**ERIC Number:**EJ909939

**Record Type:**Journal

**Publication Date:**2011

**Pages:**2

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-0148-432X

**EISSN:**N/A

Mathematical Ability Relies on Knowledge, Too

Sweller, John; Clark, Richard E.; Kirschner, Paul A.

American Educator, v34 n4 p34-35 Win 2010-2011

Recent "reform" curricula both ignore the absence of supporting data and completely misunderstand the role of problem solving in cognition. If, the argument goes, teachers are not really teaching people mathematics but rather are teaching them some form of general problem solving, then mathematical content can be reduced in importance. According to this argument, educators can teach students how to solve problems in general, and that will make them good mathematicians able to discover novel solutions irrespective of the content. The authors believe this argument ignores all the empirical evidence about mathematics learning. Although some mathematicians, in the absence of adequate instruction, may have learned to solve mathematics problems by discovering solutions without explicit guidance, this approach has never been the most effective or efficient way to learn mathematics. The alternative route to acquiring problem-solving skill in mathematics derives from the work of a Dutch psychologist, Adriaan de Groot, investigating the source of skill in chess. De Groot's results have been replicated in a variety of educationally relevant fields, including mathematics. They show that long-term memory, a critical component of human cognitive architecture, is not used to store random, isolated facts, but rather to store huge complexes of closely integrated information that results in problem-solving skill. That skill is knowledge domain-specific, not domain-general. The authors point out that domain-specific mathematical problem-solving skills can be taught by emphasizing worked examples of problem-solution strategies. Instead of continuing to waste time devising "reform" curricula based on faulty ideas, the authors suggest that mathematicians and math educators should work together to develop a sound K-12 curriculum that builds students' mathematical knowledge through carefully selected and sequenced worked examples. (Contains 11 endnotes.)

Descriptors: Mathematics Education, Elementary Secondary Education, Problem Solving, Long Term Memory, Educational Change, Mathematics, Mathematics Curriculum, Mathematics Instruction

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**Publication Type:**Journal Articles; Opinion Papers

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A