Math Exchanges


Book Description

Traditionally, small-group math instruction has been used as a format for reaching children who struggle to understand. Math coach Kassia Omohundro Wedekind uses small-group instruction as the centerpiece of her math workshop approach, engaging all students in rigorous "math exchanges." The key characteristics of these mathematical conversations are that they are: 1) short, focused sessions that bring all mathematical minds together, 2) responsive to the needs of the specific group of mathematicians, and 3) designed for meaningful, guided reflection. As in reading and writing workshop, students in math workshop become self-directed and independent while participating in a classroom community of learners. Through the math exchanges, students focus on number sense and the big ideas of mathematics. Teachers guide the conversations with small groups of students, mediating talk and thinking as students share problem-solving strategies, discuss how math works, and move toward more effective and efficient approaches and greater mathematical understanding. Although grounded in theory and research, Math Exchanges: Guiding Young Mathematicians in Small Group Meetings is written for practicing teachers and answers such questions as the following: How can I use a math workshop approach and follow a certain textbook or set of standards? How should I form small groups? How often should I meet with small groups? What should I focus on in small groups? How can I tell if my groups are making progress? What do small-group math exchanges look like, sound like, and feel like?




Counterexamples in Analysis


Book Description

These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.




A Path to Combinatorics for Undergraduates


Book Description

This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.




Concrete Mathematics


Book Description

This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.




Calculus


Book Description

Application-oriented introduction relates the subject as closely as possible to science with explorations of the derivative; differentiation and integration of the powers of x; theorems on differentiation, antidifferentiation; the chain rule; trigonometric functions; more. Examples. 1967 edition.




Math Sense


Book Description

How is that you can walk into a classroom and gain an overall sense of the quality of math instruction taking place there? What contributes to getting that sense? In Math Sense, wuthor Christine Moynihan explores some of the components that comprise the look, sound, and feel of effective teaching and learning. Does the landscape of the classroom feature such items as student work samples, a math literature collection, and a number line? Do the lessons include wait time, checks for understanding, and written feedback? Do you feel a spirit of collaboration, risk taking, and a sense of pride? In Math Sense, Moynihan provides a series of self-assessment rubrics to help you identify the earmarks of a vibrant mathematics community that will help inform and refine your practice. This practical guide offers a road map for taking stock of your teaching and building a stronger mathematics classroom environment for you and your students.




Becoming the Math Teacher You Wish You'd Had


Book Description

Ask mathematicians to describe mathematics and they' ll use words like playful, beautiful, and creative. Pose the same question to students and many will use words like boring, useless, and even humiliating. Becoming the Math Teacher You Wish You' d Had, author Tracy Zager helps teachers close this gap by making math class more like mathematics. Zager has spent years working with highly skilled math teachers in a diverse range of settings and grades and has compiled those' ideas from these vibrant classrooms into' this game-changing book. Inside you' ll find: ' How to Teach Student-Centered Mathematics:' Zager outlines a problem-solving approach to mathematics for elementary and middle school educators looking for new ways to inspire student learning Big Ideas, Practical Application:' This math book contains dozens of practical and accessible teaching techniques that focus on fundamental math concepts, including strategies that simulate connection of big ideas; rich tasks that encourage students to wonder, generalize, hypothesize, and persevere; and routines to teach students how to collaborate Key Topics for Elementary and Middle School Teachers:' Becoming the Math Teacher You Wish You' d Had' offers fresh perspectives on common challenges, from formative assessment to classroom management for elementary and middle school teachers No matter what level of math class you teach, Zager will coach you along chapter by chapter. All teachers can move towards increasingly authentic and delightful mathematics teaching and learning. This important book helps develop instructional techniques that will make the math classes we teach so much better than the math classes we took.




Implementing Guided Math: Tools for Educational Leaders


Book Description

Support the implementation of the Guided Math framework with this user-friendly professional guide written by Guided Math author, Laney Sammons. This resource provides school leaders (coaches, principals, curriculum directors, teacher leaders, etc.) with user-friendly strategies for supporting teachers as they embark on teaching components of the Guided Math framework in their classrooms. Highlights include how to use the professional learning community model effectively when implementing Guided Math, tips for creating a strategic plan for improving students’ mathematics achievement, sample implementation models, sample assessments, and planning and implementation tools.




Meaningful Small Groups in Math, Grades K-5


Book Description

Target the Math...Support the Students...Provide Access for All The need for focused small group math instruction has never been greater. Today’s education landscape is fraught with learning divides unlike anything we’ve faced in recent years. We need new ways of teaching students who have remarkably varying levels of understanding and vastly different needs. Meaningful Small Groups in Math, Grades K-5 offers practical guidance on how to meet the diverse needs of today’s students. Written for K-5 classroom teachers, math interventionists and instructional coaches, this user-friendly, accessible book provides guidance on the necessary components of small group instruction in math, trajectories for small-group instruction on specific concepts, and practical steps for getting started. Readers will find Checklists and templates for implementing small group, sample lessons in the major content domains Emphasis on flexible groups Intervention and extension ideas for differentiating learning A chapter devoted to developing small-group programs across a school or organization Small group instruction in mathematics has not been as well-developed as its counterpart in the reading world. In K-5 math classrooms, small-group instruction has typically been reduced to learning centers and rotation stations, with little emphasis on differentiated, small-group, teacher-facilitated learning. To meet the needs of today’s students, a more focused approach is needed.




Guided Math Conferences


Book Description

This professional resource provides teachers with suggestions, tips, management, and implementation methods for using effective conferencing with students within the Guided Math framework. Templates, planning tools, and other resources are provided to help teachers stay organized and effective while conferring.