Mathematics knowledge for understanding and problem solving |
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| Authors: | Ralph T. Putnam |
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| Affiliation: | 1. Department of Biomedical Sciences, University of Sassari, Viale San Pietro 43/c, 07100 Sassari, Italy;2. Department of Physical Therapy, Sackler Faculty of Medicine, Tel Aviv University, Ramat Aviv 69978, Israel;1. Division of Women''s Health, Department of Obstetrics and Gynecology, University of Washington, Box 356460, Seattle, WA 98195, USA;2. Department of Gynecology, VA Puget Sound Medical Center, 1600 South Columbian Way, Seattle, WA 98108, USA;1. Research Center for Human Tissues and Organs Degeneration, Institute of Biomedicine and Biotechnology, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, PR China;2. Department of Orthopaedic and Traumatology, The University of Hong Kong, 21 Sassoon Rd., Pokfulam, Hong Kong 999077, PR China;3. Shenzhen Key Laboratory of Marine Biomedical Materials, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, PR China;4. Shenzhen Key Laboratory for Innovative Technology in Orthopaedic Trauma, The University of Hong Kong-Shenzhen Hospital, Shenzhen 518053, PR China |
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| Abstract: | Two important aspects of transfer in mathematics learning are the application of mathematical knowledge to problem solving and the acquisition of more advanced concepts, both in mathematics and in other domains. This paper discusses general assumptions and themes of current cognitive research on mathematics learning, focusing on issues of the understanding thought to facilitate transfer of mathematical knowledge. Two studies illustrating these themes are presented, one concerning students' understanding of numerical relationships involved in basic addition and subtraction combinations, the other dealing with students' understanding of algebraic expressions and transformations. Implications of these cognitive perspectives for instruction are discussed. |
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