The basis step in the construction of the principle of mathematical induction based on APOS theory |
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| Affiliation: | 1. Departamento de Matemáticas, Universidad Católica del Norte (UCN), Avenida Angamos 0610, Antofagasta, CP 1270709, Chile;2. Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso (PUCV), Blanco Viel 596, Cerro Barón, Valparaíso, CP 2350026, Chile;1. Department of Mathematics and Application “R. Caccioppoli”, Università Federico II di Napoli, Via Cintia, Monte S. Angelo I-80126, Napoli, Italy;2. Centre for Instructional Psychology, Katholieke Universiteit Leuven, Dekenstraat 2 Box 3773, B-3000 Leuven, Belgium;3. Centre for Instructional Psychology, Katholieke Universiteit Leuven, Dekenstraat 2 Box 3773, B-3000 Leuven, Belgium;1. Faculty of Education in Science and Technology, Technion – Israel Institute of Technology, Haifa 3200003, Israel;2. Faculty of Mathematics, Lewinski College of Education, Tel Aviv 6937808, Israel;3. Department of Mathematics, Technion – Israel Institute of Technology, Haifa 3200003, Israel;1. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, P.O. Box 2014, Richmond, VA 23284, United States;2. Department of Teaching and Learning, School of Education, Virginia Commonwealth University, P.O. Box 842020, Richmond, VA 23284, United States;3. School of Continuing and Professional Studies, University of Virginia, Charlottesville, VA 22904, United States;1. Portland State University, United States;2. Virginia Tech, United States |
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| Abstract: | Using APOS theory as the framework along with a case study from a perspective within the methodological design of APOS theory, this study presents a cognitive model of the Principle of Mathematical Induction (PMI) in higher education. Based on evidence from university classrooms and the result of an initial measurement, the genetic decomposition designed by Dubinsky and Lewin for this concept was reformulated, introducing and defining the basis step in the PMI as a mental process. Using this reformulated genetic decomposition, the productions of four university students are analysed in order to support or refute the constructions it proposes. The results show that the reformulated genetic decomposition is viable and that the inclusion of the basis step as a mental process was seen in the cognitive model of the PMI shown by the students. The instruments used provide activities for a teaching sequence for the PMI at university level. |
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| Keywords: | APOS Genetic decomposition Principle of mathematical induction University education |
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