“This cannot be”—refutation feedback and its potential affordances for proof comprehension

Pinto, Alon; Cooper, Jason

doi:10.1007/s10649-022-10190-0

Cited by 3 publications

(1 citation statement)

References 22 publications

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“…Moreover, students need to be supported with the process of determining whether the problems on which they validate and verify their algorithms are sufficiently diverse and represent the global set of problems that the algorithm is expected to solve (Moala, 2019;Moala et al, 2019;Tupouniua, 2020a). To this effect, the literature and pedagogy around proofs/refutations and example/counterexample generation may be useful to consider (e.g., Lew & Zazkis, 2019;Pinto & Cooper, 2023;Sinclair et al, 2011).…”

Section: Analysis and Discussion Of Challengementioning

confidence: 99%

What challenges emerge when students engage with algorithmatizing tasks

Tupouniua

2023

JPR

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A critical part of supporting the development of students' algorithmic thinking is understanding the challenges that emerge when students engage with algorithmatizing tasks-tasks that require the creation of an algorithm. Knowledge of these challenges can serve as a basis upon which educators can build effective strategies for enhancing students' algorithmic thinking skills. This paper presents three illustrative cases of emergent challenges evident as students grapple with the process of creating an algorithm. The first challenge highlights discrepancies between the method with which students solve a problem and the algorithm they create, and claim would, when implemented, solve the same problem. The second challenge pertains to the persistence of students' normatively incorrect algorithms, despite going through multiple iterations of testing and revising. Finally, the third challenge concerns issues around the use of test problems for supporting students in their creation of generalized algorithms. These three challenges are discussed using student data (illustrative cases) from three different mathematical algorithmatizing tasks. Suggestions are put forth for addressing some of these challenges, with a particular emphasis on practical pedagogical suggestions for cultivating students' mathematical thinking in the context of algorithmatizing tasks.

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Section: Analysis and Discussion Of Challengementioning

confidence: 99%

What challenges emerge when students engage with algorithmatizing tasks

Tupouniua

2023

JPR

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Teaching practices that support revising definition drafts to adhere to mathematical norms

Vroom,

Alzaga Elizondo,

Barbosa

et al. 2024

Educ Stud Math

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Students’ Verification and Elaboration in Outdoor Mathematics: The Role of Digital Feedback in MathCityMap

Jablonski

2024

Digit Exp Math Educ

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In this article, the role of digital feedback that was provided in an outdoor mathematics education setting is taken into consideration. Using the app MathCityMap (2020) in the context of a mathematics trail, the influence of positive and/or negative feedback is examined in relation to how it influences the processes of verification and elaboration. In this context, special emphasis is placed on the students’ verification and elaboration and their relation to reasoning. In this qualitative study, 19 secondary students were filmed while solving mathematics tasks outdoors without digital support, as well as in indoor settings to enable a comparison. The results show that negative feedback in particular leads to a verification of the result. Still, an elaboration and explanation of why a result was incorrect was not often explicitly formulated by the students. Therefore, the potential of feedback is mainly seen in giving students a clear idea about the correctness of the result and searching for an alternative strategy to solve the task when in an outdoor setting.

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“This cannot be”—refutation feedback and its potential affordances for proof comprehension

Cited by 3 publications

References 22 publications

What challenges emerge when students engage with algorithmatizing tasks

What challenges emerge when students engage with algorithmatizing tasks

Teaching practices that support revising definition drafts to adhere to mathematical norms

Students’ Verification and Elaboration in Outdoor Mathematics: The Role of Digital Feedback in MathCityMap

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