{"title":"Developing (Pedagogical) content knowledge of constant rate of change: The case of Samantha","authors":"Michael A. Tallman , John Weaver , Taylor Johnson","doi":"10.1016/j.jmathb.2024.101179","DOIUrl":null,"url":null,"abstract":"<div><p>We present the results of a teaching experiment designed to foster a pre-service secondary teacher’s construction of a quantitative scheme for constant rate of change. Although the research participant developed a productive conception of constant rate of change as an interiorized ratio, images of chunky continuous covariation constrained her ability to reason efficiently across a variety of applied contexts. The participant constructed a scheme for constant rate of change at the reflected level of thought, which enabled her to become cognizant of its essential aspects and to appreciate its general applicability. Our results suggest that engaging in reflected abstraction is critical for supporting pre-service teachers’ construction of coherent and refined mathematical schemes.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Behavior","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0732312324000567","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
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Abstract
We present the results of a teaching experiment designed to foster a pre-service secondary teacher’s construction of a quantitative scheme for constant rate of change. Although the research participant developed a productive conception of constant rate of change as an interiorized ratio, images of chunky continuous covariation constrained her ability to reason efficiently across a variety of applied contexts. The participant constructed a scheme for constant rate of change at the reflected level of thought, which enabled her to become cognizant of its essential aspects and to appreciate its general applicability. Our results suggest that engaging in reflected abstraction is critical for supporting pre-service teachers’ construction of coherent and refined mathematical schemes.
期刊介绍：
The Journal of Mathematical Behavior solicits original research on the learning and teaching of mathematics. We are interested especially in basic research, research that aims to clarify, in detail and depth, how mathematical ideas develop in learners. Over three decades, our experience confirms a founding premise of this journal: that mathematical thinking, hence mathematics learning as a social enterprise, is special. It is special because mathematics is special, both logically and psychologically. Logically, through the way that mathematical ideas and methods have been built, refined and organized for centuries across a range of cultures; and psychologically, through the variety of ways people today, in many walks of life, make sense of mathematics, develop it, make it their own.
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