Backward Transfer: An Investigation of the Influence of Quadratic Functions Instruction on Students' Prior Ways of Reasoning About Linear Functions

The transfer of learning has been the subject of much scientific inquiry in the social sciences. However, mathematics education research has given little attention to a subclass called backward transfer, which is when learning about new concepts influences learners' ways of reasoning about prev...

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Bibliographic Details
Published inMathematical thinking and learning Vol. 16; no. 2; pp. 135 - 174
Main Author Hohensee, Charles
Format Journal Article
LanguageEnglish
Published Philadelphia Routledge 03.04.2014
Taylor & Francis Ltd
Subjects
Coding
Cognition & reasoning
Cognitive skills
Concept formation
Data Analysis
Influences
Learning
Mathematical Concepts
Mathematical Logic
Mathematics
Mathematics Education
Mathematics Instruction
Mathematics teaching
Middle School Students
Middle Schools
Middle years
Pretests Posttests
Prior Learning
Quadratic functions (Mathematics)
Qualitative Research
Secondary School Mathematics
Semi Structured Interviews
Teaching methods
Transfer of Training
United States (Southwest)
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Summary:The transfer of learning has been the subject of much scientific inquiry in the social sciences. However, mathematics education research has given little attention to a subclass called backward transfer, which is when learning about new concepts influences learners' ways of reasoning about previously encountered concepts. This study examined when and in what ways a quadratic functions instructional unit productively influenced middle school students' ways of reasoning about linear functions. Results showed that students' ways of reasoning about essential properties of linear functions were productively influenced. Furthermore, conceptual connections were identified linking changes in students' ways of reasoning about linear functions to what they learned during the quadratics unit. These findings suggest that it is possible to productively influence learners' ways of reasoning about previously learned-about concepts in significant respects while teaching them new material and that backward transfer offers promise as a new focus for mathematics education research.
Bibliography:Refereed article. Includes bibliographical references.
Mathematical Thinking and Learning; v.16 n.2 p.135-174; April-June 2014
ISSN:1098-6065
1532-7833
DOI:10.1080/10986065.2014.889503