Backward transfer, the relationship between new learning and prior ways of reasoning, and action versus process views of linear functions
Date
2022-02-16
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematical Thinking and Learning
Abstract
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 low-socioeconomic 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.
Description
This is an Accepted Manuscript of an article published by Taylor & Francis in Mathematical Thinking and Learning on 02/16/2022, available online: http://www.tandfonline.com/10.1080/10986065.2022.2037043. This article will be embargoed until 08/16/2023.
Keywords
transfer, functions, linear, quadratic, action view, process view
Citation
Charles Hohensee, Laura Willoughby & Sara Gartland (2022) Backward transfer, the relationship between new learning and prior ways of reasoning, and action versus process views of linear functions, Mathematical Thinking and Learning, DOI: 10.1080/10986065.2022.2037043