Powerful Problem-Solving: A transformative approach to maths teaching

In the Alcoa Champions of Maths (ACoM) program, I work with eight teachers each year to transform the way mathematics is taught in their classrooms. We’ve come to call the approach we use: Powerful Problem-Solving. It revolves around challenging tasks, deep thinking and rich discussion. 

Teachers learn to plan and deliver engaging maths lessons using challenging tasks from sources such as Challenging Mathematical Tasks, reSolve, nzmaths, NRICH and Problemo. 

Lessons are run in a three-phase thinking classroom format of ‘Launch, Explore, Discuss’. And students use mobile whiteboards to solve problems in randomly assigned groups. We place a large emphasis on the discussion phase, which runs for 15 – 20 minutes. The phase involves students in presenting their ideas, questioning and defending ideas that are presented, and seeking to understand most efficient solutions.  

Teachers construct their lessons using special lesson plan templates that walk them through the Five Practices for Orchestrating Productive Mathematics Discussions: 

• Anticipating student responses and planning prompts and questions to facilitate their thinking. 
• Monitoring students’ working and thinking, providing prompts and questions to move their thinking forward. 
• Selecting student work for presentation during discussion that highlight the important mathematical ideas in the task. 
• Sequencing the presentation of ideas for a coherent logical narrative. 
• Connecting the various mathematical ideas and strategies raised through looking at similarities and differences. 

Teachers employ Talk Moves to engage all students in active thinking throughout the discussion. 

The professional learning model for this program involves group workshops and personalised coaching which consists of pre-lesson conferences, in-class coaching and debrief. The pre-lesson conferences and debriefs provide opportunities to discuss the mathematical ideas and student thinking involved in each challenging task in detail. This enhances the teacher’s content knowledge, understanding of student misconceptions and strategies, as well as their ability to craft powerful questions and prompts to promote student understanding. In-class coaching and debriefs develop the teacher’s confidence and competence in applying the various strategies and techniques listed above. 

During their final reflections, teachers of ACoM 2021 said that by participating in the program, they have: 

• learnt how to target very specific mathematical ideas
• increased their own confidence in mathematics as well as their students’ 
• learnt how to engage students in enjoying, struggling and persisting with mathematics and tackling unfamiliar problems 
• learnt to enjoy making sense of mathematics alongside their students 
• learnt how to construct powerful questions that ignite student thinking 
• raised their expectations of students, realising they are for more capable and resilient than they had previously thought. 
• learnt how to understand the way students think about a mathematical problem and help them move their thinking forward from where they are at 
• learnt how to facilitate deep, rich discussions about mathematical ideas 
• learnt how to teach multiple concepts simultaneously and emphasising the connections between them 
• noticed both themselves and their students enjoying maths more. 

“My teaching has changed drastically. I was very much an explicit teaching kind of teacher,  giving students opportunities to practice strategies that we had learnt together on problems I know they would be able to solve. Now I understand that they need to struggle to learn. They need to discuss and collaborate with their peers so they can not only understand their own strategies but others and compare which is more efficient. There was no point in telling my students that skip counting is more efficient if they didn’t understand why and how. Previously, I didn’t ask my students questions about the maths they were doing or why they had done what they had. They had given me the answer, using the strategy I had taught them, so I didn’t feel the need to ask any more questions and they didn’t feel the need to explain their answer to me. Now I look forward to asking them questions about their maths and they look forward to explaining it to me! I have grown so much in my teaching and my students have grown so much in their understanding.”  – Year 2 Teacher, participant in Alcoa Champions of Maths.

We are extremely proud of this program and the dedicated teachers who have participated. Please look out for our upcoming final blog entry which will further discuss the student outcomes including effect on performance. 

Keep thinking and enjoy the struggle!