# Publications for Matthew Inglis

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## Journal Articles

Weiers, H,**Inglis, M**, Gilmore, C (2023) Learning artificial number symbols with ordinal and magnitude information,

*Royal Society Open Science*, 10(6), 220840, DOI: 10.1098/rsos.220840. Pickering, J, Adelman, JS,

**Inglis, M**(2023) Are Approximate Number System representations numerical?,

*Journal of Numerical Cognition*, 9(1), pp.129-144, DOI: 10.5964/jnc.8553. Sa, T, Alcock, L,

**Inglis, M**, Tanswell, FS (2023) Do mathematicians agree about mathematical beauty?,

*Review of Philosophy and Psychology*, ISSN: 1878-5158. DOI: 10.1007/s13164-022-00669-3. Woollacott, B, Alcock, L,

**Inglis, M**(2023) The spatial contiguity principle in mathematics textbooks,

*Research in Mathematics Education*, ISSN: 1479-4802. DOI: 10.1080/14794802.2022.2158122. Woollacott, B, Alcock, L,

**Inglis, M**(2023) The spatial contiguity principle in mathematics textbooks,

*Research in Mathematics Education*, pp.1-21, ISSN: 1479-4802. DOI: 10.1080/14794802.2022.2158122. Wege, T, De Smedt, B, Gilmore, C,

**Inglis, M**(2022) Counting many as one: Young children can understand sets as units except when counting,

*Journal of Experimental Child Psychology*, 225(2023), 105533, ISSN: 0022-0965. DOI: 10.1016/j.jecp.2022.105533. Evans, T, Mejía‑Ramos, JP,

**Inglis, M**(2022) Do mathematicians and undergraduates agree about explanation quality?,

*Educational Studies in Mathematics*, 111(3), pp.445-467, ISSN: 0013-1954. DOI: 10.1007/s10649-022-10164-2. Sims, S, Anders, J,

**Inglis, M**, Lortie-Forgues, H (2022) Quantifying “promising trials bias” in randomized controlled trials in education,

*Journal of Research on Educational Effectiveness*, 16(4), pp.663-680, ISSN: 1934-5747. DOI: 10.1080/19345747.2022.2090470.

**Inglis, M**and O’Hagan, S (2022) Stereotype threat, gender and mathematics attainment: A conceptual replication of Stricker & Ward,

*PLoS ONE*, 17(5), e0267699, DOI: 10.1371/journal.pone.0267699. Pickering, J, Attridge, N,

**Inglis, M**(2021) Cognitive performance in pain is predicted by effort, not goal desire,

*PLoS ONE*, 16(11), e0258874, ISSN: 1932-6203. DOI: 10.1371/journal.pone.0258874. Wege, T, Trezise, K,

**Inglis, M**(2021) Finding the subitizing in groupitizing: Evidence for parallel subitizing of dots and groups in grouped arrays,

*Psychonomic Bulletin and Review*, 29(2), pp.476-484, ISSN: 1069-9384. DOI: 10.3758/s13423-021-02015-7. Ramos, JPM, Evans, T, Rittberg, C,

**Inglis, M**(2021) Mathematicians’ assessments of the explanatory value of proofs,

*Axiomathes*, 31(5), pp.575-599, ISSN: 1122-1151. DOI: 10.1007/s10516-021-09545-8. Lortie-Forgues, H, Sio, UN,

**Inglis, M**(2021) How should educational effects be communicated to teachers?,

*Educational Researcher*, 50(6), pp.345-354, ISSN: 0013-189X. DOI: 10.3102/0013189X20987856. Wege, T, Batchelor, S,

**Inglis, M**, Mistry, H, Schlimm, D (2020) Iconicity in mathematical notation: commutativity and symmetry,

*Journal of Numerical Cognition*, 6(3), pp.378-392, ISSN: 2363-8761. DOI: 10.5964/jnc.v6i3.314.

**Inglis, M**(2020) Focusing on spontaneous focusing,

*Mathematical Thinking and Learning*, 22(4), pp.360-368, ISSN: 1098-6065. DOI: 10.1080/10986065.2020.1818472. Lortie-Forgues, H and

**Inglis, M**(2020) On the Practicality of Extremely Large Educational RCTs,

*Educational Researcher*, 49(4), pp.291-292, ISSN: 0013-189X. DOI: 10.3102/0013189X20921896.

**Inglis, M**and Aberdein, A (2020) Are aesthetic judgements purely aesthetic? Testing the social conformity account,

*ZDM*, 52(6), pp.1127-1136, ISSN: 1863-9690. DOI: 10.1007/s11858-020-01156-8. Bisson, M-J, Gilmore, C,

**Inglis, M**, Jones, I (2019) Teaching using contextualised and decontextualised representations: examining the case of differential calculus through a comparative judgement technique,

*Research in Mathematics Education*, 22(3), pp.284-303, ISSN: 1479-4802. DOI: 10.1080/14794802.2019.1692060. Lortie-Forgues, H and

**Inglis, M**(2019) The value of consensus priors: A response to Simpson,

*Educational Researcher*, 48(6), pp.385-387, ISSN: 0013-189X. DOI: 10.3102/0013189X19863426. Attridge, N, Pickering, J,

**Inglis, M**, Keogh, E, Eccleston, C (2019) People in pain make poorer decisions,

*PAIN The Journal of the International Association for the Study of Pain*, 160(7), pp.1662-1669, ISSN: 0304-3959. DOI: 10.1097/j.pain.0000000000001542. Jones, I, Bisson, M-J, Gilmore, C,

**Inglis, M**(2019) Measuring conceptual understanding in randomised controlled trials: can comparative judgement help?,

*British Educational Research Journal*, 45(3), pp.662-680, ISSN: 0141-1926. DOI: 10.1002/berj.3519.

**Inglis, M**and Mejia-Ramos, JP (2019) Functional explanation in mathematics,

*Synthese*, 198, pp.6369-6392, ISSN: 0039-7857. DOI: 10.1007/s11229-019-02234-5. Lortie-Forgues, H and

**Inglis, M**(2019) Rigorous large-scale educational RCTs are often uninformative: Should we be concerned?,

*Educational Researcher*, 48(3), pp.158-166, ISSN: 0013-189X. DOI: 10.3102/0013189X19832850. Dawkins, PC,

**Inglis, M**, Wasserman, N (2019) The use(s) of is in mathematics,

*Educational Studies in Mathematics*, ISSN: 0013-1954. DOI: 10.1007/s10649-018-9868-6. Foster, C and

**Inglis, M**(2018) Mathematics teacher professional journals: what topics appear and how has this changed over time?,

*International Journal of Science and Mathematics Education*, 17(8), ISSN: 1571-0068. DOI: 10.1007/s10763-018-9937-4.

**Inglis, M**(2018) The trials of evidence-based education: the promises, opportunities and problems of trials in education [Book review],

*Research in Mathematics Education*, 20(3), pp.316-321, ISSN: 1479-4802. DOI: 10.1080/14794802.2018.1481451. Clayton, S,

**Inglis, M**, Gilmore, C (2018) Developmental differences in approaches to nonsymbolic comparison tasks,

*Quarterly Journal of Experimental Psychology*, ISSN: 1747-0218. DOI: 10.1177/1747021818755296. Panse, A, Alcock, L,

**Inglis, M**(2018) Reading proofs for validation and comprehension: An expert-novice eye-movement study,

*International Journal of Research in Undergraduate Mathematics Education*, ISSN: 2198-9745. DOI: 10.1007/s40753-018-0077-6. Norris, JE, Clayton, S, Gilmore, C,

**Inglis, M**, Castronovo, J (2018) The measurement of approximate number system acuity across the lifespan is compromised by congruency effects,

*Quarterly Journal of Experimental Psychology*, ISSN: 1747-0218. DOI: 10.1177/1747021818779020. Bennett, A,

**Inglis, M**, Gilmore, C (2018) The cost of multiple representations: learning number symbols with abstract and concrete representations,

*Journal of Educational Psychology*, ISSN: 0022-0663. DOI: 10.1037/edu0000318.

**Inglis, M**and Foster, C (2018) Five decades of mathematics education research,

*Journal for Research in Mathematics Education*, ISSN: 0021-8251. DOI: 10.5951/jresematheduc.49.4.0462. Foster, C and

**Inglis, M**(2017) Teachers’ appraisals of adjectives relating to mathematics tasks,

*Educational Studies in Mathematics*, 95(3), pp.283-301, ISSN: 0013-1954. DOI: 10.1007/s10649-017-9750-y.

**Inglis, M**, Batchelor, S, Gilmore, C, Watson, DG (2017) Is the ANS linked to mathematics performance?,

*Behavioral and Brain Sciences*, ISSN: 0140-525X. DOI: 10.1017/S0140525X16002120. 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*, ISSN: 1754-0178. DOI: 10.1080/14794802.2017.1285720. Roy, S,

**Inglis, M**, Alcock, L (2017) Multimedia resources designed to support learning from written proofs: An eye-movement study,

*Educational Studies in Mathematics*, ISSN: 0013-1954. DOI: 10.1007/s10649-017-9754-7. 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*, pp.1-9, ISSN: 2044-5911. DOI: 10.1080/20445911.2016.1221828. Alcock, L, Ansari, D, Batchelor, S, Bisson, M-J, De Smedt, B, Gilmore, C, Goebel, SM, 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*, ISSN: 2363-8761. DOI: 10.5964/jnc.v2i1.10. Jones, I, Wheadon, C, Humphries, SM,

**Inglis, M**(2016) Fifty years of A-level mathematics: have standards changed?,

*British Educational Research Journal*, ISSN: 1469-3518. DOI: 10.1002/berj.3224. Bisson, M-J, Gilmore, C,

**Inglis, M**, Jones, I (2016) Measuring conceptual understanding using comparative judgement,

*International Journal of Research in Undergraduate Mathematics Education*, ISSN: 2198-9745. DOI: 10.1007/s40753-016-0024-3. 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, pp.100-103, DOI: 10.1515/dmvm-2016-0039. Van Dooren, W and

**Inglis, M**(2015) Inhibitory control in mathematical thinking, learning and problem solving: A survey,

*ZDM: The International Journal on Mathematics Education*, 47(5), pp.713-721, ISSN: 1863-9704. DOI: 10.1007/s11858-015-0715-2. Jones, I and

**Inglis, M**(2015) The problem of assessing problem solving: Can comparative judgement help?,

*Educational Studies in Mathematics*, 89(3), pp.337-355, DOI: 10.1007/s10649-015-9607-1. Attridge, N, Doritou, M,

**Inglis, M**(Accepted for publication) The development of reasoning skills during compulsory 16 to 18 mathematics education,

*Research in Mathematics Education*, ISSN: 1479-4802. DOI: 10.1080/14794802.2014.999014.

**Inglis, M**and Aberdein, A (2015) Beauty is not simplicity: An analysis of mathematicians' proof appraisals,

*Philosophia Mathematica*, 23(1), pp.87-109, DOI: 10.1093/philmat/nku014. Attridge, N and

**Inglis, M**(2015) Increasing cognitive inhibition with a difficult prior task: implications for mathematical thinking,

*ZDM: The International Journal on Mathematics Education*, ISSN: 1863-9704. DOI: 10.1007/s11858-014-0656-1. Alcock, L, Hodds, M, Roy, S,

**Inglis, M**(2015) Investigating and improving undergraduate proof comprehension,

*Notices of the American Mathematical Society*, ISSN: 0002-9920. DOI: 10.1090/noti1263. Attridge, N, Doritou, M,

**Inglis, M**(2015) The development of reasoning skills during compulsory 16 to 18 mathematics education,

*Research in Mathematics Education*, 17(1), pp.20-37, ISSN: 1479-4802. DOI: 10.1080/14794802.2014.999014. Batchelor, S,

**Inglis, M**, Gilmore, C (2015) Spontaneous focusing on numerosity and the arithmetic advantage,

*Learning and Instruction*, ISSN: 1873-3263. 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, pp.177-184, ISSN: 1873-6297. DOI: 10.1016/j.actpsy.2015.09.007.

**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*, ISSN: 2198-9745. DOI: 10.1007/s40753-015-0015-9. Weber, K,

**Inglis, M**, Mejia-Ramos, JP (2014) How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition,

*Educational Psychologist*, 49(1), pp.36-58, DOI: 10.1080/00461520.2013.865527. Hodds, M, Alcock, L,

**Inglis, M**(2014) Self-Explanation Training Improves Proof Comprehension,

*Journal for Research in Mathematics Education*, 45(1), pp.62-101, ISSN: 0021-8251. DOI: 10.5951/jresematheduc.45.1.0062. 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, pp.50-58, ISSN: 1041-6080. DOI: 10.1016/j.lindif.2013.10.004.

**Inglis, M**and Gilmore, C (2014) Indexing the approximate number system,

*Acta Psychol (Amst)*, 145, pp.147-155, DOI: 10.1016/j.actpsy.2013.11.009. Alcock, L,

**Inglis, M**, Attridge, N, Kenny, S (2014) Achievement and behaviour in undergraduate mathematics: personality is a better predictor than gender,

*Research in Mathematics Education*, ISSN: 1479-4802. DOI: 10.1080/14794802.2013.874094. 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), pp.1-17, ISSN: 1479-4802. DOI: 10.1080/14794802.2013.874094. Attridge, N and

**Inglis, M**(2014) Intelligence and negation biases on the Conditional Inference Task: A dual-processes analysis,

*Thinking and Reasoning*, ISSN: 1354-6783. DOI: 10.1080/13546783.2014.897254. 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(4), pp.552-565, ISSN: 0020-739X. DOI: 10.1080/0020739X.2013.855329. Attridge, N and

**Inglis, M**(2014) Intelligence and negation biases on the Conditional Inference Task: A dual-processes analysis,

*Thinking and Reasoning*, 20, pp.454-471.

**Inglis, M**, Mejia-Ramos, JP, Weber, K, Alcock, L (2013) On Mathematicians' Different Standards When Evaluating Elementary Proofs (vol 5, pg 270, 2013),

*TOPICS IN COGNITIVE SCIENCE*, 5(4), pp.844-844, ISSN: 1756-8757. DOI: 10.1111/tops.12028. Jones, I,

**Inglis, M**, Gilmore, C (Accepted for publication) Equality in the primary maths classroom,

*Primary Maths*, Summer 2013, pp.12-13. Jones, I, inglis, gilmore, Rhys, E (2013) Teaching the substitutive conception of the equals sign,

*Research in Mathematics Education*, 15, pp.34-49, DOI: 10.1080/14794802.2012.756635.

**Inglis, M**and Alcock, L (Accepted for publication) Skimming: A Response to Weber and Mejía-Ramos,

*Journal for Research in Mathematics Education*, 44, pp.471-474. Jones, I,

**Inglis, M**, Gilmore, C, Evans, R (2013) Teaching the substitutive conception of the equals sign,

*Research in Mathematics Education*, ISSN: 1479-4802.

**Inglis, M**, Mejia-Ramos, J-P, Weber, K, Alcock, L (2013) On mathematicians' different standards when evaluating elementary proofs,

*Topics in Cognitive Science*, 5, pp.270-282, DOI: 10.1111/tops.12019. Alcock, L, Gilmore, C,

**Inglis, M**(2013) Guest Editorial: Experimental methods in mathematics education,

*Research in Mathematics Education*, 15, pp.97-99. 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(6), e67374, DOI: 10.1371/journal.pone.0067374.

**Inglis, M**and Gilmore, C (2013) Sampling from the mental number line: How are Approximate Number System representations formed?,

*Cognition*, 129, pp.63-69, DOI: 10.1016/j.cognition.2013.06.003. Attridge, N and

**Inglis, M**(2013) Advanced mathematical study and the development of conditional reasoning skills,

*PLOS ONE*, 8(7), e69399, DOI: 10.1371/journal.pone.0069399. 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(1), pp.166-176, ISSN: 0022-0965. DOI: 10.1016/j.jecp.2012.05.003.

**Inglis, MJ**and Alcock, LJ (2012) Expert and novice approaches to reading mathematical proofs,

*Journal for Research in Mathematics Education*, 43(4), pp.358-390.

**Inglis, M**and Alcock, L (2012) Expert and novice approaches to reading mathematical proofs,

*Journal for Research in Mathematics Education*, 43(4), pp.358-390, ISSN: 0021-8251. DOI: 10.5951/jresematheduc.43.4.0358. 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, pp.166-176, ISSN: 0022-0965. Crisp, R,

**Inglis, M**, Mason, J, Watson, A (2012) Individual differences in generalisation strategies,

*Research in Mathematics Education*, 14(3), pp.291-292, ISSN: 1479-4802. Jones, I (2012) Early algebraization: a global dialogue from multiple perspectives,

*Research in Mathematics Education*, 14, pp.301-308, DOI: 10.1080/14794802.2012.734996. Iannone, P,

**Inglis, M**, Mejia Ramos, JP, Simpson, A, Weber, K (2011) Does generating examples aid proof production?,

*Educational Studies in Mathematics: an international journal*, 77, pp.1-14. Mejia Ramos, JP and

**Inglis, M**(2011) Semantic contamination and mathematical proof: Can a non-proof prove?,

*The Journal of Mathematical Behavior*, 30, pp.19-29. Jones, I,

**Inglis, M**, Gilmore, CK (2011) The equals sign: Operations, relations and substitutions,

*Mathematics Teaching*, 224, pp.16-17.

**Inglis, M**, Attridge, N, Batchelor, S, Gilmore, C (2011) Non-verbal number acuity correlates with symbolic mathematics achievement: but only in children,

*Psychonomic Bulletin and Review*, 18, pp.1222-1229. Gilmore, C, Attridge, N,

**Inglis, M**(2011) Measuring the Approximate Number System,

*Quarterly Journal of Experimental Psychology*, 64, pp.2099-2109.

**Inglis, M**, Palipana, A, Trenholm, S, Ward, J (2011) Individual differences in students' use of optional learning resources,

*Journal of Computer Assisted Learning*, 27, pp.490-502.

**Inglis, M**(2011) Proof in Mathematics Education: Research, Learning and Teaching,

*Research in Mathematics Education*, 13, pp.316-320.

**Inglis, M**, Palipana, A, Trenholm, S, Ward, J (2011) Individual differences in students' use of optional learning resources,

*Journal of Computer Assisted Learning*, ISSN: 0266-4909. Attridge, N, Gilmore, C,

**Inglis, M**(2010) Non-dyscalculic adults' use of the approximate number system in symbolic addition,

*Research in Mathematics Education*, 12(2), pp.149-150, ISSN: 1479-4802. DOI: 10.1080/14794802.2010.496976. Alcock, LJ and

**Inglis, M**(2010) Visual considerations in the presentation of mathematical proofs,

*Seminar.Net*, 6(1), pp.43-59.

**Inglis, M**and Simpson, A (2009) Conditional inference and advanced mathematical study: Further evidence,

*Educational Studies in Mathematics*, 72(2), pp.185-198, ISSN: 0013-1954. DOI: 10.1007/s10649-009-9187-z. Mejia Ramos, JP and

**Inglis, MJ**(2009) What are the argumentative activiities associated with proof?

*Research in Mathematics Education*, 11, pp.77-78. Alcock, LJ and

**Inglis, M**(2009) Representation systems and undergraduate proof production: A comment on Weber,

*Journal of Mathematical Behavior*, 28, pp.209-211.

**Inglis, MJ**and Simpson, A (2009) Conditional inference and advanced mathematical study: Further evidence,

*Educational Studies in Mathematics: an international journal*, 72, pp.175-198.

**Inglis, M**and Mejia Ramos, JP (2009) On the persuasiveness of visual arguments in mathematics,

*Foundations of Science*, 14, pp.97-110.

**Inglis, M**and Mejia Ramos, JP (2009) The effect of authority on the persuasiveness of mathematical arguments,

*Cognition and Instruction*, 27, pp.25-50. Alcock, LJ and

**Inglis, MJ**(2008) Doctoral students' use of examples in evaluating and proving conjectures,

*Educational Studies in Mathematics: an international journal*, 69, pp.111-129.

**Inglis, MJ**and Mejia Ramos, JP (2008) How persuaded are you? A typology of responses,

*Research in Mathematics Education*, 10, pp.119-133.

**Inglis, MJ**and Simpson, A (2008) Conditional inference and advanced mathematical study,

*Educational Studies in Mathematics: an international journal*, 67, pp.187-204.

**Inglis, MJ**and Mejia Ramos, JP (2008) Theoretical and methodological implications of a broader perspective on mathematical argumentation,

*Mediterranean Journal for Research in Mathematics Education*, 7, pp.107-119. Watson, DG and

**Inglis, MJ**(2007) Eye movements and time-based selection: Where do the eyes go in preview search?,

*Psychonomic Bulletin and Review*, 14, pp.852-857.

**Inglis, MJ**, Mejia Ramos, JP, Simpson, A (2007) Modelling mathematical argumentation:The importance of qualification,

*Educational Studies in Mathematics: an international journal*, 66, pp.3-21. Reid, D and

**Inglis, MJ**(2005) Talking about logic,

*For the Learning of Mathematics: an international journal of mathematics education*, 25(2), pp.24-25.

**Inglis, MJ**and Mejia Ramos, JP (2005) La fuerza de la asercion y el poder persuasivo en la argumentacion en matematicas,

*Revista EMA: Investigacion e Innovacion en Educacion Matematica*, 10, pp.327-352.

**Inglis, MJ**(2003) Three worlds and the imaginery sphere,

*For the Learning of Mathematics: an international journal of mathematics education*, 23(3), pp.24-27.

## Conferences

**Inglis, M**and Alcock, L (2018) Watching mathematicians read mathematics. In

*42nd Conference of the International Group for the Psychology of Mathematics Education*, Umeå, Sweden. Alcock, L,

**Inglis, M**, Lew, K, Mejia-Ramos, JP, Rago, P, Sangwin, CJ (2017) Comparing expert and learner mathematical language: A corpus linguistics approach. In

*The XX Annual Conference on Research on Undergraduate Mathematics Education*, San Diego. Mejia-Ramos, JP and

**Inglis, M**(2017) “Explanatory” talk in mathematics research papers. In

*The XX Annual Conference on Research on Undergraduate Mathematics Education*, San Diego. Attridge, N, Aberdein, A,

**Inglis, M**(2016) Does studying logic improve logical reasoning?. In

*Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education*, Szeged. Alcock, L, Kilbey, T,

**Inglis, M**(2015) How do undergraduates read mathematical texts? An eye-movement study. In

*Didactics of Mathematics in Higher Education as a Discipline*, Hannover, Germany. Alcock, LJ, Bailey, T,

**Inglis, M**, Docherty, P (2014) The ability to reject invalid logical inferences predicts proof comprehension and mathematics performance. In Fukawa-Connelly, T (ed)

*17th Conference on Research in Undergraduate Mathematics Education*, Denver, CO, USA, pp.n/a-n/a. Jones, I,

**Inglis, M**, Gilmore, C, Hodgen, J (2013) Measuring conceptual understanding: The case of fractions. In Lindmeier, AM and Heinze, A (ed)

*Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education*, Kiel, Germany, pp.113-120. Jones, I,

**Inglis, M**, Gilmore, C (2011) Imperative and punctuative operational conceptions of the equals sign. In

*Informal Proceedings of the British Society for Research into Learning Mathematics*, London Institute of Education, pp.79-84. Iannone, P and

**Inglis, M**(2011) UNDERGARDUATE STUDENTS' USE OF DEDUCTIVE ARGUMENTS TO SOLVE "PROVE THAT .." TASKS. In , PROCEEDINGS OF THE SEVENTH CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION (CERME 7), pp.2012-2021. Attridge, N, Gilmore, CK,

**Inglis, M**(2010) Symbolic addition tasts, the approximate number system and dyscalculia. In

*Proceedings of the British Society for Research into Learning Mathematics*, Proceedings of the British Society for Research into Learning Mathematics, Loughborough. Roy, S, Alcock, LJ,

**Inglis, MJ**(2010) Undergraduates' proof comprehension:. In

*Proceedings of the 13th Conference on Research in Undergraduate Mathematics Education*, A comparative study of three forms of proof presentation, Raleigh, NC, USA, pp.43-59. Iannone, P,

**Inglis, M**, Mejia Ramos, JP, Siemons, J, Weber, K (2009) How do undergraduate students generate examples of mathematical concepts?. In

*Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education*, In M. Tzekaki, M. Kaldrimidou & C. Sakonidis (eds), Thessaloniki, Green, pp.217-224.

**Inglis, MJ**and Simpson, A (2009) The defective and material conditionals in mathematics: Does it matter?. In

*Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Eduation*, In M. Tzekaki, M.Kaldrimidou & C. Sakonidis (eds), Thessaloniki, Greece, pp.225-232. Mejia Ramos, JP and

**Inglis, MJ**(2008) What are the argumentative activities associated with proof?. In

*Proceedings of the British Society for Research into Learning Mathematics*, London: BSRLM, pp.67-72. Gilmore, CK and

**Inglis, MJ**(2008) Process-and object-based thinking in arithmetic. In

*Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education*, In O. Figueras, J.L. Cortina, S. Alatorre, T. Rojana & A. Sepulveda (eds), Morelia, Mexico, pp.73-80.

**Inglis, MJ**and Simpson, A (2008) Reasoning from features or exemplars. In

*Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education*, In O. Figueras, J.L. Cortina, S. Alatorre, T. Rojana & A. Sepulveda (eds), Morelia, Mexico, pp.217-224.

**Inglis, MJ**, Watson, DG, Simpson, A (2007) Studying advanced mathematics is correlated with analytical reasoning on the Watson Selection Task. In

*12th European Conference for Research on Learning and Instruction: Developing Potential for Learning*, In B.Csapo and C. Csikos (eds), Budapest, Hungary.

**Inglis, MJ**and Simpson, A (2007) Belief bias and the study of mathematics. In

*Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education*, in D. Pitta-Pantazi & G. Philippou (eds), Larnaca, Cyprus, pp.2310-2319.

**Inglis, MJ**and Simpson, A (2006) The role of the mathematical context in evaluating conditional statements. In

*Proceedings of the 30th International Conference on the Psychology of Mathematics Education*, In J. Novotna, H. Moraova, M .Kratka & N. Stehlikova (eds), Prague, Czech Republic, pp.337-344.

**Inglis, MJ**and Mejia Ramos, JP (2006) Applying informal logic to arguments in mathematics. In

*Proceedings of the 3rd International Conference on the Teaching of Mathematics at the Undergraduate level*, tba, Istanbul, Turkey, pp.337-344.

**Inglis, MJ**and Simpson, A (2006) Characterising mathematical reasoning: Studies with the Wason Selection Task. In

*Proceedings of the Fourth Congress of the European Society for Research in Mathematics Eduation*, In M. Bosch (ed), Sant Feliu de Guixols, Spain, pp.1768-1777. Ejersbo, LR,

**Inglis, M**, Leron, U (2006) WS08: INTUITIVE VS. ANALYTICAL THINKING: A VIEW FROM COGNITIVE PSYCHOLOGY. In , PME 30: PROCEEDINGS OF THE 30TH CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION, VOL 1, pp.208-208.

**Inglis, MJ**and Simpson, A (2005) Heuristic biases in mathematical reasoning. In

*Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education*, In H.L. Chick & J.L. Vincent (eds), Melbourne, Australia, pp.177-184.

**Inglis, MJ**and Simpson, A (2004) Mathematicians and the Selection Task. In

*Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education*, In M. Johnsen Hoines & A.B. Fuglestad (eds), Bergen, Norway, pp.89-96.

## Books

Gilmore, C, Göbel, SM,**Inglis, M**(2018)

*AN INTRODUCTION TO MATHEMATICAL COGNITION*,ISBN: 9781138923942. DOI: 10.4324/9781315684758.

**Inglis, M**and Attridge, N (2016)

*Does Mathematical Study Develop Logical Thinking? Testing the Theory of Formal Discipline*, World Scientific, ISBN: 978-1-78634-068-9.

## Chapters

Weber, K and**Inglis, M**(2021) Mathematics education research on mathematical practice. In Sriraman, B (ed)

*Handbook of the History and Philosophy of Mathematical Practice*, Springer, pp.1-28, ISBN: 9783030190712. DOI: 10.1007/978-3-030-19071-2_88-1. Mejia-Ramos, JP, Alcock, L, Lew, K, Rago, P, Sangwin, CJ,

**Inglis, M**(2019) Using corpus linguistics to investigate mathematical explanation. In

*Methodological Advances in Experimental Philosophy*, Bloomsbury, pp.239-264, ISBN: 9781350068995. Batchelor, S, Gilmore, C,

**Inglis, M**(2017) Parents’ and children’s mathematics anxiety. In

*Understanding Emotions in Mathematical Thinking and Learning*, © Elsevier, pp.315-336, ISBN: 9780128024898. DOI: 10.1016/B978-0-12-802218-4.00012-1.

**Inglis, M**and Aberdein, A (2016) Diversity in proof appraisal. In

*Mathematical Cultures: The London Meetings 2012-2014*, Birkhäuser Basel © Springer International Publishing, pp.163-180, ISBN: 978-3-319-28580-1. DOI: 10.1007/978-3-319-28582-5.

**Inglis, M**and Mejia-Ramos, JP (2013) How persuaded are you? A typology of responses. In Aberdein, A and Dove, I (ed)

*The Argument of Mathematics*, Springer, pp.101-118.

**Inglis, M**and Mejia-Ramos, JP (2013) How Persuaded Are You? A Typology of Responses. In Aberdein, A and Dove, I (ed)

*The Argument of Mathematics*, pp.101-117, DOI: 10.1007/978-94-007-6534-4_7.

**Inglis, MJ**(2006) Reconsidering the Imaginary Sphere. In Simpson, A (ed)

*Retirement as Process and Concept: A Festschrift for Eddie Gray and David Tall*, Charles University, pp.119-126.

## Digital/Visual Products

**Inglis, M**and Alcock, L (2012)

*Time versus Line Number Fixation Plots*.

**Inglis, M**(Accepted for publication)

*Example e-Proof*.

## Internet Publications

**Inglis, M**(2020)

*Uninformative educational trials and their causes*. DOI: 10.5281/zenodo.4279342. O'Hagan, S and

**Inglis, M**(Accepted for publication)

*Supplementary Materials associated with “Stereotype Threat, Gender and Mathematics Attainment: A Replication of Stricker & Ward”*.

## Reports

Bairner, A and**Inglis, M**(2023)

*Professor Alan Bairner's Guide to Pubs in Loughborough*, The Mathematical Cognition and Learning Society.

**Inglis, M**, Croft, T, Matthews, J (2012)

*Graduates' Views on the Undergraduate Mathematics Curriculum*, National HE STEM Programme.

## Software

Bennett, A,**Inglis, M**, Gilmore, C (Accepted for publication)

*The Cost of Multiple Representations: Experiment 1 PsychoPy materials*. Bennett, A,

**Inglis, M**, Gilmore, C (Accepted for publication)

*The Cost of Multiple Representations: Experiment 2 PsychoPy materials*. Bennett, A,

**Inglis, M**, Gilmore, C (Accepted for publication)

*The Cost of Multiple Representations: Experiment 3 PsychoPy materials*.

**Inglis, M**(Accepted for publication)

*Non-random sampling.R*.

## Thesis/Dissertation

Weiers, H (2022)*Learning artificial number symbols: the role of ordinal and magnitude information*.

## Datasets

**Inglis, M**, Gadd, E, Stokoe, E (2023) What is a high-quality research environment?, DOI: 10.17028/rd.lboro.23912499. Pickering, J, Adelman, JS,

**Inglis, M**(2023) How numerical are ANS representations?, DOI: 10.17028/rd.lboro.19061051. Evans, T, Mejia-Ramos, JP,

**Inglis, M**(2022) Do mathematicians and undergraduates agree about explanation quality? - Dataset, DOI: 10.17028/rd.lboro.14213831. O'Hagan, S and

**Inglis, M**(2022) Data files associated with “Stereotype Threat, Gender and Mathematics Attainment: A Replication of Stricker & Ward”, DOI: 10.17028/rd.lboro.12017007. Mejia-Ramos, JP, Evans, T, Rittberg, C,

**Inglis, M**(2021) Materials associated with the manuscript "Mathematicians’ assessments of the explanatory value of proofs", DOI: 10.17028/rd.lboro.12458486. Lortie-Forgues, H, Sio, UN,

**Inglis, M**(2021) Supplemental information files for: How should educational effects be communicated to teachers?, DOI: 10.17028/rd.lboro.13385444. Wege, T, Batchelor, S,

**Inglis, M**, Mistry, H, Schlimm, D (2020) Data for Iconicity in mathematical notation, DOI: 10.17028/rd.lboro.12489731. Wege, T, DeSmedt, B,

**Inglis, M**, Gilmore, C (2020) Beyond Representation: Open Data, Materials, and Code, DOI: 10.17028/rd.lboro.12871703.

**Inglis, M**and Aberdein, A (2019) Data associated with the manuscript "Are Aesthetic Judgements Purely Aesthetic? Testing the Social Conformity Account", DOI: 10.17028/rd.lboro.9907517.

**Inglis, M**and Aberdein, A (2019) SPSS syntax associated with the manuscript "Are Aesthetic Judgements Purely Aesthetic? Testing the Social Conformity Account", DOI: 10.17028/rd.lboro.9907559. Jones, I, Gilmore, C,

**Inglis, M**, Bisson, M-J (2019) Y11_lesson_materials for Measuring Conceptual Understanding, DOI: 10.17028/rd.lboro.7830500. Lortie-Forgues, H and

**Inglis, M**(2019) Analysis scripts associated with manuscript "Rigorous Large-Scale Educational RCTs are Often Uninformative: Should We Be Concerned?", DOI: 10.6084/m9.figshare.7796711. Lortie-Forgues, H and

**Inglis, M**(2019) Data associated with the manuscript "Rigorous Large-Scale Educational RCTs are Often Uninformative: Should We Be Concerned?", DOI: 10.6084/m9.figshare.7796714. Attridge, N, Pickering, J,

**Inglis, M**, Keogh, E, Eccleston, C (2019) People in pain make poorer decisions: tasks, data files and SPSS analysis syntax, DOI: 10.17028/rd.lboro.7068413. Bennett, A,

**Inglis, M**, Gilmore, C (2018) The Cost of Multiple Representations: Experiment 1 data and scripts, DOI: 10.6084/m9.figshare.5178745. Bennett, A,

**Inglis, M**, Gilmore, C (2018) The Cost of Multiple Representations: Experiment 2 data and scripts, DOI: 10.6084/m9.figshare.5178769. Bennett, A,

**Inglis, M**, Gilmore, C (2018) The Cost of Multiple Representations: Experiment 3 data and scripts, DOI: 10.6084/m9.figshare.5178772. Bennett, A,

**Inglis, M**, Gilmore, C (2018) The Cost of Multiple Representations: Preregistrations, DOI: 10.6084/m9.figshare.7000577.

**Inglis, M**and Foster, C (2018) Five Decades of Mathematics Education Research. Panse, A, Alcock, L,

**Inglis, M**(2018) Reading Proofs for Validation and Comprehension: An Expert-Novice Eye-Movement Study: Data and Analysis, DOI: 10.6084/m9.figshare.5213326. Panse, A, Alcock, L,

**Inglis, M**(2018) Reading Proofs for Validation and Comprehension: An Expert-Novice Eye-Movement Study: Stimuli, DOI: 10.6084/m9.figshare.5217418.

**Inglis, M**and Foster, C (2017) Five Decades of Mathematics Education Research, DOI: 10.6084/m9.figshare.4877429. Alcock, L,

**Inglis, M**, Lew, K, Mejia-Ramos, JP, Rago, P, Sangwin, C (2017) Undergraduate Mathematics Learner Corpus, DOI: 10.6084/m9.figshare.5132170.

**Inglis, M**, Batchelor, S, Gilmore, C, watson, D (2016) Disclosure Table for p curve analysis on whether the ANS is causally linked to mathematics performance, DOI: 10.6084/m9.figshare.4262999.

**Inglis, M**and Aberdein, A (2015) Beauty is not simplicity: An analysis of mathematicians' proof appraisals, DOI: 10.6084/m9.figshare.1579104. Alcock, L, Attridge, N, Kenny, S,

**Inglis, M**(2013) Achievement and Behaviour in Undergraduate Mathematics: Personality is a Better Predictor than Gender, DOI: 10.6084/m9.figshare.865640.

**Inglis, M**and Aberdein, A Beauty is not simplicity: An analysis of mathematicians' proof appraisals, DOI: 10.6084/m9.figshare.1579104.v1. Alcock, L, Attridge, N, Kenny, S,

**Inglis, M**Achievement and Behaviour in Undergraduate Mathematics: Personality is a Better Predictor than Gender, DOI: 10.6084/m9.figshare.865640.v1.

**Inglis, M**, Batchelor, S, Gilmore, C, watson, D Disclosure Table for p curve analysis on whether the ANS is causally linked to mathematics performance, DOI: 10.6084/m9.figshare.4262999.v1. Lortie-Forgues, H and

**Inglis, M**Analysis scripts associated with manuscript "Rigorous Large-Scale Educational RCTs are Often Uninformative: Should We Be Concerned?", DOI: 10.6084/m9.figshare.7796711.v1. Lortie-Forgues, H and

**Inglis, M**Data associated with the manuscript "Rigorous Large-Scale Educational RCTs are Often Uninformative: Should We Be Concerned?", DOI: 10.6084/m9.figshare.7796714.v1. Bennett, A,

**Inglis, M**, Gilmore, C The Cost of Multiple Representations: Preregistrations, DOI: 10.6084/m9.figshare.7000577.v1. Alcock, L,

**Inglis, M**, Lew, K, Mejia-Ramos, JP, Rago, P, Sangwin, C Undergraduate Mathematics Learner Corpus, DOI: 10.6084/m9.figshare.5132170.v1. Bennett, A,

**Inglis, M**, Gilmore, C The Cost of Multiple Representations: Experiment 1 data and scripts, DOI: 10.6084/m9.figshare.5178745.v1. Bennett, A,

**Inglis, M**, Gilmore, C The Cost of Multiple Representations: Experiment 2 data and scripts, DOI: 10.6084/m9.figshare.5178769.v1. Bennett, A,

**Inglis, M**, Gilmore, C The Cost of Multiple Representations: Experiment 3 data and scripts, DOI: 10.6084/m9.figshare.5178772.v1. Panse, A, Alcock, L,

**Inglis, M**Reading Proofs for Validation and Comprehension: An Expert-Novice Eye-Movement Study: Stimuli, DOI: 10.6084/m9.figshare.5217418.v1.

## Filesets

Jones, I,**Inglis, M**, Gilmore, C, Bisson, M-J (2018) Y11_data, DOI: 10.17028/rd.lboro.5845683. Gilmore, C, Cragg, L, Hogan, G,

**Inglis, M**(2016) Congruency effects in dot comparison tasks: Convex hull is more important than dot area, DOI: 10.17028/rd.lboro.3582513.

## Media

**Inglis, M**and Aberdein, A (2019) Stimuli associated with the manuscript "Are Aesthetic Judgements Purely Aesthetic? Testing the Social Conformity Account".

## Other

**Inglis, M**(2023)

*The dialogical roots of deduction: historical, cognitive, and philosophical perspectives on reasoning*. DOI: 10.1080/14794802.2022.2027811.

**Inglis, M**and Crook, C (2021)

*Conversation: Uninformative randomised control trials in educational research*.

**Inglis, M**and Simms, V (2021)

*Conversation: Nature and origins of mathematics difficulties in very preterm children*. Wege, TE, Trezise, K,

**Inglis, M**(2021)

*Finding the subitizing in groupitizing: Evidence for parallel subitizing of dots and groups in grouped arrays*,

‘Groupitizing’ refers to the observation that visually grouped arrays can be accurately enumerated much faster than unstructured arrays. Previous research on groupitizing suggests that visual grouping allows participants to draw on arithmetic abilities and possibly use mental calculations to enumerate grouped arrays fast and accurately. Here we address how subitizing might be involved in finding the operands for mental calculations in grouped dot arrays. We investigated whether participants could use multiple subitizing processes to enumerate both the number of dots and the number of groups in a grouped array. We found that these multiple subitizing processes can take place within 150ms and that dots and groups seem to be subitized in parallel and with equal priority. Implications for research on mechanisms of groupitizing are discussed.

. DOI: 10.31219/osf.io/srht5. Wege, TE, Trezise, K,**Inglis, M**(2021)

*Finding the subitizing in groupitizing: Evidence for parallel subitizing of dots and groups in grouped arrays*,

‘Groupitizing’ refers to the observation that visually grouped arrays can be accurately enumerated much faster than can unstructured arrays. Previous research suggests that visual grouping allows participants to draw on arithmetic abilities and possibly use mental calculations to enumerate grouped arrays quickly and accurately. Here, we address how subitizing might be involved in finding the operands for mental calculations in grouped dot arrays. We investigated whether participants can use multiple subitizing processes to enumerate both the number of dots and the number of groups in a grouped array. We found that these multiple subitizing processes can take place within 150 ms and that dots and groups seem to be subitized in parallel and with equal priority. Implications for research on mechanisms of groupitizing are discussed.

. DOI: 10.31234/osf.io/x2ztc. Hodds, M, Alcock, L,**Inglis, M**(2014)

*Self-Explanation Training Improves Proof Comprehension: Supplementary Materials*. Alcock, L,

**Inglis, M**, Roy, S (Accepted for publication)

*Multimedia resources designed to support learning from written proofs: An eye-movement study. Supplementary Materials*, These are the supplementary materials for the article "When research-based interventions fail: Multimedia resources designed to support learning from written proofs". For Study One the material consists of: Theorem and Proof used for Immediate Post-Test; Theorem and Proof used for Delayed Post-Test; Comprehension Test; Additional Information Sheet: Definitions and Theorems. For Study Two the material consists of: Theorem, Proof and Comprehension Test 1; Theorem, Proof and Comprehension Test 2; Theorem (Rolle’s Theorem), Proof and Comprehension Test 3; Theorem (Cauchy’s GMVT), Proof and Comprehension Test 4..