Tracking Back Study - Design

Age 16 to 18

The page reports on the design issues underlying the questionnaire.

General design issues

After some thought, we concluded that finding students of exceptional mathematical ability is not straightforward without  a great deal of time and effort. Confounding factors are, for example:
  • The teachers might not be aware of the students' exceptional mathematical ability.
  • The students themselves might not be aware of their exceptional mathematical ability.
  • The exceptional mathematical ability of the students might be latent, untested or developing.
  • The students might not be connected to a wider network of mathematics support.
  • The students might be bored or disengaged from education.
  • Exceptionally mathematically able school students choose to study various mathematically intense courses and might not perceive themselves as 'mathematicians'.
  • Exceptional mathematical ability can manifest itself in students from any background.
After consideration of these points, in tracking back we decided to survey all Cambridge University students studying Natural Sciences, Mathematics, Computer Science and Engineering. The main reasons for this were:
  1. These four courses all involve a significant amount of advanced mathematics.
  2. Most students on such courses will probably be highly able mathematically; many will be exceptionally so.
  3. In line with the goal of making the most effective use of the John Templeton Foundation funding targeting this group was a quick, practical and efficient way of rapidly gathering a large amount of data concerning the target group of exceptionally gifted students.
We decided that since students come to Cambridge University with very diverse educational experiences we would ask questions very widely to gain a snapshot of the 'wider educational landscape' rather than impose our existing views of what constituted a 'good' intervention; it is only within this landscape that it will be possible to assess fully or tailor the impact of any given intervention.
General notes:
  • We interpreted 'resource' in the widest sense as something that can be used to give an input into a student's education: this included teachers, family, wider reading and other key factors.
  • We felt that student perceptions of the value, importance and nature of mathematics and education were important to help us to understand any responses concerning the significance and utility of the resources and interventions.
  • We considered all phases of schooling in the survey to provide a genuinely 'global' sense of student experience.
  • In order to assess most fully the significance of interventions we chose to open the survey to all Cambridge University students in the chosen subjects who would be reached by via email lists.
  • We designed each question to contain a wide range of common interventions but we allowed for the possibility of open-ended responses on most questions to give voice to the students.

General notes concerning method

An email announcing the online survey was sent to email lists for students who were at that time studying mathematics, engineering, natural sciences and computer science at Cambridge University. The survey was live between 5th May 2010 and 7th June 2010.
The survey was described to students as follows: "The aim of the questionnaire is to investigate the key mathematical influences for Cambridge University students studying subjects involving a significant mathematical component. We are interested in how experience of mathematics at school affects views of and success in mathematics at university level."
All entrants were offered into a prize draw: £100 was the first prize, second prize was a mathematics book.
787 students responded, with 650 giving significant levels of response. Following the June examinations, results were subsequently gathered for 465 of these respondents, including historic data for students taking their survey beyond the first year. Grades in first year (IA), second year (IB) and third year (II) were compared where available for the students. Grade data was found by reviewing class-lists and were not available in all cases due to fails, degrades and changes of course.
Most of the questions were assessed on a Likert 1 - 5 scale with the option of N/A. Where appropriate, the correlations between answers were analysed with significance determined from the number of responses provided for each particular question pair. Three phases of education were consistently targeted throughout the survey: Primary Level (ages 5 to 11), Secondary level (ages 11 to 16), Sixth form level (16 to 18).


Question groupings

The questions in the survey were broken down into these groups:

A: Course data, gender, type of schools attended, disabilities, ethnicity.                                
1: What course are you currently studying / did you study?
2: What stage of study are you at?
3: What type of schools did you attend?
4: What is your gender?
5: Do you have a disability which affects your ability to do mathematics?
6: What is your ethnic background?            
B: Examinations taken, Further Mathematics and STEP                                                  
7: Which of the following mathematics examinations did you sit?
8: Please select the Further Mathematics (FM) opportunities that were available to you, even if you did not take Further Mathematics
9: Please select the STEP opportunities that were available to you in your school, even if you did not take STEP
C: Influences and preparedness for university course                                                      
10: When did you decide that you wanted to study this sort of course?
11: Please rate how influential the following were in your decision to study your university course
12: Please rate how useful the following were in preparation for your university course
13: In hindsight, was there any intervention or support that you did not receive that would have
helped you in your university mathematics?
D: Concerning teaching received                                                                                                 
14: Was there a teacher or event that particularly influenced your view of mathematics at school?
15: Was there a teacher or event that particularly inspired you in mathematics at school?
16: How many school teachers who taught you mathematics or numeracy do you remember?
17: Of the teachers that you remember, please indicate how many were particularly memorable for
the following reasons?
18: Were you accelerated at mathematics in school (i.e. taught material from higher years or took
examinations early)
as: In addition to lesson time, please list the mathematics support you received at school.
19: Please rate your view of the amount of mathematics you learned at school and university.
20: Please rate the amount of mathematics support you received at school and university.
E: Perceptions of mathematics                                                                                                     
21: How do you view mathematics?
22: Please describe a key moment when your understanding or attitude towards a particular mathematical problem or concept shifted and how this shift occurred
23: Please rate your view of the importance of mathematics at school and university
24: Please rate your interest in mathematics at school and university.
25: Please rate your enjoyment of mathematics at school and university.
26: Please rate your view of your level of understanding of mathematics at school and university.
F: Doing mathematics                                                                                                                       
27: How would you describe the way you study and learn?
28 Please rate the difficulties you encounter when you work on mathematics
29: Please describe any key ways in which you try to overcome your most significant difficulties
30: How important to you are the following in a mathematics question?
31: How would you describe your mathematical ability at school and university relative to your peers?
32: Please rate how you found the level of difficulty of the mathematics at school and university.
G: Overall                                                                                                                                
33: Please rate the overall level of impact the following influences have had on your mathematics
34: Was there a key moment or event in your mathematics education?
35: In hindsight, please rate your level of appreciation of mathematics at school and university
36: Is there anything else that you would like to tell us about your experiences in learning mathematics?