Computer Algebra Systems CAS as a Tool for Coaxing the Emergence of Reasoning about Equivalence of Algebraic ExpressionsReportar como inadecuado




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International Group for the Psychology of Mathematics Education, Paper presented at the Conference of the International Group for the Psychology of Mathematics Education (29th, Melbourne, Australia, Jul 10-15, 2005), v3 p193-200

Equivalence of algebraic expressions is at the heart of transformational work in algebra. However, we know very little about students' understanding of equivalence. This study is part of a larger project that explores the use of CAS as a didactical tool for promoting both technical and conceptual growth in high school algebra with tasks specially designed by the research team. We report on a class of 10th graders coming to grips with the underlying theoretical ideas related to algebraic equivalence and on the role that the CAS played in the shaping of these newly emerging notions. Two different notions of equivalence of expressions were found to emerge: one was purely numerical and entailed reasoning about expressions for which some but not necessarily all numerical substitutions would yield equal values; the other entailed both numerical and common-form reasoning. Interpretation of CAS outputs (the equality test, in particular) played a role in occasioning discussions that don't normally occur in algebra classrooms and led to clarifying distinctions about equivalence for many. (Contains 3 figures.) [For complete proceedings, see ED496848.]

Descriptors: Grade 10, Algebra, Computer Assisted Instruction, Educational Technology, Mathematics Instruction, Secondary School Mathematics, Mathematical Concepts, Mathematical Logic, Thinking Skills, Comprehension, Graphing Calculators

International Group for the Psychology of Mathematics Education. 35 Aandwind Street, Kirstenhof, Cape Town, 7945, South Africa. Tel: +27-21-715-3559; Fax: +27-88-021-715-3559; e-mail: info[at]igpme.org; Web site: http://igpme.org





Autor: Kieran, Carolyn; Saldanha, Luis

Fuente: https://eric.ed.gov/?q=a&ft=on&ff1=dtySince_1992&pg=4924&id=ED496909







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