News

Teachers who receive Pot Boiler from Calculating Changes already know that a new video was added to Cube Tube at the beginning of the month. If you didn't know that, then perhaps now is the time to look. (See Link List below.) Jamie Kemp, St. Francis of Assisi, Calwell, took his Year 6 class and his camera into the school ground to explore Move Around.

This activity from Calculating Changes Free Tour easy to state, easy to start and involves heaps of mathematics related to number sense, sequencing on the number line, place value and decimals. It is an activity that can be used from Year 1 - Year 8, and beyond, depending on the range you choose on the number line. The children learnt lots about mathematics and Jamie's video makes it clear that he learnt lots about teaching and learning. The video includes a trial of the same activity with Year 3 and the two experiences, combined with what his school learnt, and continues to learn, from our Working Like a Mathematician course, has recreated how the school approaches the teaching and learning of mathematics.

Also, two of our Cube Tube videos are stored on the You Tube channel of the Association of Teachers of Mathematics (UK). One is built around Task 45, Eric The Sheep, and one around Task 154, 4 Arm Shapes. Both illustrate teaching craft likely to fascinate, captivate and absorb students in the process of Working Like a Mathematician. Links to the videos have been added to the cameos for these tasks. You can also access them through our Cube Tube link. See Link List below.

Matt Skoss, Centralian Middle School, Alice Springs has been enjoying a whole class investigation based on this Arithmagons task. He writes: A surprising strategy that arose through playing with Arithmagon problems was the kids making a decision to 'share the difference' between the two bottom vertices of the triangle. What impressed me was their sense of the three equations having to be balanced. Even though they didn't quite get to the point of using those words, they implied it by "if we add on one to each of the bottom numbers, we have to take one from the top number." Using rich problems like Arithmagons reinforces the incidental 'informal' mathematical thinking that is being developed by students. Our challenge as teachers is to be sufficiently 'tuned in' to pick up the nuances! When pressed, Matt explained further...

In the past week, I've really enjoyed my Year 7 students' reactions to working on Arithmagon problems. After a lesson of 'playing with the problem,' my students came up with the approach of picking any number for the top (say 5), and then finding the missing numbers for the bottom two vertices (13-5 and 8-5 in the example). They then turned their focus to what their total for the bottom edge was, and what the problem 'wanted the total to be.' They came up with the idea of 'sharing the difference' by halving between the two bottom vertices, which then gave them the solution immediately. Having a 'sense of power' over the problem, especially when many adults will struggle with the problem for a while, was a very powerful outcome for these students.

Ta-Daa!

The nature of this problem helped them 'take a risk' which they are normally reticent to do. We played with a few Arithmagon problems using 'Write on-Wipe off' sleeves, which are more flexible than mini-whiteboards, because they enable any template to be inserted. An unplanned journey I went on with my students was when their initial guess for the first number required them to have a negative number in one or both of the bottom vertices. I was pleasantly surprised when they were able to deal with the directed numbers in their heads, without 'breaking stride.' The fact that the need to use directed numbers was embedded in the 'story-shell' of an Arithmagon problem meant it was a tool they just drew upon without really thinking about it. The drive to find a solution didn't get in the way of them not having met directed numbers too often before.

In thinking about the very common 'classroom chestnut' of how do we differentiate learning and cater for diversity, I thought of developing an example spreadsheet to show students. This can be used to challenge students to develop their own generalised Arithmagon spreadsheet that would solve any problem. Using speech or thought bubbles on the example can help scaffold teachers or students who have limited experience in using spreadsheets in this way.

Many students won't necessarily need to or want to pursue developing a spreadsheet solution, but it would be a significant challenge for many. An extension to this problem might be to write a computer program to achieve the same outcome using free Scratch software, available from http://scratch.mit.edu.

Please feel welcome to contact me via matt@skoss.org if you'd like to follow up on the spreadsheet idea or 'Write on-Wipe off' sleeves.