Research papers

Journal articles

2018

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 Educationhttps://doi.org/10.1007/s40753-018-0077-6

2017

Roy, S., Alcock, L., & Inglis, M. (2017). Multimedia resources designed to support learning from written proofs: An eye-movement study. Educational Studies in Mathematics, 96, 249-266https://doi.org/10.1007/s10649-017-9754-7

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. https://doi.org/10.1080/14794802.2017.1285720

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

2016

Alcock, L., Ansari, D., Batchelor, S., Bisson, M.-J., De Smedt, B., Göbel, S.M., Hannula-Sormunen, M., Hodgen, J., Inglis, M., Jones, I., Mazzocco, M., McNeil, M., Schneider, M., Simms, V., & Weber, K. (2016).  Challenges in mathematical cognition: A collaboratively-derived research agenda.  Journal of Numerical Cognition, 2, 20-41.  https://doi.org/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, 47, 147-161.  https://doi.org/10.5951/jresematheduc.47.2.0147

2015

Alcock, L., Brown, G. & Dunning, T.C. (2015). Independent study workbooks for proofs in group theory.  International Journal for Research in Undergraduate Mathematics Education, 1, 3-26.  https://doi.org/10.1007/s40753-015-0009-7

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.  46, 1197-1221.  https://doi.org/10.1080/0020739X.2015.1036946

2014

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.  https://doi.org/10.1080/14794802.2013.874094

Hodds, M., Alcock, L., & Inglis, M. (2014). Self-explanation training improves proof comprehension.  Journal for Research in Mathematics Education, 45, 62-101.  https://doi.org/10.1080/03075079.2013.821974

Jones, I., & Alcock, L. (2014).  Peer assessment without assessment criteria.  Studies in Higher Education, 39, 1774-1787.  https://doi.org/10.1080/03075079.2013.821974

2013

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.  https://doi.org/10.1111/tops.12019

Inglis, M. & Alcock, L. (2013).  Skimming: A Response to Weber & Mejía-Ramos.  Journal for Research in Mathematics Education, 44, 471-474.  https://doi.org/10.5951/jresematheduc.43.4.0358

2012

Inglis, M., & Alcock, L. (2012).  Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education, 43, 358-390.  https://doi.org/10.5951/jresematheduc.43.4.0358

Trenholm, S., Alcock, L., & Robinson, C. (2012). Mathematics lecturing in the digital age.  International Journal of Mathematical Education in Science and Technology, 43, 703-716.  https://doi.org/10.1080/0020739X.2011.646325

2011

Alcock, L. and Simpson, A. (2011). Classification and concept consistency. Canadian Journal of Science, Mathematics and Technology Education, 11, 91–106.  https://doi.org/10.1080/14926156.2011.570476

Alcock, L. & Wilkinson, N. (2011).  e-Proofs: Design of a resource to support proof comprehension in mathematics.  Educational Designer, 4. http://www.educationaldesigner.org/ed/volume1/issue4/article14/index.htm.

2010

Alcock, L. & Weber, K. (2010).  Undergraduates’ example use in proof construction: Purposes and effectiveness.  Investigations in Mathematics Learning, 3(1), 1-22.  https://doi.org/10.1080/24727466.2010.11790298

Edwards, A. & Alcock, L. (2010).  Using Rasch analysis to identify uncharacteristic responses to undergraduate assessments.  Teaching Mathematics and its Applications, 29, 165-175.  https://doi.org/10.1093/teamat/hrq008

Alcock, L. & Inglis, M. (2010).  Visual considerations in the presentation of mathematical proofs.  Seminar.Net 6(1). http://seminar.net/index.php/component/ content/article/75/139-visual-considerations-in-the-presentation-of-mathematical-proofs.

Alcock, L. (2010).  Mathematicians’ perspectives on the teaching and learning of proof.  In F. Hitt, D. Holton & P.W. Thompson (Eds.) Research in Collegiate Mathematics EducationVII, Washington DC: MAA, pp.63-91. https://doi.org/10.1090/cbmath/016/03

Alcock, L. & 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 EducationVII, Washington DC: MAA, pp.93-114. https://doi.org/10.1090/cbmath/016/04

2009

Alcock, L. & Inglis, M. (2009).  Representation systems and undergraduate proof production: A comment on Weber.  Journal of Mathematical Behavior, 28, 209-211.  https://doi.org/10.1016/j.jmathb.2009.10.001

2008

Alcock, L. & Inglis, M. (2008).  Doctoral students’ use of examples in evaluating and proving conjectures.  Educational Studies in Mathematics, 69, 111-129.  https://doi.org/10.1007/s10649-008-9149-x

2005

Alcock, L.J. & Weber, K. (2005). Proof validation in real analysis: Inferring and checking warrants. Journal of Mathematical Behavior, 24, 125-134.  https://doi.org/10.1016/j.jmathb.2005.03.003

Alcock, L.J. & Simpson, A.P. (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, 77-110.  https://doi.org/10.1007/s10649-005-2813-5

Weber, K. & Alcock, L.J. (2005).  Using warranted implications to understand and validate proofs. For the Learning of Mathematics, 25, 34-38, 51.

2004

Alcock, L.J. & Simpson, A.P. (2004). Convergence of sequences and series: interactions between visual reasoning and the learner’s beliefs about their own role. Educational Studies in Mathematics, 57, 1-32.  https://doi.org/10.1023/B:EDUC.0000047051.07646.92

Weber, K. & Alcock, L.J. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56, 209-234.  https://doi.org/10.1023/B:EDUC.0000040410.57253.a1

2002

Warner, L.B., Davis, G.E., Alcock, L.J. & Coppolo, J. Jr. (2002). Flexible mathematical thinking and multiple representations in middle school mathematics. Mediterranean Journal for Research in Mathematics Education, 1, 37-61.

Alcock, L.J. & Simpson, A.P. (2002). Definitions: dealing with categories mathematically.  For the Learning of Mathematics, 22, 28-34.

Book chapters

2012

Jones, I. & Alcock, L. (2012). Summative peer assessment of undergraduate calculus using adaptive comparative judgement. In P. Iannone & A. Simpson (Eds.), Mapping University Mathematics AssessmentPractices. Norwich: University of East Anglia, pp.63-74.

2010

Alcock, L. (2010).  Interactions between teaching and research: Developing pedagogical content knowledge for Real Analysis.  In R. Leikin & R. Zazkis (Eds.), Learning through teaching: Developing mathematics teachers’ knowledge and expertise in practice.  Dordrecht: Springer, pp. 227-246.

2009

Weber, K. & Alcock, L. (2009). Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning in the Representation System of Proof.  In D.A. Stylianou, M.L. Blanton & E. Knuth (Eds.), Teaching and learning proof across the grades: A K-16 perspective.  New York: Routledge, pp. 323-338.

2001

Alcock, L.J. & Simpson, A.P. (2001).  The Warwick Analysis project: practice and theory.  In D. Holton, (Ed.), The teaching and learning of mathematics at university level, Dordrecht: Kluwer, pp. 99-111.

Conference papers

2017

Alcock, L., Inglis, M., Lew, K., Mejía-Ramos, P., Rago, P., & Sangwin, C. (2017).  Comparing expert and learner mathematical language: A corpus linguistics approach.  CRUME 20, San Diego, USA.

2016

Alcock, L., Hernandez-Martinez, P., & Godwin Patel, A. (2016).  Study habits in undergraduate mathematics: A social network analysis.  PME40.  Szeged, Hungary.

2015

Alcock, L., Kilbey, T., & Inglis, M. (2015).  How do undergraduates read mathematical texts?  An eye-movement study.  khdm Conference 2015: Didactics of Mathematics in Higher Education as a Scientific Discipline.  Hannover, Germany.

Alcock, L., Owen, A., & Allinson, R. (2015).  Diagram construction and performance in advanced mathematics.  PME 39.  Hobart, Tasmania, Australia.

2014

Alcock, L., Bailey, T., Inglis, M., & Docherty, P. (2014).  The ability to reject invalid logical inferences predicts proof comprehension and mathematics performance. CRUME 17.  Denver, CO, USA.

2010

Roy, S., Alcock, L. & Inglis, M. (2010).  Undergraduates’ proof comprehension: A comparative study of three forms of proof presentation.  CRUME 13.  Raleigh, NC, USA.

Edwards, A. & Alcock, L. (2010).  How do undergraduate students navigate their example spaces?  CRUME 13.  Raleigh, NC, USA.

2009

Alcock, L. & Simpson, A. (2009).  The role of definitions in example classification.  In M. Tzekaki, M. Kaldrimidou & H. Sakonidis (Eds.), PME 33.  Vol. 2 (pp.33-40).  Thessaloniki, Greece.

Alcock, L. (2009).  Teaching proof to undergraduates: Semantic and syntactic approaches.  Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education.  Taipei, Taiwan.  Online at http://ocs.library.utoronto.ca/index.php/icmi/8.

Alcock, L. (2009). e-Proofs: Student experience of online resources to aid understanding of mathematical proofs.  CRUME 12.  Raleigh, NC, USA.

Alcock, L. (2009).  Workbooks for independent study of group theory proofs.  CRUME 12.  Raleigh, NC, USA.

2008

Alcock, L.J. (2008). e-Proofs: Online resources to aid understanding of mathematical proofs.  CETL-MSOR Conference.  Lancaster, UK.

2007

Alcock, L.J. (2007).  How do your students think about proof?  A DVD resource for Mathematicians.  PME 31.  Seoul, South Korea.

2005

Weber, K., Alcock, L.J. & Radu, I. (2005).  Undergraduates’ use of examples in a transition to proof course.  PME-NA 27.  Roanoake, Virginia, USA.

Alcock, L.J. & Weber, K. (2005). Referential and syntactic approaches to proof: Case studies from a transition course. PME 29.  Melbourne, Australia.

2004

Weber, K. & Alcock, L.J. (2004).  How do mathematicians validate proofs? PME-NA 26. Toronto, Canada.

Alcock, L.J. (2004). Uses of example objects in proving. PME 28. Bergen, Norway.

Alcock, L.J. (2004). Mathematicians’ perspectives on the transition to formal proof. Topic Study Group 19, 10th International Congress on Mathematics Education, Copenhagen, Denmark, (http://www.icme-organisers.dk/tsg19/Alcock.htm).

2003

Warner, L.B., Alcock, L.J., Coppolo, J. & Davis, G.E. (2003). How does flexible thinking contribute to the growth of understanding? PME 27 & PME-NA 25. Honolulu, Hawaii, USA.

2002

Alcock, L.J. & Simpson, A.P. (2002). Two components in learning to reason using definitions. 2nd International Conference on the Teaching of Mathematics (at the Undergraduate Level), Hersonisoss, Greece, (www.math.uoc.gr/~ictm2/).

2001

Alcock, L.J. & Simpson, A.P. (2001). Cognitive loops and failure in university mathematics, PME 25. Utrecht, The Netherlands.

1999

Alcock, L.J. & Simpson, A.P. (1999).  The rigour prefix.  PME 23.  Haifa, Israel.

1998

Alcock, L.J. & Simpson, A.P., (1998). Definitions in university students’ perceptions of structure. Proceedings of the International Conference on the Teaching of Mathematics, Samos, Greece.