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COUNTEREXAMPLES: CHALLENGES FACED by ELEMENTARY STUDENTS WHEN TESTING A CONJECTURE about the RELATIONSHIP between PERIMETER and AREA

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journal contribution
posted on 2021-09-01, 00:00 authored by Wanty WidjajaWanty Widjaja, C Vale
One pedagogical approach to challenge a persistent misconception is to get students to test a conjecture whereby they are confronted with the misconception. A common misconception about a ‘direct linear relationship’ between area and perimeter is well-documented. In this study, Year 4-6 students were presented with a conjecture that a rectangle with a larger perimeter will always have a larger area. Eighty-two (82) students’ written responses from three elementary schools in Victoria, Australia were analyzed. The findings revealed that Year 4-6 students could find multiple examples to support the conjecture but they struggled to find counterexamples to refute the conjecture. The findings underscored the importance of developing elementary school students’ capacity to construct counterexamples and recognize that it is sufficient to offer one counterexample in refuting a conjecture about all cases. Implications for ­teaching practice to support investigating and testing a conjecture are discussed.

History

Journal

Journal on Mathematics Education

Volume

12

Pagination

487-506

Location

Palembang, Indonesia.

Open access

  • Yes

ISSN

2087-8885

eISSN

2407-0610

Language

eng

Publication classification

C1 Refereed article in a scholarly journal

Issue

3

Publisher

Indonesian Mathematical Society