{"title":"Is it a function? Generalizing from single- to multivariable settings","authors":"Allison Dorko","doi":"10.1016/j.jmathb.2023.101036","DOIUrl":null,"url":null,"abstract":"<div><p>Generalizing is a hallmark of mathematical thinking. The term ‘generalization’ is used to mean both the process of generalizing and the product of that process. This paper reports on five calculus students’ generalizing activity and what they generalized about multivariable functions. The study makes two contributions. The first is a fine-grained, actor-oriented characterization of the ways undergraduates generalized. This adds to knowledge in two areas: the use of the actor-oriented perspective and generalization in advanced mathematics. The second contribution is the products of students’ generalizing: what they generalized about what it means for a multivariable relation to represent a function). This adds to the literature about student reasoning regarding multivariable topics by characterizing the powerful ways of reasoning students possess pre-instruction.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-06-01","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/S0732312323000068","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
引用次数: 0
Abstract
Generalizing is a hallmark of mathematical thinking. The term ‘generalization’ is used to mean both the process of generalizing and the product of that process. This paper reports on five calculus students’ generalizing activity and what they generalized about multivariable functions. The study makes two contributions. The first is a fine-grained, actor-oriented characterization of the ways undergraduates generalized. This adds to knowledge in two areas: the use of the actor-oriented perspective and generalization in advanced mathematics. The second contribution is the products of students’ generalizing: what they generalized about what it means for a multivariable relation to represent a function). This adds to the literature about student reasoning regarding multivariable topics by characterizing the powerful ways of reasoning students possess pre-instruction.
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.