The Korea Society Of Educational Studies In Mathematics
[ Article ]
Journal of Educational Research in Mathematics - Vol. 30, No. 4, pp.705-732
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 30 Nov 2020
Received 08 Oct 2020 Revised 02 Nov 2020 Accepted 06 Nov 2020
DOI: https://doi.org/10.29275/jerm.2020.11.30.4.705

Secondary Students’ Reasoning about Covarying Quantities in Quadratic Function Problems

Lee, Jin Ah* ; Lee, Soo Jin**,
*Teacher, Hyowon High School, South Korea tozina@naver.com
**Professor, Korea National University of Education, South Korea sjlee@knue.ac.kr

Correspondence to: Professor, Korea National University of Education, South Korea, sjlee@knue.ac.kr

Abstract

The purpose of this study is to investigate how two 7th grade students with different concepts of ratio reason about change in covarying quantities in quadratic function problems and how these differences affect the process of expressing algebraic equations. To this end, we selected two 7th grade students who had no formal instruction in quadratic functions and four clinical interviews (each of which lasted about 90 minutes) were conducted every week from December 2019 to January 2020 with each of them. Our analysis revealed that one student whose conception of ratio was at the level of additive comparison attended to differences in amount of change in quadratic problem situations and interpreted the problems additively by repetitively adding the differences, whereas another student who operated at the interiorized ratio level could perceive the problem situations as the differences in amount of change per unit time, which resulted in their distinctive ways of expressing quadratic functions as equations. We have finalized our study by suggesting an explanatory hypothesis about students’ ratio concepts that seem highly pertinent to their ability to interpret quantitatively and to express equations of quadratic functions.

Keywords:

ratio, internalized ratio, interiorized ratio, quantification, quantitative reasoning, rate of change, quadratic function

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