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Para outros livros sobre matemática e ensino da matemática procure em:


For other books about mathematics and mathematics education try:

domingo, 19 de abril de 2009

Bringing Out the Algebraic Character of Arithmetic: From Children’s Ideas to Classroom Practic

Analucia Dias Schliemann, David William Carraher, Barbara M. Brizuela,

Lawrence Erlbaum | 2006 | 144 páginas | pdf | 1,37 Mb

Versão draft


Referência em MathEdu

Bringing Out the Algebraic Character of Arithmetic contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic reasoning in the elementary school curriculum and empirical data to support it.
The authors regard Early Algebra not as accelerated instruction but as an approach to existing topics in the early mathematics curriculum that highlights their algebraic character. Each chapter shows young learners engaged in mathematics tasks where there has been a shift away from computations on specific amounts toward thinking about relations and functional dependencies. The authors show how young learners attempt to work with mathematical generalizations before they have learned formal algebraic notation.
The book, suitable as a text in undergraduate or graduate mathematics education courses, includes a CD-ROM with additional text and video footage on how students reason about addition and subtraction as functions; on how students understand multiplication when it is presented as a function; and on how children use notations in algebraic problems involving fractions. These three videopapers (written text with embedded video footage) present relevant discussions that help identify students' mathematical reasoning. The printed text in the book includes transcriptions of the video episodes in the CD-ROM.
Bringing Out the Algebraic Character of Arithmetic is aimed at researchers, practitioners, curriculum developers, policy makers and graduate students across the mathematics education community who wish to understand how young learners deal with algebra before they have learned about algebraic notation.
Contents: Preface: Rethinking Early Mathematics Education. Interpreting Research About Learning Algebra. Part I: Interview Studies. Young Children's Understanding of Equivalences. Can Young Students Solve Equations? Part II: Classroom Studies. Addition Operations as Functions. From Quantities to Ratio, Functions, and Algebraic Notation. On Children's Written Notation to Solve Problems. Discussion.

sábado, 11 de abril de 2009

Geometry and Billiards

(Student Mathematical Library)
Serge Tabachnikov

American Mathematical Society | 2005 | 176 páginas | pdf | 1,1 Mb (link direto - versão draft)

Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. Topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course. Minimum prerequisites are the standard material covered in the first two years of college mathematics (the entire calculus sequence, linear algebra). However, readers should show some mathematical maturity and rely on their mathematical common sense. A unique feature of the book is the coverage of many diverse topics related to billiards, for example, evolutes and involutes of plane curves, the four-vertex theorem, a mathematical theory of rainbows, distribution of first digits in various sequences, Morse theory, the Poincaré recurrence theorem, Hilbert's fourth problem, Poncelet porism, and many others. There are approximately 100 illustrations. The book is suitable for advanced undergraduates, graduate students, and researchers interested in ergodic theory and geometry. This volume has been copublished with the Mathematics Advanced Study Semesters program at Penn State. 

Sam Loyd's Cyclopedia of 5000 Puzzles

Sam Loyd

Corwin Books | 1976 | 384 páginas | zip | 39,95 Mb

on-line: (imagens) (imagens em zip)

pdf - link direto

Sam Loyd was the all time greatest inventor and developer of puzzles. This is considered to be the most fabulous and exciting collection of puzzles ever assembled in one volume. The puzzles come with wonderful illustrations.

quarta-feira, 8 de abril de 2009

The Principles of Mathematics

Bertrand Russell

W. W. Norton & Company | 1996 | 534 páginas |


University press | 1903



segunda-feira, 6 de abril de 2009

Learning from TIMSS: Results of the Third International Mathematics and Science Study, Summary of a Symposium

 (Compass Series)
National Research Council

National Academy Press | 1997 | 56 páginas | 127 kb


Global Perspectives for Local Action: Using TIMSS to Improve U.S. Mathematics and Science Education

Committee on Science Education K-12 and Mathematical Sciences Education Board, National Research Council

National Academies Press | 1999 | 102 páginas | 645 kb


The Third International Mathematics and Science Study (TIMSS) raised the alarm about U.S. mathematics and science education. Most Americans are now aware that U.S. students lag behind their peers in other developed nations. In one state, the legislature reacted by lengthening the school year, assuming that more time on academic content would boost student performance. Some educators have fixed the blame on the mathematics and science curricula typically used in U.S. schools.

Does the problem lie in the curricula, instruction, or the system of support available to teachers? This book presents the first comprehensive analysis of TIMSS study--a half-million students from 15,000 schools around the world. It presents detailed reports on three major aspects of education, including curriculum issues, teaching practices, and school support.

Mathematics and Science Education Around the World

What Can We Learn From The Survey of Mathematics and Science Opportunities (SMSO) and the Third International ... and Science Study (TIMSS)?
(Compass Series)
Mathematical Sciences Education Board and Committee on Science Education K-12, National Research Council

National Academies Press | 1996 | 32 páginas