Tracking Back Study - Key Findings

Stage: 5

The survey has revealed a great richness of information concerning mathematics education: much of it is surprising and much is well in line with the philosophies of NRICH mathematics. This is very pleasing as it validates the hard work and vision of the NRICH team in its efforts to improve mathematics education for all.

The main conclusions drawn from the data gathered are found in the table below.

Note on terminology: Parts '1A, 1B and II' refer to the first, second and final year of the undergraduate degrees in Cambridge.

  Key conclusions from survey Our comment or conjecture
0 From the data gathered, an interesting and stimulating mathematical experience in everyday school classrooms appeared to be the most important factor of benefit to the respondents, across all subjects. NRICH continues its work in task development, awareness and development of teachers in this area.
1 From the data gathered there emerged a sense of the importance of the social aspects of engagement with mathematics, such as mathematics clubs and competitions, in the preparation of students for university. Do these aspects of mathematics become more important at university?
2 From the data gathered there emerged a sense that respondents who felt that they had received relatively little useful preparation for university performed relatively well in Part 1A but performed relatively poorly in Part II of tripos across all subjects. Perhaps students with little useful preparation need to demonstrate intelligence or resourcefulness to gain their places which are useful skills in tripos success; good pre-university preparation gives students the staying power and solid grounding to do well at part II, as well as helping them to get onto the course in the first place?
3 Respondents' interest in, appreciation of and enjoyment of mathematics were very strongly related at all phases of education; these were also strongly related to seeing mathematics as a beautiful subject. Note that we believe that procedural, exam-focussed teaching rarely fosters an appreciation of the beauty of mathematics.
4 From the data gathered, the school teacher was by far the most important factor in fostering an enjoyment of mathematics. This adds evidence to the thesis that NRICH CPD work is of great value to the student.
5 From the data gathered, mathematics teachers were equally likely to be memorable for being capable, inspiring, approachable, fun or providing clear explanations. In short - good teachers appeared to come in a variety of packages.
6 Respondents who said that they were accelerated (felt that they had been entered for maths exams early) at school tended to enjoy mathematics at all stages of education. It is important to understand that the respondents are students at Cambridge. They are therefore 'successful' students who have successfully navigated their school education. This result does not imply that acceleration is a 'good' option for any students; more detailed study on this point would be interesting.
7 For the respondents, early choice of university course appears to lead to improved performance in tripos. Perhaps early choice leads to deeper preparation? This has strong implications concerning Further Mathematics, which is essential for mathematics and virtually essential for engineering and physics.
 
8 Enjoyment of mathematics is a strong indicator of university success across STEM subjects. This highlights the importance of mathematics in science and engineering degrees.
9 From the data gathered, there was no evidence that one-off enrichment events or 'key moments' impact university grade. Do schools realise that one-off events which are not reinforced by stimulating classroom environment may not measurably help students?
10 The only significant differences observed between Fully Comprehensive and Independent UK schooling concerned measures of preparation for Further Mathematics, STEP and the extension of mathematics beyond the curriculum by teachers: From the data gathered Independent schools provided significantly more extension of mathematics beyond the curriculum and significantly more Further Mathematics and STEP provision. This is a very important point for high-calibre students.

Further detailed question-by question analysis can be found here.