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How Humans Learn To Think Mathematically

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Author : David Tall
Category : Education
Publisher : Cambridge University Press
Published : 2013-09-02
ISBN : 9781107035706
Type : PDF & EPUB
Page : 483
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Reviews book: How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.

Reflect Expect Check Explain Sequences And Behaviour To Enable Mathematical Thinking In The Classroom

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Author : Craig Barton
Category : Education
Publisher : Hachette UK
Published : 2020-02-28
ISBN : 9781915361936
Type : PDF & EPUB
Page : 549
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Reviews book: Some students think mathematically. They have the curiosity to notice relationships, the confidence to ask why, and the knowledge to understand the answer. They are the lucky ones.Many others just "do" maths. They look at a question, think about how to answer it, answer it, and then move on.In this book, Craig Barton, maths teacher and best-selling author of How I wish I'd taught maths, offers an approach to help all our students think mathematically. It requires the careful sequencing of questions and examples, the role of the teacher, and the mathematical behaviour of our students. It has transformed his teaching. Drawing upon research into the Self-Explanation Effect, the Hypercorrection Effect and Variation Theory, together with two years of developing this approach with teachers and students around the world, Craig describes exactly what this looks like in the classroom.But be warned: not everyone agrees. Indeed, it is this very approach that led to Craig being labelled as "the most dangerous and clueless man in maths education". If that is not a recommendation to keep reading, I don't know what is.

Mathematical Thinking

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Author : Masami Isoda
Category : Effective teaching
Publisher : World Scientific
Published : 2012
ISBN : 9789814350839
Type : PDF & EPUB
Page : 318
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Reviews book: Developing mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties developing it in the classrooms. This book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples.

Primary Came Thinking Maths Teachers Guide

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Author : David Johnson
Category : Cognition in children
Publisher : Nelson Thornes
Published : 2003-07
ISBN : 9781903142295
Type : PDF & EPUB
Page : 186
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Reviews book: This folder accompanies the Primary CAME professional development programme. The two-year programme is based on extensive research into how to promote the development of children's mathematical thinking skills. It explores not just what to teach Year 5 and 6 children but how and why.

Advanced Mathematical Thinking

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Author : David Tall
Category : Education
Publisher : Springer Science & Business Media
Published : 2006-04-11
ISBN : 9780306472039
Type : PDF & EPUB
Page : 298
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Reviews book: This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. It is highly appropriate for the college professor in mathematics or the general mathematics educator.

Thinking Mathematically

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Author : John Mason
Category : Mathematics
Publisher : Addison Wesley
Published : 1982
ISBN : STANFORD:36105003836132
Type : PDF & EPUB
Page : 244
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Reviews book: Thinking Mathematically unfolds the processes which lie at the heart of mathematics. It demonstrates how to encourage, develop, and foster the processes which seem to come naturally to mathematicians. In this way, a deep seated awareness of the nature of mathematical thinking can grow. The book is increasingly used to provide students at a tertiary level with some experience of mathematical thinking processes.

Collaborating To Meet Language Challenges In Indigenous Mathematics Classrooms

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Author : Tamsin Meaney
Category : Education
Publisher : Springer Science & Business Media
Published : 2011-10-03
ISBN : 9400719949
Type : PDF & EPUB
Page : 312
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Reviews book: Language can be simultaneously both a support and a hindrance to students’ learning of mathematics. When students have sufficient fluency in the mathematics register so that they can discuss their ideas, they become chiefs who are able to think mathematically. However, learning the mathematics register of an Indigenous language is not a simple exercise and involves many challenges not only for students, but also for their teachers and the wider community. Collaborating to Meet Language Challenges in Indigenous Mathematics Classrooms identifies some of the challenges—political, mathematical, community based, and pedagogical— to the mathematics register, faced by an Indigenous school, in this case a Mäori immersion school. It also details the solutions created by the collaboration of teachers, researchers and community members.

Teaching Mathematics Through Problem Solving In K 12 Classrooms

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Author : Matthew Oldridge
Category : Education
Publisher : Rowman & Littlefield
Published : 2018-10-31
ISBN : 9781475843347
Type : PDF & EPUB
Page : 134
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Reviews book: This book shows how problems can be the vehicle for learning mathematics itself, and presents a comprehensive pedagogy based on classroom discourse, assessment, critical and creative thinking.

Mathematizing Student Thinking

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Author : David Costello
Category : Education
Publisher : Pembroke Publishers Limited
Published : 2022-04-20
ISBN : 9781551389561
Type : PDF & EPUB
Page : 160
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Reviews book: How can you broaden student thinking and help them develop their independence and confidence as problem solvers? Real-life problems are a remarkable tool to stretch student thinking and help them develop a deeper understanding of mathematics and its role in everyday life. Rather than using textbook exercises, the book argues that solving real-world problems promotes flexibility and encourages students to adjust and grow their thinking. It inspires them to consider alternatives and apply math in authentic contexts. You will find practical ways to engage students in critical thinking, develop their independence, and make connections with the world.

Developing Thinking In Geometry

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Author : Sue Johnston-Wilder
Category : Education
Publisher : SAGE
Published : 2005-08-18
ISBN : 9781847878298
Type : PDF & EPUB
Page : 286
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Reviews book: 'Geometry is often given less time in the teaching timetable than other aspects of mathematics. This book encourages practitioners to think about and raise its profile, indeed achieving what its title suggest' - Primary Practice `This creative, innovative and fascinating book/CD package is one you "MUST BUY". All prospective, new and experienced teachers of mathematics can use it to transform their teaching. All readers can use it to reignite their fascination with mathematics' - Professor Sylvia Johnson, Sheffield Hallam University 'This book exudes activity and interactivity. Moreover, it provides challenge in the context of a significant pedagogy, one that is not just present but actually made explicit. It is undoubtedly a book to learn geometry with, but also one to learn to think more deeply about geometry, about its nature and essence, and also about its teaching and learning' - David Pimm Developing Thinking in Geometry enables teachers and their support staff to experience and teach geometric thinking. As well as discussing key teaching principles, the book and accompanying interactive CD include many activities that encourage readers to extend their own learning, and consequently their teaching practices. The book is constructed around the following key themes: - invariance; - language and points of view; - reasoning using invariance; - visualising and representing. These themes draw on teaching principles developed by the team at the Open University's Centre for Mathematics Education which has a 20-year track record of innovative approaches to teaching and learning geometry. This is a 'must have' text for all primary mathematics specialists, secondary and Further Education mathematics teachers and their support staff. Anyone who wishes to create an understanding and enthusiasm for geometry based upon firm research and effective practice, will enjoy this book. This is the course reader for the Open University Course ME627 Developing Geometric Thinking