Thinking Mathematically


Book Description




Thinking Mathematically


Book Description

In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic




Rational Numbers


Book Description

Until recently there had been relatively little integration of programs of research on teaching, learning, curriculum, and assessment. However, in the last few years it has become increasingly apparent that a more unified program of research is needed to acquire an understanding of teaching and learning in schools that will inform curriculum development and assessment. The chapters in this volume represent a first step toward an integration of research paradigms in one clearly specified mathematical domain. Integrating a number of different research perspectives is a complex task, and ways must be found to reduce the complexity without sacrificing the integration. The research discussed in this volume is tied together because it deals with a common content strand. During the last ten years specific content domains have served as focal points for research on the development of mathematical concepts in children. The areas of addition and subtraction, algebra, rational numbers, and geometry are notable examples. Whether a similar organizational structure will prevail for programs of research that integrate the study of teaching, learning, curriculum, and assessment is an open question. The perspectives presented in this volume illustrate the potential for adopting this perspective.




Teaching for Thinking


Book Description

Teaching our children to think and reason mathematically is a challenge, not because students can't learn to think mathematically, but because we must change our own often deeply-rooted teaching habits. This is where instructional routines come in. Their predictable design and repeatable nature support both teachers and students to develop new habits. In Teaching for Thinking, Grace Kelemanik and Amy Lucenta pick up where their first book, Routines for Reasoning, left off. They draw on their years of experience in the classroom and as instructional coaches to examine how educators can make use of routines to make three fundamental shifts in teaching practice: Focus on thinking: Shift attention away from students' answers and toward their thinking and reasoning Step out of the middle: Shift the balance from teacher-student interactions toward student-student interactions Support productive struggle: Help students do the hard thinking work that leads to real learning With three complete new routines, support for designing your own routine, and ideas for using routines in your professional learning as well as in your classroom teaching, Teaching for Thinking will help you build new teaching habits that will support all your students to become and see themselves as capable mathematicians.




All the Mathematics You Missed


Book Description




Learning Guide with Integrated Review Worksheets for College Algebra with Integrated Review


Book Description

This workbook is meant to be used with in tandem with the Integrated Review MyMathLab course, and provides additional practice for both the core course and prerequisite content. The Learning Guide gives students the opportunity to practice the topics, with side-by-side examples and practice problems, and guidance for test preparation. New projects foster conceptual understanding in an active classroom environment. The inclusion of Integrated Review Worksheets provide additional review and practice on the prerequisite topics that are included in the Integrated Review MyMathLab course. The Learning Guide with Integrated Review is available for students in MyMathLab, or as a printed, unbound workbook.




How Humans Learn to Think Mathematically


Book Description

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.




Thinking About Equations


Book Description

An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences. Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including: Approximation and estimation Isolating important variables Generalization and special cases Dimensional analysis and scaling Pictorial methods and graphical solutions Symmetry to simplify equations Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension. Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.




Learning Guide for Thinking Mathematically


Book Description

The new Learning Guide workbook helps students make the most of the Blitzer program. Organized by the text's learning objectives, the Learning Guide provides a note-taking section along with side-by-side examples and practice problems, offering ample opportunity to reinforce skills and concepts. Additionally, questions about the MyMathLab Check Point and MathTalk Videos are tied in to each section. If your students need to review developmental topics to prepare for your course, Integrated Review worksheets can be used in tandem with the Integrated Review MyMathLab course option. Published in an unbound, binder-ready format, the Learning Guide can serve as the foundation for a course notebook, and can be packaged with the textbook and/or a MyMathLab access code.