Essential Concepts for the First Year of Study for BSc Mathematics

Alexander Capes, Peter Rowlett

Abstract


To inform discussion about content for the first year of undergraduate mathematics, a study was completed which reviewed: the A-level Mathematics specification; published literature on the transition from A-level to university mathematics; the second and third year curricula of modules at three English universities with different foci. This aimed to investigate what students might reasonably be expected to have covered when they arrive at university, what happens in practice at the transition to university, and the role of the first year as preparation for later study. Content suggestions focus on calculus, linear algebra and analysis as core topics. There is also evidence of the need to focus on students' understanding of where formulae and solutions originated as well as their ability to produce pieces of academic and mathematical writing. Findings also include suggestion that what happens in the first year, while similar between institutions, does depend on the overall focus of the degree programme.

Keywords


undergraduate, mathematics education, transition, Further Education, Higher Education

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References


Abdulwahed, M., Jaworski, B. and Crawford, A., 2012. Innovative approaches to teaching mathematics in higher education: a review and critique. Nordic Studies in Mathematics Education, 17(2), pp. 49-68.

Biza, I., Giraldo, V., Hochmuth, R., Khakbaz, A., Rasmussen, C., 2016. Research on Teaching and Learning Mathematics at the Tertiary Level. http://dx.doi.org/10.1007/978-3-319-41814-8

Burghes, D., 1990. A-level Mathematics: A Time for Change? Teaching Mathematics and its Applications, 9(3), pp. 97-101. http://dx.doi.org/10.1093/teamat/9.3.97

Burton, L., Haines, C., 1997. Innovation in teaching and Assessing Mathematics at University Level. Teaching in Higher Education, 2(3), pp. 273-293. http://dx.doi.org/10.1080/1356215970020308

Department for Education, 2016. Mathematics AS and A Level Content. London: Department for Education.

Ellis, J., Hanson, K., Nuñez, G., Rasmussen, C., 2015. Beyond Plug and Chug: an Analysis of Calculus I Homework. International Journal of Research in Undergraduate Mathematics Education, 1(2), p. 268-287. http://dx.doi.org/10.1007/s40753-015-0012-z

Epstein, J., 2013. The Calculus Concept Inventory – Measurement of the Effect of Teaching Methodology in Mathematics. Notices of the American Mathematical Society, 60(8), pp. 1018-1026. http://dx.doi.org/10.1090/noti1033

Good, C., 2011. ‘We can’t let them graduate unless...’ In: P. Rowlett, ed., 2011. HE Mathematics Curriculum Summit. Birmingham, U.K.: Maths, Stats and OR Network. pp. 15-16.

The Guardian, 2017. Guardian University League Table 2018. [online] Available at: https://www.theguardian.com/education/ng-interactive/2017/may/16/university-league-tables-2018 [Accessed 15 October 2017].

Hoyles, C., Newman, K., Noss, R., 2001. Changing patterns of transition from school to university mathematics. International Journal of Mathematical Education in Science and Technology, 32(6), pp. 829-845. http://dx.doi.org/10.1080/00207390110067635

Iannone, P. and Simpson, A., 2011. The summative assessment diet: how we assess in mathematics degrees. Teaching Mathematics and its Applications, 30(4), pp. 186-196. http://dx.doi.org/10.1093/teamat/hrr017

Iannone, P., Simpson, A., 2012. Oral assessment in mathematics: implementation and outcomes. Teaching Mathematics and its Applications, 31(4), pp. 179-190. http://dx.doi.org/10.1093/teamat/hrs012

Jaworski, B., Mali, A., Petropoulou, G., 2017. Critical Theorising from Studies of Undergraduate Mathematics Teaching for Students’ Meaning Making in Mathematics. International Journal of Research in Undergraduate Mathematics Education, 3(1), pp. 168-197. http://dx.doi.org/10.1007/s40753-016-0044-z

Kalajdzievska, D., 2014. Taking Math Students From “Blah” to “Aha”: What can we do? PRIMUS, 24(5), pp. 375-391. http://dx.doi.org/10.1080/10511970.2014.893937

Lawson, D., 1997. What can we expect from A-level Mathematics Students? Teaching Mathematics and its Applications, 16(4), pp. 151-156 http://dx.doi.org/10.1093/teamat/16.4.151

London Mathematical Society (LMS), Institute of Mathematics and its Applications (IMA), Royal Statistical Society (RSS), 1995. Tackling the Mathematics Problem. Available at: http://mei.org.uk/files/pdf/Tackling_the_Mathematics_Problem.pdf [Accessed 15 October 2017].

Moore, R., 1994. Making the transition to formal proof. Educational Studies in Mathematics, 27(3), pp. 249-266. http://dx.doi.org/10.1007/BF01273731

Nardi, E. and Steward, S., 2003. Is Mathematics T.I.R.E.D? A Profile of Quiet Disaffection in the Secondary Mathematics Classroom. British Educational Research Journal, 30(3), pp. 345-367. http://dx.doi.org/10.1080/01411920301852

Ofsted, 2012. Mathematics: made to measure. Messages from inspection evidence (Report No. 110159). Manchester: Office for Standards in Education, Children’s Services and Skills.

Osmon, P., 2010. What maths do you need for university? Proceedings of the British Society for Research into Learning Mathematics, 30(2), pp. 41-46. Available at: http://www.bsrlm.org.uk/wp-content/uploads/2016/02/BSRLM-IP-30-2-08.pdf [Accessed 15 October 2017].

Osmon, P., 2013. A-level mathematics reform: satisfying the requirements of university courses across the range of mathematical subjects. Proceedings of the British Society for Research into Learning Mathematics, 33(1), pp. 43-48. Available at: http://www.bsrlm.org.uk/wp-content/uploads/2016/02/BSRLM-IP-33-1-08.pdf [Accessed 15 October 2017].

Prendergast, M., Faulkner, F., Breen, C., Carr, M., 2017. Mind the gap: an initial analysis of the transition of a second level curriculum reform to higher education. Teaching Mathematics and its Applications, 36(1), pp. 1-15. http://dx.doi.org/10.1093/teamat/hrw024

QAA, 2015. Subject Benchmark Statement: Mathematics, Statistics and Operational Research. Available at: http://www.qaa.ac.uk/en/Publications/Documents/SBS-Mathematics-15.pdf [Accessed 15 October 2017].

Sofronas, K., DeFranco, T., Swaminathan, H., Gorgievski, N., Vinsonhaler, C., Wiseman, B., Escolas, S., 2015. A Study of Calculus Instructors’ Perceptions of Approximation as a Unifying Thread of the First-Year Calculus. International Journal of Research in Undergraduate Mathematics Education, 1(3), pp. 386-412. http://dx.doi.org/10.1007/s40753-015-0019-5

Solomon, Y., 2006. Deficit or Difference? The Role of Students’ epistemologies of Mathematics in their Interactions with Proof. Educational Studies in Mathematics, 61(3), pp.373-393. http://dx.doi.org/10.1007/s10649-006-6927-1

Stylianou, D., Blanton, M., Rotou, O., 2015. Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof. International Journal of Research in Undergraduate Mathematics Education, 1(4), pp. 91-134. http://dx.doi.org/10.1007/s40753-015-0003-0




DOI: http://dx.doi.org/10.21100/msor.v16i2.702

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