Comparative judgement, proof summaries and proof comprehension

Davies, B. T.; Alcock, Lara; Jones, Ian

doi:10.1007/s10649-020-09984-x

Cited by 15 publications

(24 citation statements)

References 41 publications

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“…1. These proof summaries were a subset of an existing dataset, presented in Davies et al (2020), and were responses to the prompt shown in Fig. 2.…”

Section: Methodsmentioning

confidence: 99%

“…RQ3: How can these features be used to account for the consistency amongst judging mathematicians identified in Davies et al (2020)?…”

Section: Research Questionsmentioning

confidence: 99%

“…We know from Davies et al (2020) that mathematicians' judge proof summaries reliably, and that the resulting scores are likely valid reflections of students' understanding of proof. However, the literature suggests that mathematicians' often vary in their evaluations of purported proofs.…”

Section: Research Questionsmentioning

confidence: 99%

“…Second, Davies et al (2020) sought to develop assessments of comprehension of presented proofs quickly and efficiently, without the need to design and empirically validate a new multiple-choice test for every proof. Building on Mejia-Ramos and colleagues' work, they collected students' written summaries of presented proofs, and applied a comparative judgement (CJ) technique (Jones et al, 2019) to assess the summaries.…”

mentioning

confidence: 99%

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Assessing Proof Reading Comprehension Using Summaries

Davies

Jones

2021

Int. J. Res. Undergrad. Math. Ed.

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In this paper, we explore the role of mathematical proof summaries as a tool for capturing students’ reading comprehension of a given proof. We present an interview study based on mathematicians’ pairwise evaluations of student-produced summaries of a proof demonstrating the uncountability of the open unit interval. We present a thematic analysis, exploring features of mathematicians’ pairwise decision-making and their priorities in evaluating summaries. We argue that the students’ proof summaries shared several properties with traditional modes of proof-writing and were frequently evaluated against similar conventions. We consider the consequences for research and practice with proof comprehension and conclude that proof summaries have the potential to form the basis of a new approach to assessment in this area.

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“…1. These proof summaries were a subset of an existing dataset, presented in Davies et al (2020), and were responses to the prompt shown in Fig. 2.…”

Section: Methodsmentioning

confidence: 99%

“…RQ3: How can these features be used to account for the consistency amongst judging mathematicians identified in Davies et al (2020)?…”

Section: Research Questionsmentioning

confidence: 99%

Section: Research Questionsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Assessing Proof Reading Comprehension Using Summaries

Davies

Jones

2021

Int. J. Res. Undergrad. Math. Ed.

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show abstract

“…As noted above, Mejía-Ramos et al (2021) used CJ to determine mathematicians' views of the explanatory value of a collection of proofs. Other recent work has used CJ to investigate students' comprehension of proofs by judging the quality of their written summaries of proofs (Davies et al, 2020), and to investigate mathematicians' and undergraduate students written conceptions of mathematical proof (Davies et al, 2021).…”

Section: Comparative Judgementmentioning

confidence: 99%

Investigating insight and rigour as separate constructs in mathematical proof

Sangwin¹,

Kinnear²

2021

Preprint

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In this paper we investigate undergraduate mathematics students' conceptions of rigour and insight. We conducted comparative judgement experiments in which students were asked to judge different proofs of the same theorem with five separate criteria: rigour, insight, understanding, simplicity and assessment marks. We predicted, and our experiment found, that rigour is a reliable construct. We predicted that insight is also a reliable construct but asking students to judge on the basis of ``which proof gives you more insight into why a theorem is true'' did not result in a reliable judging scale. Our analysis suggests two distinct dimensions: rigour and marks contribute to one factor whereas simplicity and personal understanding relate to a second factor. We suggest three reasons why insight was related almost equally to both factors. First, while comparative judgement was suitable for assessing some aesthetic criteria it may not be suited to investigating students conceptions of insight. Second, students may not have developed an aesthetic sense in which they appreciate insight in ways which are regularly discussed by mathematics educators. Lastly, insight may not be a coherent and well-defined construct after all.

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Assessing covariation as a form of conceptual understanding through comparative judgement

2022

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This paper focuses on the importance of covariational reasoning within the processes of mathematics teaching and learning. Despite the internationally recognized relevance of covariation, research shows that only a small percentage of students and teachers is able to adopt covariational reasoning and the majority of mathematics curricula do not contain explicit references to covariational skills. In particular, when covariational reasoning manifests as conceptual knowledge, it becomes challenging to assess, and the need for innovative methods of assessment emerges; there is a need for suitable assessment to highlight the characteristics of covariation and capture the various features that characterize conceptual understanding. Comparative judgement (CJ) is an innovative assessment method based on collective expert judgements of students’ work rather than requiring scoring rubrics. Due to its holistic approach, CJ is particularly suitable for assessing complex mathematical competencies, and, as we shall see in this study, it proved to be appropriate for the covariation’s assessment. In details, our study aims to investigate the perception and relevance attributed by mathematics teachers to covariation as a theoretical construct and the way CJ can help in the assessment of covariational reasoning skills underlying a less structured modelling task.

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Comparative judgement, proof summaries and proof comprehension

Cited by 15 publications

References 41 publications

Assessing Proof Reading Comprehension Using Summaries

Assessing Proof Reading Comprehension Using Summaries

Investigating insight and rigour as separate constructs in mathematical proof

Assessing covariation as a form of conceptual understanding through comparative judgement

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