Now Playing: Ghost (Bananarama)
Well, I went to the Cambridge seminar on Tuesday - which was fun getting the students' feedback - I think the things I've gained from that has mostly been in the preparation of the materials and doing some preliminary qualitative analysis. Fatin suggested that I probably could let students who did the black-box software do it again sometime later on the glass-box to see if there were any effects ... hmm ... interesting - don't think I'll have any time for that in this PhD but something to think about for future research perhaps?
I also went to the BSRLM conference on Saturday - I was hoping to get more feedback from it - unfortunately my audience was really low (I think perhaps because the people who were interesting in my talk were mostly Cambridge students who had already seen it and I was clashing with a workshop of Geogebra). I was hoping to get some feedback on my videos. One person (Nicole) suggested I might looks at Hoyles and Noss concept of situated cognition ... and I've been doing some browsing on the concept and it might be useful but not sure how it actually fits in with the data I have ... well as I understood it situated abstraction is where students make sense of what is given to them in the situation in which they're. Noss (2002) in his paper of mathematical epistemologies that students in these abstracted situations should be able to transfer their knowledge and not be wholly confined to the situation as suggested by Resnick (1991).
Hopefully, I've looked at this correctly and I've interpreted it correctly. What was interesting when I was reading Noss's work and all other stuff on situated abstraction I was trying to figure where students were sense-making based on the software - and based on the bits of video data I've browsed through I can't say whether there was actually any abstraction based on the software perhaps in the open-box in the choice of the the variables in which students chose any variable wildly ... however, what did strike me is this notion of moving from the situated abstract and applying it in a different situation. So, I went and did an ANOVA (or rather a comparison of means) to check whether students were doing badly when they had to do the abstract problem in comparison to the real life problems.
Of course I found no difference in the 20 students (I removed the 2 outliers)! However, the means suggest that students who were doing the abstract problem (interpretive and constructive) last were students who were doing worse at it - I do have to check whether the problems that students were doing last in general - that students were doing bad in it. Because students who were doing problem 1 last also did very badly for both the interpretive and the constructive. I'm not sure whether that student's energies peter off to the last and weren't able to think ... looking at problem 2 - students also did bad when it was the last question but only for the constructive problem ... did students reach their cognitive limits? Was the time they were taking a strain on them - or were students generally couldn't handle the abstract problems? (I don't think it is the latter - I have a feeling students just do badly for the last problem!). So, much for my brief stint in checking out situative abstraction - but it still might come in useful so would keep it in mind.
Interestingly, at the BSRLM spoke about someone (I think it was on Schonfeld) who said that if students cannot work out a problem in less than 7 mins they think it is impossible - so, I need to check this out more carefully.