Concept Mapping in Mathematics

Concept Mapping in Mathematics

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  • Author: Karoline Afamasaga-Fuata'i
  • Publisher: Springer Science & Business Media
  • ISBN: 0387891943
  • Category : Education
  • Languages : en
  • Pages : 339

Concept Mapping in Mathematics: Research into Practice is the first comprehensive book on concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of concept mapping can be used innovatively and strategically to improve planning, teaching, learning, and assessment at different educational levels. This collection of research articles examines the usefulness of concept maps in the educational setting, with applications and examples ranging from primary grade classrooms through secondary mathematics to pre-service teacher education, undergraduate mathematics and post-graduate mathematics education. A second meta-cognitive tool, called vee diagrams, is also critically examined by two authors, particularly its value in improving mathematical problem solving. Thematically, the book flows from a historical development overview of concept mapping in the sciences to applications of concept mapping in mathematics by teachers and pre-service teachers as a means of analyzing mathematics topics, planning for instruction and designing assessment tasks including applications by school and university students as learning and review tools. This book provides case studies and resources that have been field tested with school and university students alike. The findings presented have implications for enriching mathematics learning and making problem solving more accessible and meaningful for students. The theoretical underpinnings of concept mapping and of the studies in the book include Ausubel’s cognitive theory of meaningful learning, constructivist and Vygotskian psychology to name a few. There is evidence particularly from international studies such as PISA and TIMSS and mathematics education research, which suggest that students’ mathematical literacy and problem solving skills can be enhanced through students collaborating and interacting as they work, discuss and communicate mathematically. This book proposes the meta-cognitive strategy of concept mapping as one viable means of promoting, communicating and explicating students’ mathematical thinking and reasoning publicly in a social setting (e.g., mathematics classrooms) as they engage in mathematical dialogues and discussions. Concept Mapping in Mathematics: Research into Practice is of interest to researchers, graduate students, teacher educators and professionals in mathematics education.


Concept Mapping in Mathematics

Concept Mapping in Mathematics

PDF Concept Mapping in Mathematics Download

  • Author: Karoline Afamasaga-Fuata'i
  • Publisher: Springer
  • ISBN: 9780387891934
  • Category : Education
  • Languages : en
  • Pages : 220

Concept Mapping in Mathematics: Research into Practice is the first comprehensive book on concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of concept mapping can be used innovatively and strategically to improve planning, teaching, learning, and assessment at different educational levels. This collection of research articles examines the usefulness of concept maps in the educational setting, with applications and examples ranging from primary grade classrooms through secondary mathematics to pre-service teacher education, undergraduate mathematics and post-graduate mathematics education. A second meta-cognitive tool, called vee diagrams, is also critically examined by two authors, particularly its value in improving mathematical problem solving. Thematically, the book flows from a historical development overview of concept mapping in the sciences to applications of concept mapping in mathematics by teachers and pre-service teachers as a means of analyzing mathematics topics, planning for instruction and designing assessment tasks including applications by school and university students as learning and review tools. This book provides case studies and resources that have been field tested with school and university students alike. The findings presented have implications for enriching mathematics learning and making problem solving more accessible and meaningful for students. The theoretical underpinnings of concept mapping and of the studies in the book include Ausubel’s cognitive theory of meaningful learning, constructivist and Vygotskian psychology to name a few. There is evidence particularly from international studies such as PISA and TIMSS and mathematics education research, which suggest that students’ mathematical literacy and problem solving skills can be enhanced through students collaborating and interacting as they work, discuss and communicate mathematically. This book proposes the meta-cognitive strategy of concept mapping as one viable means of promoting, communicating and explicating students’ mathematical thinking and reasoning publicly in a social setting (e.g., mathematics classrooms) as they engage in mathematical dialogues and discussions. Concept Mapping in Mathematics: Research into Practice is of interest to researchers, graduate students, teacher educators and professionals in mathematics education.


Concept Mapping as an Assessment Tool for Conceptual Understanding in Mathematics

Concept Mapping as an Assessment Tool for Conceptual Understanding in Mathematics

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  • Author: Haiyue JIN
  • Publisher: Routledge
  • ISBN: 100058562X
  • Category : Education
  • Languages : en
  • Pages : 181

This book investigates the practicability and effectiveness of the concept map as a tool for assessing students’ conceptual understanding in mathematics. The author first introduces concept mapping and then employs it to investigate students’ conceptual understanding of four different mathematical topics. Alongside traditional scoring methods, she adopts Social Network Analysis, a new technique, to interpret student-constructed concept maps, which reveals fresh insights into the graphic features of the concept map and into how students connect mathematical concepts. By comparing two traditional school tests with the concept map, she examines its concurrent validity and discusses its strengths and drawbacks from the viewpoint of assessing conceptual understanding. With self-designed questionnaires, interviews, and open-ended writing tasks, she also investigates students and teachers’ attitudes toward concept mapping and describes the implications these findings may have for concept mapping’s use in school and for further research on the topic. Scholars and postgraduate students of mathematics education and teachers interested in concept mapping or assessing conceptual understanding in classroom settings will find this book an informative, inspiring, and overall valuable addition to their libraries.


No Bullshit Guide to Linear Algebra

No Bullshit Guide to Linear Algebra

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  • Author: Ivan Savov
  • Publisher:
  • ISBN: 9780992001025
  • Category : MATHEMATICS
  • Languages : en
  • Pages : 596

This textbook covers the material for an undergraduate linear algebra course: vectors, matrices, linear transformations, computational techniques, geometric constructions, and theoretical foundations. The explanations are given in an informal conversational tone. The book also contains 100+ problems and exercises with answers and solutions. A special feature of this textbook is the prerequisites chapter that covers topics from high school math, which are necessary for learning linear algebra. The presence of this chapter makes the book suitable for beginners and the general audience-readers need not be math experts to read this book. Another unique aspect of the book are the applications chapters (Ch 7, 8, and 9) that discuss applications of linear algebra to engineering, computer science, economics, chemistry, machine learning, and even quantum mechanics.


Concept Mapping for Planning and Evaluation

Concept Mapping for Planning and Evaluation

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  • Author: Mary Kane
  • Publisher: SAGE Publications, Incorporated
  • ISBN:
  • Category : Social Science
  • Languages : en
  • Pages : 224

This is a complete guide to the concept mapping methodology and strategies behind using it for a broad range of social scientists - including students, researchers and practitioners.


Concept-Based Mathematics

Concept-Based Mathematics

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  • Author: Jennifer T.H. Wathall
  • Publisher: Corwin Press
  • ISBN: 150633265X
  • Category : Education
  • Languages : en
  • Pages : 307

Give math students the connections between what they learn and how they do math—and suddenly math makes sense If your secondary-school students are fearful of or frustrated by math, it’s time for a new approach. When you teach concepts rather than rote processes, you show students math’s essential elegance, as well as its practicality—and help them discover their own natural mathematical abilities. This book is a road map to retooling how you teach math in a deep, clear, and meaningful way —through a conceptual lens—helping students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and even guides you through an ideal concept-based classroom. Practical tools include: Examples from arithmetic to calculus Inquiry tasks, unit planners, templates, and activities Sample assessments with examples of student work Vignettes from international educators A dedicated companion website with additional resources, including a study guide, templates, exemplars, discussion questions, and other professional development activities. Everyone has the power to understand math. By extending Erickson and Lanning’s work on Concept-Based Curriculum and Instruction specifically to math, this book helps students achieve the deep understanding and skills called for by global standards and be prepared for the 21st century workplace. "Jennifer Wathall’s book is one of the most forward thinking mathematics resources on the market. While highlighting the essential tenets of Concept-Based Curriculum design, her accessible explanations and clear examples show how to move students to deeper conceptual understandings. This book ignites the mathematical mind!" — Lois A. Lanning, Author of Designing Concept-based Curriculum for English-Language Arts, K-12 "Wathall is a master at covering all the bases here; this book is bursting with engaging assessment examples, discussion questions, research, and resources that apply specifically to mathematical topics. Any math teacher or coach would be hard-pressed to read it and not come away with scores of ideas, assessments, and lessons that she could use instantly in the classroom. As an IB Workshop Leader and instructional coach, I want this book handy on a nearby shelf for regular referral – it′s a boon to any educator who wants to bring math to life for students." — Alexis Wiggins, Instructional Coach, IB Workshop Leader and Consultant


Concept Mapping as an Assessment Tool for Conceptual Understanding in Mathematics

Concept Mapping as an Assessment Tool for Conceptual Understanding in Mathematics

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  • Author: Haiyue JIN
  • Publisher: Taylor & Francis
  • ISBN: 1000585611
  • Category : Education
  • Languages : en
  • Pages : 223

This book investigates the practicability and effectiveness of the concept map as a tool for assessing students’ conceptual understanding in mathematics. The author first introduces concept mapping and then employs it to investigate students’ conceptual understanding of four different mathematical topics. Alongside traditional scoring methods, she adopts Social Network Analysis, a new technique, to interpret student-constructed concept maps, which reveals fresh insights into the graphic features of the concept map and into how students connect mathematical concepts. By comparing two traditional school tests with the concept map, she examines its concurrent validity and discusses its strengths and drawbacks from the viewpoint of assessing conceptual understanding. With self-designed questionnaires, interviews, and open-ended writing tasks, she also investigates students and teachers’ attitudes toward concept mapping and describes the implications these findings may have for concept mapping’s use in school and for further research on the topic. Scholars and postgraduate students of mathematics education and teachers interested in concept mapping or assessing conceptual understanding in classroom settings will find this book an informative, inspiring, and overall valuable addition to their libraries.


Teaching Science for Understanding

Teaching Science for Understanding

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  • Author: Joel J. Mintzes
  • Publisher: Academic Press
  • ISBN: 0080879241
  • Category : Psychology
  • Languages : en
  • Pages : 384

Teaching Science for Understanding


Conversations About Group Concept Mapping

Conversations About Group Concept Mapping

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  • Author: Mary Kane
  • Publisher: SAGE Publications
  • ISBN: 1506329179
  • Category : Education
  • Languages : en
  • Pages : 249

Conversations About Group Concept Mapping: Applications, Examples, and Enhancements takes a concise, practice-based approach to group concept mapping. After defining the method, demonstrating how to design a project, and providing guidelines to analyze the results, this book then dives into real research exemplars. Conversations with the researchers are based on in depth interviews that connected method, practice and results. The conversations are from a wide variety of research settings, that include mapping the needs of at-risk African American youth, creating dialogue within a local business community, considering learning needs in the 21st century, and identifying the best ways to support teens receiving Supplemental Social Security Income. The authors reflect on the commonalities between the cases and draw out insights into the overall group concept mapping method from each case.


Concept Mapping, a Technique of Analyzing a Discipline, and Its Use in the Curriculum and Instruction in a Portion of a College Level Mathematics Skills Course

Concept Mapping, a Technique of Analyzing a Discipline, and Its Use in the Curriculum and Instruction in a Portion of a College Level Mathematics Skills Course

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  • Author: Peter Francis Cardamone
  • Publisher:
  • ISBN:
  • Category : Concepts
  • Languages : en
  • Pages : 272