Counterexamples: Challenges Faced by Elementary Students When Testing a Conjecture about the Relationship between Perimeter and Area

Autor/inn/en	Widjaja, Wanty; Vale, Colleen
Titel	Counterexamples: Challenges Faced by Elementary Students When Testing a Conjecture about the Relationship between Perimeter and Area
Quelle	In: Journal on Mathematics Education, 12 (2021) 3, S.487-506 (20 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2087-8885
Schlagwörter	Foreign Countries; Elementary School Students; Geometric Concepts; Misconceptions; Mathematics Skills; Mathematical Logic; Elementary School Mathematics; Mathematics Instruction; Teaching Methods; Logical Thinking; Australia + Suchen Sie Ihr Suchwort? Ausland; Elementare Geometrie; Missverständnis; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Mathematical logics; Mathematische Logik; Elementare Mathematik; Schulmathematik; Mathematics lessons; Mathematikunterricht; Teaching method; Lehrmethode; Unterrichtsmethode; Australien
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. (As Provided).
Anmerkungen	Indonesian Mathematical Society. Jl. Padang Selasa 524, Palembang, South Sumatra 30139, Indonesia. Tel: +618-127-106777; Fax: +627-113-20310; Web site: http://jme.ejournal.unsri.ac.id/index.php/jme
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01