Supporting Mathematical Thinking

ERIC Educational Resources Information Center

Houssart, Jenny; Roaf, Caroline; Watson, Anne

2005-01-01

This book looks at how practitioners have focused on the fully educational application of intellect to the problem of developing mathematical thinking among one's pupils. Each chapter demonstrates reflective minds at work, relying on close observation, willingness to understand the student's thinking processes and patient commitment to students…

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…

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…

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…

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…

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…

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…

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…

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.

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)

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…

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…

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…

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…

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,…

Technology to Develop Algebraic Reasoning

ERIC Educational Resources Information Center

Polly, Drew

2011-01-01

Students' use of technology allows them to generate and manipulate multiple representations of a concept, compute numbers with relative ease, and focus more on mathematical concepts and higher-order thinking skills. In elementary school mathematics classrooms, students develop higher-order thinking skills by completing complex tasks that require…

Representations in Problem Solving: A Case Study with Optimization Problems

ERIC Educational Resources Information Center

Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

2009-01-01

Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

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…

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…

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.

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.

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…

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…

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…

Investigation of the Effects of Mathematical Thinking States of Form Teachers on Their Mathematics Teaching Anxieties

ERIC Educational Resources Information Center

Yorulmaz, Alper; Altintas, Sedat; Sidekli, Sabri

2017-01-01

The state of mathematical thinking is considered to have an effect on the formation of anxiety regarding teaching mathematics. It is hypothesized that with the formation of mathematical thinking, the anxiety in teachers regarding teaching mathematics will be reduced. Since mathematical thinking is a skill acquired starting from the early years of…

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…

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.

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.

Hoop Hoop Hooray!

ERIC Educational Resources Information Center

Tomsett, Ruth

2008-01-01

The author believes that Venn diagrams are a useful, yet hugely underused resource, to encourage purposeful talk, reasoning and logical thinking both within mathematics and across the curriculum. Here, she describes ways in which Venn diagrams can be used to add challenge and develop reasoning, discussion and mathematical thinking at Key Stage 2.…

The Value of Why for Student and Teacher Learning

ERIC Educational Resources Information Center

Guarino, Jody; Sykes, Marie; Santagata, Rossella

2013-01-01

The authors believe teaching for understanding begins with the development of a few essential orientations. Teachers must have an appreciation for student centered mathematics teaching, valuing an approach that builds on student thinking. In addition, teachers must appreciate the complexity of students' mathematical thinking and ideas. Once these…

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…

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.

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…

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…

Connecting Research to Teaching: The "MOST" Productive Student Mathematical Thinking

ERIC Educational Resources Information Center

Stockero, Shari L.; Peterson, Blake E.; Leatham, Keith R.; Van Zoest, Laura R.

2014-01-01

Instruction that meaningfully incorporates students' mathematical thinking is widely valued within the mathematics education community (NCTM 2000; Sherin, Louis, and Mendez 2000; Stein et al. 2008). Although being responsive to student thinking is important, not all student thinking has the same potential to support mathematical learning.…

Mathematical thinking styles of undergraduate students and their achievement in mathematics

NASA Astrophysics Data System (ADS)

Risnanosanti

2017-08-01

The main purpose of this study is to analyze the role of mathematical thinking styles in students' achievement in mathematics. On the basis of this study, it is also to generate recommendation for classroom instruction. The two specific aims are; first to observe students' mathematical thinking styles during problem solving, the second to asses students' achievement in mathematics. The data were collected by using Mathematical Thinking Styles questionnaires and test of students' achievement in mathematics. The subject in this study was 35 students from third year at mathematics study program of Muhammadiyah University of Bengkulu in academic year 2016/2017. The result of this study was that the students have three mathematical thinking styles (analytic, visual, and integrated), and the students who have analytic styles have better achievement than those who have visual styles in mathematics.

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…

A Different Perspective of the Teaching Philosophy of RL Moore

ERIC Educational Resources Information Center

Jones, Stephen L.

2017-01-01

Dr RL Moore was undoubtedly one of the finest mathematics teachers ever. He developed a unique teaching method designed to teach his students to think like mathematicians. His method was not designed to convey any particular mathematical knowledge. Instead, it was designed to teach his students to think. Today, his method has been modified to…

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…

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…

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…

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)…

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…

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.

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.

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…

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.

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.

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.

Construction of the mathematical concept of pseudo thinking students

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

This article examines the role of working memory, attention shifting, and inhibitory control executive cognitive functions in the development of mathematics knowledge and ability in children. It suggests that an examination of the executive cognitive demand of mathematical thinking can complement procedural and conceptual knowledge-based…

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.

Defining Computational Thinking for Mathematics and Science Classrooms

NASA Astrophysics Data System (ADS)

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

2016-02-01

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 urgency has come to the challenge of defining computational thinking and providing a theoretical grounding for what form it should take in school science and mathematics classrooms. This paper presents a response to this challenge by proposing a definition of computational thinking for mathematics and science in the form of a taxonomy consisting of four main categories: data practices, modeling and simulation practices, computational problem solving practices, and systems thinking practices. In formulating this taxonomy, we draw on the existing computational thinking literature, interviews with mathematicians and scientists, and exemplary computational thinking instructional materials. This work was undertaken as part of a larger effort to infuse computational thinking into high school science and mathematics curricular materials. In this paper, we argue for the approach of embedding computational thinking in mathematics and science contexts, present the taxonomy, and discuss how we envision the taxonomy being used to bring current educational efforts in line with the increasingly computational nature of modern science and mathematics.

The co-development and interrelation of proof and authority: The case of Yana and Ronit

NASA Astrophysics Data System (ADS)

Fried, Michael N.; Amit, Miriam

2008-12-01

Students' mathematical lives are characterized not only by a set of mathematical ideas and the engagement in mathematical thinking, but also by social relations, specifically, relations of authority. Watching student actions and speaking to students, one becomes cognizant of a `web of authority' ever present in mathematics classrooms. In past work, it has been shown how those relations of authority may sometimes interfere with students' reflecting on mathematical ideas. However, "…by shifting the emphasis from domination and obedience to negotiation and consent…" (Amit & Fried, 2005, p.164) it has also been stressed that these relations are fluid and are, in fact, a sine qua non in the process of students' defining their place in a mathematical community. But can these fluid relations be operative also in the formation of specific mathematical ideas? It is my contention that they may at least coincide with students' thinking about one significant mathematical idea, namely, the idea of proof. In this talk, I shall discuss both the general question of authority in the mathematics classroom and its specific connection with students' thinking about proof in the context of work done in two 8th grade classrooms.

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.

The Impact of a Professional Development Program on Teachers' Mathematical Knowledge for Teaching, Instruction, and Student Achievement

ERIC Educational Resources Information Center

Jacob, Robin; Hill, Heather; Corey, Doug

2017-01-01

In this paper, we describe findings from a three-year evaluation of a well-developed mathematics professional development program that is commercially available on a wide scale. The professional development is designed to improve teachers' mathematical knowledge for teaching and to enable them to elicit more student thinking and reasoning during…

Corresponding Habits of Mind and Mathematical Ability

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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.

Extending Students' Mathematical Thinking during Whole-Group Discussions

ERIC Educational Resources Information Center

Cengiz, Nesrin; Kline, Kate; Grant, Theresa J.

2011-01-01

Studies show that extending students' mathematical thinking during whole-group discussions is a challenging undertaking. To better understand what extending student thinking looks like and how teachers' mathematical knowledge for teaching (MKT) supports teachers in their efforts to extend student thinking, the teaching of six experienced…

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.

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.

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:…

A Mathematical Analysis of Semantic Maps, with Theoretical and Applied Implications for Blended Learning Software

ERIC Educational Resources Information Center

Tang, Michael; David, Hyerle; Byrne, Roxanne; Tran, John

2012-01-01

This paper is a mathematical (Boolean) analysis a set of cognitive maps called Thinking Maps[R], based on Albert Upton's semantic principles developed in his seminal works, Design for Thinking (1961) and Creative Analysis (1961). Albert Upton can be seen as a brilliant thinker who was before his time or after his time depending on the future of…

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…

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…

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…

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…

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…

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…

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

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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.

Mathematics creative thinking levels based on interpersonal intelligence

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Kuncorowati, R. H.; Mardiyana; Saputro, D. R. S.

2017-12-01

Creative thinking ability was one of student’s ability to determine various alternative solutions toward mathematics problem. One of indicators related to creative thinking ability was interpersonal intelligence. Student’s interpersonal intelligence would influence to student’s creativity. This research aimed to analyze creative thinking ability level of junior high school students in Karanganyar using descriptive method. Data was collected by test, questionnaire, interview, and documentation. The result showed that students with high interpersonal intelligence achieved third and fourth level in creative thinking ability. Students with moderate interpersonal intelligence achieved second level in creative thinking ability and students with low interpersonal intelligence achieved first and zero level in creative thinking ability. Hence, students with high, moderate, and low interpersonal intelligence could solve mathematics problem based on their mathematics creative thinking ability.

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…

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…

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…

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…

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…

What Matters Most: A Comparison of Expert and Novice Teachers' Noticing of Mathematics Classroom Events

ERIC Educational Resources Information Center

Huang, Rongjin; Li, Yeping

2012-01-01

In this study, we examined 10 expert and 10 novice teachers' noticing of classroom events in China. It was found that both expert and novice teachers, who were selected from two cities in China, highly attended to developing students' mathematics knowledge coherently and developing students' mathematical thinking and ability; they also paid…

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

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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.

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…

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…

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…

Mathematics in Finance and Economics: Importance of Teaching Higher Order Mathematical Thinking Skills in Finance

ERIC Educational Resources Information Center

Tularam, Gurudeo Anand

2013-01-01

This paper addresses the importance of teaching mathematics in business and finance schools of tertiary institutions of Australia. The paper explores the nature of thinking and reasoning required for advancement financial or economic studies involves the use of higher order thinking and creativity skills (HOTS) for teaching in mathematics classes.…

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…

Investigating students' perceptions of graduate learning outcomes in mathematics

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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.

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…

Developing Assessment through Lesson Study

ERIC Educational Resources Information Center

Fischman, Davida; Wasserman, Kelli

2017-01-01

Lesson study cultivates teachers' capacity for formative assessment by placing student thinking front and center throughout. Lesson study is a form of professional development in which a team of teachers determines a mathematical focus, collaboratively studies student thinking about the topic, designs a lesson about this content, implements the…

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.

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…

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…

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…

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

ERIC Educational Resources Information Center

Olkun, Sinan; Altun, Arif; Deryakulu, Deniz

2009-01-01

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

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…

Helping Mathematics Teachers Develop Noticing Skills: Utilizing Smartphone Technology for One-on-One Teacher/Student Interviews

ERIC Educational Resources Information Center

Chao, Theodore; Murray, Eileen; Star, Jon R.

2016-01-01

Teaching mathematics for understanding requires listening to each student's mathematical thinking, best elicited in a one-on-one interview. Interviews are difficult to enact in a teacher's busy schedule, however. In this study, the authors utilize smartphone technology to help mathematics teachers interview a student in a virtual one-on-one…

The Co-Development and Interrelation of Proof and Authority: The Case of Yana and Ronit

ERIC Educational Resources Information Center

Fried, Michael N.; Amit, Miriam

2008-01-01

Students' mathematical lives are characterized not only by a set of mathematical ideas and the engagement in mathematical thinking, but also by social relations, specifically, relations of authority. Watching student actions and speaking to students, one becomes cognizant of a "web of authority" ever present in mathematics classrooms. In…

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.…

Using Students' Interests as Algebraic Models

ERIC Educational Resources Information Center

Whaley, Kenneth A.

2012-01-01

Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…

Systems Engineering of Education I: The Evolution of Systems Thinking in Education, 2nd Edition.

ERIC Educational Resources Information Center

Silvern, Leonard C.

This document methodically traces the development of the fundamental concepts of systems thinking in education from Harbert to contemporary innovators. The discussion explains narrative models, concentrating on educational flowcharting techniques and mathematical models related to developments in engineering and physical science. The presentation…

Mathematics Teachers' Views of Accountability Testing Revealed through Lesson Study

ERIC Educational Resources Information Center

Yarema, Connie H.

2010-01-01

The practice of lesson study, a professional development model originating in Japan, aligns well with recommendations from research for teacher professional development. Lesson study is also an inductive research method that uncovers student thinking and, in parallel, grants teacher-educators the opportunity to study teachers' thinking about…

Advanced Mathematical Thinking

ERIC Educational Resources Information Center

Dubinsky, Ed; McDonald, Michael A.; Edwards, Barbara S.

2005-01-01

In this article we propose the following definition for advanced mathematical thinking: Thinking that requires deductive and rigorous reasoning about mathematical notions that are not entirely accessible to us through our five senses. We argue that this definition is not necessarily tied to a particular kind of educational experience; nor is it…

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.

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…

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…

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…

Conditional Inference and Advanced Mathematical Study: Further Evidence

ERIC Educational Resources Information Center

Inglis, Matthew; Simpson, Adrian

2009-01-01

In this paper, we examine the support given for the "theory of formal discipline" by Inglis and Simpson (Educational Studies Mathematics 67:187-204, "2008"). This theory, which is widely accepted by mathematicians and curriculum bodies, suggests that the study of advanced mathematics develops general thinking skills and, in particular, conditional…

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…

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…

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 Cognitive Theory Driven New Orientation of Indonesian Lessons

ERIC Educational Resources Information Center

Nowinska, Edyta

2014-01-01

The main focus of this design research was on students' mathematical thinking and skills and on their understanding of mathematical concepts and methods. The mathematical content our project starts with is the introduction of integers. For this content new learning environments have been developed, implemented and evaluated. An important question…

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…

Mathematical Modeling and Computational Thinking

ERIC Educational Resources Information Center

Sanford, John F.; Naidu, Jaideep T.

2017-01-01

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

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.…

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…

Including Students' Diverse Perspectives on Classroom Interactions into Video-Based Professional Development for Teachers

ERIC Educational Resources Information Center

Vogler, Anna-Marietha; Prediger, Susanne

2017-01-01

Video is often used in professional development courses to sensitize mathematics teachers to students' thinking and issues of classroom interaction. This article presents an approach that incorporates students' perspectives on mathematics classroom interactions into video-based professional development in order to enhance teachers' reflection on…

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…

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…

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…

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…

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

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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 teachers decided to modify a task. Moreover, relationships between and among the various factors were identified. The emergent framework from this study offers insight into decompositions of the two teaching practices of interest, and, in particular, the utility of the number choices made by the teachers.

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…

Developing and Evaluating a Kindergarten to Third Grade CBM Mathematics Assessment

ERIC Educational Resources Information Center

Lee, Young-Sun; Lembke, Erica

2016-01-01

The present study examined the technical adequacy of curriculum-based measurement (CBM) measure of early numeracy for kindergarten through third grade students. Our CBM measures were developed to reflect broad and theoretically derived categories of mathematical thinking: quick retrieval, written computation, and number sense. The mastery of these…

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…

Developing the Practice of Teacher Questioning through a K-2 Elementary Mathematics Field Experience

ERIC Educational Resources Information Center

Schwartz, Catherine

2015-01-01

This article presents findings from research on a field experience designed to help elementary preservice teachers learn the practice of teacher questioning during formal and informal interviews to analyze student mathematical thinking in K-2 classrooms. The practice of teacher questioning is framed as choosing a mathematical goal, analyzing…

Testing the Immediate and Long-Term Efficacy of a Tier 2 Kindergarten Mathematics Intervention

ERIC Educational Resources Information Center

Clarke, Ben; Doabler, Christian T.; Smolkowski, Keith; Kurtz-Nelson, Evangeline; Fien, Hank; Baker, Scott K.; Kosty, Derek

2016-01-01

This study examined the efficacy of a kindergarten mathematics intervention program, ROOTS, focused on developing whole-number understanding in the areas of counting and cardinality and operations and algebraic thinking for students at risk in mathematics. The study utilized a randomized block design with students within classrooms randomly…

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…

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

ERIC Educational Resources Information Center

Nivera, Gladys C.

2017-01-01

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

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…

Canonical Images

ERIC Educational Resources Information Center

Hewitt, Dave

2007-01-01

In this article, the author offers two well-known mathematical images--that of a dot moving around a circle; and that of the tens chart--and considers their power for developing mathematical thinking. In his opinion, these images each contain the essence of a particular topic of mathematics. They are contrasting images in the sense that they deal…

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…

The Differences in Scores and Self-Efficacy by Student Gender in Mathematics and Science

ERIC Educational Resources Information Center

Louis, Rachel A.; Mistele, Jean M.

2012-01-01

Typically, mathematics and science are seen as linked together, where both subjects involve numbers, critical thinking, and problem solving. Our study aims to develop a better understanding of the connections between student's achievement scores in mathematics and science, student gender, and self-efficacy. We used the Trends in International…

Using Internet Aesthetic Mathematical Texts to Develop Secondary School Learners' Thinking Skills

ERIC Educational Resources Information Center

Nyaumwe, Lovemore J.

2011-01-01

This paper presents some internet aesthetic texts collected over a period of two years through chain message communications with colleagues located in different parts of the world. The aesthetic texts are grouped into four themes of mathematical magic, values, beauty, and prediction. Mathematical magic aesthetics show fascinating things that can…

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

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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.

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…

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…

The Use of Questions within In-the-Moment Coaching in Initial Mathematics Teacher Education: Enhancing Participation, Reflection, and Co-Construction in Rehearsals of Practice

ERIC Educational Resources Information Center

Averill, Robin; Drake, Michael; Anderson, Dayle; Anthony, Glenda

2016-01-01

Managing mathematical discussion is known to be challenging for novice teachers. Coaching within student teacher rehearsals of teaching has been shown to develop mathematics teaching practice, but can be time consuming. To examine how coaching using questions could assist novice teachers to promote mathematical thinking and discussions within…

Preserving Pelicans with Models That Make Sense

ERIC Educational Resources Information Center

Moore, Tamara J.; Doerr, Helen M.; Glancy, Aran W.; Ntow, Forster D.

2015-01-01

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

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…

Focusing of Students' Mathematical Thinking

ERIC Educational Resources Information Center

Breyfogle, M. Lynn; Herbel-Eisenmann, Beth A.

2004-01-01

Suggestions and ideas that enable teachers to take a closer look at students' thinking are discussed. A teacher should periodically reflect on his or her own classroom practices in order to increase attention on students' mathematical thinking.

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…

Information Technology and Mathematics: Opening New Representational Windows.

ERIC Educational Resources Information Center

Kaput, James J.

Higher order thinking skills are inevitably developed or exercised relative to some discipline. The discipline may be formal or informal, may or may not be represented in a school curriculum, or relate to a wide variety of domains. Moreover, the development or exercise of thinking skills may take place at differing levels of generality. This paper…

Modeling the Development Process of Dialogical Critical Thinking in Pupils Aged 10 to 12 Years

ERIC Educational Resources Information Center

Daniel, Marie-France; Lafortune, Louise; Pallascio, Richard; Splitter, Laurance; Slade, Christina; de la Garza, Teresa

2005-01-01

This research project investigated manifestations of critical thinking in pupils 10 to 12 years of age during their group discussions held in the context of Philosophy for Children Adapted to Mathematics. The objective of the research project was to examine, through the pupils' discussions, the development of dialogical critical thinking…

Naptime Data Meetings to Increase the Math Talk of Early Care and Education Providers

ERIC Educational Resources Information Center

Trawick-Smith, Jeffrey; Oski, Heather; DePaolis, Kim; Krause, Kristen; Zebrowski, Alyssa

2016-01-01

Classroom conversations about mathematics--math talk--between early care and education providers and young children have been associated with growth in mathematical thinking. However, professional development opportunities to learn about math teaching and learning are limited in many community-based child development centers. New approaches that…

Knowing and Teaching Middle School Mathematics: A Professional Development Course for In-Service Teachers

ERIC Educational Resources Information Center

Anderson, Celia Rousseau; Hoffmeister, April M.

2007-01-01

This article describes a professional development course intended to improve the content understanding of middle school mathematics teachers. The design of the course included three professional learning strategies: problem solving, examination of student thinking, and discussion of research. The concepts studied in the course included multi-digit…

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…

Towards the Construction of a Framework to Deal with Routine Problems to Foster Mathematical Inquiry

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Camacho-Machin, Matias

2009-01-01

To what extent does the process of solving textbook problems help students develop a way of thinking that is consistent with mathematical practice? Can routine problems be transformed into problem solving activities that promote students' mathematical reflection? These questions are used to outline and discuss features of an inquiry framework…

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…

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…

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…

The Mathematics and Mathematical Thinking of Seamstresses.

ERIC Educational Resources Information Center

Hancock, Sabrina J. C.

This study documents the mathematics practiced by four women in the context of sewing. The study describes the mathematics recognized in the skills, thinking and strategies used by the seamstresses. Through their work, the seamstresses exhibited an understanding of the concepts of angles, direction, parallel, reflection, symmetry, proportion,…

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 …

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)

Student’s thinking process in solving word problems in geometry

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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.

The Increase of Critical Thinking Skills through Mathematical Investigation Approach

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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.

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…

The role of local theories: teacher knowledge and its impact on engaging students with challenging tasks

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Choppin, Jeffrey

2011-03-01

This study explores the extent to which a teacher elicited students' mathematical reasoning through the use of challenging tasks and the role her knowledge played in doing so. I characterised the teacher's knowledge in terms of a local theory of instruction, a form of pedagogical content knowledge that involves an empirically tested set of conjectures situated within a mathematical domain. Video data were collected and analysed and used to stimulate the teacher's reflection on her enactments of an instructional sequence. The teacher, chosen for how she consistently elicited student reasoning, showed evidence of possessing a local theory in that she articulated the ways student thinking developed over time, the processes by which that thinking developed, and the resources that facilitated the development of student thinking. Her knowledge informed how she revised and enacted challenging tasks in ways that elicited and refined student thinking around integer addition and subtraction. Furthermore, her knowledge and practices emphasised the progressive formalisation of students' ideas as a key learning process. A key implication of this study is that teachers are able to develop robust knowledge from enacting challenging tasks, knowledge that organises how they elicit and refine student reasoning from those tasks.

Learning by Doing: A Manual for Teaching and Assessing Higher-Order Thinking in Science and Mathematics.

ERIC Educational Resources Information Center

National Assessment of Educational Progress, Princeton, NJ.

The National Assessment of Educational Progress (NAEP), the Nation's Report Card, has developed and pilot-tested a variety of hands-on science and mathematics tasks. These tasks were developed as prototypes for use in future national assessments, but the concepts measured and the innovative approaches used are equally suitable for classroom…

Making Numbers Come to Life: Two Scoring Methods for Creativity in Aurora's Cartoon Numbers

ERIC Educational Resources Information Center

Tan, Mei; Mourgues, Catalina; Bolden, David S.; Grigorenko, Elena L.

2014-01-01

Although creativity has long been recognized as an important aspect of mathematical thinking, both for the advancement of the field and in students' developing expertise in mathematics, assessments of student creativity in that domain have been limited in number and focus. This article presents an assessment developed for creativity that…

The Role of Dynamic Software in the Identification and Construction of Mathematical Relationships

ERIC Educational Resources Information Center

Santos-Trigo, Manuel

2004-01-01

What features of mathematical thinking do students exhibit when they use dynamic software in their problem solving approaches? To what extent does the systematic use of technology favour students' development of problem solving competences? What type of reasoning do students develop as a result of using a particular tool? This study documents…

Early Childhood Teachers' Professional Learning in Early Algebraic Thinking: A Model that Supports New Knowledge and Pedagogy

ERIC Educational Resources Information Center

Warren, Elizabeth

2009-01-01

The implementation of a new mathematics syllabus in the elementary context is problematic, especially if it contains a new content area. A professional development model, Transformative Teaching in the Early Years Mathematics (TTEYM) was specifically developed to support the implementation of the new Patterns and Algebra strand. The model was…

The Cognitive Underpinnings of Emerging Mathematical Skills: Executive Functioning, Patterns, Numeracy, and Arithmetic

ERIC Educational Resources Information Center

Lee, Kerry; Ng, Swee Fong; Pe, Madeline Lee; Ang, Su Yin; Hasshim, Muhammad Nabil Azhar Mohd; Bull, Rebecca

2012-01-01

Background: Exposure to mathematical pattern tasks is often deemed important for developing children's algebraic thinking skills. Yet, there is a dearth of evidence on the cognitive underpinnings of pattern tasks and how early competencies on these tasks are related to later development. Aims: We examined the domain-specific and domain-general…

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…

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…

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

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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.

Riding the RAFT

ERIC Educational Resources Information Center

Gunter, Melissa D.

2016-01-01

Writing about mathematics holds a wealth of benefits for students. When students are given opportunities to write in math class, it helps develop mathematical thinking and language, encourages self-reflection, and provides a better way to organize ideas. Many teachers incorporate journaling and other types of reflective writing into their…

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…

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…

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

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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.

Developing Mathematical Knowledge and Skills through the Awareness Approach of Teaching and Learning

ERIC Educational Resources Information Center

Cherif, Abour H.; Gialamas, Stefanos; Stamati, Angeliki

2017-01-01

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

An Experimental Text in Transformational Geometry, Student Text; Cambridge Conference on School Mathematics Feasibility Study No. 43a.

ERIC Educational Resources Information Center

Cambridge Conference on School Mathematics, Newton, MA.

This is part of a student text which was written with the aim of reflecting the thinking of The Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for mathematics. The instructional materials were developed for teaching geometry in the secondary schools. This document is chapter six and titled Motions and…

Examining the Impact of a Framework to Support Prospective Secondary Teachers' Transition from 'Doer' to 'Teacher' of Mathematics

ERIC Educational Resources Information Center

Lee, Hea-Jin; Özgün-Koca, S. Asli; Meagher, Michael; Edwards, Michael Todd

2018-01-01

A transition from "doer" to "teacher" for prospective teachers requires them to reorient from thinking about how they do mathematics to engaging with students and their work, understanding student representations, and planning instruction accordingly. To scaffold a transition, we developed a five-step mathematics as teacher…

In Pursuit of a Connected Way of Knowing: The Case of One Mathematics Teacher

ERIC Educational Resources Information Center

Agudelo-Valderrama, Cecilia; Martínez, Diana

2016-01-01

In this paper, we offer illustrations of a mathematics teacher's difficulties with content knowledge when trying to find connections between school mathematics and science; we do so by describing the development of this teacher's thinking and learning in her pursuit of connections between the concepts of slope of a line and density of matter. The…

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

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron

2016-01-01

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

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,…

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,…

Improving High-Level Thinking Skills by Development of Learning PBL Approach on the Learning Mathematics for Senior High School Students

ERIC Educational Resources Information Center

Surya, Edy; Syahputra, Edi

2017-01-01

This study aims to improve the ability of high-level thinking by developing learning models based on problems in senior high school students. The type study is research development. The subject of dissemination consists in 3 district/city in North Sumatera, namely: SMK Negeri 6 Medan, MAN Deli Serdang Distric and SMA Yapim Taruna Langkat Distric,…

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…

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…

Focal Event, Contextualization, and Effective Communication in the Mathematics Classroom

ERIC Educational Resources Information Center

Nilsson, Per; Ryve, Andreas

2010-01-01

The aim of this article is to develop analytical tools for studying mathematical communication in collaborative activities. The theoretical construct of contextualization is elaborated methodologically in order to study diversity in individual thinking in relation to effective communication. The construct of contextualization highlights issues of…

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…

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…

Fostering the Development of Logico-Mathematical Thinking in a Card Game at Ages 5-6

ERIC Educational Resources Information Center

Kamii, Constance; Kato, Yasuhiko

2005-01-01

A class of 14 kindergartners in Japan was videotaped while playing a card game in groups of three involving the placement of cards in numerical order. The children were followed up in first grade, and it was found that development in one area of logico-mathematical knowledge (for example, the making of temporal relationships) stimulates…

Developing design-based STEM education learning activities to enhance students' creative thinking

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Pinasa, Siwa; Siripun, Kulpatsorn; Yuenyong, Chokchai

2018-01-01

Creative thinking on applying science and mathematics knowledge is required by the future STEM career. The STEM education should be provided for the required skills of future STEM career. This paper aimed to clarify the developing STEM education learning activities to enhance students' creative thinking. The learning activities were developed for Grade 10 students who will study in the subject of independent study (IS) of Khon Kaen Wittayayon School, Khon Kaen, Thailand. The developing STEM education learning activities for enhancing students' creative thinking was developed regarding on 6 steps including (1) providing of understanding of fundamental STEM education concept, (2) generating creative thinking from prototype, (4) revised ideas, (5) engineering ability, and (6) presentation and discussion. The paper will clarify the 18 weeks activities that will be provided based these 6 steps of developing learning activities. Then, these STEM learning activities will be discussed to provide the chance of enhancing students' creative thinking. The paper may have implication for STEM education in school setting.

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

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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.

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

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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.

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.

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

NASA Astrophysics Data System (ADS)

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.

Patterns of Interaction and Mathematical Thinking of High School Students in Classroom Environments That Include Use of Java-Based, Curriculum-Embedded Software

ERIC Educational Resources Information Center

Fonkert, Karen L.

2012-01-01

This study analyzes the nature of student interaction and discourse in an environment that includes the use of Java-based, curriculum-embedded mathematical software. The software "CPMP-Tools" was designed as part of the development of the second edition of the "Core-Plus Mathematics" curriculum. The use of the software on…

Developing the Area of a Trapezoid

ERIC Educational Resources Information Center

Manizade, Agida G.; Mason, Marguerite M.

2014-01-01

A mathematics classroom that reflects the vision of NCTM's "Principles and Standards for School Mathematics" will have the teacher posing problems, asking questions that build on students' thinking, and encouraging students to explore different solutions. In teaching about area, it is not sufficient to give students the…

Model Eliciting Activities: A Home Run

ERIC Educational Resources Information Center

Magiera, Marta T.

2013-01-01

An important goal of school mathematics is to enable students to formulate, approach, and refine problems beyond those they have studied, allowing them to organize and consolidate their mathematical thinking. To achieve this goal, students should be encouraged to develop expertise in a variety of areas, such as problem solving, reasoning and…

Differentiated Success: Combining Theories to Explain Learning

ERIC Educational Resources Information Center

Jorgensen, Robyn; Larkin, Kevin

2015-01-01

This paper explores the value of different paradigms to explain dispositions towards mathematics among primary school students from different social backgrounds. As part of a larger project designed to elicit students' thinking and attitudes towards mathematics, we seek to develop an explanatory model for the socially-differentiated outcomes in…

Not Just for Computation: Basic Calculators Can Advance the Process Standards

ERIC Educational Resources Information Center

Moss, Laura J.; Grover, Barbara W.

2007-01-01

Simple nongraphing calculators can be powerful tools to enhance students' conceptual understanding of mathematics concepts. Students have opportunities to develop (1) a broad repertoire of problem-solving strategies by observing multiple solution strategies; (2) respect for other students' abilities and ways of thinking about mathematics; (3) the…

Programming in Preschool--With a Focus on Learning Mathematics

ERIC Educational Resources Information Center

Palmér, Hanna

2017-01-01

This article presents a teaching intervention where programming was used to facilitate preschoolers' learning of mathematics, especially in their development of spatial thinking. In the intervention, the programming was made with a small programmable robot especially designed for young students. The results indicate that the children developed…

Cognitive Tutor®. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2016

2016-01-01

"Cognitive Tutor"® is a secondary mathematics curriculum developed by Carnegie Learning that focuses on how students think about and learn mathematics. Teachers facilitate student learning as students acquire and apply new information and discuss their work. The curriculum can be implemented using a textbook, adaptive software, or…

Learning Trajectories in Teacher Education: Supporting Teachers' Understandings of Students' Mathematical Thinking

ERIC Educational Resources Information Center

Wilson, P. Holt; Mojica, Gemma F.; Confrey, Jere

2013-01-01

Recent work by researchers has focused on synthesizing and elaborating knowledge of students' thinking on particular concepts as core progressions called learning trajectories. Although useful at the level of curriculum development, assessment design, and the articulation of standards, evidence is only beginning to emerge to suggest how learning…

Think Aloud: Using Cognitive Interviewing to Validate the PISA Assessment of Student Self-Efficacy in Mathematics

ERIC Educational Resources Information Center

Pepper, David; Hodgen, Jeremy; Lamesoo, Katri; Kõiv, Pille; Tolboom, Jos

2018-01-01

Cognitive interviewing (CI) provides a method of systematically collecting validity evidence of response processes for questionnaire items. CI involves a range of techniques for prompting individuals to verbalise their responses to items. One such technique is concurrent verbalisation, as developed in Think Aloud Protocol (TAP). This article…

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…

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…

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

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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.

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…

"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.…

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.

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.

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,…

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…

Gestures and Insight in Advanced Mathematical Thinking

ERIC Educational Resources Information Center

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

2011-01-01

What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…

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…

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,…

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…

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.

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…

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…

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…

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.

Thinking beyond the Obvious Boundaries in Mathematics: An Exploration of Joyous Discovery.

ERIC Educational Resources Information Center

de Vries, Marianne E.

1992-01-01

Ideas for the development of creative exploration in mathematics are offered, including games to play in class (e.g., card games and tangrams), competitions (sample problems), clubs and math evenings (math relays and treasure hunts), projects (possible topics in patchwork quilting, art, and music), and math camps. (DB)

Math Process Standards Series, Grades PreK-2 [with CD-ROMs

ERIC Educational Resources Information Center

O'Connell, Susan, Ed.

2007-01-01

The National Council of Teachers of Mathematics (NCTM)'s Process Standards support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every primary teacher the opportunity to explore each standard in depth. With language and examples that don't require…

An Inquiry Approach to Construct Instructional Trajectories Based on the Use of Digital Technologies

ERIC Educational Resources Information Center

Santos-Trigo, Manuel

2008-01-01

There are diverse ways to construct instructional activities that teachers can use to foster their students' development of mathematical thinking. It is argued that the use of computational tools offers teachers the possibility of designing and exploring mathematical tasks from distinct perspectives that might lead their students to the…

Mathematically Gifted Children: Developmental Brain Characteristics and Their Prognosis for Well-Being

ERIC Educational Resources Information Center

O'Boyle, Michael W.

2008-01-01

Research in cognitive neuroscience suggests that the brains of mathematically gifted children are quantitatively and qualitatively different from those of average math ability. Math-gifted children exhibit signs of enhanced right-hemisphere development, and when engaged in the thinking process, tend to rely on mental imagery. They further manifest…

Teaching Mathematics by Comparison: Analog Visibility as a Double-Edged Sword

ERIC Educational Resources Information Center

Begolli, Kreshnik Nasi; Richland, Lindsey Engle

2016-01-01

Comparing multiple solutions to a single problem is an important mode for developing flexible mathematical thinking, yet instructionally leading this activity is challenging (Stein, Engle, Smith, & Hughes, 2008). We test 1 decision teachers must make after having students solve a problem: whether to only verbally discuss students' solutions or…

Vamos a Jugar Counters! Learning Mathematics through Funds of Knowledge, Play, and the Third Space

ERIC Educational Resources Information Center

Razfar, Aria

2012-01-01

Drawing on Cultural Historical Activity Theory (CHAT), funds of knowledge, and third space, this article presents a model for practitioners and researchers to think about how Latina/o, bilingual children develop explicit mathematics strategies through multilingual and multigenerational interactions. Using data collected through fieldwork in an…

Programming-Languages as a Conceptual Framework for Teaching Mathematics

ERIC Educational Resources Information Center

Feurzeig, Wallace; Papert, Seymour A.

2011-01-01

Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively…

Thinking and Reasoning with Data and Chance: 68th NCTM Yearbook (2006)

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, 2006

2006-01-01

The 2006 NCTM Sixty-eighth Yearbook focuses on students' and teachers' learning in statistics centered on a set of activities. Topics include the relation between mathematics and statistics, the development and enrichment of mathematical concepts through the use of statistics, and a discussion of the research related to teaching and learning…

Initial Understandings of Fraction Concepts Evidenced by Students with Mathematics Learning Disabilities and Difficulties: A Framework

ERIC Educational Resources Information Center

Hunt, Jessica H.; Welch-Ptak, Jasmine J.; Silva, Juanita M.

2016-01-01

Documenting how students with learning disabilities (LD) initially conceive of fractional quantities, and how their understandings may align with or differ from students with mathematics difficulties, is necessary to guide development of assessments and interventions that attach to unique ways of thinking or inherent difficulties these students…

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

ERIC Educational Resources Information Center

Rahman, Abdul; Ahmar, Ansari Saleh

2016-01-01

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

Middle School Students' Mathematics Knowledge Retention: Online or Face-To-Face Environments

ERIC Educational Resources Information Center

Edwards, Clayton M.; Rule, Audrey C.; Boody, Robert M.

2017-01-01

Educators seek to develop students' mathematical knowledge retention to increase student efficacy in follow-on classwork, improvement of test scores, attainment of standards, and preparation for careers. Interactive visuals, feedback during problem solving, and incorporation of higher-order thinking skills are known to increase retention, but a…

Such Low Temperatures in the Arctic Region: How Can the Polar Bears Call It Home?

ERIC Educational Resources Information Center

Pringle, Rose M.

2005-01-01

Science requires active learning--it is something that children do, rather than something that is done to them. The learning process involves students' thinking and doing to develop higher-order thinking skills, strengthen their reading and mathematical skills, and attain scientific knowledge. In the elementary grades, children learn biological…

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…

Reflection on the Analytic Geometry Courses: The Geogebra Software and Its Effect on Creative Thinking

ERIC Educational Resources Information Center

Yildiz, Avni; Baltaci, Serdal; Demir, Betül Küçük

2017-01-01

Creativity has a significant role in individuals' lives. This research aims to examine the reflection of the learning process of analytic geometry concepts through GeoGebra software and its effect upon the development of preservice mathematics teachers' creative thinking skills. This effect is expected to make a significant contribution to the…

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…

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…

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…

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…

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…

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.

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 engineering program outcomes set by the Engineering Accreditation Council.

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…

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…

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

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.

An Early Mathematical Patterning Assessment: identifying young Australian Indigenous children's patterning skills

NASA Astrophysics Data System (ADS)

Papic, Marina

2015-12-01

This paper presents an Early Mathematical Patterning Assessment (EMPA) tool that provides early childhood educators with a valuable opportunity to identify young children's mathematical thinking and patterning skills through a series of hands-on and drawing tasks. EMPA was administered through one-to-one assessment interviews to children aged 4 to 5 years in the year prior to formal school. Two hundred and seventeen assessments indicated that the young low socioeconomic and predominantly Australian Indigenous children in the study group had varied patterning and counting skills. Three percent of the study group was able to consistently copy and draw an ABABAB pattern made with coloured blocks. Fifty percent could count to six by ones and count out six items with 4 % of the total group able to identify six items presented in regular formations without counting. The integration of patterning into early mathematics learning is critical to the abstraction of mathematical ideas and relationships and to the development of mathematical reasoning in young children. By using the insights into the children's thinking that the EMPA tool provides, early childhood educators can better inform mathematics teaching and learning and so help close the persistent gap in numeracy between Indigenous and non-Indigenous children.

Introducing computational thinking through hands-on projects using R with applications to calculus, probability and data analysis

NASA Astrophysics Data System (ADS)

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

2017-04-01

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 analysis. We present nine computer experiments and suggest a few more, with applications to calculus, probability and data analysis, which engage computational thinking through simulations, visualizations and data analysis. We are using the free (open-source) statistical programming language R. Our goal is to give a taste of what R offers rather than to present a comprehensive tutorial on the R language. In our experience, these kinds of interactive computer activities can be easily integrated into a smart classroom. Furthermore, these activities do tend to keep students motivated and actively engaged in the process of learning, problem solving and developing a better intuition for understanding complex mathematical concepts.

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…

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…

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…

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…

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…

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.

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…

Introduction to Communication, Grades 6-8 [with CD-ROM]. The Math Process Standards, Grades 6-8 Series

ERIC Educational Resources Information Center

O'Connell, Susan; Croskey, Suzanne G.

2008-01-01

The National Council of Teachers of Mathematics' (NCTM's) Process Standards support teaching that helps students develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every middle grades math teacher the opportunity to explore each standard in depth. The series offers friendly,…

A Tool for Rethinking Teachers' Questioning

ERIC Educational Resources Information Center

Simpson, Amber; Mokalled, Stefani; Ellenburg, Lou Ann; Che, S. Megan

2014-01-01

In this article, the authors present a tool, the Cognitive Rigor Matrix (CRM; Hess et al. 2009), as a means to analyze and reflect on the type of questions posed by mathematics teachers. This tool is intended to promote and develop higher-order thinking and inquiry through the use of purposeful questions and mathematical tasks. The authors…

Assessing Translation Misconceptions inside the Classroom: A Presentation of an Instrument and Its Results

ERIC Educational Resources Information Center

Mangulabnan, Pauline Anne Therese M.

2013-01-01

This is a descriptive research on the difficulties of Filipino high school students in translating algebraic word problems into mathematical equations. This research is composed of three parts: (1) development of an 11-page "Filipinized" questionnaire; (2) analysis of the mathematical thinking processes of the respondents based on the answers to…

Using a Framework for Three Levels of Sense Making in a Mathematics Classroom

ERIC Educational Resources Information Center

Moss, Diana L.; Lamberg, Teruni

2016-01-01

This discussion-based lesson is designed to support Year 6 students in their initial understanding of using letters to represent numbers, expressions, and equations in algebra. The three level framework is designed for: (1) making thinking explicit, (2) exploring each other's solutions, and (3) developing new mathematical insights. In each level…

Introduction to Problem Solving, Grades 6-8 [with CD-ROM]. The Math Process Standards, Grades 6-8 Series

ERIC Educational Resources Information Center

Schackow, Joy Bronston; O'Connell, Susan

2008-01-01

The National Council of Teachers of Mathematics' (NCTM's) Process Standards support teaching that helps students develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every middle grades math teacher the opportunity to explore each standard in depth. The series offers friendly,…

Developing Conceptual Understanding and Definitional Clarity in Linear Algebra through the Three Worlds of Mathematical Thinking

ERIC Educational Resources Information Center

Hannah, John; Stewart, Sepideh; Thomas, Michael

2016-01-01

Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall's three worlds (embodied, symbolic and…

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.

Problem Solving-based Learning Materials on Fraction for Training Creativity of Elementary School Students

NASA Astrophysics Data System (ADS)

Widhitama, Y. N.; Lukito, A.; Khabibah, S.

2018-01-01

The aim of this research is to develop problem solving based learning materials on fraction for training creativity of elementary school students. Curriculum 2006 states that mathematics should be studied by all learners starting from elementary level in order for them mastering thinking skills, one of them is creative thinking. To our current knowledge, there is no such a research topic being done. To promote this direction, we initiate by developing learning materials with problem solving approach. The developed materials include Lesson Plan, Student Activity Sheet, Mathematical Creativity Test, and Achievement Test. We implemented a slightly modified 4-D model by Thiagajan et al. (1974) consisting of Define, Design, Development, and Disseminate. Techniques of gathering data include observation, test, and questionnaire. We applied three good qualities for the resulted materials; that is, validity, practicality, and effectiveness. The results show that the four mentioned materials meet the corresponding criteria of good quality product.

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.

On the use of history of mathematics: an introduction to Galileo's study of free fall motion

NASA Astrophysics Data System (ADS)

Ponce Campuzano, Juan Carlos; Matthews, Kelly E.; Adams, Peter

2018-05-01

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year university students through Galileo's experiments designed to investigate the motion of falling bodies, and his geometrical explanation of his results, via simple dynamic geometric applets designed with GeoGebra. Our goal was to enhance the students' development of mathematical thinking. Through a scholarship of teaching and learning study design, we captured data from students before, during and after the activity. Findings suggest that the historical development presented to the students helped to show the growth and evolution of the ideas and made visible authentic ways of thinking mathematically. Importantly, the activity prompted students to question and rethink what they knew about speed and acceleration, and also to appreciate the novel concepts of instantaneous speed and acceleration at which Galileo arrived.

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…

Lily Pad Doubling: Proportional Reasoning Development

ERIC Educational Resources Information Center

Robichaux-Davis, Rebecca R.

2017-01-01

Progressing from additive to multiplicative thinking is critical for the development of middle school students' proportional reasoning abilities. Yet, many middle school mathematics teachers lack a thorough understanding of additive versus multiplicative situations. This article describes a sequence of instructional activities used to develop the…

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…

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.

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.

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.

Assessing the Mathematical Thinking of Young Children in New Zealand: The Initial School Years

ERIC Educational Resources Information Center

Young-Loveridge, Jenny

2011-01-01

This paper provides an overview of assessment policy and practice in mathematics for early years classrooms in New Zealand between 1993 and the present day. It describes the introduction of school entry assessment for children starting school at age five. A numeracy initiative, the Numeracy Development Projects (NDP), for students in Years 1-10…

The Power of Colombian Mathematics Teachers' Conceptions of Social/Institutional Factors of Teaching

ERIC Educational Resources Information Center

Agudelo-Valderrama, Cecilia

2008-01-01

In this paper I shall discuss data from a study on Colombian mathematics teachers' conceptions of their own teaching practices of beginning algebra, which led to the development of a theoretical model of teachers' thought structures designed as a thinking tool at the initial stage of the study. With a focus on the perspectives of teachers, the…

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…

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

Supporting Productive Struggle with Communication Moves

ERIC Educational Resources Information Center

Freeburn, Ben; Arbaugh, Fran

2017-01-01

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014, p. 10) contains eight research-informed teaching practices that have been shown to support students' mathematical thinking and learning. Two teaching practices highlighted herein are "to elicit and use evidence of students' thinking" and "support…

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.…

Adding structure to the transition process to advanced mathematical activity

NASA Astrophysics Data System (ADS)

Engelbrecht, Johann

2010-03-01

The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical deductive reasoning, required in advanced mathematics. It is necessary to assist students in this transition process, in moving from general to mathematical thinking. In this article some structure is suggested for this transition period. This essay is an argumentative exposition supported by personal experience and international literature. This makes this study theoretical rather than empirical.

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…

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.

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…

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.

Reasoning with Geometric Shapes

ERIC Educational Resources Information Center

Seah, Rebecca

2015-01-01

Geometry belongs to branches of mathematics that develop students' visualisation, intuition, critical thinking, problem solving, deductive reasoning, logical argument and proof (Jones, 2002). It provides the basis for the development of spatial sense and plays an important role in acquiring advanced knowledge in science, technology, engineering,…

Microcomputers and Preschoolers.

ERIC Educational Resources Information Center

Evans, Dina

Preschool children can benefit by working with microcomputers. Thinking skills are enhanced by software games that focus on logic, memory, problem solving, and pattern recognition. Counting, sequencing, and matching games develop mathematics skills, and word games focusing on basic letter symbol and word recognition develop language skills.…

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.

Development of a Framework to Characterise the Openness of Mathematical Tasks

ERIC Educational Resources Information Center

Yeo, Joseph B. W.

2017-01-01

Educators usually mean different constructs when they speak of open tasks: some may refer to pure-mathematics investigative tasks while others may have authentic real-life tasks in mind; some may think of the answer being open while others may refer to an open method. On the other hand, some educators use different terms, e.g. open and open-ended,…

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

NASA Astrophysics Data System (ADS)

Bektasli, Behzat

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

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…

Thinking Process of Pseudo Construction in Mathematics Concepts

ERIC Educational Resources Information Center

Subanji; Nusantara, Toto

2016-01-01

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

Teachers' 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…

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…

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…

Professional development in statistics, technology, and cognitively demanding tasks: classroom implementation and obstacles

NASA Astrophysics Data System (ADS)

Foley, Gregory D.; Bakr Khoshaim, Heba; Alsaeed, Maha; Nihan Er, S.

2012-03-01

Attending professional development programmes can support teachers in applying new strategies for teaching mathematics and statistics. This study investigated (a) the extent to which the participants in a professional development programme subsequently used the techniques they had learned when teaching mathematics and statistics and (b) the obstacles they encountered in enacting cognitively demanding instructional tasks in their classrooms. The programme created an intellectual learning community among the participants and helped them gain confidence as teachers of statistics, and the students of participating teachers became actively engaged in deep mathematical thinking. The participants indicated, however, that time, availability of resources and students' prior achievement critically affected the implementation of cognitively demanding instructional activities.

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

Of Nasa and Neanderthals, Elephants and Machines: Metaphors and the Conceptualization of Homeland Security

DTIC Science & Technology

2013-12-01

study of nature, just as they have in mathematics . Hence, even in our day of hyper abstract thinking , mathematics continues to be the language of...way of thinking . 2. Those successfully completing education and apprenticeship have professed a self-sacrificing commitment to serving society...overreaches. Pinker points out that the contextual school ignores the predictive reality of science and mathematics .73 This does not mean that metaphors

National Science Resources Center Project to Improve Science Teaching in Elementary Schools with Special Emphasis on Department of Defense Dependents Schools and Other Schools Serving Children of Military Personnel

DTIC Science & Technology

1992-10-01

science and mathematics education: • DOD Apprenticeship Programs * DOD Teacher Internship Programs * DOD Partnership Programs * DOD Dependents Schools ...corporate sponsors. curriculum and instruction in school mathematics For further information about the project or for were developed in a comprehensive... students develop critical thinking skills and to enhance their ability to solve problems through hands-on activities. The staff and participants were most

Polygon Properties: What Is Possible?

ERIC Educational Resources Information Center

Rodrigue, Paulette R.; Robichaux, Rebecca R.

2010-01-01

Sorting shapes and solving riddles develop and advance children's geometric thinking and understanding while promoting mathematical communication, cooperative learning, and numerous representations. This article presents a brief summary of how children develop an understanding of the properties of geometric shapes as well as a description of the…

Learning with touchscreen devices: game strategies to improve geometric thinking

NASA Astrophysics Data System (ADS)

Soldano, Carlotta; Arzarello, Ferdinando

2016-03-01

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 theoretical background of our study lies in the works of J. Hintikka, a Finnish logician, who developed a new type of logic, based on game theory, called the logic of inquiry. In order to experiment with this new approach to the teaching and learning of mathematics, we have prepared five game-activities based on geometric theorems in which two players play against each other in a multi-touch dynamic geometric environment (DGE). In this paper, we present the design of the first game-activity and the relationship between it and the logic of inquiry. Then, adopting the theoretical framework of the instrumental genesis by Vérillon and Rabardel (EJPE 10: 77-101, 1995), we will present and analyse significant actions and dialogues developed by students while they are solving the game. We focus on the presence of a particular way of playing the game introduced by the students, the "reflected game", and highlight its functions for the development of the task.

Gender differences in algebraic thinking ability to solve mathematics problems

NASA Astrophysics Data System (ADS)

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.

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.

Mathematics Performance and Cognition (MPAC) Interview: Measuring First- and Second-Grade Student Achievement in Number, Operations, and Equality in Spring 2014. Research Report No. 2016-01

ERIC Educational Resources Information Center

Schoen, Robert C.; LaVenia, Mark; Champagne, Zachary M.; Farina, Kristy

2017-01-01

This report provides an overview of the development, implementation, and psychometric properties of a student mathematics interview designed to assess first- and second-grade student achievement and thinking processes. The student interview was conducted with 622 first- or second-grade students in 22 schools located in two public school districts…

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…

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…

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…

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,…

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.…

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…

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)…

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…

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…

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.

Developing workshop module of realistic mathematics education: Follow-up workshop

NASA Astrophysics Data System (ADS)

Palupi, E. L. W.; Khabibah, S.

2018-01-01

Realistic Mathematics Education (RME) is a learning approach which fits the aim of the curriculum. The success of RME in teaching mathematics concepts, triggering students’ interest in mathematics and teaching high order thinking skills to the students will make teachers start to learn RME. Hence, RME workshop is often offered and done. This study applied development model proposed by Plomp. Based on the study by RME team, there are three kinds of RME workshop: start-up workshop, follow-up workshop, and quality boost. However, there is no standardized or validated module which is used in that workshops. This study aims to develop a module of RME follow-up workshop which is valid and can be used. Plopm’s developmental model includes materials analysis, design, realization, implementation, and evaluation. Based on the validation, the developed module is valid. While field test shows that the module can be used effectively.

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…

Gathering Circles: An Experience in Creativity and Variety.

ERIC Educational Resources Information Center

Nakagomi, Koji

2000-01-01

Presents materials and methods that maintain student interest and encourage them to think creatively, develop mathematical reasoning, and look at problems from different perspectives, all within an open-ended approach to problem solving. Includes questions for discussion. (KHR)

Noticing numeracy now! Examining changes in preservice teachers' noticing, knowledge, and attitudes

NASA Astrophysics Data System (ADS)

Fisher, Molly H.; Thomas, Jonathan; Schack, Edna O.; Jong, Cindy; Tassell, Janet

2018-06-01

This study examined the impact of an intervention, focused on professional noticing of children's conceptual development in whole number and arithmetic reasoning, on preservice elementary teachers' (PSETs') professional noticing skills, attitudes toward mathematics, and mathematical knowledge for teaching mathematics. A video-based professional noticing module, situated in the pedagogies of practice framework, was used with 224 PSETs from five universities. Comparison data was also collected with similar groups not participating in the instructional module. Through pre- and post-assessments, findings indicated that PSETs can develop sound professional noticing skills as a result of participation in a video-based module. The impact on attitudes toward mathematics was less convincing as significant changes were revealed in intervention as well as comparison groups. We hypothesized the potential for professional noticing of children's mathematical thinking to serve as a mechanism for increasing the capabilities of PSETs to negotiate the complexities of mathematics teaching and learning; however, mathematics knowledge for teaching showed no significant increase for either group.

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.

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).…

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…

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…

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.…

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…

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…

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…

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…

The essence of student visual-spatial literacy and higher order thinking skills in undergraduate biology.

PubMed

Milner-Bolotin, Marina; Nashon, Samson Madera

2012-02-01

Science, engineering and mathematics-related disciplines have relied heavily on a researcher's ability to visualize phenomena under study and being able to link and superimpose various abstract and concrete representations including visual, spatial, and temporal. The spatial representations are especially important in all branches of biology (in developmental biology time becomes an important dimension), where 3D and often 4D representations are crucial for understanding the phenomena. By the time biology students get to undergraduate education, they are supposed to have acquired visual-spatial thinking skills, yet it has been documented that very few undergraduates and a small percentage of graduate students have had a chance to develop these skills to a sufficient degree. The current paper discusses the literature that highlights the essence of visual-spatial thinking and the development of visual-spatial literacy, considers the application of the visual-spatial thinking to biology education, and proposes how modern technology can help to promote visual-spatial literacy and higher order thinking among undergraduate students of biology.

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.

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.

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)

Investigating and developing engineering students' mathematical modelling and problem-solving skills

NASA Astrophysics Data System (ADS)

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-09-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced problem solvers, unaware of the importance of understanding the problem and exploring alternatives, and impeded by inappropriate beliefs, attitudes and expectations. Important impacts of the course belong to the metacognitive domain. The nature of the problems, the supervision and the follow-up lectures were emphasised as contributing to the impacts of the course, where students show major development. We discuss these empirical results in relation to a framework for mathematical thinking and the notion of cognitive apprenticeship. Based on the results, we argue that this kind of teaching should be considered in the education of all engineers.

Silent method for mathematics instruction: An overview of teaching subsets

NASA Astrophysics Data System (ADS)

Sugiman, Apino, Ezi

2017-05-01

Generally, teachers use oral communication for teaching mathematics. Taking an opposite perspective, this paper describes how instructional practices for mathematics can be carried out namely a silent method. Silent method uses body language, written, and oral communication for classroom interaction. This research uses a design research approach consisting of four phases: preliminary, prototyping and developing the instruction, and assessment. There are four stages of silent method. The first stage is conditioning stage in which the teacher introduces the method and makes agreement about the `rule of the game'. It is followed by the second one, elaborating stage, where students guess and explore alternative answers. The third stage is developing mathematical thinking by structuring and symbolizing. Finally, the method is ended by reinforcing stage which aims at strengthening and reflecting student's understanding. In this paper, every stage is described on the basis of practical experiences in a real mathematics classroom setting.

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.

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.

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.

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

ERIC Educational Resources Information Center

Yilmaz, Rezan; Argun, Ziya

2018-01-01

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

The 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…

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…

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…

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…

Listening Responsively

ERIC Educational Resources Information Center

Callahan, Kadian M.

2011-01-01

Standards documents, such as the Common Core State Standards for Mathematics and "Principles and Standards for School Mathematics", expect teachers to foster mathematics learning by engaging students in meaningful mathematical discourse to expose students to different ways of thinking about and solving problems and positively influence their…

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…

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…

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…

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…

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…

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…

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

ERIC Educational Resources Information Center

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

2018-01-01

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

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)

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…

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…

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.

Integrating Science and Mathematics Curricula Using Computer Mediated Communications: A Vygotskian Perspective.

ERIC Educational Resources Information Center

Charnitski, Christina Wotell; Harvey, Francis A.

This paper presents the theories of L.S. Vygotsky as a conceptual framework for implementing instruction that supports concept development and promotes higher level thinking skills in students. Three major components (i.e., language, scientific and spontaneous concepts, and the zone of proximal development) of Vygotsky's socio-cultural-historical…

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.

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.

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)

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…

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…

Students’ Creativity: Problem Posing in Structured Situation

NASA Astrophysics Data System (ADS)

Amalina, I. K.; Amirudin, M.; Budiarto, M. T.

2018-01-01

This is a qualitative research concerning on students’ creativity on problem posing task. The study aimed at describing the students’ creative thinking ability to pose the mathematics problem in structured situations with varied condition of given problems. In order to find out the students’ creative thinking ability, an analysis of mathematics problem posing test based on fluency, novelty, and flexibility and interview was applied for categorizing students’ responses on that task. The data analysis used the quality of problem posing and categorized in 4 level of creativity. The results revealed from 29 secondary students grade 8, a student in CTL (Creative Thinking Level) 1 met the fluency. A student in CTL 2 met the novelty, while a student in CTL 3 met both fluency and novelty and no one in CTL 4. These results are affected by students’ mathematical experience. The findings of this study highlight that student’s problem posing creativity are dependent on their experience in mathematics learning and from the point of view of which students start to pose problem.

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…

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…

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.

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…

The Expert Mathematician. Revised. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2006

2006-01-01

"The Expert Mathematician" is designed to help middle school students develop the thinking processes for mathematical applications and communication. A three-year program of instruction, "The Expert Mathematician" uses a software and consumable print materials package with 196 lessons that teach the "Logo" programming…

Earth Algebra: Real-Life Mathematics in Navajoland.

ERIC Educational Resources Information Center

Schaufele, Christopher; Srivastava, Ravindra

1995-01-01

An algebra class at Navajo Community College (Shiprock, New Mexico) uses traditional algebra topics to study real-life situations, focuses on environmental issues, encourages collaborative learning, uses modern technology, and promotes development of critical thinking and decision-making skills. Students follow principles of Dine educational…

Learning and Teaching Measurement (2003 Yearbook)

ERIC Educational Resources Information Center

Clements, Douglas H., Ed.

2003-01-01

Measurement can develop in the earliest years from children's experience, and it readily lends itself to real-world application. Focusing on research and practice, NCTM's 2003 Yearbook presents current thinking about the learning and teaching of measurement, including students' understanding, the mathematics of measurement, estimation and…

Learning by Heart.

ERIC Educational Resources Information Center

Rist, Marilee C.

1992-01-01

Although rote learning is a heretical notion to many educators, memorizing, reciting, and drilling may be what is needed to improve test scores and provide students with the necessary skills for solving problems and developing complex thinking skills. Sidebars summarize direct-teaching methods for mathematics and a Core Knowledge curriculum…

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…

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…

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…

Reflections on Language and Mathematics Problem Solving: A Case Study of a Bilingual First-Grade Teacher

ERIC Educational Resources Information Center

Musanti, Sandra I.; Celedon-Pattichis, Sylvia; Marshall, Mary E.

2009-01-01

This case study investigates a professional development initiative in which a first-grade bilingual teacher engages in learning and teaching Cognitively Guided Instruction, a framework for understanding student thinking through context-rich word-problem lessons. The study explores (a) the impact of classroom-based professional development on a…

Mathvision: A Mobile Video Application for Math Teacher Noticing of Learning Progressions

ERIC Educational Resources Information Center

Lewis, Stephen T.; Chao, Theodore; Battista, Michael

2017-01-01

We report on the development and evaluation of MathVision, a mobile-application designed to develop Virtual Professional Learning Communities through asynchronous discussion about 2nd, 3rd, 4th, and 5th grade students' mathematical thinking. MathVision allows teachers to upload videos of problems solving sessions using Cognition Based Assessment…

Impact of Online Professional Development on Teacher Quality and Student Achievement in Fifth Grade Mathematics

ERIC Educational Resources Information Center

Dash, Sheralyn; de Kramer, Raquel Magidin; O'Dwyer, Laura M.; Masters, Jessica; Russell, Michael

2012-01-01

Despite the ever-increasing number of online professional development (OPD) programs, relatively few studies have been conducted to examine the efficacy of such programs for teachers and students. This manuscript presents findings from an impact study of OPD courses in fractions, algebraic thinking, and measurement on 79 fifth grade teachers'…

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…

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…

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

NASA Astrophysics Data System (ADS)

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.

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.

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…

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)…

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…

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…

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…

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…

Thinking Conics

ERIC Educational Resources Information Center

Lewis, Richard

2008-01-01

For their course, mathematics students at Bath Spa University were asked to choose a topic and explore the mathematics. As well as learning some mathematics, the author hoped that the assignment would shed light on the process of mathematical investigation itself. Their course leader had suggested that the topic of conic sections was rich, and…

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…

Math Process Standards Series, Grades 3-5

ERIC Educational Resources Information Center

O'Connell, Susan, Ed.

2008-01-01

NCTM's Process Standards support teaching that helps upper elementary level children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every intermediate-grades teacher the opportunity to explore each standard in depth. With language and examples that don't require prior math…

Math "Rules" Prompt Reflection on Teachers' Identity

ERIC Educational Resources Information Center

Yagi, Seanyelle; Venenciano, Linda

2017-01-01

In their ongoing professional development project, the authors had an opportunity to work with a group of teachers who were particularly insightful. These teachers shared written reflections about their thinking, prior experiences, and changing self-awareness of their mathematics practice. In one session, teachers were provided the…

Math 3011--College Algebra and Trigonometry. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for a college level mathematics course designed to provide the necessary foundation for success in calculus, develop logical thinking skills, and enhance analytic skills through problem solving. Topics include relations and functions; inequalities; complex numbers;…

Teaching Data Handling in Foundation Phase: Teachers' Experiences

ERIC Educational Resources Information Center

Naidoo, Jayaluxmi; Mkhabela, Nokuphiwa

2017-01-01

Data handling plays an important role within mathematics education since it encompasses real-world situations and assists in developing critical thinking skills in learners. However, globally international assessments disclose that learners are not performing well in data handling. This article explores foundation phase South African teachers'…

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…

A cognitive framework for analyzing and describing introductory students' use and understanding of mathematics in physics

NASA Astrophysics Data System (ADS)

Tuminaro, Jonathan

Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics. In this thesis I propose a theoretical framework to analyze and describe students' mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events. The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework. Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of mathematical use in the context physics, and (2) a detailed understanding, in terms of the proposed theoretical framework, of the errors that students make when using mathematics in the context of physics.

Using Integer Manipulatives: Representational Determinism

ERIC Educational Resources Information Center

Bossé, Michael J.; Lynch-Davis, Kathleen; Adu-Gyamfi, Kwaku; Chandler, Kayla

2016-01-01

Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some…

Sharing a Birthday Cake

ERIC Educational Resources Information Center

Switzer, J. Matt

2016-01-01

National Council of Teachers of Mathematics' (NCTM's) "Principles to Actions: Ensuring Mathematical Success for All" outlines eight teaching practices for effective teaching and learning of mathematics (NCTM 2014). One of the teaching practices, "elicit and use evidence of student thinking," states, "Effective teaching of…

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…

Data Modeling for Preservice Teachers and Everyone Else

ERIC Educational Resources Information Center

Petrosino, Anthony J.; Mann, Michele J.

2018-01-01

Although data modeling, the employment of statistical reasoning for the purpose of investigating questions about the world, is central to both mathematics and science, it is rarely emphasized in K-16 instruction. The current work focuses on developing thinking about data modeling with undergraduates in general and preservice teachers in…

Do You Hear What I Hear

ERIC Educational Resources Information Center

Adams, Krista L.; Pedersen, Jon; Narboni, Nicole

2014-01-01

Ask many elementary school teachers or principals, and they will say that science and music are not the top priority in their classrooms. Teachers need to know "how" they can incorporate the necessary mathematics and reading goals and objectives while still engaging students in the critical and aesthetic thinking developed through…

Dancing with STEAM: Creative Movement Generates Electricity for Young Learners

ERIC Educational Resources Information Center

Simpson Steele, Jamie; Fulton, Lori; Fanning, Lisa

2016-01-01

The integration of science, technology, engineering, arts, and mathematics (STEAM) serves to develop creative thinking and twenty-first-century skills in the classroom (Maeda 2012). Learning through STEAM promotes novelty, innovation, ingenuity, and task-specific purposefulness to solve real-world problems--all aspects that define creativity. Lisa…

Examining Student Work in the Preparation of Preservice Elementary School Teachers

ERIC Educational Resources Information Center

Busi, Rich; Jacobbe, Tim

2014-01-01

This study investigated preservice teachers' perceptions of their knowledge and development resulting from analyzing student work in an undergraduate mathematics education course. Participants were given opportunities to view and analyze student work examples that portrayed errors in thinking as well as alternative solution methods. Thirty-eight…

Investigating the Effectiveness of Group Work in Mathematics

ERIC Educational Resources Information Center

Sofroniou, Anastasia; Poutos, Konstantinos

2016-01-01

Group work permits students to develop a range of critical thinking, analytical and communication skills; effective team work; appreciation and respect for other views, techniques and problem-solving methods, all of which promote active learning and enhance student learning. This paper presents an evaluation of employing the didactic and…

Professional Noticing: Learning to Teach Responsively

ERIC Educational Resources Information Center

Thomas, Jonathan; Fisher, Molly H.; Jong, Cindy; Schack, Edna O.; Krause, Lisa R.; Kasten, Sarah

2015-01-01

In the buzzing activity of the mathematics classroom, teaching in a way that effectively responds to and furthers students' thinking can be quite challenging. Given that teachers' instructional decisions will directly influence students' learning, it is extremely important to develop the sorts of practices that lead to productive in-the-moment…

The Math Master Level 2. Ages 6-8.

ERIC Educational Resources Information Center

Levy, Barbara W.

This booklet, designed for ages 6-8, is the second in a series designed to help teachers develop a more positive and creative approach to giving work on mathematics skills to children. It is based on objectives concerning creativity, fostering independent thinking, using experiences, using mastery, reinforcing previously learned skills,…

The Math Master Level 4. Ages 10-12.

ERIC Educational Resources Information Center

Levy, Barbara W.

This booklet, designed for ages 10-12, is the fourth in a series designed to help teachers develop a more positive and creative approach to giving work on mathematics skills to children. It is based on objectives concerning creativity, fostering independent thinking, using experiences, using mastery, reinforcing previously learned skills,…

The Math Master Level 1. Preschool-Age 6.

ERIC Educational Resources Information Center

Levy, Barbara W.

This booklet, designed for preschool through age 6, is the first in a series designed to help teachers develop a more positive and creative approach to giving work on mathematics skills to children. It is based on objectives concerning creativity, fostering independent thinking, using experiences, using mastery, reinforcing previously learned…

The Math Master Level 3. Ages 8-10.

ERIC Educational Resources Information Center

Levy, Barbara W.

This booklet, designed for ages 8-10, is the third in a series designed to help teachers develop a more positive and creative approach to giving work on mathematics skills to children. It is based on objectives concerning creativity, fostering independent thinking, using experiences, using mastery, reinforcing previously learned skills,…

Forgotten Fundamentals of the Energy Crisis

ERIC Educational Resources Information Center

Bartlett, Albert A.

1978-01-01

Explains using exponential mathematics, the effect of growth on rate of consuming energy resources. Concludes that we are running out of energy resources at a greater rate than many people think. Lists few options left such as conservation by stopping growth of consumption, recycling, and research to develop alternate sources. (GA)

STEM Education: Proceed with Caution

ERIC Educational Resources Information Center

Williams, P. John

2011-01-01

The STEM (science, technology, engineering and mathematics) movement has developed from a non-educational rationale. Although some think it may enliven the delivery of maths and science in classrooms, the social and economic rationales are those that have initiated this movement. Spurred on by the global financial crisis, it is hoped that…

The Leap from Patterns to Formulas

ERIC Educational Resources Information Center

Beigie, Darin

2011-01-01

Initial exposure to algebraic thinking involves the critical leap from working with numbers to thinking with variables. The transition to thinking mathematically using variables has many layers, and for all students an abstraction that is clear in one setting may be opaque in another. Geometric counting and the resulting algebraic patterns provide…

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…

Canadian Mathematics Education Study Group = Groupe Canadien d'etude en didactique des mathematiques. Proceedings of the Annual Meeting (22nd, Vancouver, British Columbia, Canada, May 29-June 2, 1998).

ERIC Educational Resources Information Center

Pothier, Yvonne M., Ed.

This proceedings includes the following papers: (1) "Structure of Attention in Teaching Mathematics" (John Mason); (2) "Communicating Mathematics or Mathematics Storytelling" (Kathy Heinrich); (3) "Assessing Mathematical Thinking" (Florence Glanfield and Pat Rogers); (4) "From Theory to Observational Data (and…

The roles of lesson study in the development of mathematics learning instrument based on learning trajectory

NASA Astrophysics Data System (ADS)

Misnasanti; Dien, C. A.; Azizah, F.

2018-03-01

This study is aimed to describe Lesson Study (LS) activity and its roles in the development of mathematics learning instruments based on Learning Trajectory (LT). This study is a narrative study of teacher’s experiences in joining LS activity. Data collecting in this study will use three methods such as observation, documentations, and deep interview. The collected data will be analyzed with Milles and Huberman’s model that consists of reduction, display, and verification. The study result shows that through LS activity, teachers know more about how students think. Teachers also can revise their mathematics learning instrument in the form of lesson plan. It means that LS activity is important to make a better learning instruments and focus on how student learn not on how teacher teach.

Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

Third Graders' Mathematical Thinking of Place Value through the Use of Concrete and Virtual Manipulatives

ERIC Educational Resources Information Center

Burris, Justin T.

2010-01-01

As one research priority for mathematics education is "to research how mathematical meanings are structured by tools available," the present study examined mathematical representations more closely by investigating instructional modes of representation (Noss, Healy & Hoyles, 1997). The study compared two modes of instruction of place value with…

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.…

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…

Identity and Ethnomathematics Projects in Papua New Guinea

ERIC Educational Resources Information Center

Owens, Kay

2012-01-01

Indigenous students may find mathematics in schools difficult because there is discontinuity between cultural mathematics and school mathematics. One of the reasons for this is that their teacher's identity as a mathematical thinker may not link to their cultural ways of thinking. In Papua New Guinea, there is a subject to assist student teachers…

Adding Structure to the Transition Process to Advanced Mathematical Activity

ERIC Educational Resources Information Center

Engelbrecht, Johann

2010-01-01

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

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…

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…

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…

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.

Learning from Our Own Lessons: Pre-Service Teachers' Narratives of Teaching as an Experiment

ERIC Educational Resources Information Center

Wickstrom, Megan H.; Wilm, Stephanie; Mills, Emily; Johnson, Alexis; Leonard, Nicole; Larberg, Raegan

2018-01-01

Pre-service teachers need to develop habits of mind that allow them to grow as new teachers. This article describes an elementary mathematics methods course in which teaching as an experiment was used a framework for pre-service teachers to participate in action research by developing learning goals, observing and analyzing student thinking,…

The Effect of Differentiation Approach Developed on Creativity of Gifted Students: Cognitive and Affective Factors

ERIC Educational Resources Information Center

Altintas, Esra; Özdemir, Ahmet S.

2015-01-01

The aim of the study is to develop a differentiation approach for the mathematics education of gifted middle school students and to determine the effect of the differentiation approach on creative thinking skills of gifted students based on both cognitive and affective factors. In this context, the answer to the following question was searched:…

Assessing the Relationship Between Questioning and Understanding to Improve Learning and Thinking (QUILT) and Student Achievement in Mathematics: A Pilot Study

ERIC Educational Resources Information Center

Craig, Jim; Cairo, III, Leslie

2005-01-01

Good questions, effectively delivered are a key feature of learning and teaching. QUILT is a research-based, field-tested professional development program designed to assist teachers in developing and implementing effective questioning skills to facilitate student learning. The QUILT framework presents classroom questioning as a five-stage…

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…

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.

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…

On inferentialism

NASA Astrophysics Data System (ADS)

Radford, Luis

2017-12-01

This article is a critical commentary on inferentialism in mathematics education. In the first part, I comment on some of the major shortcomings that inferentialists see in the theoretical underpinnings of representationalist, empiricist, and socioconstructivist mathematics education theories. I discuss in particular the criticism that inferentialism makes of the social dimension as conceptualized by socioconstructivism and the question related to the objectivity of knowledge. In the second part, I discuss some of the theoretical foundations of inferentialism in mathematics education and try to answer the question of whether or not inferentialism overcomes the individual-social divide. In the third part, I speculate on what I think inferentialism accomplishes and what I think it does not.

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…

What secondary teachers think and do about student engagement in mathematics

NASA Astrophysics Data System (ADS)

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.

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.

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.

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…

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…

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…

The Impact of a Teacher Education Culture-Based Project on Identity as a Mathematically Thinking Teacher

ERIC Educational Resources Information Center

Owens, Kay

2014-01-01

Identity as a mathematics teacher is enhanced when a teacher explores the cultural setting of their mathematics. The reports of projects that link culture and mathematics were analysed to explore the impact of sociocultural situations together with affective and cognitive aspects of self-regulation on identity. The reports were written by…

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)…

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…

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:…

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…

Enhancing Student Engagement through the Affordances of Mobile Technology: A 21st Century Learning Perspective on Realistic Mathematics Education

ERIC Educational Resources Information Center

Bray, Aibhín; Tangney, Brendan

2016-01-01

Several recent curriculum reforms aim to address the shortfalls traditionally associated with mathematics education through increased emphasis on higher-order-thinking and collaborative skills. Some stakeholders, such as the US National Council of Teachers of Mathematics and the UK Joint Mathematical Council, advocate harnessing the affordances of…

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…

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…

Warning Signs!

ERIC Educational Resources Information Center

Jacobs, Victoria R.; Martin, Heather A.; Ambrose, Rebecca C.; Philipp, Randolph A.

2014-01-01

In this article the authors explain that when engaging in a problem-solving conversation with a child, their goal goes beyond helping the child reach a correct answer. They want to learn about the child's mathematical thinking, support that thinking, and extend it as far as possible. This exploration of children's thinking is central to…

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.

Internal process: what is abstraction and distortion process?

NASA Astrophysics Data System (ADS)

Fiantika, F. R.; Budayasa, I. K.; Lukito, A.

2018-03-01

Geometry is one of the branch of mathematics that plays a major role in the development of science and technology. Thus, knowing the geometry concept is needed for students from their early basic level of thinking. A preliminary study showed that the elementary students have difficulty in perceiving parallelogram shape in a 2-dimention of a cube drawing as a square shape. This difficulty makes the students can not solve geometrical problems correctly. This problem is related to the internal thinking process in geometry. We conducted the exploration of students’ internal thinking processes in geometry particularly in distinguishing the square and parallelogram shape. How the students process their internal thinking through distortion and abstraction is the main aim of this study. Analysis of the geometrical test and deep interview are used in this study to obtain the data. The result of this study is there are two types of distortion and abstraction respectively in which the student used in their internal thinking processes.

Supporting Common Core Sense Making

ERIC Educational Resources Information Center

Keazer, Lindsay; Gerberry, Carla

2017-01-01

Imagine a mathematics classroom in which students engage in sharing ideas and reasoning through solutions to interesting mathematical problems. They are excited about mathematics and working on challenging problems that encourage collaboration and critical thinking. These are things that teachers want, but sometimes they do not know how to achieve…

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…

Math in Your Classroom: Math Magic

ERIC Educational Resources Information Center

Naylor, Michael

2005-01-01

Mathematics truly is magical, especially for students with strong number sense and algebra skills. This paper describes a variety of mathematical surprises that will capture students' interest and motivate exploration of mathematical ideas. While the tricks themselves are fascinating, push students to think about the reasons why these stunning…

Designing a Better Experience: A Qualitative Investigation of Student Engineering Internships

ERIC Educational Resources Information Center

Paknejad, Mohammad R.

2016-01-01

Science, Technology, Engineering and Mathematics (STEM) education play a very important role in preparing students with skills necessary to obtain better jobs, solve real-world challenges, and compete in the global economy. STEM education develops critical thinking and the ability to solve complex problems. Research showed that 8 out of 10 most…

Engineering Play: Exploring Associations with Executive Function, Mathematical Ability, and Spatial Ability in Preschool

ERIC Educational Resources Information Center

Gold, Zachary Samuel

2017-01-01

Engineering play is a new perspective on preschool education that views constructive play as an engineering design process that parallels the way engineers think and work when they develop engineered solutions to human problems (Bairaktarova, Evangelou, Bagiati, & Brophy, 2011). Early research from this perspective supports its use in framing…

Language Skills, Mathematical Thinking, and Achievement Motivation in Children with ADHD, Disruptive Behavior Disorders, and Normal Controls

ERIC Educational Resources Information Center

Gut, Janine; Heckmann, Carmen; Meyer, Christine Sandra; Schmid, Marc; Grob, Alexander

2012-01-01

Recent models of attention deficit/hyperactivity disorder (ADHD) suggest that the association between achievement motivation and school performance may be stronger in children with ADHD than in typically developing children. Therefore, the present study investigated associations between achievement motivation and performance on language skills and…

Ugandan Mathematics: An Unsolvable Problem?

ERIC Educational Resources Information Center

Eveleigh, Tobias

2011-01-01

This author is on a journey--hoping that his expertise might have some small local impact. He shares his experiences that might relate to those who are thinking about volunteering abroad, or trying to modernise a system that is cemented in place. Creating change, developing teaching styles, and working for a charity are some of the challenges he…

Responsive Teaching from the Inside Out: Teaching Base Ten to Young Children

ERIC Educational Resources Information Center

Empson, Susan B.

2014-01-01

Decision making during instruction that is responsive to children's mathematical thinking is examined reflexively by the researcher in the context of teaching second graders. Focus is on exploring how the research base on learning informs teaching decisions that are oriented to building on children's sound conceptions. The development of four…

GRID[subscript C] Renewable Energy Data Streaming into Classrooms

ERIC Educational Resources Information Center

DeLuca, V. William; Carpenter, Pam; Lari, Nasim

2010-01-01

For years, researchers have shown the value of using real-world data to enhance instruction in mathematics, science, and social studies. In an effort to help develop students' higher-order thinking skills in a data-rich learning environment, Green Research for Incorporating Data in the Classroom (GRID[subscript C]), a National Science…

Integrating Literacy and Math: Strategies for K-6 Teachers

ERIC Educational Resources Information Center

Fogelberg, Ellen; Skalinder, Carole; Satz, Patti; Hiller, Barbara; Bernstein, Lisa; Vitantonio, Sandra

2008-01-01

Many K-6 teachers and students still think of mathematics as a totally separate subject from literacy. Yet incorporating math content into the language arts block helps students gain skills for reading many kinds of texts. Bringing reading, writing, and talking into the math classroom supports the development of conceptual knowledge and problem…

Self-Grading: A Simple Strategy for Formative Assessment in Activity-Based Instruction.

ERIC Educational Resources Information Center

Ulmer, M. B.

This paper discusses the author's personal experiences in developing and implementing a problem-based college mathematics course for liberal arts majors. This project was initiated in response to the realization that most students are dependent on "patterning" learning algorithms and have no expectation that self-initiated thinking is a…

Creativity in the Fifth Grade High-Stakes Mathematics Environment

ERIC Educational Resources Information Center

Dominguez, Adriana

2011-01-01

Since the implementation of No Child Left Behind (NCLB), there has been a decrease of creative outlets (Berliner, 2009; Pederson, 2007) for pre-teen students to develop a positive self concept in public schools; creatively implemented technology along with critical thinking skills are no longer emphasized contributing to the notion that only…

Research and Teaching: WikiED--Using Web 2.0 Tools to Teach Content and Critical Thinking

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Frisch, Jennifer K.; Jackson, Paula C.; Murray, Meg C.

2013-01-01

WIKIed Biology is a National Science Foundation Transforming Undergraduate Education in Science, Technology, Engineering, and Mathematics interdisciplinary project in which the authors developed and implemented a model for student centered, inquiry-driven instruction using Web 2.0 technologies to increase inquiry and conceptual understanding in…

Proposing and Testing a Model to Explain Traits of Algebra Preparedness

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Venenciano, Linda; Heck, Ronald

2016-01-01

Early experiences with theoretical thinking and generalization in measurement are hypothesized to develop constructs we name here as logical reasoning and preparedness for algebra. Based on work of V. V. Davydov (1975), the Measure Up (MU) elementary grades experimental mathematics curriculum uses quantities of area, length, volume, and mass to…

Development of a Short-Form Measure of Science and Technology Self-Efficacy Using Rasch Analysis

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Lamb, Richard L.; Vallett, David; Annetta, Leonard

2014-01-01

Despite an increased focus on science, technology, engineering, and mathematics (STEM) in U.S. schools, today's students often struggle to maintain adequate performance in these fields compared with students in other countries (Cheek in "Thinking constructively about science, technology, and society education." State University of New…

A Sequence of Cylinders

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Johnson, Erica

2006-01-01

Hoping to develop in her students an understanding of mathematics as a way of thinking more than a way of doing, the author of this article describes how her students worked on a spatial reasoning problem stemming from an iteratively constructed sequence of cylinders. She presents an activity of making cylinders out of paper models, and for every…

The Impact of an Interdisciplinary Learning Community Course on Pseudoscientific Reasoning in First-Year Science Students

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Franz, Timothy M.; Green, Kris H.

2013-01-01

This case study examined the development and evaluation of an interdisciplinary first-year learning community designed to stimulate scientific reasoning and critical thinking. Designed to serve the needs of scholarship students majoring in mathematics and natural sciences, the six-credit learning community course was writing-intensive and…

Duality of Mathematical Thinking When Making Sense of Simple Word Problems: Theoretical Essay

ERIC Educational Resources Information Center

Polotskaia, Elena; Savard, Annie; Freiman, Viktor

2015-01-01

This essay proposes a reflection on the learning difficulties and teaching approaches associated with arithmetic word problem solving. We question the development of word problem solving skills in the early grades of elementary school. We are trying to revive the discussion because first, the knowledge in question--reversibility of arithmetic…

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…

Guide to Mathematics Released Items: Understanding Scoring

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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…

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…

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

ERIC Educational Resources Information Center

Prediger, Susanne; Zindel, Carina

2017-01-01

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

A 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…

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…

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…

Synopses for Modern Secondary School Mathematics.

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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…

Mathematical Thinking: Challenging Prospective Teachers to Do More than "Talk the Talk"

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Prendergast, Mark; Johnson, Patrick; Fitzmaurice, Olivia; Liston, Miriam; O'Keeffe, Lisa; O'Meara, Niamh

2014-01-01

This paper reports on a research project which aims to improve prospective mathematics teachers' relational understanding and pedagogical beliefs for teaching in second-level Irish classrooms. Prospective mathematics teachers complete their teacher education training with varying pedagogical beliefs, and often little relational understanding of…

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…

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…

CASMI: Virtual Learning Collaborative Environment for Mathematical Enrichment

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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…

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…

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…

Capturing Thinking on the Talk Frame

ERIC Educational Resources Information Center

Casa, Tutita M.

2013-01-01

The National Council of Teachers of Mathematics (NCTM 1991, 2000) recommends that students be positioned as sense makers who weigh one another's ideas and judge their mathematical validity. The instructional tool discussed in this article helps students engage in discussions that foster student reasoning, then settle on correct mathematics.…

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…

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…

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,…

"I Think I Can, but I'm Afraid to Try": The Role of Self-Efficacy Beliefs and Mathematics Anxiety in Mathematics Problem-Solving Efficiency

ERIC Educational Resources Information Center

Hoffman, Bobby

2010-01-01

This study investigated the role of self-efficacy beliefs, mathematics anxiety, and working memory capacity in problem-solving accuracy, response time, and efficiency (the ratio of problem-solving accuracy to response time). Pre-service teachers completed a mathematics anxiety inventory measuring cognitive and affective dispositions for…

Students' Intentions to Study Non-Compulsory Mathematics: The Importance of How Good You Think You Are

ERIC Educational Resources Information Center

Sheldrake, Richard; Mujtaba, Tamjid; Reiss, Michael J.

2015-01-01

Increasing the number of students who study mathematics once it is no longer compulsory remains a priority for England. A longitudinal cohort from England (1085 students) was surveyed at Years 10 and 12. Students' self-beliefs of ability influenced their GCSE mathematics grades and their intended and actual mathematics subject-choices; the degree…

A Study of Students' Conceptual, Procedural Knowledge, Logical Thinking and Creativity during the First Year of Tertiary Mathematics

ERIC Educational Resources Information Center

Tularam, Gurudeo Anand; Hulsman, Kees

2015-01-01

This study focuses on students in first year environmental science degree programs, where traditionally mathematical emphasis has been much less than within the strict science or math majors. The importance now placed on applied mathematics, however, means that students need to gain more conceptual and quantitative knowledge of mathematics in not…

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…

Cooperative learning model with high order thinking skills questions: an understanding on geometry

NASA Astrophysics Data System (ADS)

Sari, P. P.; Budiyono; Slamet, I.

2018-05-01

Geometry, a branch of mathematics, has an important role in mathematics learning. This research aims to find out the effect of learning model, emotional intelligence, and the interaction between learning model and emotional intelligence toward students’ mathematics achievement. This research is quasi-experimental research with 2 × 3 factorial design. The sample in this research included 179 Senior High School students on 11th grade in Sukoharjo Regency, Central Java, Indonesia in academic year of 2016/2017. The sample was taken by using stratified cluster random sampling. The results showed that: the student are taught by Thinking Aloud Pairs Problem-Solving using HOTs questions provides better mathematics learning achievement than Make A Match using HOTs questions. High emotional intelligence students have better mathematics learning achievement than moderate and low emotional intelligence students, and moderate emotional intelligence students have better mathematics learning achievement than low emotional intelligence students. There is an interaction between learning model and emotional intelligence, and these affect mathematics learning achievement. We conclude that appropriate learning model can support learning activities become more meaningful and facilitate students to understand material. For further research, we suggest to explore the contribution of other aspects in cooperative learning modification to mathematics achievement.

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…

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…

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…