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Reflecting on the journey
Last week we had our most successful problem-solving lesson of the year and it had little to do with ‘solving the problem’. It was successful because the students were talking. All of them were talking about the problem. They were pointing to their working out – there was working out! There were diagrams to support their number sentences, they were justifying their solutions and even the students who struggle most in maths were explaining their thinking.
This lesson had me reflect on how far they’ve come, how much I’ve learnt, and most importantly, what got us here.
At the start of our journey, there were tears and a sense of failure. A lot of tears!
They would cry when they were wrong.
They would cry when they made a mistake.
They would cry when they were confused.
They would cry when their ideas were challenged.
Somewhere in the ‘explore phase’ of my first problem solving lesson, I realised I had fallen deep into the learning pit. Many lessons later it seemed I would never make the steep climb back up to success. My students were stuck in the pit with me. They sensed my lack of confidence and didn’t trust themselves to find their own way out.
Each lesson, I’d introduce a problem and the students and I would slide into confusion and become overwhelmed. The very capable students would climb their way out of the pit to success, but I was struggling to guide the rest of the students out of the pit. They were left feeling discouraged and I was beginning to doubt my ability to guide them.
In last week’s lesson they were wrong. They made mistakes. They were confused. And they had their ideas challenged. However, in this lesson, no one cried. In this lesson they had the skills to collaborate, to problem solve, to reason and to justify. They shared their thinking and built on each others’ ideas. In this lesson they climbed out of the pit.
Creating a success criteria and initiating deep math talks have had an incredible impact on our problem solving journey. Both are responsible for last week’s success.
Introducing a success criteria was the catalyst to change in our classroom. It offered all students the opportunity for success – something many had never experienced in maths. With a success criteria, students could understand that making mistakes was ok. This gave them the confidence to try. It made the over-confident students more aware of the learning process, rather than the race to the answer. It gave those lacking confidence a sense of pride in their efforts, despite mistakes or lacking a solution.
Before last week’s problem-solving lesson, students selected a ‘goal’ as their focus. Goals included things like: ‘my strategy didn’t work so I tried a new one’, ‘I changed my mind’ or ‘I collaborated with a peer to find a solution’.
Following the lesson, students reflected on their goal. They journaled whether they met their goal and why. Alternatively, they reflected on why they didn’t achieve their goal and considered what they can do differently next time in order to achieve their goal.
This gave all students the opportunity to feel like successful learners and made them confident enough to engage in problem solving. It has been a key part of successful problem solving in our class.
I thought I was doing maths talks. I wasn’t. Sure, some were talking about maths, but it wasn’t deepening their understanding. During the launch phase of this recent problem, students ‘turned and talked’ to a neighbour to discuss what the problem and constraints were. This allowed time to clarify the problem before actually attempting to solve it.
This time, as students formed their groups, they discussed strategies to approach the problem before delving into the ‘explore’ phase. The big difference that I noticed in last week’s lesson was that students of varying levels were attempting to solve the problem. Previously, weaker students would stand watching while the more confident mathematicians strategised. This time however, I noticed all students were finding ways to reach a solution. They were using diagrams and were able to explain their working out. Most excitingly, they could explain why they’d selected their particular strategy and justify their solutions.
The ‘discussion’ phase of problem solving has taken a while for the students to get the hang of. Initially, many students would consider their job done at the end of the ‘explore’ phase and wouldn’t engage actively in the discussion. In last week’s lesson, students successfully participated in discussions. As a group explained their strategy and solution, others were able to add on to the explanation and demonstrate their understanding. Students were also able to explain other groups’ working out and justify the efficiency of their strategies. Students were now asking their peers questions about the work.
The true value of these talk moves is that they guide students to the intended learning focus. In last week’s lesson, the focus was the relationship between multiplication and division. While students had found solutions during the ‘explore’ phase, I found it was the ‘discussion’ phase that really consolidated their understanding of multiplication and division. Students were able to represent their understanding of the concept through demonstrating their working out. If problem solving ended when the solution was found, the students’ attention would have been on the solution and misconceptions may not have been addressed. In this lesson, the discussion phase ensured that the students’ attention . It ensured misconceptions were addressed and students understood the reasoning behind their solutions.
In last week’s lesson there were no tears.
Nobody cried when they were wrong.
Nobody cried when they made a mistake.
Nobody cried when they were confused.
Nobody cried when their ideas were challenged.
This week they cried when our problem-solving lesson was cancelled.