As the school year draws to a close, I am reflecting on the problem-solving journey my class went on this year.
What have I learned by teaching problem–solving?
I have learned that kids are capable of really hard things. They are incredibly resilient. That resilience is strengthened by a classroom culture that embraces it. A culture where trying, failing, and trying a new strategy is encouraged. Developing this culture early in our journey was crucial to the students’ willingness to embrace problem-solving and persevere through challenging learning tasks.
I learned that all students are capable of hard things. At the beginning of the journey, I insisted that hard maths wasn’t accessible to all students because some students don’t have the mindset to benefit from such challenging tasks. I learned that I was wrong. Problem-solving is accessible to all students, of all capabilities. Problem-solving challenges and benefits the kids who are working below the standards for their year level, as well as those who are working well above their year level. All students have shown progress after a year of regular problem-solving challenges.
It is also clear that my approach to maths is critical to the students’ relationship with maths. Importantly, I have realised that my approach to teaching maths has the potential to make students feel excited, instead of intimated, by maths. I am excited by maths, so they are excited by maths. I am confident in their ability to persevere through challenging tasks, so they are confident in their success. I am excited to have nurtured a class of students who are excited, rather than intimidated, by maths. My students are now eager to confront challenges and have self–efficacy in their success.
What has changed for me as a teacher since introducing problem solving?
I am less intimidated by maths. I am more confident in my ability to question and lead discussions that will focus my students’ attention on the intended learning area.
Previously, my maths followed a pattern of explicitly teaching a strategy, and then encouraging the students to use this strategy to solve multiple problems in exactly the same way. We mostly focused on problems that only had one solution. If students correctly solved the problem, I considered the teaching successful. While explicit teaching of concepts and strategies is still core to my program, I have learned that providing students with the opportunity to apply these strategies, and their own, to challenging problems is invaluable to consolidating their understanding.
Problem-solving lessons are also important in revealing student misconceptions and understanding. They provide an opportunity to confront misconceptions and address them through collaboration and teacher discussion. Through problem-solving, I can make informed judgements of my students. By observing the students’ discussion and work, I have a far deeper understanding of each of my students’ strengths and weaknesses.
My teaching has also changed in the way that I question students. I am more aware of how to shape a question so that it directs a student’s thinking, rather than give them an answer. I have also realised just how capable and resilient students are when faced with very challenging maths. As a result, I have started to expect more from myself and my students. In doing so, my students achieve more.
How problem-solving methods changed my approach to maths lessons
For me, teaching used to be about teaching students a strategy, then having them practise it over and over. Now I understand that maths teaching is about the understanding, not the answer. It is about the students finding a strategy on their own and being able to articulate why their solution is valid. Through proving their solution and explaining it, they are demonstrating a deep understanding of the concept. It is through this journey that I have learned that this is what all learning is about. Understanding, not just having the answer.
I have learned that questioning is where the magic happens. It’s where the learning is consolidated and misconceptions are addressed. It’s where students have the opportunity to consolidate their understanding and share it with their peers. As Liljedahl states, the goal of thinking classrooms is to build the student’s will to think about any task.
What has changed in the students?
In Term 1, many groaned at the mention of maths. Some cried at the thought of not immediately being ‘right’ and many believed that they were ‘no good at maths’.
By facing challenging maths tasks, collaborating and sharing their thinking in maths discussions, many of the students have increased their self-confidence in maths. My students are now excited to participate in maths and are genuinely proud to share their thinking with their class.
They’ve learned how to set and achieve learning goals. They’ve learned that it’s ok to make a mistake. They’ve learned that they can do hard things.
In Term 4, my students are excited by problem-solving. They participate in class discussions. Some are even asking if they can ‘add on’ to a peer’s statement. They can also accept feedback from a teacher or peer and adjust their thinking.
Through problem-solving, I’ve learned that hard maths is accessible and critical to the development of all students. I’ve come to know my students better through problem-solving. And thanks to problem-solving, my students have learned that they’re all good at maths.