widjaja-counterexamples-2021.pdf (511.7 kB)
COUNTEREXAMPLES: CHALLENGES FACED by ELEMENTARY STUDENTS WHEN TESTING A CONJECTURE about the RELATIONSHIP between PERIMETER and AREA
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 EducationVolume
12Issue
3Pagination
487 - 506Publisher
Indonesian Mathematical SocietyLocation
Palembang, Indonesia.Publisher DOI
ISSN
2087-8885eISSN
2407-0610Language
engPublication classification
C1 Refereed article in a scholarly journalUsage metrics
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