Discussion is Critical to Understanding

Hi, my name is Jodie Walton and I am a teacher at Australind Primary School. I’m currently teaching a Year 6 class, but have had the opportunity to teach all year groups during my career. I have always loved mathematics and in particular seeing students suddenly understand concepts and gain new insights. Even though I love maths, I am aware of how difficult I find it to teach different concepts in interesting and practical ways which will enable students to have a deeper understanding.

At the beginning of the year, I became a member of the Alcoa Champions of Maths Program. I was thrilled to be selected into this program as it seemed to correspond with many of my beliefs and understandings of good mathematical teaching practices. I hoped it would help me become a better teacher of mathematics.

The activity that I would like to talk about in this blog was a simple activity by Jo Boaler called Growing Patterns.

How do you see the shapes growing?

The students were put into random groups and given a whiteboard per group to try and identify all the different ways this pattern grew. The students were given a set time to come up with several ways the pattern grew (with much sideline encouragement) and then we opened up a class discussion.

At the beginning of the year, I started working with my students about being respectful towards each other during discussion times. We have looked at ways to voice our opinions and being careful to discuss the ‘action’ and not to belittle and criticise the ‘person’. Before we started the discussion I reminded the students about respecting each other and to remember it is the pattern that we are talking about not the individual speakers/presenters. I also reminded the students not to be defensive if they don’t agree with something that is being said. Each group had an opportunity to share with the class about how they saw the pattern changing.

After some discussion one of my students asked the following question “I am confused when you said add one on top – because that could be anywhere – where do you mean on top?” This question prompted some great in-depth discussion about where the blocks were placed and how the pattern changed.

It thrilled me that not only were the students eager to participate in the discussion, but they were also thinking critically about the pattern and acknowledging other students’ understandings. Through asking this question, in this way, the student was saying that the answer had value and was then allowing the presenter to clarify his thoughts without embarrassment.

During the course of ‘Champions of Maths’, it has been emphasised that discussion is an important element in the gaining and reinforcement of understanding. This was clearly illustrated during the above discussion. The student who presented to the class had to think more deeply and clarify his thoughts in order to share his understandings. The audience were demonstrating active listening by asking relevant and open questions and not just presuming they know what the person is trying to say.

I personally gained two very important understandings from this simple lesson. Firstly, giving the students time to discuss their understandings is very important. It demonstrates what they know and how deeply they understand. It also illustrates any misconceptions they may have, so that the misconceptions can be dealt with immediately. The second point is that by giving students the skills and opening promts to have civil and open discussions means that they can all get a deeper understanding of the mathematical concepts covered in class.

Find out more about the Alcoa Maths Enrichment Program or read the next article.

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