Recently, Dr Kit Yates, a lecturer at the school of mathematical sciences at the University of Bath, caused a stir when he expressed frustration at what he sees as the disconnection between school maths and maths taught at university.
According to an article which appeared on The Guardian website on Saturday 20 February 2021, “…what he finds frustrating is the lying. The curriculum is forcing teachers to deliberately teach children lies … which then have to be unpicked later. For example, after years of being taught there are no numbers between zero and one, his seven-year-old is suddenly expected to understand that are such things as fractions.”
While many will find Kit Yates’ position extreme and his expression clumsy and unhelpful, this article did generate some very good Twitter discussion involving maths teachers at school and university about the transition between A level Mathematics and Further Mathematics, and undergraduate maths.
For instance, Dr Vicky Neale, maths lecturer at the University of Oxford, put it nicely when she tweeted, “Otherwise, I think my students and I are looking at different perspectives on ideas, rather than ‘correcting’ or ‘unteaching’ half-truths.” She went on to give the example of a function: the university perspective on this is any suitable rule; at school, it’s more likely to be seen as something with a neat formula and a graph.
Reflecting on the transition between A level Mathematics and Further Mathematics, and undergraduate maths, I find the diagram below, devised by the AMSP’s Phil Chaffé, useful. Phil places various exams – AS Mathematics, A level Mathematics and A level Further Mathematics, along with university admissions tests TMUA, MAT, (the now defunct) STEP 1, STEP 2 and STEP 3 – in a two-dimensional space with axes labelled ‘routine techniques’ and ‘problem-solving skills’. Also pictured is the red ‘landing area’ of undergraduate maths. The idea the diagram is trying to convey is that the problem-solving demands of the university entrance exams makes them excellent preparation for those A level students who have ambitions to study maths at university. Moreover, while MAT, TMUA and some STEP papers cover less content than, say, A level Further Mathematics, perhaps the advanced problem-solving skills they demand make them an excellent complement to A levels for students who are intending to study maths at university.
The question of the role of university admissions tests in preparing students to study maths at university is directly addressed in the paper, ‘What benefits could extension papers and admissions tests have for university mathematics applicants?’ by Dr Ellie Darlington from Cambridge Assessments.
In the paper, Dr Ellie Darlington attempts to classify questions from A level Mathematics, university admissions papers and undergraduate exam papers according to a taxonomy involving three basic groups:
- Group A (factual recall and routine procedures)
- Group B (using mathematical knowledge and techniques in new ways)
- Group C (application of conceptual knowledge to construct mathematical arguments)
According to this analysis, the exams which most closely resemble university undergraduate exams are the STEP and MAT papers. For example, more than 50% of the available marks on the papers sat by undergraduates belong to the Group C category (constructing mathematical arguments), and many marks on STEP and MAT papers are also awarded for constructing mathematical arguments, whereas in the A level papers of 2015, only a small percentage of marks were awarded for mathematical reasoning.
Dr Darlington’s paper is from 2015, and so, while her analysis of A levels is pertinent to the old specifications, it may not be as relevant to the reformed A levels – for what it’s worth, my feeling is that newer A level papers are more demanding. Her paper also misses out on TMUA, which is a much newer admissions test. It would be interesting to read an up-to-date analysis.
It would be interesting to hear your opinions, perhaps at one of our upcoming Teacher Network meetings.