Student Teachers, Tasks & Students

Tamsin Meaney
Charles Sturt University, Wagga Wagga, New South Wales

Through a weekly Maths Club run by the University for students from local primary schools, Tamsin perceived that teachers were looking for ways to extend their more interested mathematics students. She was also looking for ways to support her student teachers to get more 'up close and personal' with children at work. An idea evolved...

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...What about adding maths tasks to the Maths Club resources, then running a workshop day for the two groups of learners based around using the tasks to develop confidence in learning to work like a mathematician? The idea grew ... much bigger than expected.

The photo summary below outlines how the day played out for 80 student teachers, 80 Years 4-6 students from various schools plus a few teachers and accompanying adults. The promotional blurb for the day turned out to appeal to many teachers and students:

Interest, Challenge & Depth: A Framework for Gifted & Talented Learners
It doesn't matter what the problem is. It does matter that the learners are interested in tackling it. In this full day program, which will be based around the many lives of a Mathematics Task Centre resource, the focus will be on both the teaching craft likely to engage students and the problems themselves. Our inspiration is professional mathematicians, who report that their work begins when they are given an interesting problem.

We invite you to bring your G & T mathematics students, or even just the ones who shine a little, and yourselves, to join with our student teachers in making a community of learners for a day. Sometimes we will work together on the same problem. Sometimes we will work in groups on different problems. Always we will be moving beyond the initial problem by asking mathematicians' questions such as:

  • Can I check this another way?
  • What happens if...?
  • How many solutions are there?
  • How will I know if I have found them all?
Characteristics of the day will be hands-on learning, mathematical conversation and development of the process of working like a mathematician. You may well find much of it supports your work with all the students in your class.
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Workshop day at Charles Sturt University, Wagga Wagga, NSW for 80 primary kids, 80 first year teacher trainees and the odd teacher or two. We made teams of around 4 kids and 4 student teachers. The kids were the captains and could ask advice. The student teachers were the coaches and could ask questions.

The opening activity was a Poster Problem Clinic using the Farmer's Puzzle, Maths300 Lesson 14. Journal's were both individual and group.

One strategy suggested was to start with units of $12.50 because one of each animal would cost that much.

Teams worked well together.

Another approach showing recognition of unstated conditions in the problem.

Next we explored Crosses, Task 35, together before opening Cafe Conundrum, which offered a menu of problems using digits from 1 to 9.

This table has developed an hypothesis about Crosses.

This table has recorded several solutions to Crosses. How do you know which number is in the middle of the cross in each solution?

Another way of recording.

Truth Tiles, Task 30, was on the Cafe Conundrum menu.

As students developed solutions to Crosses, they could test and record them using the partner Maths300 software. By morning break (two hour session to start) the students had found 16 unique solutions. There are only 18, as we discovered by running Option 3 of the software over lunchtime.

Later, the university's task set was used to broaden the range of problems. Perfect for an extended menu of 'desserts'.

We're exploring What's In The Bag? First we put in a combination of colours, then I draw out a sample...

...and record it until I get enough data to predict what's in the bag.

This team is working on Truth Tiles 2, Task 17, and has found that they can make families of solutions by exchanging digits in the subtractions.

After lunch we discussed the things that helped us learn and made table lists so the teachers could learn from the kids.

The final activity was to explore Trisquares together.

Each table made a 4 Trisquare shape and drew its outline in the smallest possible scale by joining dots. Then drawings were exchanged to see if others could figure out how the Trisquares had been arranged.

Excitement reached a peak when we discovered that 4 Trisquares make a Trisquare and we could go on building from Size 1 to Size 2 to Size 4 to ... and make really humongous Trisquares to cover the whole floor.

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