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Approaches to Integration Based on Quantitative Reasoning: Adding Up Pieces and Accumulation from Rate
- Source :
-
International Journal of Research in Undergraduate Mathematics Education . Apr 2023 9(1):8-35. - Publication Year :
- 2023
-
Abstract
- Calculus education research on integration is coalescing around the theme that teaching integration based on quantitative reasoning is crucial for robust understanding of and usage of integrals. This paper contributes to this International Journal for Research in Undergraduate Education special issue on the teaching and learning of definite integrals by reviewing the research literature on quantitatively-based approaches to integration, in order to pull together the ideas that are spread across many papers in many outlets. We note that the literature in this area has largely developed along two distinct paradigms, which we call "adding up pieces and accumulation from rate." While they are both based in quantitative reasoning, there are critical differences between them that have important ramifications for teaching and learning integration. We use these two paradigms to organize our review and we use the literature to discuss the meanings, formalizations, foci, reasoning, and modeling in these approaches.
Details
- Language :
- English
- ISSN :
- 2198-9745 and 2198-9753
- Volume :
- 9
- Issue :
- 1
- Database :
- ERIC
- Journal :
- International Journal of Research in Undergraduate Mathematics Education
- Publication Type :
- Academic Journal
- Accession number :
- EJ1377711
- Document Type :
- Journal Articles<br />Information Analyses<br />Reports - Evaluative
- Full Text :
- https://doi.org/10.1007/s40753-022-00203-x