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Vale, Colleen
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COUNTEREXAMPLES: CHALLENGES FACED BY ELEMENTARY STUDENTS WHEN TESTING A CONJECTURE ABOUT THE RELATIONSHIP BETWEEN PERIMETER AND AREA Widjaja, Wanty; Vale, Colleen
Journal on Mathematics Education Vol 12, No 3 (2021)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.12.3.14526.487-506

Abstract

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.
COUNTEREXAMPLES: CHALLENGES FACED BY ELEMENTARY STUDENTS WHEN TESTING A CONJECTURE ABOUT THE RELATIONSHIP BETWEEN PERIMETER AND AREA Widjaja, Wanty; Vale, Colleen
Journal on Mathematics Education Vol. 12 No. 3 (2021): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

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.
Co-Authors Wanty Widjaja