The Mathematics Needs of Higher Education

The Mathematics Needs of Higher Education

This article was originally featured in 'Mathematics Today' Vol. 52

A-level Mathematics Reform

As part of an ongoing A Level reform programme in England, A Level Mathematics and A Level Further Mathematics will undergo subject-specific changes in addition to general A Level changes which will see the qualification move from a modular to a linear system (DfE, 2014a, 2014b).

"...reformed A Level Mathematics will have 100% prescribed content."

Currently, in the modular system of A Level Mathematics and A Level Further Mathematics students are able to specialise in a particular branch of applied mathematics (statistics, mechanics or decision mathematics) or to study a mixture. This flexibility means different students will have taken different module combinations by the time they reach university, thus engendering variability in new undergraduates’ mathematical backgrounds.

Planned for first teaching in 2017, the reformed A Level Mathematics will have 100% prescribed content, with compulsory mechanics and statistics topics, which should reduce disparities in students’ mathematical knowledge. Furthermore, half of the Further Mathematics content will be prescribed pure mathematics (ALCAB, 2014). The remaining 50% will be decided by the awarding bodies. Some of this is likely to be applied mathematics, due to the reduction in the amount of mechanics and statistics students can study in the new A Level Mathematics. "Most students who had taken Further Mathematics were enthusiastic about it."



To assist with developments of A Level Further Mathematics modules, a study was conducted to investigate how students and lecturers perceive the current Mathematics A-levels as preparation for degrees with a mathematical component.

Method

This study comprised three strands:

1. A comparison of the applied mathematics content in curricula in other jurisdictions considered equivalent to A Level Mathematics and Further Mathematics.

2. Semi-structured interviews with university lecturers regarding their opinions about the existing Mathematics A Levels and the mathematical competency of their new undergraduates.

3. An online questionnaire for undergraduates who had taken at least AS Level Mathematics. Students were surveyed about their perceived mathematical preparedness for university study, their experiences of Further Mathematics, and their opinions about the utility of the applied mathematics modules they studied.

Participants from a variety of subject areas were involved in the study, with particular focus on architecture, bioscience, business studies, chemistry, computer science, economics, engineering, geography, mathematics, medicine, physics and psychology.

Findings

The international comparisons revealed notable differences between A Level Mathematics and its counterparts overseas relating to applied mathematics. England was "International comparisons revealed notable differences between A Level Mathematics and its counterparts overseas."

the only jurisdiction to include mechanics in mathematics (rather than physics) curricula, and there was significant variation in the volume and type of statistical content in A Level equivalents. This raises questions regarding what and how much applied mathematics should be taught at the pre-university level, and whether mechanics content might be more appropriately placed in physics.

The interviews showed that university lecturers were generally satisfied with the existing content of A Level Mathematics and A Level Further Mathematics. However, most encountered significant problems with new undergraduates’ abilities to apply mathematics in unfamiliar contexts, and to translate effectively between mathematics and science problems. This was attributed to numerous factors, such as the modularisation of A Levels and the nature of assessment.

Finally, the questionnaires garnered an enthusiastic response from over 4,000 students. Participants’ opinions about post-compulsory mathematics varied substantially across degree subjects, particularly regarding the applied modules they considered most useful as preparation for the mathematical component of their degrees. Generally, students in the physical sciences preferred mechanics; those in the biological and social sciences preferred statistics; and computer scientists preferred decision mathematics. Most students who had taken Further Mathematics were enthusiastic about it, but there was variability in how useful it was perceived to be as preparation for university. Mathematics, chemistry, physics and economics undergraduates found it very useful and, whilst students of medicine and architecture found it enjoyable, they reported that Further Mathematics had little relevance to their degrees.

Implications

Students wishing to specialise in a particular area of applied mathematics will have to take Further Mathematics in future, as the reformed A Level Mathematics will "...reformed A Level mathematics will not permit specialisation."

not permit specialisation. Therefore careful attention to the outcomes of this study may help to increase participation in Further Mathematics. It will be important for teachers, careers advisers and universities to signpost to prospective undergraduates the areas of applied mathematics which will be most useful in order to ease the transition to university-level study of particular subjects.

The reforms to the Mathematics A Levels and the introduction of a new Core Mathematics qualification provide an opportunity for universities to revise their guidance to prospective students. A formal entry requirement of A Level Mathematics and/or A Level Further Mathematics may not always be appropriate, but proper guidance of prospective undergraduates could help to ensure they are better informed about – and prepared for – the mathematical demands of certain degree subjects.

Publications

A short article in the informal proceedings of the British Society for Research into Learning Mathematics is now available regarding undergraduate mathematicians’ perceptions of A Level Further Mathematics (Darlington, 2015). An analysis and comparison of international curricula equivalent to A Level Mathematics with regards to their applied mathematics content has also been published (Munro, 2015). Further findings of this project will be published in due course.

Anyone interested in receiving updates on when publications will be made available should contact darlington.e@cambridgeassessment.org.uk

References

Bowyer, J. & Darlington, E. (2017) Mathematical struggles and ensuring success: post-compulsory mathematics as preparation for undergraduate bioscience. Journal of Biological Education, online, 1-12. DOI: http://dx.doi.org/10.1080/00219266.2017.1285803

Darlington, E. & Bowyer, J. (2017). The mathematics needs of prospective geography undergraduates. Journal of Research in Social Sciences, 5(2), 11-35

Darlington, E. & Bowyer, J. (2017). Students’ views of A-level Mathematics as preparation for degree-level economics. Citizenship, Social and Economics Education. DOI: http://dx.doi.org/10.1177%2F2047173417716423

Bowyer, J. & Darlington, E. (2017) Should I take Further Mathematics? Physics undergraduates’ experiences of post-compulsory Mathematics. Physics Education, 52(1), 1-9. DOI: http://dx.doi.org/10.1088/1361-6552/52/1/015007

Darlington, E. and Bowyer, J. (2017) Decision Mathematics as Preparation for Undergraduate Computer Science. International journal of Modern Education and Computer Science, 9(4), 1-11. DOI: 10.5815/ijmecs.2017.04.01

Darlington, E. & Bowyer, J. (2017). The role of ‘extension papers’ in preparation for undergraduate mathematics: students’ views of the MAT, AEA and STEP. Teaching Mathematics and its Applications, advance online access. https://doi.org/10.1093/teamat/hrx009
 
Darlington, E. & Bowyer, J. (2016) Accounting for students’ mathematical preparedness for Finance and Business degrees. Research Matters, 22 (Summer), 9-16. Available: http://www.cambridgeassessment.org.uk/Images/322752-research-matters-22-summer-2016.pdf

Darlington, E. (2016) I want to study science, maths or social science at university… what maths options should I take? The Student Room. Available from: https://www.thestudentroom.co.uk/content.php?r=27234-I-want-to-study-science-maths-or-social-science-at-university%E2%80%A6-what-maths-options-should-I-take

Bowyer, J. and Darlington, E. (2016) “Applications, applications, applications”: Lecturers’ perceptions of students’ mathematical preparedness for STEMM and Social Science degrees. Cambridge: Cambridge Assessment. Available from: http://www.cambridgeassessment.org.uk/Images/419688-lecturers-perceptions-of-students-mathematical-preparedness-for-stemm-and-social-science-degrees.pdf

Darlington, E. & Bowyer, J. (2016) Engineering undergraduates’ views of A-level Mathematics and Further Mathematics as preparation for their degree. Teaching Mathematics and its Applications, DOI: https://doi.org/10.1093/teamat/hrw020

Darlington, E. & Bowyer, J. (2016) How well does A-level Mathematics prepare students for the mathematical demands of chemistry degrees? Chemistry Education Research and Practice, 17, 1190-1202. DOI: http://dx.doi.org/10.1039/C6RP00170J

Darlington, E. & Bowyer, J. (2016) Students’ views of, and motivations for, studying A-level Further Mathematics. MSOR Connections, 15(1), 4-13. Available: https://journals.gre.ac.uk/index.php/msor/article/view/329

Darlington, E. & Bowyer, J. (2016) The Mathematics needs of prospective Architecture undergraduates. Research Matters, 21 (Winter), 11-16. Available: http://www.cambridgeassessment.org.uk/Images/294145-research-matters-21-winter-2016.pdf

Darlington, E. (2015) The Mathematics Needs of Higher Education. Sigma Network Newsletter, 9. Available: http://www.sigma-network.ac.uk/wp-content/uploads/2015/12/sigmanewsletter9_Dec15.html#MathsHE

Darlington, E. (2015). Students' Perceptions of A-level Further Mathematics as Preparation for Undergraduate Mathematics. Paper presented at the British Society for Research into Learning Mathematics, Durham University, UK.

Munro, J. (2015). Statistics & Mechanics: Comparing the Applied Mathematics of International Mathematics Qualifications. Research Matters: A Cambridge Assessment Publication, 20, 27-34.

ALCAB. (2014). Report of the ALCAB Panel on Mathematics & Further Mathematics. Retrieved 16 July, 2014, from https://alevelcontent.files.wordpress.com/2014/07/alcab-report-on-mathematics-and-further-mathematics-july-2014.pdf

DfE. (2014a). Further Mathematics: GCE AS & A Level Subject Content. London: Department for Education.

DfE. (2014b). Mathematics: GCE AS & A Level Subject Content. London: Department for Education.