Calculus Education: Aspects of Order, Continuity, and Reconceptualization
The triad order, continuity, and reconceptualization that appears in the title of this paper refers to a juxtaposition of three aspects of calculus education. Order refers to differentiation followed by integration (DI approach) versus integration followed by differentiation (ID approach) versus Tho...
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| Udgivet i: | URI:https://journals.openedition.org/adsc, |
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| Format: | Article ou chapitre numérique |
| Sprog: | Anglais |
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Annales de Didactique et de Sciences Cognitives
2025
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| Online adgang: | Accès Université d'Orléans et IFPM Accès Université d'Orléans et IFPM |
| Summary: | The triad order, continuity, and reconceptualization that appears in the title of this paper refers to a juxtaposition of three aspects of calculus education. Order refers to differentiation followed by integration (DI approach) versus integration followed by differentiation (ID approach) versus Thompson’s integrated approach (TI approach) which view differentiation and integration inseparable. Continuity refers to the impact of these approaches on student learning as they transition from high school to university. Reconceptualization refers to the effort to reform calculus learning and teaching by reeducating future secondary teachers relearn calculus concepts and ideas through the lens of quantitative reasoning. This is an analytic paper. It begins with an analysis of the cognitive and pedagogical features of the three approaches, DI, ID, and TI, and continues with a discussion of the continuity problem concerning the transition from school mathematics to university mathematics, focusing on the difficulty to reform calculus education in the U.S. To advance this reform, it is necessary to examine in depth the current approaches to calculus education in the U.S., as well as alternative approaches advocated by mathematicians and mathematics education scholars. The analysis of the three approaches, DI, ID, and TI, aims at contributing to this essential examination. As part of this examination, the paper offers a calculus module for prospective secondary teachers who have already taken the “mainstream” calculus sequence. The module, while akin to the TI approach, its development and implementation rest on a separate theoretical framework. |
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