I’m writing these summaries to help me organise my thoughts on these meetings and, hopefully, make the most out of the module. The last week or two of term was a bit mental between general work stuff and more specific marking of M2 papers for Edexcel. Planning on using the first day of half-term to get caught up on more blue sky things like this.
So, the second session was set-up to be a bit contrast to the first. Like the first we watched an extended video sequence – this time it was legacy Teachers’ TV material which is being curated by TeachersMedia.co.uk. We watched, “World of Maths – The Ice Rink” and I started to react badly almost immediately. This clip was narrated extensively, it had voice-overs, interviews and questions. The format made me switch off immediately. I wanted to discover the Maths, to generate my own questions – I don’t want to be told what to be curious about. I was recoiling and frustrated that this use of media seemed equivalent to a textbook exercise, except one with multimedia.
The video did give some more data to help with those questions that they were asking and could probably be used as a first step towards more open ended, questioning, Mathematical exploration. If we are equipping students with tools they can use in real-life we need to get them into the habit of working out what information they need, gathering it or making realistic estimates based on past experience, but maybe this is a skill that needs to grow over time. I felt that this situation was way too artificial – the questions that were being asked were too “So, what?”. I think that unless the students have felt the itch of a problem, picked a question that interested them and persevered with it for a while, then there will be a greater problem with engagement.
I tried to express this a little afterwards, not sure many people were with me – l probably wasn’t very clear – but one suggestion was to use the clip without sound. That would definitely alter what was happening and I think I’d like to watch it without sound to check that out. The other point that was made was that either clip would be frustrating when played in one go – splitting it into sections would be much more meaningful and useful.
We then thought a little about real life and how Maths might relate to that. I’m guessing this is going to be something we’ll be engaging with more and more over the course of this module. It got me thinking about the difference between the two main ways ‘realistic’ Maths is explored
The first: we have the concept we want to teach and we layer over a thin veneer of realism (see the Boaler article linked at the end for a better exploration of this) – share these cakes, work out the height of this building, are there enough buses for the school trip?
Is it disingenuous to wrap the Maths in a context to make it more engaging? If that is the only motivation rather than meaningful finding ways in which the subject is relevant and helpful. This is obviously a harder goal to achieve for some topic areas but does that mean we shouldn’t try? The other issue this throws up is the meaningless links between “context areas” – here is a linear growth problem in geometry, in shopping, in gardening, etc. This does allow some links between areas of Mathematics but each problem is normally only dealt with to the level that an atomised skill is drilled and practiced. Again, a veneer of relevance rather than the real thing.
The second: we have a real situation and we explore the Maths that can be found inherent in the situation.
This allows us to take a context and unpack the mathematics that helps us to understand and answer questions that grow out of it. This lets us suck the marrow out of a situation – letting us really dig in and see what Maths might be there. By nature, it has the potential to be more uncertain, particularly if student questions are directed differently from yours.
I think there is a need for a combination of the two approaches. The need to practise Mathematical skills in an atomised and skill based way, and a need to integrate these distinct skills into a coherent way to solve meaningful problems.
Is there a difference between realistic and real? If I use Quidditch from Harry Potter as a way to discuss probability, does the fact this isn’t a real game make it less meaningful? Does the use of taxes and mortgages, of loans and bills create a more meaningful task because it is real? Is it real real or pretend real and does that matter?
I think the answer to that lies somewhere with the person answering the question. If it is real to the person who asks it, it can be meaningful.
Boaler, Jo: “The Role of Contexts in the Mathematics Classroom: Do They Make Mathematics More “Real”?” (1993)