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Outputs (65)

Brokering knowledge from laboratory experiments in evidence‐based education: The case of interleaving (2024)
Journal Article
Rowlandson, P., & Simpson, A. (2024). Brokering knowledge from laboratory experiments in evidence‐based education: The case of interleaving. British Educational Research Journal, https://doi.org/10.1002/berj.4037

The turn to ‘evidence‐based education’ in the past three decades favours one type of evidence: experiment. Knowledge brokers ground recommendations for classroom practice on reports of experimental research. This paper distinguishes field and laborat... Read More about Brokering knowledge from laboratory experiments in evidence‐based education: The case of interleaving.

A recipe for disappointment: policy, effect size and the winner’s curse (2022)
Journal Article
Simpson, A. (2023). A recipe for disappointment: policy, effect size and the winner’s curse. Journal of Research on Educational Effectiveness, 16(4), 643-662. https://doi.org/10.1080/19345747.2022.2066588

Evidence-based education aims to support policy makers choosing between potential interventions. This rarely involves considering each in isolation; instead, sets of evidence regarding many potential policy interventions are considered. Filtering a s... Read More about A recipe for disappointment: policy, effect size and the winner’s curse.

Making sense of ‘mastery’: Understandings of a policy term among a sample of teachers in England (2022)
Journal Article
Simpson, A., & Wang, Y. (2023). Making sense of ‘mastery’: Understandings of a policy term among a sample of teachers in England. International Journal of Science and Mathematics Education, 21(2), 581-600. https://doi.org/10.1007/s10763-021-10178-x

This paper considers the term ‘mastery’ as used in mathematics education across different times and locations. A case study from England is offered to show how these pedagogical approaches morph as they move from one territory to another, in the cont... Read More about Making sense of ‘mastery’: Understandings of a policy term among a sample of teachers in England.

How we assess mathematics degrees: the summative assessment diet a decade on (2021)
Journal Article
Iannone, P., & Simpson, A. (2022). How we assess mathematics degrees: the summative assessment diet a decade on. Teaching Mathematics and its Applications: An International Journal of the IMA, 41(1), 22-31. https://doi.org/10.1093/teamat/hrab007

Two previous studies mapping university mathematics students’ summative assessment diet in the UK revealed a clear picture. In general there was a dominance of closed book examinations with a strong relationship to departmental league table position.... Read More about How we assess mathematics degrees: the summative assessment diet a decade on.

Benchmarking a misnomer: A note on “Interpreting effect sizes in education interventions” (2021)
Journal Article
Simpson, A. (2023). Benchmarking a misnomer: A note on “Interpreting effect sizes in education interventions”. Educational Researcher, 52(3), 180-182. https://doi.org/10.3102/0013189x20985448

A recent article calculates new benchmarks from the distribution of effect sizes in a dataset, without accounting for signed values or sampling appropriately. In addition, the focus-narrowing approach it takes does little to address the issues highli... Read More about Benchmarking a misnomer: A note on “Interpreting effect sizes in education interventions”.

Mathematics and Statistics (2019)
Book Chapter
Iannone, P., & Simpson, A. (2019). Mathematics and Statistics. In S. Marshall (Ed.), A Handbook for Teaching and Learning in Higher Education: Enhancing Academic Practice. Routledge

Developing Pre-service Teachers’ Professional Vision with Video Interventions: A Divergent Replication (2019)
Journal Article
Simpson, A., & Vondrová, N. (2019). Developing Pre-service Teachers’ Professional Vision with Video Interventions: A Divergent Replication. Journal of Education for Teaching, 45(5), 567-584. https://doi.org/10.1080/02607476.2019.1674563

Much research on teachers’ professional vision examines development through video interventions. Evidence suggests they change focus towards specifics, subject matter and students and away from the evaluation. This study was designed to examine wheth... Read More about Developing Pre-service Teachers’ Professional Vision with Video Interventions: A Divergent Replication.

Whose Prior is it Anyway? A Note on 'Rigorous Large-Scale Educational RCTs are Often Uninformative' (2019)
Journal Article
Simpson, A. (2019). Whose Prior is it Anyway? A Note on 'Rigorous Large-Scale Educational RCTs are Often Uninformative'. Educational Researcher, 48(6), 382-384. https://doi.org/10.3102/0013189x19855076

A recent paper uses Bayes factors to argue a large minority of rigorous, large-scale education RCTs are ‘uninformative’. The definition of ‘uninformative’ depends on the authors’ hypothesis choices for calculating Bayes factors. These arguably over-a... Read More about Whose Prior is it Anyway? A Note on 'Rigorous Large-Scale Educational RCTs are Often Uninformative'.

Separating arguments from conclusions: The mistaken role of effect size in educational policy research (2019)
Journal Article
Simpson, A. (2019). Separating arguments from conclusions: The mistaken role of effect size in educational policy research. Educational Research and Evaluation, 25(1-2), 99-109. https://doi.org/10.1080/13803611.2019.1617170

Effect size is the basis of much evidence-based education policymaking. In particular, it is assumed to measure the educational effectiveness of interventions. Policy is being driven by the influential work of John Hattie, the Education Endowment Fou... Read More about Separating arguments from conclusions: The mistaken role of effect size in educational policy research.

The relation between mathematics students' discipline-based epistemological beliefs and their summative assessment preferences (2019)
Journal Article
Simpson, A. (2019). The relation between mathematics students' discipline-based epistemological beliefs and their summative assessment preferences. International Journal of Research in Undergraduate Mathematics Education, 5(2), 147-162. https://doi.org/10.1007/s40753-019-00086-5

Existing research posits a relationship between undergraduate mathematics students’ mathematics-related epistemological beliefs and their perceptions of summative assessment. This paper reports a study investigating whether there is indeed such a rel... Read More about The relation between mathematics students' discipline-based epistemological beliefs and their summative assessment preferences.

Unmasking the unasked: correcting the record about assessor masking as an explanation for effect size differences (2018)
Journal Article
Simpson, A. (2018). Unmasking the unasked: correcting the record about assessor masking as an explanation for effect size differences. Educational Research and Evaluation, 24(1-2), 3-12. https://doi.org/10.1080/13803611.2018.1520131

Ainsworth et al.’s paper “Sources of Bias in Outcome Assessment in Randomised Controlled Trials: A Case Study” examines alternative accounts for a large difference in effect size between 2 outcomes in the same intervention evaluation. It argues that... Read More about Unmasking the unasked: correcting the record about assessor masking as an explanation for effect size differences.

Princesses are bigger than Elephants: effect size as a category error in evidence based education (2018)
Journal Article
Simpson, A. (2018). Princesses are bigger than Elephants: effect size as a category error in evidence based education. British Educational Research Journal, 44(5), 897-913. https://doi.org/10.1002/berj.3474

Much of the evidential basis for recent policy decisions is grounded in effect size: the standardised mean difference in outcome scores between a study's intervention and comparison groups. This is interpreted as measuring educational influence, impo... Read More about Princesses are bigger than Elephants: effect size as a category error in evidence based education.

Sources of Shifts in Pre-Service Teachers' Patterns of Attention: The Roles of Teaching Experience and of Observational Experience (2017)
Journal Article
Simpson, A., Vondrová, N., & Žalská, J. (2018). Sources of Shifts in Pre-Service Teachers' Patterns of Attention: The Roles of Teaching Experience and of Observational Experience. Journal of Mathematics Teacher Education, 21(6), 607-630. https://doi.org/10.1007/s10857-017-9370-6

A key requirement of successful initial teacher education is the development of professional vision, which includes shifting attention to features of the situation relevant to the specialized goals of teaching. Existing research hints at the value of... Read More about Sources of Shifts in Pre-Service Teachers' Patterns of Attention: The Roles of Teaching Experience and of Observational Experience.

The misdirection of public policy: comparing and combining standardised effect sizes (2017)
Journal Article
Simpson, A. (2017). The misdirection of public policy: comparing and combining standardised effect sizes. Journal of Education Policy, 32(4), 450-466. https://doi.org/10.1080/02680939.2017.1280183

Increased attention on ‘what works’ in education has led to an emphasis on developing policy from evidence based on comparing and combining a particular statistical summary of intervention studies: the standardised effect size. It is assumed that thi... Read More about The misdirection of public policy: comparing and combining standardised effect sizes.

The Structure of Surveys and the Peril of Panels (2016)
Journal Article
Simpson, A. (2018). The Structure of Surveys and the Peril of Panels. Studies in Higher Education, 43(8), 1334-1347. https://doi.org/10.1080/03075079.2016.1252321

University league tables give the image that there is a single dimension along which institutions can be placed. Most derive rankings from an aggregate score of multiple items, which often include opinion responses which has the potential to introduc... Read More about The Structure of Surveys and the Peril of Panels.

Three concepts or one? Students' understanding of basic limit concepts (2016)
Journal Article
Fernández-Plaza, J., & Simpson, A. (2016). Three concepts or one? Students' understanding of basic limit concepts. Educational Studies in Mathematics, 93(3), 315-332. https://doi.org/10.1007/s10649-016-9707-6

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these... Read More about Three concepts or one? Students' understanding of basic limit concepts.

Interactions between defining, explaining and classifying: The case of increasing and decreasing sequences (2016)
Journal Article
Alcock, L., & Simpson, A. (2017). Interactions between defining, explaining and classifying: The case of increasing and decreasing sequences. Educational Studies in Mathematics, 94(1), 5-19. https://doi.org/10.1007/s10649-016-9709-4

This paper describes a study in which we investigated relationships between defining mathematical concepts — increasing and decreasing infinite sequences — explaining their meanings and classifying consistently with formal definitions. We explored th... Read More about Interactions between defining, explaining and classifying: The case of increasing and decreasing sequences.

University students’ perceptions of summative assessment: the role of context (2016)
Journal Article
Iannone, P., & Simpson, A. (2017). University students’ perceptions of summative assessment: the role of context. Journal of Further and Higher Education, 41(6), 785-801. https://doi.org/10.1080/0309877x.2016.1177172

We report on a mixed-method study that compared students’ perceptions of summative assessment across two distinct disciplines – education and mathematics, at two research-intensive institutions in the UK. The disciplines chosen represent opposing pos... Read More about University students’ perceptions of summative assessment: the role of context.

Teaching and Learning Mathematics and Statistics (2015)
Book Chapter
Iannone, P., & Simpson, A. (2015). Teaching and Learning Mathematics and Statistics. In H. Fry, S. Ketteridge, & S. Marshall (Eds.), A Handbook for Teaching and Learning in Higher Education. Routledge

The Surprising Persistence of Biglan's Classification Scheme (2015)
Journal Article
Simpson, A. (2015). The Surprising Persistence of Biglan's Classification Scheme. Studies in Higher Education, 1520-1531. https://doi.org/10.1080/03075079.2015.1111323

Within higher education systems, different institutions deliver different patterns of disciplines. A simple analysis of the structure of that pattern of disciplines across institutions in one higher education system uncovers a surprising relationship... Read More about The Surprising Persistence of Biglan's Classification Scheme.

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.

A survey of current assessment practices. (2012)
Book Chapter
Ianone, P., & Simpson, A. (2012). A survey of current assessment practices. In P. Iannone, & A. Simpson (Eds.), Mapping university mathematics assessment practices. Norwich: HEA

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.

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

Natural, conflicting and alien (1993)
Journal Article
Duffin, J., & Simpson, A. (1993). Natural, conflicting and alien. Journal of Mathematical Behavior, 12(4), 313-320

The infidel is innocent (1990)
Journal Article
Simpson, A. (1990). The infidel is innocent. Mathematical Intelligencer, 12(3), 43-51