A Hypothesis Framework for Students’ Difficulties with Proof By Contradiction

Quarfoot, David; Rabin, Jeffrey M.

doi:10.1007/s40753-021-00150-z

Cited by 3 publications

(2 citation statements)

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“…One significant challenge in achieving the ideal learning outcomes for the formal definition of limit places an emphasis on students constructing proofs processes engaging with epsilon and delta (Arzarello & Soldano, 2019;Quarfoot & Rabin, 2022;Slavíčková & Vargová, 2023). As an illustration, when students are asked to identify the value of delta for any positive epsilon given, they should be able to determine the required delta for any given epsilon.…”

Section: Introductionmentioning

confidence: 99%

Cognitive load scale in learning formal definition of limit: A rasch model approach

Oktaviyanthi,

Agus,

Garcia

et al. 2024

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Constructing proofs for the limit using the formal definition induces a high cognitive load. Common assessment tools, like cognitive load scales, lack specificity for the concept of limits. This research aims to validate an instrument tailored to assess cognitive load in students focused on the formal definition of limits, addressing the need for diverse strategies in education. The research employs a quantitative survey design with a Rasch model approach, utilizing a data collection instrument in the form of a questionnaire. Subsequently, the data are analyzed by focusing on three aspects: (1) item fit to the Rasch model, (2) unidimensionality, and (3) rating scale. A total of 315 students from three private universities in Banten participated as research respondents. The findings of this study affirm the validity of the cognitive load scale centered on the formal definition of limit, meeting the stringent standards set by Rasch modeling. Additionally, the results of the study provide evidence of the scale’s adherence to the monotonic principle of the Rasch model. These outcomes contribute to a comprehensive understanding of cognitive load in the context of learning formal definition of limit, providing a solid foundation for instructional design and assessment strategies.

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Section: Introductionmentioning

confidence: 99%

Cognitive load scale in learning formal definition of limit: A rasch model approach

Oktaviyanthi,

Agus,

Garcia

et al. 2024

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“…Therefore, it is not surprising that research interest in aspects of mathematical reasoning, such as proof, continues to grow, particularly regarding teaching proof to younger learners in secondary school (Goos & Kaya, 2020). Consequently, students' difficulties when learning different aspects of mathematical proof have been thoroughly explored by prior and recent research (Brunner, 2014;Quarfoot & Rabin, 2021;Weber, 2001).…”

Section: Introductionmentioning

confidence: 99%

Teaching and Learning Proofs of the Pythagorean Theorem during Distance Learning and in the Flipped

Rothe

2022

Kor Soc Edu Stu Mathematics -J Edu Re Mathematics

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This paper presents the findings of two design research cycles on learning and teaching different proofs of the Pythagorean theorem in German secondary schools during distance learning in the first research cycle and a flipped classroom in the second research cycle. The study explores students' difficulties when learning proofs in the different scenarios by analyzing students' proof schemes, occurring error patterns, the students' descriptions of their proof comprehension, and evaluations of the learning scenarios. The findings indicate that typical difficulties occur less in the flipped setting, especially for students with a low or average level of prior knowledge. Further analysis of the evaluation of the learning activities suggests that this can be attributed to the implemented adaptations of the learning scenario when changing it from a distance learning setting to a flipped learning setting, in particular, the opportunity to work collaboratively and direct support the teacher. These results have implications regarding the potential of the flipped classroom as a way for educators to integrate instructional approaches they developed during the COVID-19 pandemic into their in-person teaching in the future.

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