The work of Jo Boaler (Boaler 2013) and Carol Dweck (Dweck 2006) shows us that the main hinderance to students learning maths is the belief that they cannot do it (i.e. an emotional response). This concept was introduced to me through the TED talk ‘How you can be good at maths, and other surprising facts about learning’ presented by Jo Boaler (Below). She argues that a ‘fixed mindset’ has arisen for many in maths through the misguided perception that it is an ability you either have or you do not.
Praising students for their intelligence instead of their effort will only result in the student valuing the praise rather than the process of learning. A lesson based on proving ones knowledge through rapid question answering or worksheets fosters the former attitude, however a lesson based on inquiry, making mistakes and coming to an answer through one’s own investigation fosters the later.
If a student bases their self-worth in praise and reward, they are at risk of developing a fixed mindset where failure becomes the enemy and therefore it makes sense to only try things you are competent in and sure not to fail. I was one of these students who developed a ‘fixed’ mindset, it was only much later in university that I was able to work hard to reverse this trend and truly enjoy making mistakes that I developed a growth mindset.
“Our brains – and our lives – are highly adaptable”Jo Boaler
Moser and his team (Moser et. al. 2011) take this a step further by demonstrating in their paper through a measurement of electroencephalographic activity (or electrical activity of the brain) called ‘error positivity component’ that a person’s beliefs about learning and intelligence determine how they will react to mistakes and setbacks. A person with a growth mindset, as defined by Dweck (2006), will see mistakes as opportunities to improve and believe improvement results from effort. A person with a fixed mindset, however, believes that ability is set, and a mistake is proof of a lack of ability (Moser et. al. 2011). Basically, when someone with a growth mindset gets an answer wrong, they work hard to get it right. When someone with a fixed mindset gets an answer wrong, they give up.
Related to the discussion of mindsets is a powerful analogy called ‘The Learning Pit’ by educator James Nottingham (pictured above). The learning pit represents a challenge, something a student does not understand or perhaps something the student might have a few conflicting ideas about (i.e. stepping inside Vygotsky’s ‘Zone of Proximal Development’). The students are supposed to fall into the pit, representing uncertainty or being out of one’s comfort zone, and here engage in some deep thinking about a topic. They are then supposed to use selected ‘Habits of Mind’ in order to climb back out of the pit (The Learning Challenge: How to Guide Your Students Through the Learning Pit 2017).
I think many adults fall into the trap of rarely taking on something completely new to learn, and we forget how much of a struggle it is to develop brand new neural pathways and enter into a new way of knowing. I myself had. Queue the beginning of my Masters… Every single time I start a new essay I find myself in the pit and for the first few weeks I definitely forgot my ‘growth mindset’. Learning about the pit was a turning point for me and I have used the chart above many, many times. I hope that this experience will give me a good reminder of what being in the pit is like – and help me to guide students out of it!
Boaler, J 2013, ‘Ability and Mathematics: the mindset revolution that is reshaping education’, Forum, vol. 55, no. 1.
Dweck, C 2006, ‘Mindset: the new psychology of success’, Ballantine Books.
Moser, J, Schroder, H, Heeter, C, Moran, T and Lee, Y 2011, ‘Mind your errors: Evidence for a neural mechanism linking growth mindset to adaptive posterror adjustments’, Psychological Science, vol. 22, no. 12.