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The Anatomy of a Mathematical Proof: Implications for Analyses with Toulmin's Scheme (2015)
Journal Article
Simpson, A. (2015). The Anatomy of a Mathematical Proof: Implications for Analyses with Toulmin's Scheme. Educational Studies in Mathematics, 90(1), 1-17. https://doi.org/10.1007/s10649-015-9616-0

A model solution to a proof question on an examination is explored and subjected to a detailed analysis in terms of Toulmin’s scheme of argumentation. In doing so, the ways in which the scheme has been variously used in the mathematics education and... Read More about The Anatomy of a Mathematical Proof: Implications for Analyses with Toulmin's Scheme.

Assessment and its outcomes: the influence of disciplines and institutions (2015)
Journal Article
Simpson, A. (2016). Assessment and its outcomes: the influence of disciplines and institutions. Assessment & Evaluation in Higher Education, 41(6), 917-937. https://doi.org/10.1080/02602938.2015.1052369

Existing research provides evidence at the module level of systematic differences in patterns of assessment, marks achieved and distributions of marks between different disciplines. This paper examines those issues at the degree course level, and sug... Read More about Assessment and its outcomes: the influence of disciplines and institutions.

Mathematics lecturers’ views of examinations: tensions and possible resolutions (2014)
Journal Article
Iannone, P., & Simpson, A. (2015). Mathematics lecturers’ views of examinations: tensions and possible resolutions. Teaching Mathematics and its Applications: An International Journal of the IMA, 34(2), 71-82. https://doi.org/10.1093/teamat/hru024

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 article uses a mi... Read More about Mathematics lecturers’ views of examinations: tensions and possible resolutions.

Students’ views of oral performance assessment in mathematics: straddling the ‘assessment of’ and ‘assessment for’ learning divide (2014)
Journal Article
Iannone, P., & Simpson, A. (2015). Students’ views of oral performance assessment in mathematics: straddling the ‘assessment of’ and ‘assessment for’ learning divide. Assessment & Evaluation in Higher Education, 40(7), 971-987. https://doi.org/10.1080/02602938.2014.961124

This paper explores the views of a group of students who took an oral performance assessment in a first-year mathematics module. Such assessments are unusual for most subjects in the UK, but particularly within the generally homogenous assessment die... Read More about Students’ views of oral performance assessment in mathematics: straddling the ‘assessment of’ and ‘assessment for’ learning divide.

Students' preferences in undergraduate mathematics assessment (2014)
Journal Article
Iannone, P., & Simpson, A. (2015). Students' preferences in undergraduate mathematics assessment. Studies in Higher Education, 40(6), 1046-1067. https://doi.org/10.1080/03075079.2013.858683

Existing research into students' preferences for assessment methods has been developed from a restricted sample: in particular, the voice of students in the ‘hard-pure sciences’ has rarely been heard. We conducted a mixed method study to explore math... Read More about Students' preferences in undergraduate mathematics assessment.

Students' perceptions of assessment in undergraduate mathematics (2013)
Journal Article
Iannone, P., & Simpson, A. (2013). Students' perceptions of assessment in undergraduate mathematics. Research in Mathematics Education, 15(1), 17-33. https://doi.org/10.1080/14794802.2012.756634

A consistent message emerges from research on undergraduate students' perceptions of assessment which describes traditional assessment as detrimental to learning. However this literature has not included students in the pure sciences. Mathematics edu... Read More about Students' perceptions of assessment in undergraduate mathematics.

Oral assessment in mathematics: implementation and outcomes (2012)
Journal Article
Iannone, P., & Simpson, A. (2012). Oral assessment in mathematics: implementation and outcomes. Teaching Mathematics and its Applications: An International Journal of the IMA, 31(4), 179-190. https://doi.org/10.1093/teamat/hrs012

In this article, we report the planning and implementation of an oral assessment component in a first-year pure mathematics module of a degree course in mathematics. Our aim was to examine potential barriers to using oral assessments, explore the adv... Read More about Oral assessment in mathematics: implementation and outcomes.

The summative assessment diet: how we assess in mathematics degrees (2011)
Journal Article
Iannone, P., & Simpson, A. (2011). The summative assessment diet: how we assess in mathematics degrees. Teaching Mathematics and its Applications: An International Journal of the IMA, 30(4), 186-196. https://doi.org/10.1093/teamat/hrr017

Much research and many papers on mathematics pedagogy have discussed assessment and, in particular, the need to provide a varied diet of methods by which students are assessed for the award of their degree. In this article, we explore the mix of asse... Read More about The summative assessment diet: how we assess in mathematics degrees.

Classification and concept consistency (2011)
Journal Article
Alcock, L., & Simpson, A. (2011). Classification and concept consistency. Canadian Journal of Science, Mathematics and Technology Education, 11(2), 91-106. https://doi.org/10.1080/14926156.2011.570476

This article investigates the extent to which undergraduates consistently use a single mechanism as a basis for classifying mathematical objects. We argue that the concept image/concept definition distinction focuses on whether students use an accept... Read More about Classification and concept consistency.

Does generating examples aid proof production? (2011)
Journal Article
Iannone, P., Inglis, M., Mejia-Ramos, J., Simpson, A., & Weber, K. (2011). Does generating examples aid proof production?. Educational Studies in Mathematics, 77(1), 1-14. https://doi.org/10.1007/s10649-011-9299-0

Many mathematics education researchers have suggested that asking learners to generate examples of mathematical concepts is an effective way of learning about novel concepts. To date, however, this suggestion has limited empirical support. We asked u... Read More about Does generating examples aid proof production?.

The thinking styles of university mathematics students (2010)
Journal Article
Moutsios-Rentzos, A., & Simpson, A. (2010). The thinking styles of university mathematics students. Acta Didactica Napocensia, 3(4), 1-10

In this paper, we focus on the relationship between studying university mathematics and the ‘thinking styles’ of both undergraduate and postgraduate mathematics students. A crosssectional quantitative study (N = 238) was conducted in a large Greek un... Read More about The thinking styles of university mathematics students.

Conditional inference and advanced mathematical study: Further evidence (2009)
Journal Article
Inglis, M., & Simpson, A. (2009). Conditional inference and advanced mathematical study: Further evidence. Educational Studies in Mathematics, 72(2), 185-198. https://doi.org/10.1007/s10649-009-9187-z

In this paper, we examine the support given for the ‘theory of formal discipline’ by Inglis and Simpson (Educational Studies Mathematics 67:187–204, 2008). This theory, which is widely accepted by mathematicians and curriculum bodies, suggests that t... Read More about Conditional inference and advanced mathematical study: Further evidence.

Conditional inference and advanced mathematical study (2008)
Journal Article
Inglis, M., & Simpson, A. (2008). Conditional inference and advanced mathematical study. Educational Studies in Mathematics, 67(3), 187-204. https://doi.org/10.1007/s10649-007-9098-9

Many mathematicians and curriculum bodies have argued in favour of the theory of formal discipline: that studying advanced mathematics develops one’s ability to reason logically. In this paper we explore this view by directly comparing the inferences... Read More about Conditional inference and advanced mathematical study.

Modelling mathematical argumentation: the importance of qualification (2007)
Journal Article
Inglis, M., Mejia-Ramos, J., & Simpson, A. (2007). Modelling mathematical argumentation: the importance of qualification. Educational Studies in Mathematics, 66(1), 3-21. https://doi.org/10.1007/s10649-006-9059-8

In recent years several mathematics education researchers have attempted to analyse students’ arguments using a restricted form of Toulmin’s [The Uses of Argument, Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report da... Read More about Modelling mathematical argumentation: the importance of qualification.

Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring (2006)
Journal Article
Simpson, A., & Stehlikova, N. (2006). Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring. Educational Studies in Mathematics, 61(3), 347-371. https://doi.org/10.1007/s10649-006-1300-y

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit... Read More about Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring.

Cognitive Empathy and the Transition to Independent Graduate Study in Mathematics (2005)
Journal Article
Duffin, J., & Simpson, A. (2005). Cognitive Empathy and the Transition to Independent Graduate Study in Mathematics. Educational Studies in Mathematics, 58(1), 121-135. https://doi.org/10.1007/s10649-005-2384-5

Thirteen PhD students took part in interviews focussed on the nature of their own learning of mathematics. In analysing these interviews an unexpected category emerged concerning the students' awareness of others as having particular types of learnin... Read More about Cognitive Empathy and the Transition to Independent Graduate Study in Mathematics.

Convergence of Sequences and Series 2: Interactions between Nonvisual Reasoning and the Learner's Beliefs about their own Role (2005)
Journal Article
Alcock, L., & Simpson, A. (2005). Convergence of Sequences and Series 2: Interactions between Nonvisual Reasoning and the Learner's Beliefs about their own Role. Educational Studies in Mathematics, 58(1), 77-100. https://doi.org/10.1007/s10649-005-2813-5

this paper examines the work of students who, when reasoning about real analysis, do so almost exclusively by means of verbal and algebraic reasoining, and tend not to incorporate visual images into their work. It examines the work of students from t... Read More about Convergence of Sequences and Series 2: Interactions between Nonvisual Reasoning and the Learner's Beliefs about their own Role.