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Flexible thinking and met-befores : impact on learning mathematics
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McGowen, Mercedes A. and Tall, David (2013) Flexible thinking and met-befores : impact on learning mathematics. The Journal of Mathematical Behavior, Volume 32 (Number 3). pp. 527-537. doi:10.1016/j.jmathb.2013.06.004 ISSN 0732-3123.
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Official URL: http://dx.doi.org/10.1016/j.jmathb.2013.06.004
Abstract
In this paper we study the difficulties resulting from changes in meaning of the minus sign, from an operation on numbers, to a sign designating a negative number, to the additive inverse of an algebraic symbol on students in two-year colleges and universities. Analysis of the development of algebra reveals that these successive meanings that the student has met before often become problematic, leading to a fragile knowledge structure that lacks flexibility and leads to confusion and long-term disaffection. The problematic aspects that arise from changes in meaning of the minus sign are identified and the iconic function machine is utilized as a supportive strategy, along with formative assessment to encourage teachers and learners to seek more flexible and effective ways of making sense of increasingly sophisticated mathematics.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Social Sciences > Institute of Education ( -2013) | ||||
Journal or Publication Title: | The Journal of Mathematical Behavior | ||||
Publisher: | Pergamon | ||||
ISSN: | 0732-3123 | ||||
Official Date: | September 2013 | ||||
Dates: |
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Volume: | Volume 32 | ||||
Number: | Number 3 | ||||
Page Range: | pp. 527-537 | ||||
DOI: | 10.1016/j.jmathb.2013.06.004 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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