Mathematics Education Centre

Loughborough University

Loughborough

Leicestershire

LE11 3TU

+44 (0) 1509 228213

m.j.inglis@lboro.ac.uk

Mathematics Education Centre

Loughborough University

Loughborough

Leicestershire

LE11 3TU

+44 (0) 1509 228213

m.j.inglis@lboro.ac.uk

I am a professor in the Mathematics Education Centre at Loughborough University, and an honorary research fellow in the Learning Sciences Research Institute at the University of Nottingham. I currently serve on the Editorial Boards of *Educational Studies in Mathematics*, *Research in Mathematics Education* and the *International Journal of Research in Undergraduate Mathematics Education*. From 2010-2015 I was a Royal Society Worshipful Company of Actuaries Research Fellow, in 2014 I was awarded the Annie and John Selden Prize by the Mathematical Association of America, and in 2017 I was named the *Times Higher Education* Outstanding Research Supervisor of the Year.

In 2014 I appeared on Radio 4's *A History of Ideas* programme, talking about my research on mathematicians' perceptions of mathematical beauty. Earlier in the same year the Royal Society recorded a Café Scientifique talk I gave about the relationship between mathematical study and reasoning development. In 2017 I appeared on the Math Ed Podcast talking about the book Nina Attridge and I wrote on reasoning development.

The main focus of my research is on mathematical thinking and reasoning. Some questions I am currently interested in include:

- How do numerical symbols acquire their meaning? (Main collaborators: Nina Attridge, Camilla Gilmore & Theresa Wege).
- What are mathematical explanations, how are they generated, and how do they effect learning? (Main collaborator: Pablo Mejia-Ramos).
- How do students and mathematicians read and evaluate mathematics? (Main collaborators: Andrew Aberdein, Lara Alcock & Beth Woollacott).
- How does pain influence mathematical cognition? (Main collaborators: Nina Attridge & Jayne Pickering).

Depending on the number of students I'm currently working with, I may be able to supervise PhD research degrees in these or related areas. Please email me to discuss possibilities. Details about PhD study in the Mathematics Education Centre at Loughborough is available here.

Jump to: journal papers, book chapters, conference papers, book reviews, commissioned reports, short reports, other or links.

Gilmore, C., Göbel, S., & Inglis, M. (2018). *An Introduction to Mathematical Cognition.* Abingdon: Routledge.

Aberdein, A. & Inglis, M. (Eds.) (in press). *Advances in Experimental Philosophy of Logic and Mathematics.* London: Bloomsbury.

Inglis, M. & Attridge, N. (2016). *Does Mathematical Study Develop Logical Thinking? Testing the Theory of Formal Discipline.* London: World Scientific. [publisher's page] [errata].

Dawkins, P. C., Inglis, M. & Wasserman, N. (in press). The use(s) of 'is' in mathematics. *Educational Studies in Mathematics*.

Foster, C. & Inglis, M. (in press). Mathematics teacher professional journals: What topics appear and how has this changed over time? *International Journal of Science and Mathematics Education*. [open access version].

Bennett, A., Inglis, M., & Gilmore, C. (in press). The cost of multiple representations: Learning number symbols with abstract and concrete representations. *Journal of Educational Psychology*. [preprint, 704k].

Inglis, M. & Foster, C. (2018). Five decades of mathematics education research. *Journal for Research in Mathematics Education, 49*, 462-500. [preprint, 1.4MB].

Norris, J. E., Clayton, S., Gilmore, C., Inglis, M., & Castronovo, J. (in press). The measurement of Approximate Number System acuity across the lifespan is compromised by congruency effects. *Quarterly Journal of Experimental Psychology*. [journal version].

Panse, A., Alcock, L., & Inglis, M. (2018). Reading proofs for validation and comprehension: An expert-novice eye-movement study. *International Journal for Research in Undergraduate Mathematics Education, 4,* 357-375. [preprint, 770k] [journal version].

Clayton, S., Inglis, M., & Gilmore, C. (2018). Developmental differences in approaches to nonsymbolic comparison tasks. *Quarterly Journal of Experimental Psychology*. [preprint, 1.5MB] [journal version].

Inglis, M., Batchelor, S., Gilmore, C., Watson, D. (2017). Is the ANS linked to mathematics performance? *Behavioral and Brain Sciences, 40*, 26-27. [preprint, 349k] [journal version].

Roy, S., Inglis, M., & Alcock, L. (2017). Multimedia resources designed to support learning from written proofs: An eye-movement study. *Educational Studies in Mathematics, 96*, 249-266. [open access version].

Foster, C. & Inglis, M. (2017). Teachers' appraisals of adjectives relating to mathematics tasks. *Educational Studies in Mathematics, 95*, 283-301. [open access version].

Wainwright, E., Attridge, N., Wainwright, D., Alcock, L., & Inglis, M. (2017). Support with caveats: Advocates' views of the Theory of Formal Discipline as a reason for the study of advanced mathematics. *Research in Mathematics Education, 19*, 20-41. [journal version].

Gilmore, C., Cragg, L., Hogan, G., & Inglis, M. (2016). Congruency effects in dot comparison tasks: Convex hull is more important than dot area. *Journal of Cognitive Psychology, 28,* 923-931. [journal version].

Jones, I., Wheadon, C., Humphries, S., & Inglis, M. (2016). Fifty years of A-level mathematics: Have standards changed? *British Educational Research Journal, 42*, 543-560. [preprint, 1.6 MB] [journal version].

Bisson, M.-J., Gilmore, C., Inglis, M. & Jones, I. (2016). Measuring conceptual understanding using comparative judgement. *International Journal of Research in Undergraduate Mathematics Education, 2,* 141-164. [preprint, 1MB] [journal version].

Alcock, L., Ansari, D., Batchelor, S., Bisson, M.-J., De Smedt, B., Gilmore, C., Goebel, S. M., Hannula-Sormunen, M., Hodgen, J., Inglis, M., Jones, I., Mazzocco, M., McNeil, N., Schneider, M., Simms, V., & Weber, K. (2016). Challenges in mathematical cognition: A collaboratively-derived research agenda. *Journal of Numerical Cognition, 2*, 20-41. [open access version]. Commentaries by: Daniel Berch, Kerry Lee, Steve Chinn.

Batchelor, S., Inglis, M., & Gilmore, C. (2015). Spontaneous focusing on numerosity and the arithmetic advantage. *Learning and Instruction. 40*, 79-88. [open access version].

Clayton, S., Gilmore, C., & Inglis, M. (2015). Dot comparison stimuli are not all alike: The effect of different visual controls on ANS measurement. *Acta Psychologica, 161*, 177-184. [preprint, 1.1MB] [journal version].

Van Dooren, W. & Inglis, M. (2015). Inhibitory control in mathematical thinking, learning and problem solving: A survey. *ZDM Mathematics Education, 47*, 713-721. [journal version].

Attridge, N. & Inglis, M. (2015). Increasing cognitive inhibition with a difficult prior task: Implications for mathematical thinking. *ZDM Mathematics Education, 47*, 723-734. [preprint, 359k] [journal version].

Jones, I. & Inglis, M. (2015). The problem of assessing problem solving: Can comparative judgement help? *Educational Studies in Mathematics, 89*, 337-355. [preprint, 6.9MB] [journal version].

Attridge, N., Doritou, M., & Inglis, M. (2015). The development of reasoning skills during compulsory 16 to 18 mathematics education. *Research in Mathematics Education, 17*, 20-37. [journal version].

Alcock, L., Hodds, M., Roy, S., & Inglis, M. (2015). Investigating and improving undergraduate proof comprehension. *Notices of the American Mathematical Society, 62*, 742-752. [open access version, 7.7MB].

Inglis, M. & Aberdein, A. (2015). Beauty is not simplicity: An analysis of mathematicians' proof appraisals. *Philosophia Mathematica, 23*, 87-109. [preprint, 484k] [journal version].

Attridge, N. & Inglis, M. (2014). Intelligence and negation biases on the Conditional Inference Task: A dual-processes analysis. *Thinking and Reasoning, 20*, 454-471. [preprint, 213k] [journal version].

Alcock, L., Attridge, N., Kenny, S. & Inglis, M. (2014). Achievement and behaviour in undergraduate mathematics: Personality is a better predictor than gender. *Research in Mathematics Education, 16*, 1-17. [preprint, 271k]
[journal version].

Weber, K., Inglis, M. & Mejia-Ramos, J. P. (2014). How mathematicians obtain conviction: Implications for mathematics instruction and research on epistemic cognition. *Educational Psychologist, 49*, 36-58. [preprint, 433k] [journal version].

Duah, F., Croft, T., & Inglis, M. (2014). Can peer-assisted learning be effective in undergraduate mathematics? *International Journal of Mathematical Education in Science and Technology, 45,* 552-565. [repository version] [journal version].

Inglis, M. & Gilmore, C. (2014). Indexing the Approximate Number System. *Acta Psychologica, 145*, 147-155. [repository version] [journal version].

Hodds, M., Alcock, L., & Inglis, M. (2014). Self-explanation training improves proof comprehension. *Journal for Research in Mathematics Education, 45*, 62-101. [preprint, 609k] [supporting materials, 106k] [journal version].

Gilmore, C., Attridge, N., De Smedt, B., & Inglis, M. (2014). Measuring the Approximate Number System in children: Exploring the relationships among different tasks. *Learning and Individual Differences, 29,* 50-58. [repository version] [journal version].

Attridge, N. & Inglis, M. (2013). Advanced mathematical study and the development of conditional reasoning skills. *PLOS ONE, 8*, e69399. [open access version].

Inglis, M. & Gilmore, C. (2013). Sampling from the mental number line: How are Approximate Number System representations formed? *Cognition, 129,* 63-69. [repository version] [journal version].

Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., Simms, V., & Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. *PLOS ONE, 8*, e67374. [open access version].

Alcock, L., Gilmore, C., & Inglis, M. (2013). Guest Editorial: Experimental methods in mathematics education. *Research in Mathematics Education, 15,* 97-99. [repository version] [journal version].

Inglis, M., Mejia-Ramos, J. P., Weber, K., & Alcock, L. (2013). On mathematicians' different standards when evaluating elementary proofs. *Topics in Cognitive Science, 5, *270-282. [preprint, 573k] [journal version].

Jones, I., Inglis, M., Gilmore, C., & Evans, R. (2013). Teaching the substitutive conception of the equals sign. *Research in Mathematics Education, 15*, 34-49. [preprint, 424k] [journal version].

Inglis, M. & Alcock, L. (2013). Skimming: A response to Weber and Mejia-Ramos. *Journal for Research in Mathematics Education, 44*, 471-474. [preprint, 134k].

Jones, I., Inglis, M., Gilmore, C., & Dowens, M. (2012). Substitution and sameness: Two components of a relational conception of the equals sign. *Journal of Experimental Child Psychology, 113*, 166-176. [repository version] [journal version].

Inglis, M. & Alcock, L. (2012). Expert and novice approaches to reading mathematical proofs. *Journal for Research in Mathematics Education, 43*, 358-390 [preprint, 1.1MB] [journal version].

Inglis, M., Attridge, N., Batchelor, S., & Gilmore, C. (2011). Non-verbal number acuity correlates with symbolic mathematics achievement: But only in children. *Psychonomic Bulletin & Review, 18,* 1222-1229. [repository version] [journal version].

Gilmore, C., Attridge, N., & Inglis, M. (2011). Measuring the approximate number system. *Quarterly Journal of Experimental Psychology, 64,* 2099-2109. [repository version] [journal version].

Inglis, M., Palipana, A., Trenholm, S., & Ward, J. (2011). Individual differences in students' use of optional learning resources. *Journal of Computer Assisted Learning, 27*, 490-502. [preprint, 365k] [journal version].

Iannone, P., Inglis, M., Mejia-Ramos, J. P., Simpson, A. & Weber, K. (2011). Does generating examples aid proof production? *Educational Studies in Mathematics, 77*, 1-14. [repository version] [journal version].

Mejia-Ramos, J. P. & Inglis, M. (2011). Semantic contamination and mathematical proof: Can a non-proof prove? *Journal of Mathematical Behavior, 30,* 19-29. [repository version] [journal version].

Alcock, L. & Inglis, M. (2010). Visual considerations in the presentation of mathematical proofs. *Seminar.net - International Journal of Media, Technology and Lifelong Learning, 6*, 43-59. [repository version] [journal version].

Alcock, L. & Inglis, M. (2009). Representation systems and undergraduate proof production: A comment on Weber. *Journal of Mathematical Behavior, 28*, 209-211. [repository version] [journal version].

Inglis, M. & Simpson, A. (2009). Conditional inference and advanced mathematical study: Further evidence. *Educational Studies in Mathematics, 72*, 185-198. [repository version] [journal version].

Inglis, M. & Mejia-Ramos, J. P. (2009). The effect of authority on the persuasiveness of mathematical arguments. *Cognition and Instruction, 27*, 25-50. [repository version] [journal version].

Inglis, M. & Mejia-Ramos, J. P. (2009). On the persuasiveness of visual arguments in mathematics. *Foundations of Science, 14,* 97-110. [repository version] [journal version].

Alcock, L. & Inglis, M. (2008). Doctoral students' use of examples in evaluating and proving conjectures. *Educational Studies in Mathematics, 69*, 111-129. [repository version] [journal version].

Inglis, M. & Mejia-Ramos, J. P. (2008). How persuaded are you? A typology of responses. *Research in Mathematics Education, 10,* 119-133. [repository version] [journal version].

*Republished as:* Inglis, M., & Mejia-Ramos, J. P. (2013). How persuaded are you? A typology of responses. In A. Aberdein & I. Dove (Eds.), *The Argument of Mathematics*, (pp. 101-118). Springer: Dordrecht.

Inglis, M. & Simpson, A. (2008). Conditional inference and advanced mathematical study. *Educational Studies in Mathematics, 67*, 187-204. [repository version] [journal version].

Inglis, M. & Mejia-Ramos, J. P. (2008). Theoretical and methodological implications of a broader perspective
on mathematical argumentation. *Mediterranean Journal for Research in Mathematics Education, 7*, 107-119.

Watson, D. G. & Inglis, M. (2007). Eye movements and time-based selection: Where do the eyes go in preview search? *Psychonomic Bulletin & Review, 14*, 852-857. [repository version] [journal version].

Inglis, M., Mejia-Ramos, J. P. & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. *Educational Studies in Mathematics, 66*, 3-21. [repository version] [journal version].

Reid, D. & Inglis, M. (2005). Talking about logic. *For the Learning of Mathematics, 25*(2), 24-25.

Inglis, M. & Mejia-Ramos, J. P. (2005). La fuerza de la asercion y el poder persuasivo en la argumentacion en matematicas. *Revista EMA: Investigacion e Innovacion en Educacion Matematica, 10*, 327-352.

Inglis, M. (2003). Three worlds and the imaginary sphere. *For the Learning of Mathematics, 23*(3), 24-27, [360k].

Batchelor, S., Gilmore, C., & Inglis, M. (2017). Parents' and children's mathematics anxiety. In U. Xolocotzin (Ed.) *Understanding Emotions in Mathematical Thinking and Learning* (pp. 315-336). Academic Press: London.

Inglis, M., & Aberdein, A. (2016). Diversity in proof appraisal. In B. Larvor (Ed.), *Mathematical Cultures: The London Meetings 2012-2014*, (pp. 163-179). Birkhäuser Science. [preprint, 465k] [full book].

Inglis, M., & Mejia-Ramos, J. P. (2013). How persuaded are you? A typology of responses. In A. Aberdein & I. Dove (Eds.), *The Argument of Mathematics*, (pp. 101-118). Springer: Dordrecht.

*Reprint of:* Inglis, M. & Mejia-Ramos, J. P. (2008). How persuaded are you? A typology of responses. *Research in Mathematics Education, 10,* 119-133.

Inglis, M. (2006). Reconsidering the Imaginary Sphere. In A. Simpson (Ed.), Retirement as Process and Concept: A Festschrift for Eddie Gray and David Tall (pp. 119-126). Prague, Czech Republic.

*The whole Festschrift is available from David's site.*

Inglis, M. (in press). Review of "The trials of evidence-based education: the promises, opportunities and problems of trials in education". *Research in Mathematics Education*. [journal version].

Inglis, M. (2015). Review of "APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education, Arnon et al. (2014)." *International Journal of Research in Undergraduate Mathematics Education, 1*, 413-417. [preprint, 92k] [journal version].

Inglis, M. (2011). Review of "Proof in Mathematics Education: Research, Learning and Teaching". *Research in Mathematics Education, 13,* 316-320. [preprint, 118k] [repository version] [journal version].

Inglis, M. & Alcock, L. (2018). Watching mathematicians read mathematics. In E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter (Eds.), *Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education*. (Vol. 3, pp. 139--146). Umeå, Sweden.

Xolocotzin, U., Inglis, M., & Medrano, A. (2018, July). Elementary and secondary students? functional thinking with tables and diagrams. In E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter (Eds.), *Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education*. (Vol. 4, pp. 451--458). Umeå, Sweden.

Attridge, N., Aberdein, A. & Inglis, M. (2016). Does studying logic improve logical reasoning? In C. Csíkos, A. Rausch & J. Szitányi (Eds.), *Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education.* (Vol. 2, pp. 27-34). Szeged, Hungary. [preprint, 935k].

Jones, I., Inglis, M., Gilmore, C, and Hodgen, J. (2013). Measuring conceptual understanding: The case of fractions. In A. M. Lindmeier and A. Heinze (Eds.), *Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education.* (Vol. 3, pp. 113-120). Kiel, Germany. [preprint, 405k].

Iannone, P., Inglis, M., Mejia-Ramos, J. P., Siemons, J. & Weber, K. (2009). How do undergraduate students generate examples of mathematical concepts? In M. Tzekaki, M. Kaldrimidou & H. Sakonidis (Eds.), *Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education* (Vol. 3, pp. 217-224). Thessaloniki, Greece.

Inglis, M. & Simpson, A. (2009). The defective and material conditionals in mathematics: Does it matter? In M. Tzekaki, M. Kaldrimidou & H. Sakonidis (Eds.), *Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education* (Vol. 3, pp. 225-232). Thessaloniki, Greece.

Mejia-Ramos, J. P. & Inglis, M. (2009). Argumentative and proving activities in mathematics education research. In F.-L. Lin, F.-J. Hsieh, G. Hanna & M. de Villiers (Eds.), *Proceedings of the ICMI Study 19 conference: Proof and Proving in Mathematics Education* (Vol. 2, pp. 88-93), Taipei, Taiwan.

Gilmore, C. K. & Inglis, M. (2008). Process- and object-based thinking in arithmetic. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojana & A. Sepulveda (Eds.), *Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education* (Vol. 3, pp. 73-80). Morelia, Mexico. [repository version].

Inglis, M. & Simpson, A. (2008). Reasoning from features or exemplars. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojana & A. Sepulveda (Eds.), *Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education* (Vol. 3, pp. 217-224). Morelia, Mexico.

Inglis, M. & Simpson, A. (2007). Belief bias and the study of mathematics. In D. Pitta-Pantazi & G. Philippou (Eds.), *Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education* (pp. 2310-2319). Larnaca, Cyprus.

Inglis, M. & Simpson, A. (2006). The role of mathematical context in evaluating conditional statements. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), *Proceedings of the 30th International Conference on the Psychology of Mathematics Education* (Vol. 3, pp. 337-344). Prague, Czech Republic. [repository version].

Inglis, M. & Mejia-Ramos, J. P. (2006). Applying informal logic to arguments in mathematics. *Proceedings of the 3rd International Conference on the Teaching of Mathematics at the Undergraduate Level*. Istanbul, Turkey.

Inglis, M. & Simpson, A. (2006). Characterising mathematical reasoning: Studies with the Wason Selection Task. In M. Bosch (Ed.), *Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education* (pp. 1768-1777). Sant Feliu de Guixols, Spain.

Inglis, M. & Simpson, A. (2005). Heuristic biases in mathematical reasoning. In H.L. Chick & J.L. Vincent (Eds.), *Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education* (Vol. 3, pp. 177-184). Melbourne, Australia.

Inglis, M. & Simpson, A. (2004). Mathematicians and the Selection Task. In M. Johnsen Hoines & A.B. Fuglestad (Eds.), *Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education* (Vol. 3, pp. 89-96). Bergen, Norway.

Inglis, M., Croft, T., & Matthews, J. (2012). *Graduates' Views on the Undergraduate Mathematics Curriculum.* Birmingham: HE STEM Programme. [final report, 392k].

*Erratum: Figures 7 and 8 in the published version of this report displayed the "Written Communication" data incorrectly. The correct figures are here: Figure 7 and Figure 8. The version linked to here is correct. Apologies for the confusion.*

Crisp, R., Inglis, M., Mason, J., & Watson, A. (2012). Individual differences in generalisation strategies. *Research in Mathematics Education, 14,* 291-292.

Attridge, N., Gilmore, C. K. & Inglis, M. (2010). Non-dyscalculic adults use of the approximate number system in symbolic addition. *Research in Mathematics Education, 12,* 149-150. [journal version].

Mejia-Ramos, J. P. & Inglis, M. (2009). What are the argumentative activities associated with proof? *Research in Mathematics Education, 11*, 77-78. [journal version].

Inglis, M., Watson, D. G., and Simpson, A. (2007). Studying advanced mathematics is correlated with analytical reasoning on the Wason Selection Task. In B. Csapo and C. Csikos (Eds.) *12th European Conference for Research on Learning and Instruction: Developing Potentials for Learning*, 132.

Jones, I., Wheadon, C., Humphries, S., & Inglis, M. (2016). Wie vergleicht man den Anspruch mathematischer Prüfungen? Die A levels in England, Wales und Nordirland. *Mitteilungen der Deutschen Mathematiker-Vereinigung, 24*, 100-103. [journal version].

Jones, I., Inglis, M. & Gilmore, C. (2011). The equals sign: Operations, relations and substitutions. *Mathematics Teaching, 224,* 16-17. [journal version].

Jones, I., Inglis, M. & Gilmore, C. (2011). Imperative and punctuative operational conceptions of the equals sign. *Proceedings of the British Society for Research into Learning Mathematics, 31*(1), 79-84. [online version].

Attridge, N., Gilmore, C. & Inglis, M. (2010). Symbolic addition tasks, the approximate number system and dyscalculia. *Proceedings of the British Society for Research into Learning Mathematics, 29*(3), 7-12. [online version].

Mejia-Ramos, J. P. & Inglis, M. (2008). What are the activities associated with proof? *Proceedings of the British Society for Research into Learning Mathematics, 28*(2). [online version].

Inglis, M. & Mejia-Ramos, J. P. (2006). Is it ever appropriate to judge an argument by its author? *Proceedings of the British Society for Research into Learning Mathematics, 26*(2), 43-48. [preprint, 46k].