Last Saturday I attended the 25th annual Primary Maths Association conference at the beautiful Waipuna Conference Center. Though I don't recall it being said (that of course, doesn't mean it wasn't said) there was a clear theme running throughout the day: Proportional thinking. Now this doesn't necessarily mean proportions, ratios and percent - but it does refer to multiplicative thinking. This, according to many speakers, is something we need to focus on as many learners are yet unable to think this way.
The keynote speaker, Shelley Dole, spoke of a three-step process of representing mathematical thinking for learners. The first is enactive - acting out the problems. This is probably something that is lacking in my practice at the moment. In the week since, I've tried to bring this back into my problem solving. The second is iconic - using diagrams or manipulatives that represent real life things. For example, this would be using things like counters, place value cubes, etc. I've been doing this to a degree, though including diagrams is something that I will work on adding (pun intended). The last is symbolic - which is using numbers and symbols to represent those mathematical ideas. This is something that we rely on quite a bit, and while necessary, it's important to remember that that doesn't have to be the only thing we do.
To be honest, a few of the big ideas in the sessions were not new to me, but it's always good to get a reminder of these things AND there were some practical things that I can use in my teaching.
One session I attended, called Learning Through Play, had a few ideas of things we as educators could use to make the learning of our learners more interesting. There was a lot of talk about using literacy to connect with mathematical ideas. A lot of this was about using stories to create math investigations. I like this idea, though it was very juniors based (read: Year 2 or under). It did remind me of the wonderful (American) resource of the Math Start books. Despite the obvious issues with the currency books, these are really great. I've brought my set back into school and am planning to share them with my learners shortly.
Another really important tip that was shared in this session was that learners should be encouraged to answer their questions in full sentences - not just in one-word answers. The facilitator mentioned that this can have wonderful effects across all learning areas.
The last session of the day included a massive amount of practical real world maths problems. The facilitator gave us heaps of example questions using ratios and proportions that are real world problems. What I liked best about this session was that we had time to go around and have a go at solving them (note to any presenters out there: get us doing stuff or at some point, most of us will just tune out).
It was a good day to spark some thinking in me. I've always enjoyed math as a student, though that can be a challenge when it comes to teaching learners who don't share my excitement. I hope to use a good deal of the ideas in the coming weeks!