As a primary school teacher, I did not have the same level of confidence in teaching maths as I had in other curriculum areas.
My own experience of maths at school was mixed. I was an average student in primary school but became lost with maths in high school. Looking back, the content was too abstract, and we moved through the concepts too quickly for me to consolidate. When I began my career as a teacher, I still thought I was not very good at mathematics. As a consequence, compared to other curriculum areas, I spent more time preparing maths lessons – thinking about how I was going to explain concepts and differentiate content. When I had the opportunity to participate in the Alcoa Champions of Maths program, I looked forward to being coached by experts to develop my expertise and understanding to refine my maths lessons. When working on maths problems, I am now able to explain my methods and reasoning which allows me to guide students to do the same.
The pre-lesson coaching sessions where I learned how to explicitly plan for a problem-solving lesson and pre-empt my students’ responses were a game changer. I have a deeper understanding of how to plan for and look for specific mathematical concepts and strategies when working with my students on a problem-solving task. My problem-solving lessons are more challenging but supported by links to real world experiences, prior knowledge and collaborative teams. I now have the confidence to move from explicit teaching to more flexible arrangements and activities. The randomized groupings have worked beautifully, and we use this strategy to form groups for other activities in the classroom.
All the elements we have learnt have been important to my development as a maths teacher. However, the discussion during and at the culmination of the lessons have had the most impact on my professional growth and consequently the learning of my students. The opportunity for students to talk about and explain their thinking allows for a very clear understanding of what they know, any misconceptions they have, and where they need to go next with their learning. Shyam showed us how to structure our lessons to plan for productive discussions throughout the lessons to find out where students were at in their thinking, share and discuss their understandings. This gave me the opportunity to re-direct students to a particular concept or direction while allowing the students to see, hear and sometimes challenge different perspectives. My class was used to the cooperative learning structures and the language of sharing respectfully, but Shyam refined these by helping me ensure they were always focused on the mathematical goal.
After introducing my class to the ‘Magic V’, I presented them with this problem taken from re(Solve):
Sam said, “It is impossible to make a Magic V with an even number at the bottom with the set of numbers 1 to 5.” Is Sam right? Explain why or why not.
During the Launch phase, I used a visual to explain what a magic V is and showed an example and a non-example (concept attainment strategy). I asked students to use their whiteboards to draw a Magic V and then decide if it was an example or non-example. I asked students to stand on the line – examples, non-examples facing each other. Each group checked with the other participants and decided whether to stay or change sides. I randomly asked for students to share their Magic V and give thumbs up or down to agree or disagree.
I presented the task, reading the prompt three times, discussing vocabulary and key words. The students were then sorted into random groups of four and given three minutes of discussion time, before being sent to an upright whiteboard to begin working on the problem. After 20 minutes I stopped the students and chose three groups to share their work. After each presentation, the class were given time to discuss what they noticed. The students’ work on the vertical whiteboards was left overnight. The next day, I explained that they would be completing an individual reflection to show their understanding of the task. They used the example from re(Solve), which I then marked using the reasoning rubric. I looked at their ability to analyse (looking at the problem), generalize (give examples) and justify (offer counter examples). This continuum of growth from cooperative collaboration to individual accountability gave students a clear understanding of how they would be expected to show their understanding.
I used to fake confidence and competence in teaching maths, telling students it was my favourite subject. Now I have parents coming up to me and asking me if I am “that maths teacher” their children talk about and how much they are loving maths. What more can you ask for?