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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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High School Students’ Use of Technology to Make Sense of Functions Within the Context of Geometric Transformations
Although geometric transformations are functions, few studies have examined students’ reasoning about these two important concepts. The purpose of this study was to examine the various ways students reasoned about functions in the context of preconstructed, dynamic sketches of geometric transformations. We found that, regardless of prior experience, all students were able to reason about important aspects of the notion of function through dragging. Specifically, by using the idea of the semiotic potential of the artifact (the dragging tool), we were able to examine ways in which students with different backgrounds reasoned about functions and how the use of the dragging tool and semiotic mediation contributed to their descriptions of geometric transformations and functions.
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- Award ID(s):
- 0929543
- PAR ID:
- 10221335
- Date Published:
- Journal Name:
- Digital Experiences in Mathematics Education
- ISSN:
- 2199-3246
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s40751-021-00085-9
