Mathematical problem solving in didactic institutions as a complex system: The case of elementary calculus |
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| Institution: | 1. Department of Liver Transplantation, King Faisal Specialist Hospital and Research Center, Riyadh, Saudi Arabia;2. Department of Medicine, Ipswich Hospital Trust, Heath Rd, Ipswich, UK;3. Perfect Statistics, Hubli, India;4. Multi Organ Transplant, King Fahad Specialist Hospital, Dammam, Saudi Arabia;5. Liver Failure Group, UCL Institute for Liver and Digestive Health, UCL Medical School, Royal Free Campus, London, UK;1. San Diego State University, United States;2. University of Illinois at Urbana-Champaign, United States;3. Temple University, United States;1. Department of Mechanical Engineering, Ray W. Herrick Laboratories, Purdue University, 177 S Russell St, West Lafayette, IN 47907, USA;2. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA |
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| Abstract: | The question of problem-solving activities in didactic institutions is critical in mathematics education for two important reasons. It is a main factor of learning according to Piaget, and it is a means for students to try to align their behaviors to expected institutional references. Mathematical reasoning during problem solving in didactic institutions is studied in the present work as a complex system of interfering constraints. Results tend to show that this system may be understood as being ruled by ternary interactions between three poles: the student, the teacher, and the knowledge itself. Simultaneously, theoretical and pragmatic considerations are focused on problem solving in mathematics: the specific epistemological difficulties of each domain of knowledge to be studied, the computational asymmetry between mathematical concepts and procedures, and the influence of implicit teacher expectations through students' decoding of local “didactic contracts.” |
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