Stories below illustrate teachers getting excited by the tools or methods used in Calculating Changes just as Nicholas Dale does in his article Threading Works which features in the In Brief link. Members have access to more stories. If you would like to contribute to these stories, email Doug.Williams: doug@blackdouglas.com.au
Doug. WilliamsProject Manager, Mathematics CentreSometimes I wonder whether the 'aha' moments in Calculating Changes are meant for teachers rather than children. I have had the opportunity to work in a couple of classrooms recently and in both I have been surprised by what I have learnt from, and about, children.In Meekatharra, Western Australia, I was working in a K-2 class. It was their first time with Poly Plug so I started with Free Play. That went well - each pair around the circle made something different and I was able to challenge each with a question or two based on their own exploration. My plan was to move from here to a more structured activity and I had chosen Counting Frames. I wanted to find out how these young ones would go counting by twos. Using my own red board as an example I asked each pair to make this:
Then, thinking to myself what a wonderful teacher I was, I stuck my fingers two at a time through the gaps and we counted happily to 10 by twos. Next I called on the mathematician's question What happens if...?:
...and make a sort of road train, can we count the gaps now?Road train's move through this town daily so I was making a connection with the children's experience. I felt I was right on target when the little girl next to me immediately said to her partner Look at all the windows. Not that road trains have windows like this - perhaps she just heard 'train'. But now the kids were hooked. The collective drawing in of breath at the challenge of counting all these windows by twos was audible, but they were excited. So was I. It lasted about four milliseconds. One Grade 1 boy went 2, 4, 6, 8, 10 ... 20, 30, ... and the others all went Oh yeah. Once again I had been to focussed on what I wanted to teach and had risked being insufficiently aware of what the children had to offer. My second experience was at Dederang Primary, a small rural school on the way to Victoria's High Country. In a Year 3/4 class I introduced Highest Number, an investigation from the Mathematics Task Centre that is included in Working Mathematically with Infants. It's a well known game requiring the children to quickly sketch a hundreds/tens/ones board big enough to place a playing card in each column. Players take turns to roll a 6-sided dice, perhaps revealing a 5, and have to decide whether this is 5 hundreds, 5 tens or 5 ones. Each player only has one of each card from 1 to 6 and the higher 'score' after three rolls is the winner. But being the winner wasn't enough. The pair had to work out by how much the winner won. And, calling again on the Working Mathematically process, had to check their answer another way. They used materials in the room such as MAB 10, Unifix and calculators and displayed insightful mental arithmetic with comments like: It would have been 100 because of that column but the ones column is 6 for the winner and 8 for the loser, so the total is 2 less, so 98. The children enjoyed the game much more because of the added challenges and the learning was much deeper than it would have been had I simply expected them to keep track of how many times each person won.
 Robyn AndersonPrincipal Project Officer, Mathematics, Metropolitan Region, Queensland
All in all the 30-40 participants in each workshop were engaged and positive about the activities and Poly Plug and worked to establish how it might best fit with their planning for young students developing problem solving skills. 'Inspiring' and 'interesting' were among the comments and feedback from the participants. July 2010Just a quick catch up. I did the WM with Infants workshop Bits and Bobs with 25 teachers/maths leaders from various parts of the state involved in an Early Years Numeracy Project in mid-June. It went very well.Also did a Problem Solving workshop with your materials at QAMTAC 2010 Functioning Mathematically. I drew the last workshop slot of the conference but still had 18 attend. My thesis was that we must teach students to make choices - empower them to make the choices as to how they are going to solve problems - as against the teacher knowing the 'best' or often only 'one' way and then remembering it. I used several investigations from WM with Infants which confounded the secondary teachers when the source was revealed. The participants got to choose from:
I have loved doing these workshops with your materials. There is so much work still to be done. If the Australian Curriculum can drive the agenda for the necessity of frequency, and access, for teachers to good quality professional learning in mathematics pedagogy, bring it on!
Sue DavisG.A.T.E.Ways TeacherG.A.T.E.Ways is an independent organisation offering challenging and enriching activities and experiences to develop and extend highly able children. Sue Davis designed a course titled Problem Solving Polypluggers made up of four 2.5 hour sessions, and was blown away by the kids' responses. Here is what she wrote after her first course with Year 1 & 2 children:WEEK 1
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