Tracking Back Study

Age 16 to 18
Article by Steve Hewson

Published September 2012.

Between 2010 and 2012 NRICH undertook a programme of research concerning the mathematics education of exceptionally gifted students. The research was split into parallel strands of ongoing tracking activity.

These pages report on the 'tracking back study of exceptionally talented students' strand to analyse the mathematical learning experiences of those who successfully gain a place to study a mathematically intense course at Cambridge University.

The explicit goals of this strand of the research were to

  • Give formative information to feed into the creation of an online programme about how best NRICH can develop resources to support  exceptionally able students.
  • Highlight aspects of mathematical experience worth sharing with and disseminating to other interested projects and organisations.
  • Give us indications of the proportions of students who know they have used NRICH.
  • Provide useful contextual background data and the importance (students) attach to this experience as well as more detailed information on the impact that the use of NRICH resources has had on their learning development.

To attempt to address these questions in May 2010 NRICH ran on online questionnaire open to all Cambridge University students studying mathematics, natural sciences, engineering and computer science.  The questionnaire was designed to gain a snapshot, on which subsequent research might be based, of the mathematical factors leading to success in university STEM courses for exceptionally talented students, along with the associated perceptions of mathematics and mathematics interventions held by such students.

This ambitious and innovative questionnaire incorporated questions covering many aspects of students’ experiences of mathematics education from primary school level through to the mathematics involved in their university courses.

750 students responded to the questionnaire from a broad cross-section of subjects, grades, school-types and year-groups, including 23% of 1st year mathematicians and 25% of 1st year engineers – this was a high response rate for an optional questionnaire. The questionnaire elicited response from students across the spectrum of grades, from firsts to thirds, with a slight bias towards higher grades and the survey drew response from a representative sample of schools. The findings as presented here are formed from a mixture of qualitative and quantitative analysis and present a good starting point for further focussed research and the development of a school-university intervention package.

Note concerning levels of giftedness

Issues concerning ability are controversial and we understand that students, including those of great talent, are difficult to box and label in a fully representative way. However, in order to engage in discussion about gift it is very useful to have some sense of the scarcity of the student about which we speak. We use the following working definition about levels of gift:
  • Gifted – Top 5 percent; Top few in a typical large secondary school top set.
  • Highly gifted – Top 1 percent; Best student in a large secondary school year group.
  • Exceptionally gifted – Top 0.1 percent; Best student in a large secondary school.
We use the terms ‘able’, ‘gifted’ and ‘talented’ interchangeably as synonyms.



We have discussed the survey with many educationalists, mathematicians and scientists outside of the Millennium Mathematics Project. We would particularly like to thank Keith Johnstone, Ron Horgan and Paul Andrews. We would like to thank the members of the Ask NRICH community for their input into the early design stages of the questionnaire. We are indebted to the respondents who generously gave their time to answer the questionnaire. This research work was funded by the Templeton Foundation and many of the materials produced in parallel with the research, which have informed the development of the project, were funded by DAMTP and the Transskills project.