An assessment model for proof comprehension in undergraduate mathematics

Mejía-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron

doi:10.1007/s10649-011-9349-7

Cited by 97 publications

(58 citation statements)

References 21 publications

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“…After reaching the BHolisticstructural^level, students become able not only to reconstruct previously taught proofs, but are also able to plan and construct their own proofs. In addition, students become aware of the hierarchical structure of the theorems they use and understand the modular structure of their proofs (Mejia-Ramos et al, 2012). Figure 2 illustrates our overall framework.…”

Section: Three Levels Of Understanding Of the Structure Of Deductive mentioning

confidence: 99%

Students’ understanding of the structure of deductive proof

2016

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While proof is central to mathematics, difficulties in the teaching and learning of proof are well-recognised internationally. Within the research literature, a number of theoretical frameworks relating to the teaching of different aspects of proof and proving are evident. In our work, we are focusing on secondary school students learning the structure of deductive proofs and, in this paper, we propose a theoretical framework based on this aspect of proof education. In our framework, we capture students' understanding of the structure of deductive proofs in terms of three levels of increasing sophistication: Prestructural, Partial-structural, and Holistic-structural, with the Partial-structural level further divided into two sub-levels: Elemental and Relational. In this paper, we apply the framework to data from our classroom research in which secondary school students (aged 14) tackled a series of lessons that provided an introduction to proof problems involving congruent triangles. Using data from the transcribed lessons, we focus in particular on students who displayed the tendency to accept a proof that contained logical circularity. From the perspective of our framework, we illustrate what we argue are two independent aspects of Relational understanding of the Partial-structural level, those of universal instantiation and hypothetical syllogism, and contend that accepting logical circularity can be an indicator of lack of understanding of syllogism. These findings can inform how teaching approaches might be improved so that students develop a more secure understanding of deductive proofs and proving in geometry.

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Section: Three Levels Of Understanding Of the Structure Of Deductive mentioning

confidence: 99%

Students’ understanding of the structure of deductive proof

2016

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“…Thus the issue may be to look at the design of written examinations and see if questions can be designed to differentiate on the basis of abilities mathematicians value, without leaving weaker students with discouragingly low marks. One might, for example, look to questions that test comprehension of proofs rather than reproduction or construction (Mejia-Ramos, Fuller, Weber, Rhoads and Samkoff, 2012) or consider the wide range of different examination questions and dimensions on which they can vary discussed in Griffiths and McLone (1984). Such approaches may enable us to relieve the understanding-competence tension, while maintaining the pattern of assessment peculiar to mathematics.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Mathematics lecturers' views of examinations: tensions and possible resolutions

Iannone

Simpson

2014

Teaching Mathematics and its Applications

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract: If assessment drives learning and the closed book examination dominates the pattern of assessment for undergraduate mathematics (as it does in the UK), lecturers need to ensure that examinations reflect the learning they value. This paper uses a mixed method approach to explore lecturers' views of the closed book examination in relation to other assessment methods, their preferences for different types of methods and the extent to which they discriminate between stronger and weaker students. A survey of staff views confirms the dominance of closed book examinations, but an accompanying interview study shows hidden complexity to this view. In particular a tension between the potential and the reality of examinations is uncovered and suggestions are made for resolving that tension.

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“…yang tidak lengkap. Hal tersebut karena pemahaman bukti yang bersifat lokal maupun pemahaman bukti yang bersifat holistik banyak yang tidak tepat dilakukan kedua subjek ini (Mejia-Ramos et al, 2012). Hal itu terjadi karena kedua subjek ini bernalar secara induktif dan mengalami kesulitan berpikir deduktif (Recio & Godino, 2001).…”

Section: Hasil Dan Pembahasanunclassified

Karakteristik Pemahaman Mahasiswa dalam Mengonstruksi Bukti Matematis

Syamsuri

Santosa

2017

JRPM

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The teaching and learning process in the mathematics undergraduate program emphasizes on the use of an axiomatic system and formal deduction. In this process, the students learn continuously about mathematical evidence, which can be referred to as the ability to build arguments based on their mathematical understanding. This article aims at describing the characteristics of students' comprehension in constructing a mathematical evidence. A qualitative approach is applied in this study, which involves third year students of Mathematics Education Department at the state university in Banten. Interviews are conducted to find out and clarify how the students construct and build mathematical evidence. The result shows that the students' mathematical proof of comprehension can be classified into three types: holistic-global, partial-global, and partial-local. It is expected that the result of the study can be used as a source of consideration in determining appropriate learning strategies that can overcome students' difficulties in constructing a mathematical evidence. Keywords:Proof of comprehension; Holistic-global; Partial-global; partiallocal. PENDAHULUANPembelajaran matematika di perguruan tinggi menekankan pada sistem aksiomatik dan deduksi-formal. Pada pembelajaran matematika tingkat lanjut ini, para mahasiswa banyak mempelajari bukti-bukti matematis. Bukti matematis tersebut terdapat dalam buku-buku teks maupun disampaikan oleh para dosen di depan kelas saat pembelajaran. Oleh karena itu, diperlukan pemahaman matematis agar para mahasiswa tersebut mampu menguasai materi matematika pada tingkat ini.Pembelajaran tentang pembuktian matematis di perguruan tinggi telah banyak dikaji oleh para peneliti

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An assessment model for proof comprehension in undergraduate mathematics

Cited by 97 publications

References 21 publications

Students’ understanding of the structure of deductive proof

Students’ understanding of the structure of deductive proof

Mathematics lecturers' views of examinations: tensions and possible resolutions

Karakteristik Pemahaman Mahasiswa dalam Mengonstruksi Bukti Matematis

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