Resources for Refining Mathematical Conceptions: Case Studies in Learning About Linear Functions

In this article, I describe the refinement of a conception in the domain of linear functions, the use of the x-intercept in equations of the form y = mx + b, to illustrate the resources used by students to refine a conception. The examples presented show how students refined their use of the x-inter...

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Bibliographic Details
Published in:The Journal of the learning sciences 1998-01, Vol.7 (2), p.209-237
Main Author: Moschkovich, Judith N.
Format: Article
Language:English
Subjects:
Algebra
Case Studies
Classroom observations
Concept Formation
Educational Theories
Geometric lines
Graph theory
Industrial refining
Learning Strategies
Mathematical Concepts
Mathematical Formulas
Mathematics
Mathematics education
Mathematics Instruction
Misconception
Posttests
Pretests
Resource Materials
Secondary Education
Secondary School Mathematics
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Summary:In this article, I describe the refinement of a conception in the domain of linear functions, the use of the x-intercept in equations of the form y = mx + b, to illustrate the resources used by students to refine a conception. The examples presented show how students refined their use of the x-intercept by (a) narrowing the problem contexts in which they applied this conception, (b) making connections between conceptions, (c) using a mathematical procedure, and (d) refining their verbal descriptions of how the graph of a line changes as a result of a change in the equation. The analysis draws on diSessa's (1993) theory of science learning and the recommendations made by Smith, diSessa, and Roschelle (1993) for describing conceptual change. The results extend this prior work from science to mathematics and identify resources used by students that teachers can draw on to support the learning of mathematical concepts.
ISSN:1050-8406
1532-7809
DOI:10.1207/s15327809jls0702_3