Tracking Back Study - Detailed Findings

Stage: 5

This page details the main findings from the study on a question-by-question basis. The main findings can be found here.

Note that in Cambridge University the terminology Parts IA, IB and II typically correspond to the first, second and third year of courses.

  1. For the data gathered from the Mathematics respondents:
  1. Part IA grade was most strongly related to interest, enjoyment and appreciation of mathematics.
  2. Part II grade was most strongly related to the perceived usefulness of students' teachers whilst at school along with an appreciation of mathematics and enjoying the challenge of mathematics.
  1. For the data gathered from the Natural Sciences respondents:
  1. In part 1A the most significant correlation with grade was the Total Influence of NRICH. These respondents may have been exposed to the trial university preparation pages on NRICH, as funded by DAMTP - This statistic provides evidence for the potential effectiveness of interventions of this type.
  2. Enjoyment of mathematics was a strong indicator of tripos success.
  1. For the data gathered from both the Natural Sciences and Engineering respondents:
  1. Part II grade was very strongly related to students' enjoyment of their university mathematics.
  2. Respondents who believed that good mathematics questions challenge them to think or to stimulate curiosity do well in tripos, especially in part II.
  1. For the data gathered from the Computer Sciences respondents:
  1. In part 1A Usefulness of NRICH and mathematics competitions were the two factors most strongly correlated with grade.
  2. In part 1B Usefulness of NRICH and holiday mathematics programmes were the two factors most strongly correlated with grade.
  1. For the data gathered from the Engineering respondents
  1. In Part I strength in mathematics was the main indicator of tripos success.
  2. Part II success was strongly related to the influence of external information sources: Wider reading, the internet and television.

Summary of other conclusions by question groups

Useful preparations for university courses

  1. From  the data gathered, the most important general factors/interventions in terms of positive university grade impact were:
  1. All subjects: Wider reading, internet, mathematics competitions
  2. Natural Sciences: NRICH website/Ask NRICH (for part 1A), wider Reading, enjoyment of mathematics.
  3. Mathematics: Teaching, attitudes towards mathematics.
  4. Computer Science: NRICH , mathematics clubs.
  5. Engineering : Strength in mathematics, wider reading,  internet, television, science festivals.
  1. Sixth form teachers, wider reading, internet, materials provided by the university, secondary school teachers and family were clearly perceived by respondents to be the most useful preparations for university course.
  2. 90% of respondents were exposed to mathematics competitions whilst at school; these were by far the most common 'optional' preparation and they were generally viewed very positively by the respondents.
  3. From the data gathered, there is some evidence that those preparations which focus on the social aspects of mathematics, particularly mathematics competitions, led to sustained improvement in tripos across all subjects.
  4. Overall, respondents with very little pre-university preparation tended to perform  slightly better in part IA than those with lots of pre-university preparation.
  5. Overall, respondents with lots of useful pre-university preparation tended to perform better in part II than those with little pre-university preparation.

Choice of university course

  1. Large numbers of respondents chose their degree course early on in their school career; 1 in 13 whilst at primary school. Large numbers (2 in 5) of respondents only chose their degree course after making their choice of A-levels - this has strong implications concerning Further Mathematics, which is essential for mathematics and virtually essential for engineering and physics.
  2. Respondents who chose their sort of course early in their school career tended to consider themselves to be strong at mathematics, tended to have been accelerated and tended do better in part II.
  3. Sixth form teachers, wider reading, family, internet and secondary Sshool teachers are clearly perceived by respondents to be the key influences in choice of university course


  1. Relatively few respondents had heard of NRICH or Ask NRICH, but around 25% of respondents who knew that they had used NRICH or Ask NRICH used them monthly or more - this suggests a strong appeal of NRICH to exceptional students, but more work needs to be done concerning awareness.
  2. Whether or not Ask NRICH / NRICH had been viewed was related to the maximum level of mathematics learned at school - note that many respondents will have been unknowingly exposed to NRICH via their teachers, particularly in primary and secondary schools. It is difficult for NRICH to get a clear picture of the extent of its impact as many teachers embed ideas from the website in their schemes of work and do not necessarily return to the site when using these embedded resources in the classroom. We plan to survey teachers to gain an indication of the prevalence of use.
  3. NRICH and Ask NRICH were perceived as equally useful, important and influential by respondents - either positively or negatively - this seems to suggest that students either tend to make good use of NRICH or not to use NRICH at all.

Concerning School Teachers

  1. Around one third of respondents reported no influential or inspirational teachers or events (concerning mathematics) during their entire school educational experience - is this acceptable?
  2. There were significant numbers of memorable primary teachers.
  3. There were disappointingly significant numbers of non-memorable secondary and sixth form teachers.
  4. Good teaching somewhat increased enjoyment, interest and positive views of mathematics.
  5. Teachers who extended mathematics beyond the curriculum and provide enrichment opportunities tended to create respondents who would not have wanted additional intervention in hindsight.
  6. Good teachers were equally likely to have been remembered by respondents for being mathematically capable, inspiring, approachable, fun or explaining things clearly - this seems to suggest that good, memorable teaching comes in a variety of packages.
  7. Respondents exposed to good teachers tended also to have more STEP support and FM support - this is an interesting point, as schools offering FM and STEP need mathematically high-calibre teachers .

University Course Influences

  1. Respondents studying Mathematics had been exposed to more mathematical influences whilst at school than respondents studying other subjects - given the late subject choice of many respondents might we conjecture the effectiveness of mathematical influences in university subject choice?

Type of schooling - Independent, Comprehensive, Overseas

  1. School type played little part in inspiration or influence concerning mathematics for the respondents - From the data gathered Independent and Comprehensive schools were equally likely to provide a good or bad educational experience regarding inspiration or influence.
  2. 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.
  3. From the data gathered there is some evidence that independent school teaching propagated through to somewhat improved success in part II, whereas the impact of comprehensive school teaching perceived as useful had little impact on success in part II.
  4. School type did not appear to be a factor in the number of key moments respondents experienced in mathematics.
  5. Comprehensive schooled respondents were slightly less likely to enjoy mathematics then independent or overseas schooled respondents.
  6. From the data gathered, independent 6th forms provided significantly more STEP support than Comprehensive 6th forms.
  7. From the data gathered there was little difference between the amount of preparation for university perceived as useful by Independent/Comprehensive schooled respondents; Overseas respondents received notably more Useful preparation.


  1. At each stage (primary, secondary, 6th form) of education around 1/3 of respondents were accelerated.  Respondents who were accelerated typically enjoyed and appreciated mathematics, made early choice of their degree course and considered their teaching to be good and influential.
  2. Respondents who had been accelerated in primary school were somewhat more likely to enjoy mathematics.
  3. From the data gathered, acceleration in secondary school was somewhat positively related to: good teaching; levels of enrichment; extending the curriculum; mathematics was made fun; mathematics was made enjoyable - this indicates a relationship between received enrichment and received acceleration at secondary school and a positive student view of these factors.
  4. Respondents who had been accelerated in sixth form felt somewhat more interested  in mathematics.

Perceptions of mathematics

  1. From the data gathered, interest, enjoyment and appreciation of mathematics were very strongly related across all stages of education.
  2. Respondents who enjoyed university mathematics tended to see it as a beautiful subject.
  3. NST and Engineering respondents who didn't find their mathematics at university beautiful found it hard to maintain interest and motivation - this indicates that procedural teaching and viewing mathematics as a 'service subject' are damaging to performance.
  4. From the data gathered, mathematics was clearly and significantly important to success in STEM subjects - there was a strong relationship between enjoying mathematics in NST, ENG and CS and doing well in tripos. From the data gathered, this was not the case for success in Part II Mathematics - are students sufficiently aware of the fundamental importance of mathematics whilst at school?
  5. Views of the importance of mathematics from 6th Form to university were very static for the respondents - it is important to foster positive views of mathematics whilst still at school.

Views of design of mathematics questions

  1. An interesting, stimulating challenge in a useful context is very important to all respondents.
  2. 'Stimulating' and 'challenging' were important factors which should be in a mathematics question, ideally one which leads to a new technique. Overall, other factors were neither good nor bad for the respondents.
  3. Respondents with a procedural, exam-focussed view of mathematics performed relatively poorly in tripos and were less likely to enjoy their degree course  - in other words, passive, spoon-fed respondents tended to perform poorly and not enjoy their degree course.
  4. From the data gathered, there was strong evidence that respondents who did well in tripos saw the value of challenge in mathematics questions and enjoyed aspects of 'rich tasks'.

Approaches to learning

  1. There was very little difference in learning preferences profiles between respondents. The most significant differences in learning preferences concerned preference working with others: mathematics respondents as a group had a higher preference toward solitary working than did other subject groups.
  2. There was no evidence from the data gathered that preferred learning style affected views of mathematics or what makes a good mathematics question - this seems to imply that tasks do not need to be designed with learning style in mind.
  3. Visual learners were a significant majority over aural and kinaesthetic learners.
  4. All-rounders performed slightly better in part IA than those with a strong preference for one of the particular learning styles.
  5. Highly visual learners tended to perform slightly better than audio or kinaesthetic learners in part II
  6. Linear (sequential) vs. non-linear (big-picture) thinkers were present in equal measures.
  7. Big picture learners performed slightly better than linear learners in part II.
  8. Most respondents strongly enjoy learning and enjoy a challenge although, notably, 14% of respondents do not particularly enjoy learning and 16% do not enjoy a challenge.

Key moments in mathematics

  1. 69% of respondents experienced no key moment in mathematics whilst at school.
  2. There was no evidence of correlation between the number of key moments experienced and success at university - the concept of the light-bulb or flash of inspiration does not seem to be of importance and not worthy of further investigation.

Additional support in mathematics needed

  1. One third of respondents felt that they need more mathematics support at university than they get; around one fifth of respondents felt that they needed more support whilst at school - it seems  important to understand what the students perceive is lacking.
  2. Large numbers of respondents received no additional mathematics support outside of lesson time whilst at school - it seems that the in-lesson activity is the key factor.
  3. From the data gathered, the amount of additional support in mathematics received out of lesson times was independent of UK school type.
  4. There was no evidence of additional support received by respondents leading to improved performance at university or improved contentedness in hindsight - this is more evidence for the argument that  the in-lesson activity is the key factor which leads to success.

Views of ability

  1. Self-views of mathematical ability of the respondents were reasonably static from primary to secondary.
  2. Respondents tended to have an accurate understanding of their relative level of mathematical skill university: those who perceived themselves as mathematically weak tended to perform relatively poorly in tripos.
  3. Respondents who viewed themselves as good at mathematics at primary school enjoyed mathematics at primary school .
  4. There was a gender difference between self-perception of ability and actual ability relative to peers at university - female respondents as a group were less confident than male respondents as a group.

Would additional intervention have helped in hindsight?

  1. One third of respondents believed that in hindsight additional intervention whilst at school would have helped them with their university mathematics; this was independent of the amount of additional mathematics support they had received outside of lessons and was weakly negatively correlated with the number of key moments they had experienced - this is a very significant proportion of respondents;  can we use their experiences as detailed in the textual data to help to devise suitable intervention packages?
  2. 'Teachers enriching or extending the mathematics beyond the curriculum' were the two most significant factors in creating respondents who did not believe that additional intervention in hindsight would have been useful - NRICH's work with teachers appears to be a natural way to help to create 'contented' students; this issue will become more pressing as costs of education increase and funding into education decreases in the UK.


  1. Overall, there were very few significant differences observed between the group of female respondents and the group of male respondents.
  2. The group of female respondents rated almost all aspects of their received school teaching significantly higher than the group of male respondents. This was the only significant difference arising between the two groups in the survey.
  3. The group of female respondents somewhat underestimated their mathematical ability compared with the group of male respondents (see point 73).
  4. The only observed gender difference concerning realised tripos grades was in Part IA Engineering, where the Female group underperformed compared with the Male group.


  1. Respondents reporting disabilities affecting their ability to learn mathematics tended to be influenced by external factors whilst at school and were affected by memory in terms of remembering formulae.
  2. Respondents reporting disabilities affecting their ability to learn mathematics tended to underperform in part IA of tripos, although no difference was observed in parts IB and II.


  1. White British respondents had received significantly better teaching and results at GCSE than Non-(White British) respondents. Non-(White British) respondents were significantly more influenced by external factors, such as wider reading and mathematics competitions.
  2. Non-(White British) respondents under-performed slightly relative to White British respondents in part IA of tripos, although no difference was observed in parts IB and II.