Concept Mapping in Mathematics
Concept Mapping in Mathematics

Author: Karoline Afamasaga-Fuata'i

Publisher: Springer Science & Business Media

Published: 2009-04-21

Total Pages: 339

ISBN-13: 0387891943

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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 for Planning and Evaluation
Concept Mapping for Planning and Evaluation

Author: Mary Kane

Publisher: SAGE Publications, Incorporated

Published: 2007

Total Pages: 224

ISBN-13:

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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.

No Bullshit Guide to Linear Algebra
No Bullshit Guide to Linear Algebra

Author: Ivan Savov

Publisher:

Published: 2020-10-25

Total Pages: 596

ISBN-13: 9780992001025

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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 as an Assessment Tool for Conceptual Understanding in Mathematics
Concept Mapping as an Assessment Tool for Conceptual Understanding in Mathematics

Author: Haiyue JIN

Publisher: Taylor & Francis

Published: 2022-05-05

Total Pages: 223

ISBN-13: 1000585611

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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.

Visualizing Social Science Research
Visualizing Social Science Research

Author: Johannes Wheeldon

Publisher: SAGE

Published: 2011-07-12

Total Pages: 225

ISBN-13: 145223955X

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This introductory text presents basic principles of social science research through maps, graphs, and diagrams. The authors show how concept maps and mind maps can be used in quantitative, qualitative, and mixed methods research, using student-friendly examples and classroom-based activities. Integrating theory and practice, chapters show how to use these tools to plan research projects, "see" analysis strategies, and assist in the development and writing of research reports.

Concept-Based Mathematics
Concept-Based Mathematics

Author: Jennifer T.H. Wathall

Publisher: Corwin Press

Published: 2016-01-14

Total Pages: 307

ISBN-13: 150633265X

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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

Conceptual Mathematics
Conceptual Mathematics

Author: F. William Lawvere

Publisher: Cambridge University Press

Published: 2009-07-30

Total Pages: 409

ISBN-13: 0521894859

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This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

Learning, Creating, and Using Knowledge
Learning, Creating, and Using Knowledge

Author: Joseph D. Novak

Publisher: Routledge

Published: 2010-02-02

Total Pages: 334

ISBN-13: 1135184461

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This fully revised and updated edition of Learning, Creating, and Using Knowledge recognizes that the future of economic well being in today's knowledge and information society rests upon the effectiveness of schools and corporations to empower their people to be more effective learners and knowledge creators. Novak’s pioneering theory of education presented in the first edition remains viable and useful. This new edition updates his theory for meaningful learning and autonomous knowledge building along with tools to make it operational ─ that is, concept maps, created with the use of CMapTools and the V diagram. The theory is easy to put into practice, since it includes resources to facilitate the process, especially concept maps, now optimised by CMapTools software. CMapTools software is highly intuitive and easy to use. People who have until now been reluctant to use the new technologies in their professional lives are will find this book particularly helpful. Learning, Creating, and Using Knowledge is essential reading for educators at all levels and corporate managers who seek to enhance worker productivity.

Pedagogy for Conceptual Thinking and Meaning Equivalence: Emerging Research and Opportunities
Pedagogy for Conceptual Thinking and Meaning Equivalence: Emerging Research and Opportunities

Author: Etkind, Masha

Publisher: IGI Global

Published: 2019-11-08

Total Pages: 154

ISBN-13: 1799819876

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Research in neuroscience and brain imaging show that exposure of learners to multi-semiotic problems enhance cognitive control of inter-hemispheric attentional processing in the lateral brain and increase higher-order thinking. Multi-semiotic representations of conceptual meaning are found in most knowledge domains where issues of quantity, structure, space, and change play important roles, including applied sciences and social science. Teaching courses in History and Theory of Architecture to young architecture students with pedagogy for conceptual thinking allows them to connect analysis of historic artifact, identify pattern of design ideas extracted from the precedent, and transfer concepts of good design into their creative design process. Pedagogy for Conceptual Thinking and Meaning Equivalence: Emerging Research and Opportunities is a critical scholarly resource that demonstrates an instructional and assessment methodology that enhances higher-order thinking, deepens comprehension of conceptual content, and improves learning outcomes. Based on the rich literature on word meaning and concept formation in linguistics and semiotics, and in developmental and cognitive psychology, it shows how independent studies in these disciplines converge on the necessary clues for constructing a procedure for the demonstration of mastery of knowledge with equivalence-of-meaning across multiple representations. Featuring a wide range of topics such as curriculum design, learning outcomes, and STEM education, this book is essential for curriculum developers, instructional designers, teachers, administrators, education professionals, academicians, policymakers, and researchers.