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A constructive and metacognitive teaching path at university level on the Principle of Mathematical Induction: focus on the students' behaviours, productions and awareness
Published October 14, 2021

We present the main results about a teaching/learning path for engineering university students devoted to the Principle of Mathematical Induction (PMI). The path, of constructive and metacognitive type, is aimed at fostering an aware and meaningful learning of PMI and it is based on providing students with a range of explorations and activities, after which the formulation of the statement of the PMI is devolved to the students themselves, organized in working groups. A specific focus is put on the quantification in the statement of PMI to bring students to a deep understanding and a mature view of PMI as a convincing method of proof. The results show the effectiveness of the metacognitive reflections on each phase of the path for what concerns a) students' handling of structural complexity of the PMI, b) students' conceptualization of quantification as a key element for the reification of the proving process by PMI; c) students' perception of the PMI as a convincing method of proof.

Subject Classification: 97B40, 97C70

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Promoting a meaningful learning of double integrals through routes of digital tasks
Published September 13, 2022

Within a wider project aimed at innovating the teaching of mathematics for freshmen, in this study we describe the design and the implementation of two routes of digital tasks aimed at fostering students' approach to double integrals. The tasks are built on a formative assessment frame and classical works on problem solving. They provide facili...tative and response-specific feedback and the possibility to request different hints. In this way, students may be guided to the development of well-connected knowledge, operative and decision-making skills. We investigated the effects of the interaction with the digital tasks on the learning of engineering freshmen, by comparing the behaviours of students who worked with the digital tasks (experimental group, N=19) and students who did not (control group, N=19). We detected that students in the experimental group showed more exibility of thinking and obtained better results in the final exam than students in the control group. The results confirmed the effectiveness of the experimental educational path and offered us interesting indications for further studies.

Subject Classification: 97D40, 97U70, 44A45

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