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 Effects on Action and Process Views of Functions
This study was conducted to gain understanding about potential influences that learning about quadratic functions has on high school algebra students’ action versus process views of linear functions. Pre/post linear functions tests were given to two classrooms of Algebra II students (N=57) immediately before and immediately after they participated in a multi-day unit on quadratic functions. The purpose was to identify ways that their views of linear functions had changed. Results showed that on some measures, students across both classes shifted their views of linear functions similarly. However, on other measures, the results were different across the classes. These findings suggest that learning about quadratic functions can influence students’ action or process views of linear. Furthermore, the instructional differences between classes provide insights into how to promote those influences that are productive for students’ views.
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- Award ID(s):
- 1651571
- PAR ID:
- 10149097
- Date Published:
- Journal Name:
- Proceedings of the Forty-First Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
- Page Range / eLocation ID:
- 1415-1423
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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