The difficulty of “length × width”: Is a square the unit of measurement? |
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| Authors: | Constance Kamii Judith Kysh |
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| Institution: | a School Of Education Dean's Office, EB 116A, 1530 3rd Ave S, University of Alabama at Birmingham, Birmingham, AL 35294-1250, USA
b San Francisco State University, USA |
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| Abstract: | In individual interviews, 220 students in grades 4, 6, 8, and 9 were given one task, and 72 eighth graders were given three tasks to answer two questions: (a) Is a square the unit of measurement for an area for students in grades 4-8? and (b) Does a square have a space-covering characteristic for students in grade 8? The answers to both questions were No (except for eighth (and ninth) graders in advanced sections of mathematics). The difficulty of “length × width” is explained in light of Piaget's theory, and educational implications are discussed. |
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| Keywords: | Measurement of area Area of a rectangle A square as a unit of measurement Length × width Piaget's theory The infinitely small |
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