Lapses in Mathematical Reasoning
Lapses in Mathematical Reasoning

Author: V. M. Bradis

Publisher: Courier Dover Publications

Published: 2016-10-28

Total Pages: 225

ISBN-13: 0486816575

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Unique, effective system for teaching mathematical reasoning leads students toward clearly false conclusions. Students then analyze problems to correct the errors. Covers arithmetic, algebra, geometry, trigonometry, and approximate computations. 1963 edition.

Classroom-Ready Rich Math Tasks, Grades 4-5
Classroom-Ready Rich Math Tasks, Grades 4-5

Author: Beth McCord Kobett

Publisher: Corwin Press

Published: 2021-04-14

Total Pages: 348

ISBN-13: 1071841068

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Detailed plans for helping elementary students experience deep mathematical learning Do you work tirelessly to make your math lessons meaningful, challenging, accessible, and engaging? Do you spend hours you don’t have searching for, adapting, and creating tasks to provide rich experiences for your students that supplement your mathematics curriculum? Help has arrived! Classroom Ready-Rich Math Tasks for Grades 4-5 details more than 50 research- and standards-aligned, high-cognitive-demand tasks that will have your students doing deep-problem-based learning. These ready-to-implement, engaging tasks connect skills, concepts and practices, while encouraging students to reason, problem-solve, discuss, explore multiple solution pathways, connect multiple representations, and justify their thinking. They help students monitor their own thinking and connect the mathematics they know to new situations. In other words, these tasks allow students to truly do mathematics! Written with a strengths-based lens and an attentiveness to all students, this guide includes: • Complete task-based lessons, referencing mathematics standards and practices, vocabulary, and materials • Downloadable planning tools, student resource pages, and thoughtful questions, and formative assessment prompts • Guidance on preparing, launching, facilitating, and reflecting on each task • Notes on access and equity, focusing on students’ strengths, productive struggle, and distance or alternative learning environments. With concluding guidance on adapting or creating additional rich tasks for your students, this guide will help you give all of your students the deepest, most enriching and engaging mathematics learning experience possible.

Mathematical Reasoning
Mathematical Reasoning

Author: Raymond Nickerson

Publisher: Taylor & Francis

Published: 2011-02-25

Total Pages: 597

ISBN-13: 1136945393

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The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.

Introduction to Reasoning and Proof
Introduction to Reasoning and Proof

Author: Denisse Rubilee Thompson

Publisher: Math Process Standards

Published: 2008

Total Pages: 0

ISBN-13: 9780325017334

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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, reassuring advice and ready-to-use examples to any teacher ready to embrace the Process Standards. In Introduction to Reasoning and Proof, Denisse Thompson and Karren Schultz-Ferrell familiarize you with ways to help students explore their reasoning and support their mathematical thinking. They offer an array of entry points for understanding, planning, and teaching, including strategies for encouraging middle grades students to describe their reasoning about mathematical activities. Thompson and Schultz-Ferrell also provide methods for questioning students about their conclusions and their thought processes in ways that help support classroom-wide learning. The book and accompanying CD-ROM are filled with activities that are modifiable for immediate use with students of all levels customizable to match your specific lessons. In addition, a correlation guide helps you match the math content you teach with the mathematical processes it utilizes. If your students could benefit from more opportunities to develop their reasoning about math concepts, or if you're simply looking for new ways to work the reasoning and proof standards into your curriculum, read, dog-ear, and teach with Introduction to Reasoning and Proof. And if you'd like to learn about any of NCTM's process standards, or if you're looking for new, classroom-tested ways to address them in your math teaching, look no further than Heinemann's Math Process Standards Series. You'll find them explained in the most understandable and practical way: from one teacher to another.