News

Our contribution to the recent Mathematical Association of Victoria (MAV) Gippsland Conference was the keynote address and three workshops.

The keynote was titled Fascinating, Captivating and Absorbing Kids in Mathematics and the workshops, for early years, primary and secondary teachers, were focussed on working like a mathematician at that level. MAV consultants Helen Haralambous and Jen Bowden added to the workshop choices with their own sparkling sessions. Through our sessions teachers were invited to reconsider the narrative around mathematics education through two questions: Is it time to stop teaching mathematics and start creating classrooms where students are learning to work like a mathematician? Is it time to stop talking about engaging kids and start talking passionately about fascinating, captivating and absorbing them?

The history of teaching mathematics indicates that it hasn't usually offered the greatest good to the greatest number. The word 'engage' comes with too many variations in meaning:

• engaged to be married
• engaging gears
• engaging in war
• engaging the enemy
• engaging in conversation
• engaged to carry out a task
• ...

We went on to offer evidence that choosing teaching craft designed to captivate, fascinate and absorb students in the process of working like a mathematician is successful and often encourages unexpected outcomes. Two examples follow - the first was used in the conference, the second was contributed during the past month with no connection at all to the conference.

Evidence A: Truth Tiles 2
This story is an example of an unexpected outcome when students are offered the opportunity to choose and explore their own investigation, in the same way as students are freely allowed to, in fact expected to, choose their own reading books. The story belongs to Blair and Alexander, but first we need to develop a sense of what they were working on.

Tear a strip of paper into 5 pieces and number the pieces from 3 to 7. Now place them into these boxes to make the equation true.

+ - =

• Find one solution.
• Find another solution.
• Find five solutions.
• How many solutions are there?
• How do you know when you have found them all?

Play with this for as long as you like. When you are ready to hear Blair and Alexander's story take the Cube Tube link in the Link List below.

Evidence B: Poster Problem Clinic
This story is an example of an unexpected outcome when students are offered a whole class investigation in the same sense as a teacher will choose a book and read it to the class as a literary adventure. Ellen Corovic begins this story with the email below, but the story really belongs to Jane Lockwood and her Year 4/5 students at Albanvale Primary School.

Hi Doug,
I just had to forward you this email. As you may remember I have been working with a school this term specifically on reading and understanding problems. A part of this was introducing teachers to poster puzzles.

We've been focusing on slowing down the initial part of problem solving so that everyone really understands. Student discussions and drawing out the mathematical language has been a feature.

OMG Ellen, I wish you had a live feed into my room. I just introduced the 100 animals for $100 poster problem (Maths 300), and it was amazing, going through the process, they really slowed down this week, but you still had a few who wanted to dive into solving it. The conversations and mathematical language and problem solving being used was incredible, they were really frustrated and they loved it. I told them it is good they were frustrated, because if this was easy it wouldn't be a problem, they were soooo engaged.

Task 183, Pizza Toppings

It is amazing that such a simple looking task can open up such a deep investigation. The context of making or eating pizza is familiar to most students. I have even been invited to help deliver pizza around Milikapiti, Melville Island, on a Friday evening. It was flown in from Darwin and was still warm. For further confirmation of the interest the problem can generate, consider Oliver's journal record in the article Recording at Ashburton Primary School. See Link List below. Perhaps because of this 'old friend' context the task initiates interest, then at all levels from Years 2 - 12 it is possible to uncover more and more depth in the iceberg. From

physically making as many pizzas as possible using counters, to asking What happens if...?, to seeking and seeing patterns, to linking the patterns to Pascal's Triangle, to exploring the expansion of (1 + x)^t, t = no. of toppings, and relating its coefficients to the patterns in the problem.