عنوان

The roles of representation in school mathematics /

0873534956

9780873534956

b783820

The roles of representation in school mathematics /

[Book]

Albert A. Cuoco, 2001 yearbook editor ; Frances R. Curcio, general yearbook editor.

Reston, Va. :

National Council of Teachers of Mathematics,

©2001.

xiii, 282 pages :

illustrations ;

24 cm.

Yearbook ;

2001

Includes bibliographical references.

pt. 1. Roles for representations. Systems of representations and the development of mathematical concepts / Gerald Goldin, Nina Shteingold -- Representation and abstraction in young children's numerical reasoning / Constance Kamii, Lynn Kirkland, Barbara A. Lewis -- Algebra : what are we teaching / Mark Saul -- Attending to transparent features of opaque representations of natural numbers / Rina Zazkis, Karen Gadowsky -- pt. 2. Tools for thinking. The influence of language on mathematical representations / Irene T. Miura -- The role of tools in supporting students' development measuring conceptions / Michelle Stephan [and others] --Promoting the use of diagrams as tools for thinking / Carmel Diezmann, Lyn English -- Constructing a foundation for the fundamental theorem of calculus / Mary J. Schnepp, Ricardo Nemirovsky -- Mapping diagrams : another view of functions / Mark Bridger, Maxine Bridger -- A multirepresentational journey through the law of cosines / Daniel Scher -- Representations of reversal : an exploration of Simpson's paradox / Lawrence Mark Lesser.

pt. 3. Symbols and symbol systems. Presenting and representing : from fractions to rational numbers / Susan J. Lamon -- Representations of patterns and functions : tools for learning / Wendy N. Coulombe, Sarah B. Berenson -- Promoting multiple representations in algebra / Alex Friedlander, Michal Tabach -- From Fibonacci numbers to fractals : recursive patterns and subscript notation / Deborah S. Franzblau, Lisa B. Warner -- Tracing the origins and extensions of Michael's representation / Regina D. Kiczek, Carolyn A. Maher, Robert Speiser -- pt. 4. The role of context. Listen to their pictures : an investigation of children's mathematical drawings / Kristine Reed Woleck -- Using literature to invite mathematical representations / Phyllis Whitin, David Whitin -- Representation in realistic mathematics education / Margaret R. Meyer -- Charting a visual course to the concept of function / Michal Yerushalmy, Beba Shternberg -- Teaching mathematical modeling and the skills of representation / Joshua Paul Abrams.

0

0

Educators and scholars discuss the roles of "invented" and "presented" representations, the kind the child creates versus the kind the teacher gives to students, as an aspect of the internalization of mathematical reasoning. Representations are the devices which people use to help them gain insights, and by examining the interplay between modeling and representation, the roles for representation can be defined.

Roles of representation in school mathematics.

Mathematics-- Study and teaching.

Mental representation.

Mathematics-- Study and teaching-- Psychological aspects.

Mathematics-- Study and teaching.

Mathematics-- Study and teaching.

Mathématiques-- Étude et enseignement.

Mental representation.

Mental representation.

Cuoco, Albert.

Curcio, Frances R.

20201206220452.0

[Book]

Y