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Backward transfer is defined as the influence that new learning has on individuals’ prior ways of reasoning. In this article, we report on an exploratory study that examined the influences that quadratic functions instruction in real classrooms had on students’ prior ways of reasoning about linear functions. Two algebra classes and their teachers at two comprehensive high schools served as the participants. Both schools drew from lowsocioeconomic urban populations. The study involved paper-and-pencil assessments about linear functions that were administered before and after a four- to five-week instructional unit on quadratic functions. The teachers were instructed to teach the quadratic functions unit using their regular approach. Qualitative analysis revealed three kinds of backward transfer influences and each influence was related to a shift in how the students reasoned about functions in terms of an action or process view of functions. Additionally, features of the instruction in each class provided plausible explanations for the similarities and differences in backward transfer effects across the two classrooms. These results offer insights into backward transfer, the relationship between prior knowledge and new learning, aspects of reasoning about linear functions, and instructional approaches to teaching functions.
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Backward Transfer and Students’ Performance on Linear Functions Problems
This study examines the phenomenon of backward transfer in the context of high school students learning and reasoning about linear and quadratic functions. Using quantitative methods, this study provides statistical evidence that it is possible to produce intended productive backward transfer effects on students’ prior ways of reasoning about linear functions with quadratic functions instruction that emphasizes quantitative and covariational reasoning. Using qualitative methods, this study characterizes the quality of the backward transfer effects on students’ quantitative and covariational reasoning. The significance of these results is that if intended productive backward transfer is possible, then it represents a new way for mathematics education to be improved.
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- Award ID(s):
- 1651571
- PAR ID:
- 10503463
- Publisher / Repository:
- NCTM
- Date Published:
- Journal Name:
- NCTM Research Conference
- Format(s):
- Medium: X
- Location:
- Washington, DC
- Sponsoring Org:
- National Science Foundation
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