Acquiring new use of multiplication through classroom teaching: an exploratory study |
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| Authors: | Keiko Hino |
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| Institution: | 1. Department of Sociology, Indiana University, United States;2. Network Science Institute, Indiana University, United States;3. Indianapolis Alzheimer Disease Center, Indiana University, United States;1. Environmental Radioactivity Assessment Team, Korea Atomic Energy Research Institute, Yuseong, Daejeon 305-353, Republic of Korea;2. Department of Physics Education, College of Education, Kongju National University, Kongju 314-701, Republic of Korea;1. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, IL 61801, USA;2. Department of Mechanical Engineering, University of Akron, Akron, OH 44325, USA;3. Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, 104 S. Wright Street, Urbana, IL 61801, USA;1. Department of Orthodontics, Barts and the London School of Medicine and Dentistry, Queen Mary University, London, United Kingdom;2. Division of Dentistry, Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom;1. Department of Mechanical Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 120-749, South Korea;2. Green Chemistry Process Research Division, Korea Research Institute of Chemical Technology, 141 Gajeongro, Yuseong, Daejeon 305-600, South Korea |
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| Abstract: | This article analyzes the process in which pupils acquire new uses of multiplication to measure area. Behaviors of five 4th-grade pupils in a series of lessons on areas were studied in depth by qualitative case-study methodology. Their use of multiplication changed as the lesson evolved, characterized conceptually as “using multiplication as a label,” “using it positively to approach problems which have not been solved before,” and “using it effectively to achieve the goal of measuring areas.” These three phases show the pupils’ understanding of multiplication in the context of measuring areas from a secondary accompaniment to a powerful tool of thinking. The phases observed and the students’ progress between the phases differs noticeably among the pupils. Factors that foster learners’ progress are investigated by comparing their behaviors. |
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| Keywords: | Acquisition of new symbol-use Mathematics classroom Qualitative research |
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