Changing my IA Mindset

This blog post is a kind of confession! I apologise in advance, but hope others of you might be able to relate. When I first started teaching IB and IB maths studies in particular I was really taken with that course. It seemed to have such an excellent spirit of 'mathematics for all' and offer another opportunity to those whose experience with mathematics had been troubled. I loved teaching it and dived head first in to all the resources, workshops and so on. I also loved contributing to the curriculum review that gave rise to these new courses. The challenge was to accept that some things needed to change whist keeping as much of that spirit I mentioned. Now we are seeing our third cohort go through, I confess that transition has been hard. I do feel some of the spirit has been lost but I also really like the new applications course and see all its upsides. Many of our challenges as teachers remain and it has definitely been harder to squeeze in the syllabus whilst being faithful to the philosophy of mathematics teaching. This transition has also been made more difficult to navigate because of the global pandemic and the impact that has had on the whole assessment process. It has left many of us feeling a little bit in the dark. This is a whole other discussion.

My confession is that through all of this I have struggled to make the necessary shift in mindset regarding Internal Assessment. The comments in last Mays examiners report suggests I was not the only one. Don't get me wrong, I worked hard to understand the task and its criteria and worked with my colleagues to get on top of this. It is just that the transition of this knowledge in to practise has been hard for me and demanded quite a lot more of my time to help students produce suitable work. I am now acutely aware of the dangers of writing a blog post now that suggests I have made a break through, before I see the results of this years moderation! I have stopped believing I have control of this process. I work hard to interpret the criteria, read reports, look at sample work and do my best to mark as the criteria demand and am always happy to learn. That's enough.

I have just noticed that this year I was freer of some of the 'Maths studies' shackles that I found hard to let go in the past. For example, the old 'information' criterion lent itself much more to a formulaic approach and the unofficial rules that flew around like '50 ordered pairs'. I noticed that I saw potential in more and more varied ideas and that it was potential for fruitful exploration, rather than criteria ticking potential. The criteria, I think, can reward fruitful mathematical exploration. Who knows, maybe I'll be writing a follow up blog post after results in July taking all this back! I suppose what I am saying is that, regardless of the outcome, I have found the process more rewarding and less formulaic for both myself and my students. Probably a little bit harder and more time consuming as a result, but definitely more rewarding. I hope it continues this way. 

I am sure that many of you, especially those of you that already used the exploration criteria, were here before me and I don't claim that any of the following were particularly revolutionary ideas, but rather just examples of types of exploration I found more interesting and that would have been less viable with the maths studies criteria.

Basketball

Goodness knows we have seen some variations on basketball and quadratic modelling. What I particularly enjoyed about this one was that it entered on finding critical paths for a basketball that meant the angle of approach would be big enough let the ball clear the front rim. This involved some trigonometry and geometry to determine that critical angle, the generation of a family of quadratics that would take a ball from a height of 2m on the 3 point line to the basket and then the use of calculus to deduce the limit on that family such that the gradient on the path the quadratic would be sufficient to make the critical angle. It was a lovely coming together of mathematical ideas and a fruitful journey from conception of a problem to a general solution.

Parkours

I have student who is very accomplished at this. Previously I would have been a bit frightened by the potential for complication and lack of focus that could have come from a project based around this kind of movement. The candidate did well to settle on a simple focus of the impact height has on the distance they can jump from a standing position. For example, consider a standing jump on a flat surface, then consider how much further you might be able to jump if you started on a box that was 30 cm off the ground, and so on. The candidate used a motion tracker and video to collect the data and the exploration focussed on the different nature of the jumps, their potentially quadratic paths and the outcome. It was very doable and involved some linear and quadratic modelling along with some calculus to look at theoretical maximum height reached on the jumps and how this changed. 

Trampolining

Similarly, another candidate, who is successful competitor in trampolining, looked at the damping pattern from a given height. What happens to the height of a jumper who slows down from their maximum height. They had imagined some kind of geometric/exponential model. the results were intriguing and fruitful.

Product Life cycles

A student picked up on some news about the 'vinyl revival' and when through some analysis of the product life cycles of the vinyl the first time, the CD and album downloads as a means of trying to predict what this new vinyl revival might look like over time. There was some good use of stats here which culminated in the devising of a couple of excellent goodness of fit tests aimed at trying to determine the nature, distribution and similarity of these product life cycles. This was a great example of an exploration that took shape very much as it went.

Tea

A student looked at the cooling curve of a cup of tea but with an interesting angle. They set up a little challenge for themselves by asking a friend to boil the kettle and pour the tea and then bring it to them an unknown time later. The student then collected cooling data and modelled it to try and deduce the time it was boiled. It was good fun.

Thoughts on statistics

It does feel like the increased emphasis on hypothesis testing has opened more doors for students and is better suited the reality that often they only have 'samples'. There is care to be taken about the required assumptions for T-tests and it is not always easy to conceive of a meaningful test, but there are avenues.

Last May's Examiners Report was fairly derisory about 'Maths studies style projects' and whilst I think the language was not so helpful, I do get the point they are trying to make and meaningful application and interpretation. It does not mean that such topics are no longer appropriate, it just means that we have to make a small mindset shift that I think is well reflected in the criteria.

It can be both fascinating and frustrating to constantly be thinking about what we do and why we do it and there is lots of pressure on us to make sure we hive our students the best we can. I reserve the right to change my mind in the future and I accept that last years have been a scramble to stay on top which is a huge factor, but this year, I have rediscovered some enjoyment in the IA process!