Term 3 Summary

hourglassWe are halfway through the Exploring Mathematics course – and I hope you’ve enjoyed learning some really interesting and unusual mathematical ideas! This seemed like a good time to make sure everyone is on the same page with the current assessments that you’re all working on.

AT1: Class Discussion
At this stage in the course, you have (including today’s lesson, listed below) TEN posts that you should have written in response to concepts and work done during our lessons. Here they are for those who can’t remember:

  1. Introductory lesson
  2. The Golden Ratio
  3. 3 videos (Beauty & Mathematics)
  4. Fractals
  5. Artwork ideas
  6. Set Theory topic review
  7. Discovery or invention?
  8. Comparing the sizes of sets (rational vs. natural numbers)
  9. Division by zero (What is 0 divided by 0? How about 0 to the power of 0?)
  10. Video ideas (today’s lesson)

Please check back through all the posts and make sure you are up-to-date. Don’t forget to participate in the dialogue too by actively discussing and questioning the ideas posted by others.

AT4: Video Composition
You have already formed your groups for this, and you’ve already been issued the assessment outline. Today your task is to identify three potential ideas to make your video about and then create storyboards for each. You must then write individually about:

  • The pros and cons of each idea
  • Which idea you like best and why
  • How you (personally – not the whole group) will contribute to the project in the lead-up to submitting Stage 1 (draft)

Happy holidays everyone!

TER Podcast follow-up: the big issues

2014 has been a year full of firsts for me. First year teaching in a comprehensive school (student teacher placements notwithstanding). First year as a head teacher (which has produced a whole lot of firsts of its own). First time recognised in public because of the videos I make. And as I type this, I’m at my first MANSW Annual Conference (arguably the biggest gathering of maths teachers in the state all year), my head spinning from considering new ideas and meeting new people (or in some cases, seeing people face-to-face who I’ve been interacting with online for a long time now).

Another first happened last month, when I participated in a phone interview with Corinne Campbell (@corisel) for the TER Podcast. The topic was Is Maths Education Broken?, and I was there to provide a sort of foil to an interview that Corinne had with the luminary Conrad Wolfram (of Wolfram Alpha fame). You can listen to the entire episode (and if you’re in education and haven’t subscribed to the podcast, you really ought to). It was an interesting experience, not least because it was so unusual to actually interact with a voice that I was so used to just listening to passively through a podcast.

I’m the kind of person who thinks of the perfect witty comeback or joke ten minutes after the conversation is over. So even though I had prepared my own thoughts and notes before the interview and tried my best to cover everything that would be important, I found myself in the shower that evening thinking, “Oh, _this_ would have been the perfect answer to that question!” and “How on earth did I forget to say _that_?” So here are a few of the things that I should have said, but forgot to. In this post I’m going to talk about the large-scale issues that are related to the “STEM crisis” Australia is experiencing, and in a follow-up post I’ll talk about some of the smaller practical strategies that can be employed in the classroom to help our students from day to day.

How do we improve STEM skills in Australian schools?
There’s no simple solution to this one – so you can know with a fair degree of certainty that if someone tells you they have a straightforward way to fix this problem, they’re probably just oversimplifying the situation. The so-called STEM crisis is a perfect storm of different factors and so there won’t be a single actionable item to fix things.

But there are definitely many identifiable aspects of the challenge. For instance, the syllabus is by-and-large divorced from real mathematical practice (both in everyday life and in vocational contexts). Here’s a great little quote from Optimising the Future with Mathematics (via The Conversation):

Current mathematics education, in schools and universities, is satisfied with programming students to carry out certain mathematical processes, and assessment rewards students who can calculate everything even if they understand nothing.

So what can we work on at the ground level? Firstly, it’s vital to recognise the enormous continuity of learning in maths. All key learning areas exhibit a degree of intra-dependence within their skills and knowledge, but it seems to be especially noticeable in maths where a single “weak link” in the chain can be disastrous! Once student confidence is lost, it is hard (not impossible, but significantly challenging) to rebuild it.

Secondly, top-down (syllabus level) change is required, but we can’t wait for that to happen. Policy is always hard and slow to change (it must be in a democratic and bureaucratic environment), but we can push the envelope of our daily practices right now and see what works. We can undertake action research projects into what is effective and helpful. Another insightful quote:

We need mathematics “to be taught more like it is done” by those engaged in it, in both the innovations economy and research. This is a cultural change that involves the discipline itself, one that must be mainstreamed into school and university systems.

These cultural changes almost never come as mandates from above – they are typically born out of grassroots movements from below that are then recognised and ratified by authorities.