By Albert A. Cuoco, Frances R. Curcio

The focal point of NCTM's 2001 Yearbook is one point of ways scholars research arithmetic specifically, how they discover ways to shape abstractions and construct mathematical representations of phenomena. It explains how scholars come to boost mathematical behavior of brain, or even how they strengthen misunderstandings approximately arithmetic. Discussions at the nature and roles of illustration, using illustration instruments for gaining insights, a variety of image platforms utilized in arithmetic, and the position of context within the interaction among modeling and illustration make this a superb source for academics who intend to make shrewdpermanent judgements approximately content material and pedagogy.

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**Extra info for The Roles of Representation in School Mathematics: 2001 Yearbook (Yearbook National Council of Teachers of Mathematics)**

**Sample text**

Barry followed this reasoning and could do a few more problems like this. But he balked when the reasoning was expressed algebraically. 2 x =123 42 THE ROLES OF REPRESENTATION IN SCHOOL MATHEMATICS This was just to please me. For the longest time, it had no meaning at all for Barry. "). This situation improved with time, and Barry was eventually able to solve simple linear equations with numbers for which he could not use trial and error. An essential part of this process was played by the calculator.

No formal, academic instruction was given at that time in public kindergartens in Geneva. " This request was carefully worded to avoid using terms such as "how many" and "number" that would have suggested quantification. " These requests were made to find out if the child could write numerals when explicitly asked to do so in the absence of objects. The following six types of notations were found (see fig. 1): 1. Global representation of quantity Examples of this type Types Three balls Two balls Five houses are "/1/1" for three 1.

In Learning by Discovery:A CriticalAppraisal, edited by Lee S. Shulman and Evan R. Keislar, pp. 114-28. Chicago: Rand McNally, 1966. LearningMathematics:The Cognitive Science Approach to MathematicsEducation. : Ablex, 1984. , and Carolyn A. Maher. " In MathematicalReasoning: Analogies, Metaphors, and Images, edited by Lyn English, pp. 93-115. : Lawrence Erlbaum Associates, 1997. DeBellis, Valerie M. Interactionsbetween Affect and Cognition duringMathematical Problem Solving. , Rutgers University.