A comparison of equality in computer algebra and correctness in mathematical pedagogy (II)

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Abstract

A perennial problem in computer-aided assessment is that “a right answer”, pedagogically speaking, is not the same thing as “a mathematically correct expression”, as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was “the right answer”, typically calculus questions. Here we look at some other cases, notably in linear algebra, where there can be many “right answers”, but still there can be answers that are mathematically right but pedagogically wrong. We reformulate the problem in terms of articulating the sought-after properties, which may include both mathematical equivalence and algebraic form.
Original languageEnglish
Pages (from-to)93-98
Number of pages6
JournalInternational Journal for Technology in Mathematics Education
Volume17
Issue number2
Publication statusPublished - Apr 2010

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Algebra
equality
Linear algebra
equivalence
speaking
evaluation

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title = "A comparison of equality in computer algebra and correctness in mathematical pedagogy (II)",
abstract = "A perennial problem in computer-aided assessment is that “a right answer”, pedagogically speaking, is not the same thing as “a mathematically correct expression”, as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was “the right answer”, typically calculus questions. Here we look at some other cases, notably in linear algebra, where there can be many “right answers”, but still there can be answers that are mathematically right but pedagogically wrong. We reformulate the problem in terms of articulating the sought-after properties, which may include both mathematical equivalence and algebraic form.",
author = "Russell Bradford and Davenport, {James H} and C Sangwin",
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