Reshaping School Mathematics A Philosophy and Framework for Curriculum (1990) / Chapter Skim
Currently Skimming:
Redesign from a Research Perspective
Redesign from a Research Perspective
Pages 27-34
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From page 27... ...
American -textbooks tend to develop ideas very slowly by progressing through a hierarchy of small, straightforward learning tasks. Texts from Asian countries and from the Soviet Union immerse students in much more demanding problem situations from the beginning (Fuson et al., 1988~.
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From page 28... ...
The findings of international comparisons are confirmed by National Assessments of Eclucational Progress (Dossey et al., 1988~. Ail studies consistently show disappointing levels of sTudent performance in areas of mathematical power, unclerstancling, and relevant applications.
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From page 29... ...
, "To understand is to invent." Topics in school should be arranged to exploit intuitions and informal numerical notions that students bring with them to school. Moreover, teaching methocis must adapt to the notion of the child as interpreter and constructor of (possibly wrong)
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From page 30... ...
reveals that many mistakes students make follow predictable patterns. Such consistent but mistaken procedures learning bugs-have a natural origin in the invention of the student: they are intelligent attempts to modify memorized procedures that ore poorly understood.
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From page 31... ...
that students who know more than enough subject matter often fail to solve problems because they do not use their knowlecig0 wisely. They may jump info problems, doggedly pursuing a particular ill-chosen approach to the exclusion of anything else; they may raise profitable alternatives, but fail to pursue them; they may get side-trackecl into focusing on trivia while ignoring the "big picture." Research indicates that such "executive" skills can be learnecO, resulting in significant improvements in problemsolving performance.
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From page 32... ...
In a report of the Thircl National Assessment of Educational Progress (Carpenter et al., 1983) , nearly 30% of children reported the answer of "31 remainder 12" to the problem: An Army bus holds 36 solcliers.
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From page 33... ...
The goal of teaching sense-making via mathematics should be a central concern of all curricular reform. To "see" abstract ideas such as limits, it is helpful to use pictures.
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