# Publications for Matthew Inglis

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## Journal Articles

Bennett, A,**Inglis, M**, Gilmore, C (Accepted for publication) The Cost of Multiple Representations: Learning Number Symbols with Abstract and Concrete Representations,

*Journal of Educational Psychology*, ISSN: 1939-2176. 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.,

*Q J Exp Psychol (Hove)*, pp.1747021818779020-1747021818779020, DOI: 10.1177/1747021818779020. Alcock, LJ, Panse, A,

**Inglis, M**(Accepted for publication) Reading Proofs for Validation and Comprehension: An Expert-Novice Eye-Movement Study,

*International Journal of Research in Undergraduate Mathematics Education*, ISSN: 2198-9745.

**Inglis, M**and Foster, C (Accepted for publication) Five Decades of Mathematics Education Research,

*Journal for Research in Mathematics Education*, ISSN: 0021-8251. Clayton, S,

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

*Quarterly Journal of Experimental Psychology*, ISSN: 1747-0218.

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

*Behavioral and Brain Sciences*, 40, 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*, 19(1), pp.20-41, ISSN: 1754-0178. DOI: 10.1080/14794802.2017.1285720. Roy, S,

**Inglis, M**, Alcock, LJ (Accepted for publication) Multimedia resources designed to support learning from written proofs: An eye-movement study,

*Educational Studies in Mathematics*. Foster, C and

**Inglis, M**(Accepted for publication) Teachers’ appraisals of adjectives relating to mathematics tasks,

*Educational Studies in Mathematics*. 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, LJ, Batchelor, S, Gilmore, C,

**Inglis, M**, Jones, I, Ansari, D, Bisson, M-J, De Smedt, B, Goebel, SM, Hannula-Sormunen, M, Hodgen, J, 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(1), pp.20-41. Bisson, Gilmore, C,

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

*International Journal of Research in Undergraduate Mathematics Education*, 2, pp.141-164. Jones, I, Wheadon, C, Humphries, S,

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

*British Educational Research Journal*, ISSN: 1469-3518. 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.

**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*, DOI: 10.1007/s40753-015-0015-9. 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. Batchelor, S,

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

*Learning and Instruction*, 40, pp.79-88, ISSN: 1873-3263. DOI: 10.1016/j.learninstruc.2015.09.005. 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**(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. Alcock, LJ, Hodds, M, Roy, S,

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

*Notices of the American Mathematical Society*, 62, pp.742-752, Full text: http://www.ams.org/notices/201507/rnoti-p742.pdf . 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*, 47, pp.723-734, ISSN: 1863-9704. DOI: 10.1007/s11858-014-0656-1.

**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. 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.

**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. 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. 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. Weber, K,

**Inglis, M**, Mejia-Ramos, JP (2014) How mathematicians obtain conviction: Implications for mathematics instruction and research on epistemic cognition,

*Educational Psychologist*, 49, pp.36-58. 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. Hodds, M, Alcock, L,

**Inglis, M**(2014) Self-explanation training improves proof comprehension,

*Journal for Research in Mathematics Education*, 45, pp.98-137, ISSN: 0021-8251. Jones, I,

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

*Primary Maths*, Summer 2013, pp.12-13. 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.

**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. 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. Alcock, L, Gilmore, C,

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

*Research in Mathematics Education*, 15, pp.97-99.

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

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

**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.

**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. 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.

**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*, 27, pp.490-502. Gilmore, C, Attridge, N,

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

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

**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. Jones, I,

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

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

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

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

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

*Foundations of Science*, 14, pp.97-110. Alcock, LJ and

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

*Journal of Mathematical Behavior*, 28, pp.209-211. Mejia Ramos, JP and

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

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

**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.

**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) How persuaded are you? A typology of responses,

*Research in Mathematics Education*, 10, pp.119-133. 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**, Mejia Ramos, JP, Simpson, A (2007) Modelling mathematical argumentation:The importance of qualification,

*Educational Studies in Mathematics: an international journal*, 66, pp.3-21. 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**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. 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**(2003) Three worlds and the imaginery sphere,

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

## Conferences

Alcock, LJ and**Inglis, M**(Accepted for publication) Watching mathematicians read mathematics. In

*42nd Conference of the International Group for the Psychology of Mathematics Education*, Umeå, Sweden. Mejia-Ramos, JP and

**Inglis, M**(Accepted for publication) “Explanatory” Talk in Mathematics Research Papers. In

*The XX Annual Conference on Research on Undergraduate Mathematics Education*, San Diego. Alcock, L,

**Inglis, M**, Lew, K, Mejia-Ramos, JP, Rago, P, Sangwin, C (Accepted for publication) Comparing Expert and Learner Mathematical Language: A Corpus Linguistics Approach. 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 Csíkos, C, Rausch, A, Szitányi, J (ed)

*40th Conference of the International Group for the Psychology of Mathematics Education*, Szeged, Hungary, pp.27-34.

**Inglis, M**, Kilbey, T, Alcock, LJ (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. 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. 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. 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.217-224. 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.

**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. 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 (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. 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. 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.

**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**, 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 (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.

**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.1768-1777.

**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 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

**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. Full text: http://www.worldscientific.com/worldscibooks/10.1142/q0020 .

## Chapters

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

*Understanding Emotions in Mathematical Thinking and Learning*, Elsevier, pp.315-336.

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

*Mathematical Cultures: The London Meetings 2012-2014*, Bikhauser, pp.163-180.

**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

Roy, S,**Inglis, M**, Alcock, L (2016)

*An example e-Proof*.

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

*Time versus Line Number Fixation Plots*.

## Other

Alcock, LJ,**Inglis,**, Roy, S (2017)

*Multimedia resources designed to support learning from written proofs: An eye-movement study: Supplementary Materials*. Hodds, M, Alcock, L,

**Inglis, M**(2014)

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

## Reports

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

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