Mathematical Reflections after the SGIS Education Conference

A few hand-picked highlights and reflections from the SGIS Conference 2016. Just to qualify some of the points made here, Rob Eastaway delivered sessions to both maths and non-maths specialists in a fun and dynamic way with some great ideas. There is no way that he could have, or should have, delved deeply into some of the points I am making.

1. The Creative Side of Maths (Rob Eastaway)

Some lovey ideas from Rob and some of my own reflection points in this fun packed opening keynote.

• I loved how he used jumping up stairs to teach his children about prime numbers (e.g. 13 stairs: Can you get to the top in equal jumps? What about with 12 stairs?)
• “How to measure the height of a tree with a walkers crisp packet?” was a lovely open problem with many different solution strategies. Some great hands on maths there.
• Another maths teacher said at one point during this talk that it is okay to make mistakes. I think this is somewhat dangerous if we aren’t clear on the types of mistakes being made. I’ve found it helpful with my classes to refer to sloppy mistakes and stretch mistakes. Sloppy mistakes aren’t great. They tend to refer to things like numerical errors, not reading the question properly or issues with algebraic manipulation. Stretch mistakes are great. They can happen when someone tries a new strategy or provides a strategy for the class to analyse. Mathematics is both creative and rigorous after-all!
• Rob said that we should be encouraging any solution strategy so as not to make students believe there is only one way to solve problems. I completely agree, but I also agree with the Japanese philosophy of ensuring that the class reflects on the most efficient strategy and/or the strategy that could be applied to a larger proportion of different problems – we are ultimately also trying to help students become effective mathematicians.
• When Rob referred to Pythagoras as being about lengths, I understand why he would say that, ultimately we use the idea of the triangle inequality (and Pythagoras) when walking around everyday. However, I do love how it is a beautiful theorem about area and it therefore can be applied to calculating lengths (sorry for being pedantic here – I just can’t help it – see one of my previous posts).

2. An Inquiry into the Brain (Dr Robert Greenleaf)

• Manipulatives and visuals are only good if students are engaged and focused. Otherwise they can be a distraction and learning can become confused [I guess just like any form of teaching and learning].
• Never define anything that you can get students to define themselves. One example that came to mind here for me is showing lots of trapezia and asking students to develop the simplest and shortest definition possible. This makes the students active participants in the defining process.
• Whenever possible, get students to analyse and collaborate on the similarities and differences between things. I believe that he claimed this to have the highest understanding and retention effect size over any other learning strategy. A classic mathematical example here would be in ascertaining the odd one out from a group of quadratics.

3. Maths, Magic and Mind-Reading (Rob Eastaway)

Lots of lovely mathematical magic tricks in this workshop to astound students and then get them working out the ‘how’ of the trick. I won’t share the magic tricks but I think Rob’s point about introducing algebra with mathematical magic really does engage students in understanding what a variable is. This is one he shared but also one I have used in the past during initial algebra units.

E.g. Think of a number -> Multiply it by 2 -> Add 10 -> Divide your current answer by two -> subtract the original number you thought of. The answer is always 5 – why?

4. The Importance of Puzzles in Maths (Rob Eastaway)

Again, so many great ideas for ‘low floor, high ceiling” tasks here. I decided to take one of them and extend it into a more meaty investigation.

Imagine a football field with a length of 100 m. Two teams are playing a cup final and a team assistant is asked to run and grab some bunting before the end of the game. Since the bunting needs to pass across the entire length of the pitch (100 m), but be pulled upwards in the centre so that players can fit underneath it, the manager asks the assistant to get more than 100m of bunting. The assistant comes back with 101 m which appears to be way too short.

1. Can the players fit under the bunting?
2. What would be the minimum length of bunting needed for the players to fit underneath? (given to an appropriate accuracy and assuming an averaged height person)
3. Can you find a general formula for the length of bunting needed for any length football pitch and for players of any height?

(This isn’t at all intuitive. It would make a nice 3 ACT task for anyone good enough to make the ACT 1 animation)

Summary

If you haven’t attended one of Rob Eastaway’s presentations before then I’d highly recommend that you do! If not, check out some of his books. I personally loved “Why do buses come in threes?” – see previous blog post on this.