Problem solving and mathematics: Promoting cognitive dissonance

A couple of weeks ago I came across the term ‘cognitive dissonance’ in relation to teaching and learning mathematics and I have been thinking about it ever since. It reminded me of something a colleague of mine talks about with his primary class – the idea of getting a ‘sweaty brain’ when something is challenging or difficult during maths lessons. It’s that uncomfortable feeling you get, that feeling of disequilibrium, when you’re grappling to learn something new – something that is slightly out of reach.

Do you celebrate cognitive dissonance or ‘sweaty brains’ in your classroom? I think this is something that we have to promote – we need our students to value the struggle that takes place as part of the learning process and particularly when we engage in the problem solving process. Problem solving is a central part of the mathematics curriculum, and explicitly listed as one of the four Proficiencies of the Australian Curriculum: Mathematics and as a Working Mathematically component in New South Wales schools.

Another important aspect of the problem solving process and one that is closely related to the idea of cognitive dissonance is the development of perseverance in our students – when tasks are challenging it’s important not to give up – what some might refer to as having ‘grit’. So how do students develop perseverance when it comes to problem solving? There are things we can do as part of our pedagogical repertoires that promote perseverance and help celebrate having a ‘sweaty brain’. First, we need to understand the struggle that students are experiencing. By knowing your students well and developing a positive pedagogical relationship where you have a strong understanding of the learning needs of each individual student, you can set tasks and problems that are at an appropriate level of cognitive challenge for each child – not too difficult, but not too easy!

Set up opportunities for your class to work collaboratively on challenging problems – this gives students a chance to share their thinking and hear you model the thinking processes that occur when tasks are challenging. Use a growth mindset approach and focus on the language of ‘yet’. Often in mathematics classes we expect to begin and end a task within one mathematics lesson – giving students a very limited amount of time to work on what could be a complex problem. Why not allow students to walk away from the problem and think about it overnight before continuing to work on it the following day?

Use reflection as a natural part of the learning process, and model reflection for your students – very often we assume students can ‘do’ reflection, yet often they don’t really engage in metacognition because they haven’t practiced it or seen someone else engage in the process of reflection.

Finally, consider where problem solving fits into your classroom routines – is it part of your daily routine, and do you use problem solving as an opportunity to provide purpose for learning mathematical concepts and processes? Do you promote a classroom culture where mistakes are regarded as learning opportunities and cognitive dissonance is celebrated?