Skip to main content

Research Repository

Advanced Search

All Outputs (65)

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.

The transition to independent graduate studies in mathematics (2006)
Book Chapter
Duffin, J., & Simpson, A. (2006). The transition to independent graduate studies in mathematics. In A. Selden, F. Hitt, G. Harel, & S. Hauk (Eds.), Research in Collegiate Mathematics Education (233-246). Oxford University Press

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.

Pseudo-solutioning (2004)
Journal Article
de Hoyos, M., Gray, E., & Simpson, A. (2004). Pseudo-solutioning. Research in Mathematics Education, 6(1), 101-113

Convergence of sequences and series: interactions between visual reasoning and the learner's beliefs about their own role (2004)
Journal Article
Alcock, L., & Simpson, A. (2004). Convergence of sequences and series: interactions between visual reasoning and the learner's beliefs about their own role. Educational Studies in Mathematics, 57(1), 1-32. https://doi.org/10.1023/b%3Aeduc.0000047051.07646.92

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and se... Read More about Convergence of sequences and series: interactions between visual reasoning and the learner's beliefs about their own role.

The Warwick analysis project: practice and theory (2002)
Book Chapter
Alcock, L., & Simpson, A. (2002). The Warwick analysis project: practice and theory. In D. Holton (Ed.), The Teaching and Learning of Mathematics at the University Level (99-111). Springer: Dordrecht

Definitions: Dealing with Categories Mathematically (2002)
Journal Article
Alcock, L., & Simpson, A. (2002). Definitions: Dealing with Categories Mathematically. For the learning of mathematics, 22(2), 28-34

Explores differences between mathematical definitions and non-mathematical definitions by contrasting three approaches to mathematical reasoning. Examines the consequences of the use of those approaches in a first course in real analysis. Analyzes st... Read More about Definitions: Dealing with Categories Mathematically.

When does a way of working become a methodology? (2000)
Journal Article
Duffin, J., & Simpson, A. (2000). When does a way of working become a methodology?. Journal of Mathematical Behavior, 19(2), 175-188. https://doi.org/10.1016/s0732-3123%2800%2900043-2

We discuss the question of how to determine what are valid methodologies in mathematics education and the problems associated with developing new ways of working into acceptable research methods. We develop the idea of a two-stage validation process... Read More about When does a way of working become a methodology?.

A search for understanding (2000)
Journal Article
Duffin, J., & Simpson, A. (2000). A search for understanding. Journal of Mathematical Behavior, 18(4), 415-427. https://doi.org/10.1016/s0732-3123%2800%2900028-6

We discuss an important breakthrough for us in our search for a technical meaning of “understanding” in mathematics education. In this article, we describe the background to this discovery, the catalyst for the breakthrough, and a concise explanation... Read More about A search for understanding.

Teaching mathematics as a way of life (1999)
Book Chapter
Houston, K., Rogers, P., & Simpson, A. (1999). Teaching mathematics as a way of life. In C. Rust (Ed.), Improving Student Learning through the Disciplines. OCSLD