Having posted about Tall’s Three Worlds of Mathematics last week, I think it’s a good idea to keep the maths education theme going this week. And I’ve been thinking about my (Master’s) thesis, and in the last few weeks a whole bunch of ideas and things have started coming together. Which is really nice. And means I now have a Plan. And I am going to share my plan with you, so here goes:
Research Question (slightly tongue-in-cheek):
“Your first term as a Cambridge Mathmo – what does it do to you? (a) what does it do to your view of mathematics? (b) what does it do to your view of yourself?”
Essentially, my aim is to carefully provide a small number (3 or 4) of illustrative case studies that will provide a data point for other people wondering about this sort of thing. This is the scale that is feasible within the constraints of a Master’s thesis (20 000 words, and of course there are time constraints). I want to write in a way that will be accessible to other people in Education but more importantly accessible to undergrad mathmos, their supervisors, DoSs and lecturers – because maths students and the people immediately around them are actually the people I care about most.
Phase 0:<– this is the one I am currently in
Find and read relevant literature from stuff that’s been published in Maths Education. Talk to lots of people e.g. my peers, friends in various years doing maths/ who did maths, etc. about my plans to see if they think they are reasonable and those people offer a chance to critique my plan / suggest improvements, possibly including asking people to think a bit about their answers to my questions. Important things: 1) connect to literature, 2) collect themes that I should keep an eye out for during phase 1.
Phase 1: find and interview 3 or 4 new Cambridge maths freshers who will be willing to give up 3 hours of their Michelmas term (one in week 0/1, one in week 4/5, one in week 8/9) out of the goodness of their hearts and general wonderfulness (I don’t have the money to pay them, but am planning recompense in a sort of “Here is some fancy apple juice / cake / nice chocolate” sort of way). Interviews will be semi-structured and questions asked will be based on findings from phase 0.
Phase 2: analyse data. Look for emergent themes. (I’m not sure on methods of data analysis yet – obviously that has to depend on the questions which has to depend on the reading which I have to do). This phase will probably be the most work.
Phase 3? put together a very short online survey to be sent out to all first year mathmos (assuming I can be nice to the department and they will send a link out via email). I am thinking sort of quotations/statements followed by a 5-point scale from strongly agree to strongly disagree. e.g. “in my first term at Cambridge I felt I could really talk to people on my level about maths for the first time, which was liberating” (but probably better than that). The aim of this is to take the themes I have found in phases 0-2, and get a very crude idea of how general they are – just an crude indication of whether these are general, widespread themes, or whether I have somehow managed to find 4 completely atypical completely unrepresentative people. Despite taking the longest to describe, this will be the shortest/easiest phase (unless something goes very wrong)!
Phase 4: write it all up. Arg. Cross that bridge when I get there … (maybe this phase will actually be the most work).
So. What do you think? (Please be gentle! :))