Middle School Students' Reasoning in Nonlinear Proportional Problems in Geometry

AYAN R., Bostan M.

INTERNATIONAL JOURNAL OF SCIENCE AND MATHEMATICS EDUCATION, vol.16, no.3, pp.503-518, 2018 (SSCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.1007/s10763-016-9777-z
  • Journal Name: INTERNATIONAL JOURNAL OF SCIENCE AND MATHEMATICS EDUCATION
  • Journal Indexes: Social Sciences Citation Index (SSCI), Scopus
  • Page Numbers: pp.503-518
  • Keywords: Additive reasoning, Area and volume, Illusion of linearity, Linear and nonlinear proportionality, Proportional reasoning, LINEARITY
  • Middle East Technical University Affiliated: Yes

Abstract

In this study, we investigate sixth, seventh, and eighth grade students' achievement in nonlinear (quadratic or cubic) proportional problems regarding length, area, and volume of enlarged figures. In addition, we examine students' solution strategies for the problems and obstacles that prevent students from answering the problems correctly by using a mixed method research design. A total of 935 middle school students were given a paper-pencil test and 12 of them were interviewed. Findings indicated that achievement of the participants were low and that students used a limited number of strategies for solving the problems. In addition, these strategies were found to have lacked the argument of the linear proportional and nonlinear proportional relationships among length, area, and volume concepts for most of the participants' answers. Moreover, analysis revealed that the confusion of linear proportional and nonlinear proportional relationships and misinterpretation of additive and multiplicative relationships were serious obstacles while solving the nonlinear proportional problems related to the area and volume of enlarged figures.