different cognitive structures. In this paper, the subject matter is a "cognitive obstacle", a phenomenon that occurs in the procedures of solving mathematical tasks. Each task in…

Neurocognitive mechanisms of mathematical giftedness: A literature review.

PubMed

Zhang, Li; Gan, John Q; Wang, Haixian

2017-01-01

Mathematically gifted children/adolescents have demonstrated exceptional abilities and traits in logical reasoning, mental imagery, and creative thinking. In the field of cognitive neuroscience, the past studies on mathematically gifted brains have concentrated on investigating event-related brain activation regions, cerebral laterality of cognitive functions, functional specialization that is uniquely dedicated for specific cognitive purposes, and functional interactions among discrete brain regions. From structural and functional perspectives, these studies have witnessed both "general" and "unique" neural characteristics of mathematically gifted brains. In this article, the theoretical background, empirical studies, and neurocognitive mechanisms of mathematically gifted children/adolescents are reviewed. Based on the integration of the findings, some potential directions for the future research are identified and discussed.

Using Technology To Enhance Problem Solving and Critical Thinking Skills.

ERIC Educational Resources Information Center

Mingus, Tabitha; Grassl, Richard

1997-01-01

Secondary mathematics teachers participated in a problem-solving course in which technology became a means to develop as teachers and as problem solvers. Findings indicate a delineation between technical competence and metatechnology--thinking about how and when to apply technology to particular problems. (PVD)

Advanced Mathematics Communication beyond Modality of Sight

ERIC Educational Resources Information Center

Sedaghatjou, Mina

2018-01-01

This study illustrates how mathematical communication and learning are inherently multimodal and embodied; hence, sight-disabled students are also able to conceptualize visuospatial information and mathematical concepts through tactile and auditory activities. Adapting a perceptuomotor integration approach, the study shows that the lack of access…

Teaching Critical Thinking: Sense-Making, Explanations, Language, and Habits

ERIC Educational Resources Information Center

Maloney, David

2015-01-01

The conjunction of three events has encouraged me to devote significant time to thinking about the pedagogical framework in my introductory courses. The three events were: doing a workshop addressing the Advanced Placement restructuring of the Physics B course with a stronger focus on critical thinking, finding out that "The Physics…

Helping Students to Recognize and Evaluate an Assumption in Quantitative Reasoning: A Basic Critical-Thinking Activity with Marbles and Electronic Balance

ERIC Educational Resources Information Center

Slisko, Josip; Cruz, Adrian Corona

2013-01-01

There is a general agreement that critical thinking is an important element of 21st century skills. Although critical thinking is a very complex and controversial conception, many would accept that recognition and evaluation of assumptions is a basic critical-thinking process. When students use simple mathematical model to reason quantitatively…

The "Verbification" of Mathematics: Using the Grammatical Structures of Mi'kmaq to Support Student Learning

ERIC Educational Resources Information Center

Borden, Lisa Lunney

2011-01-01

As part of a larger project focused on transforming mathematics education for Aboriginal students in Atlantic Canada, this paper reports on the role of the Mi'kmaw language in mathematics teaching. Examining how mathematical concepts are described in Mi'kmaq gives insight into ways of thinking. Shifting classroom discussions to reflect Mi'kmaw…

Utilising a construct of teacher capacity to examine national curriculum reform in mathematics

NASA Astrophysics Data System (ADS)

Zhang, Qinqiong; Stephens, Max

2013-12-01

This study involving 120 Australian and Chinese teachers introduces a construct of teacher capacity to analyse how teachers help students connect arithmetic learning and emerging algebraic thinking. Four criteria formed the basis of our construct of teacher capacity: knowledge of mathematics, interpretation of the intentions of official curriculum documents, understanding of students' thinking, and design of teaching. While these key elements connect to what other researchers refer to as mathematical knowledge for teaching, several differences are made clear. Qualitative and quantitative analyses show that our construct was robust and effective in distinguishing between different levels of teacher capacity.

Using Task Like PISA's Problem to Support Students' Creativity in Mathematics

ERIC Educational Resources Information Center

Novita, Rita; Putra, Mulia

2016-01-01

Creativity is one of keys to success in the evolving global economy and also be a fundamental skill that is absolutely necessary in the 21st century. Also in mathematics, creativity or thinking creatively is important to be developed because creativity is an integral part of mathematics. However, limiting the use of creativity in the classroom…

Is There a Role for Executive Functions in the Development of Mathematics Ability?

ERIC Educational Resources Information Center

Blair, Clancy; Knipe, Hilary; Gamson, David

2008-01-01