Definite integral registers using infinitesimals |
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| Affiliation: | 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. 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 |
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| Abstract: | I propose a theoretical model of representation registers for definite integral notation. The two registers, adding up pieces (AUP) and multiplicatively-based summation (MBS), are developed from modes of interpreting integral notation identified by S. Jones (2015). In this model, the AUP register affords modeling with definite integral notation, while the MBS register affords sense-making with and evaluation of integrals. These registers are illustrated in the context of a Calculus I class that used an informal infinitesimals approach; in this class differentials such as dx directly represented infinitesimal quantities instead of serving as a reminder of a quantity that existed before a limit was taken. Theoretical implications of extending Duval’s register theory (2006) in this way are also explored. |
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| Keywords: | Register Integral Calculus Infinitesimal Differential Modeling |
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