# Publications for Lara Alcock

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## Journal Articles

**Alcock, L**and Attridge, N (2023) Refutations and reasoning in undergraduate mathematics,

*International Journal of Research in Undergraduate Mathematics Education*, ISSN: 2198-9745. DOI: 10.1007/s40753-023-00220-4. Sa, T,

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

*Review of Philosophy and Psychology*, 15(1), 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. Davies, B,

**Alcock, L**, Jones, I (2020) What do mathematicians mean by proof? A comparative-judgement study of students’ and mathematicians’ views,

*The Journal of Mathematical Behavior*, 61, 100824, ISSN: 0732-3123. DOI: 10.1016/j.jmathb.2020.100824. Davies, B,

**Alcock, L**, Jones, I (2020) Comparative judgement, proof summaries and proof comprehension,

*Educational Studies in Mathematics*, 105, ISSN: 0013-1954. DOI: 10.1007/s10649-020-09984-x.

**Alcock, L**, Hernandez-Martinez, P, Patel, AG, Sirl, D (2020) Study Habits and Attainment in Undergraduate Mathematics: A Social Network Analysis,

*Journal for Research in Mathematics Education*, 51(1), pp.26-49, ISSN: 0021-8251. DOI: 10.5951/jresematheduc.2019.0006.

**Alcock, L**(2018) Tilting the classroom,

*London Mathematical Society Newsletter*, 474, pp.22-27. 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.

**Alcock, L**and Simpson, A (2017) Interactions between defining, explaining and classifying: The case of increasing and decreasing sequences,

*Educational Studies in Mathematics*, ISSN: 0013-1954. DOI: 10.1007/s10649-016-9709-4. 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.

**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. Trenholm, S,

**Alcock, L**, Robinson, C (2016) The instructor experience of fully online tertiary mathematics: a challenge and an opportunity,

*Journal for Research in Mathematics Education*, ISSN: 1945-2306. DOI: 10.5951/jresematheduc.47.2.0147. Trenholm, S,

**Alcock, L**, Robinson, C (2015) An investigation of assessment and feedback practices in fully asynchronous online undergraduate mathematics courses,

*International Journal of Mathematical Education in Science and Technology*, ISSN: 0020-739X. DOI: 10.1080/0020739X.2015.1036946.

**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.

**Alcock, L**, Brown, G, Dunning, C (2015) Independent study workbooks for proofs in group theory,

*International Journal of Research in Undergraduate Mathematics Education*, ISSN: 2198-9745. DOI: 10.1007/s40753-015-0009-7. 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.

**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.

**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. 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 and

**Alcock, L**(2013) Peer assessment without assessment criteria,

*Studies in Higher Education*, 39(10), pp.1774-1787, ISSN: 0307-5079. DOI: 10.1080/03075079.2013.821974. 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. 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. Trenholm, S,

**Alcock, L**, Robinson, CL (2012) Mathematics lecturing in the digital age,

*International Journal of Mathematical Education in Science and Technology*, 43(6), pp.703-716, ISSN: 0020-739X. DOI: 10.1080/0020739X.2011.646325. 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.

**Alcock, LJ**and Simpson, A (2011) Classification and concept consistency,

*Canadian Journal of Science, Mathematics and Technology Education*, 11, pp.91-116.

**Alcock, LJ**and Wilkinson, N (2011) e-Proofs: Design of a resource to support proof comprehension in mathematics,

*Educational Designer*, 1(4), pp.none-none.

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

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

**Alcock, LJ**(2010) Mathematicians' perspectives on the teaching and learning of proof,

*F.Hitt, D.Holton & P.W. Thompson(Eds) Research in Collegiate Mathematics Education VII, Washington DC: MAA*, pp.63-92.

**Alcock, LJ**and Weber, K (2010) Referential and syntactic approaches to proof: Case studies from a transition-to-proof course,

*In F. Hitt, D. Holton & P.W. Thompson (Eds) Research in Collegiate Mathematics Education VII, Washington DC: MAA*, pp.93-114.

**Alcock, LJ**and Weber, K (2010) Undergraduates' example use in proof construction: Purposes and effectiveness,

*Investigations in Mathematics Learning*, 3(1), pp.1-22. Edwards, A and

**Alcock, LJ**(2010) Using Rasch analysis to identify uncharacteristic responses to undergraduate assessments,

*Teaching Mathematics and its Applications*, 29, pp.165-175.

**Alcock, L**and Weber, K (2010) Undergraduates’ Example Use in Proof Construction: Purposes and Effectiveness,

*Investigations in Mathematics Learning*, 3(1), pp.1-22, ISSN: 1947-7503. DOI: 10.1080/24727466.2010.11790298.

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

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

**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.

**Alcock, LJ**and Weber, K (2005) Proof validation in real analysis: Inferring and checking warrants,

*Journal of Mathematical Behaviour*, 24(2), pp.125-134, ISSN: 0732-3123. DOI: 10.1016/j.jmathb.2005.03.003.

**Alcock, LJ**and Simpson, AP (2005) Convergence of sequences and series 2: Interactions between non-visual reasoning and the learner's beliefs about their own role,

*Educational Studies in Mathematics*, 58(1), pp.77-110, ISSN: 1573-0816. DOI: 10.1007/s10649-005-2813-5. Weber, K and

**Alcock, LJ**(2005) Using warranted implications to understand and validate proofs,

*For the Learning of Mathematics*, 25(1), pp.34-38, 51.

**Alcock, LJ**and Simpson, AP (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), pp.1-32, ISSN: 1573-0816. DOI: 10.1023/B:EDUC.0000047051.07646.92. Weber, K and

**Alcock, LJ**(2004) Semantic and syntactic proof productions,

*Educational Studies in Mathematics*, 56(3), pp.209-234, ISSN: 1573-0816. DOI: 10.1023/B:EDUC.0000040410.57253.a1.

## Conferences

Woollacott, B,**Alcock, L**, Inglis, M (2024) DOES HIGHLIGHTING KEY INFORMATION HELP OR HINDER MATHEMATICAL READING?. In , Proceedings of the International Group for the Psychology of Mathematics Education, p.238.

**Alcock, L**and Davies, B (2023) Believability in mathematical conditionals: generating items for a conditional inference task. In

*26th Conference on Research in Undergraduate Mathematics Education; Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education*, Omaha, Nebraska, USA.

**Alcock, L**and Attridge, N (2022) Counterexamples and refutations in undergraduate mathematics. In Karunakaran, SS and Higgins, A (ed)

*2022 Conference on Research in Undergraduate Mathematics Education; Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education*, Boston, Massachusetts, USA, pp.1-9. 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.

**Alcock, L**, Hernandez-Martinez, P, Patel, AG (2016) Study habits in undergraduate mathematics: a social network analysis. In

*40th Annual Conference of the International Group for the Psychology of Mathematics Education*, Szeged, Hungary.

**Alcock, L**, Owen, A, Allinson, R (2015) Diagram construction and performance in advanced mathematics. In

*39th Conference of the International Group for the Psychology of Mathematics Education*, Hobart, Tasmania, Australia.

**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. Trenholm, S,

**Alcock, L**, Robinson, C (2011) MATHEMATICS LECTURING IN THE DIGITAL AGE. In , PROCEEDINGS OF THE 35TH CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION, VOL. 1: DEVELOPING MATHEMATICAL THINKING, pp.404-404. 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.93-114. Edwards, A and

**Alcock, LJ**(2010) How do undergraduate students navigate their example spaces?. In

*Proceedings of the 32nd Conference on Research in Undergraduate Mathematics Education*, Raleigh, NC, USA.

**Alcock, LJ**and Simpson, A (2009) The role of definitions in example classification. In

*Proceedings of the 33rd Conference of the International Group for the Psychology of the Mathematics Education*, In M. Tzekaki, M. Kaldrimidou & Sakonidis (Eds), Thessaloniki, Greece, pp.33-40.

**Alcock, LJ**(2009) e-Proofs: Student experience of online resources to aid understanding of mathematical proofs. In

*Proceedings of the 12th Conference on Research in Undergraduate Mathematics Education*, Online at http://mathed.asu.edu/crume2009/proceedings.html, Raleigh, NC, USA, pp.33-40.

**Alcock, LJ**(2009) Workbooks for independent study of group theory proofs. In

*Proceedings of the 12th Conference on Research in Undergraduate Mathematics Education*, Online at http://mathed.asu.edu/crume2009/proceedings.html, Raleigh, NC, USA, pp.33-40.

**Alcock, LJ**(2009) Teaching proof to undergraduates:Semantic and syntactic approaches. In

*Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education*, Online at http://ocs.library/utoronot.ca/index.php/icmi/8, Taipei,Taiwan, pp.33-40.

**Alcock, LJ**(2009) e-Proofs: Online resources to aid understanding of mathematical proofs. In

*CETL-MSOR Conference*, tba, Lancaster, UK, pp.33-40.

**Alcock, LJ**, Brown, GD, Dunning, C (2009) Workbooks for Independent Study of Group Theory Proofs. In

*Proceedings of the Conference on Research in Undergraduate Mathematics Education*, Raleigh, North Carolina, 12 .

**Alcock, LJ**(2007) Watching students construct proofs. Invited plenary address. In

*3rd Irish Symposium for Undergraduate Mathematics Education*, Galway, Ireland.

**Alcock, LJ**(2007) Proving styles in advanced mathematics. Contributed talk with Keith Weber and Luliana Radu. In

*SIGMMA on RUME 10*, San Diego, USA, pp.34-38, 51.

**Alcock, LJ**(2007) Engaging mathematics professors in discussions about learning via annotated video of student proof attempts. Preliminary report with Keith Weber and Anne Seery. In

*SIGMAA on RUME 10*, San Diego, USA.

**Alcock, LJ**(2007) How do students think about proof? A DVD resource for Mathematicians. In

*PME 31*, Seoul, South Korea.

**Alcock, LJ**(2006) How do students think about proof? A professional development DVD for mathematicians. In

*Mathematicians and Mathematics Educationalists: Can we collaborate?*, Warwick, UK.

**Alcock, LJ**(2005) Proving: The use of instantiations. Contributed talk with Keith Weber. In

*SIGMAA on RUME 8*, Arizona, USA. Weber, K,

**Alcock, LJ**, Radu, I (2005) Undergraduates' use of examples in a transition to proof course. In

*PME-NA 27*, Roanoake, Virginia, USA, pp.99-111.

**Alcock, LJ**(2005) Undergraduates' use of examples in a transition to proof course. In

*PME-NA 27*, Roanoake, Virginia, USA.

**Alcock, LJ**(2004) Using a warranted conception of implication to validate proofs. Short oral report with Keith Weber. In

*PME-NA 26*, Toronto, Canada.

**Alcock, LJ**(2004) Large numbers and generalization in the absence of algebraic notation. Short oral report with Rahul Malhotra. In

*PME-NA 26*, Toronto, Canada.

**Alcock, LJ**(2004) Symbolic cognition and non-visual reasoning in real analysis. Invited presentation in working group on symbolic cognition in advanced mathematics. In

*PME 28*, Bergen, Norway. Weber, K and

**Alcock, LJ**(2004) How do mathematicians validate proofs?. In

*PME-NA 26*, Toronto, Canada, pp.209-234.

**Alcock, LJ**(2004) Uses of example objects in proving. In

*PME 28*, Bergen, Norway.

## Books

**Alcock, L**(2017)

*Mathematics Rebooted A Fresh Approach to Understanding*, Oxford University Press, ISBN: 9780198803799.

**Alcock, L**(2016)

*Wie man erfolgreich Mathematik studiert Besonderheiten eines nicht-trivialen Studiengangs*, Springer Spektrum, ISBN: 9783662503843.

**Alcock, L**(2014)

*How to Think about Analysis*, Oxford University Press, ISBN: 9780198723530.

**Alcock, L**(2012)

*How to Study for a Mathematics Degree*, OUP Oxford, ISBN: 9780191637377.

**Alcock, LJ**and Simpson, A (2009)

*Ideas from mathematics education: An introduction for mathematicians*, MSOR Network.

## Chapters

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. Jones, I and Alcock, (2012) Summative peer assessment of undergraduate calculus using Adaptive Comparative Judgement. In Iannone, P and Simpson, A (ed)

*Mapping University Mathematics Assessment Practices*, University of East Anglia, pp.63-74, ISBN: 9781870284011.

**Alcock, LJ**(2010) Interactions between teaching and research: Developing pedagogical content knowledge for Real Analysis. In Leikin, IR and Eds, RZ (ed)

*Learning through teaching: Developing mathematics teachers' knowledge adn expertise in practice*, Dordrecht: Springer, pp.227-246. Weber, K and

**Alcock, L**(2010) Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning in the Representation System of Proof. In

*Teaching and Learning Proof Across the Grades: A K-16 Perspective*, pp.323-338, DOI: 10.4324/9780203882009-19. Weber, K and

**Alcock, LJ**(2009) Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning in the Representation System of Proof. In Stylianou, IDA, Blanton, ML, Eds, EK (ed)

*Teaching and learning proof across the grades: A K-16 perspective*, pp.33-40.

**Alcock, LJ**and Simpson, AP (2001) The Warwick Analysis project: practice and theory. In Ed, DH (ed)

*The teaching and learning of mathematics at university level,*, Dordrecht: Kluwer, pp.99-111.

## Internet Publications

Davies, B,**Alcock, L**, Jones, I (Accepted for publication)

*Students' and mathematicians' written conceptions of proof*. Davies, B,

**Alcock, L**, Jones, I (Accepted for publication)

*Comparative judgment and proof comprehension: supplementary material*.

**Alcock, L**and Sa, R (Accepted for publication)

*How do Introduction-to-Proof Textbooks Explain Conditionals and Implications? Supplementary Materials*.

## Other

Hodds, M,**Alcock, L**, Inglis, M (2014)

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

**Alcock, LJ**, Robinson, CL (2013)

*Development of a Summated Scale for Measuring Approaches to Assessment Practice of Undergraduate Mathematics Lecturers*.

**Alcock, LJ**(2009)

*Students and proof: bounds and functions*, DVD.

**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..