The effect of using Transparent Pseudo-Proofs in Linear Algebra

Malek, Aliza; Movshovitz-Hadar, Nitsa

doi:10.1080/14794802.2011.550719

Cited by 24 publications

(3 citation statements)

References 22 publications

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“…We have analyzed the works of different authors to determine the foundation for further research. A. Malek & N. Movshovitz-Hadar [13] [14] studied the effect of using a "Transparent Pseudo-Proofs" (TPP). A Transparent Proof (TP) is a proof of a particular case which is small enough to serve as a concrete example, yet large enough to be considered a non-specific representative of the flow of arguments in the proof of the general case; one can see the formal proof through it since nothing specific to the particular case enters the transparent proof (N. Movshovitz-Hadar [14[14], p.29]).…”

Section: Background Of the Studymentioning

confidence: 99%

Factors Affecting Techniques of Teaching Theorem Proof

Tarasenkova¹,

Akulenko²,

Burda³

et al. 2020

ujer

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Students' mastering the art of proof is one of the most important educational results of teaching Mathematics in the secondary school. The study shows that there are significant challenges, gaps, and weaknesses in the practice of teaching reasoning and proving. The goal of the research is to determine the way of using traditional teaching practices to present reasoning and proving, the way of organizing the review and mastery of the theorem proofs. In addition, the obvious and hidden factors affecting the students' productivity in these activities were identified. To study the problem, a survey that involved 136 Mathematics teachers across Ukraine was carried out. A standard close-ended questionnaire was developed. Factor analysis was used to analyze the results of the survey. The important factors determining the time efficiency when a teacher organizes teaching and learning of a theorem proof, were discovered. The analysis of the factors and numerical loadings of variables forming them, result in the conclusions presented in this paper.

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Section: Background Of the Studymentioning

confidence: 99%

Factors Affecting Techniques of Teaching Theorem Proof

Tarasenkova¹,

Akulenko²,

Burda³

et al. 2020

ujer

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“…At this point, Rina feels like she is having a breakthrough (S14). Next, without being aware of it, she applies the transparent proof technique [34,35] (S16-S18). "A Transparent Proof is a proof of a particular case which is small enough to serve as a concrete example, yet large enough to be considered a non-specific representative of the flow of arguments in the proof of the general case; one can see the formal proof through it since nothing specific to the particular case enters the transparent proof" (p. 29, [34]).…”

mentioning

confidence: 99%

On Reading Mathematical Texts, Question-Asking and Cognitive Load

Lavy

Shriki

2023

Education Sciences

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In this study, we examined aspects relating to the impact of integrating question-asking activities and providing answers to these questions while reading historical mathematical texts on prospective mathematics teachers’ self-reported cognitive load. The research design of the study was quasi-experimental. The study participants included two groups of 20 students each (experimental and control). The experimental group was instructed to ask questions while coping with the texts, whereas the control group received no special instructions. The experimental group participants were asked to think aloud while coping with the texts and audio record themselves. These records were transcribed into written protocols. Both groups had to respond to a self-esteem index questionnaire in which they had to report the level of difficulty they experienced during their attempts to cope with the texts, as an indicator of their sense of cognitive load. This process was repeated at three time points, relating to three different texts. The data were analyzed using quantitative and qualitative methods. Two main observations were obtained: (1) A significant difference was found between the control and the experimental groups regarding the decrease in cognitive load along the time points. Because the only difference between the control and experimental groups was the activity of question-asking, it might be concluded that question-asking affects the reduction in cognitive load. (2) Question-asking supports the assimilation of new information up to a specific limit, depending on the gap between existing knowledge and new information.

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“…We introduce the term generic proving to denote any mathematical or educational activity surrounding a generic proof. The notions of generic example, generic proof, and proof by generic example have been discussed by a number of scholars (e.g., Balacheff, 1988;Mason & Pimm, 1984;Rowland, 1998;Malek & Movshovitz-Hadar, 2011). All acknowledge the role of proof not only in terms of validating the conclusion of a theorem but, just as importantly, as a means to gain insights to why the theorem is true.…”

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confidence: 99%