Dr Jenny Koenig from the university of Cambridge was the presenter at one of our regular PedR meetings (pedagogical research group) recently. Now, I actually like maths. One of the first Open University courses I did was ‘MS283 An Introduction to Calculus’ so it was interesting to look at maths from a different perspective. The title was ‘Teaching and Learning Maths in the Biosciences’ and dealt with the challenges and issues surrounding quantitative skills in the biosciences, which fell into two main areas. First was content, the mathematical knowledge that a student arrived at university with, which varied according to the subjects and level they studied to and the grades they achieved. What this meant in practice was a very wide range in knowledge and ability from a bare pass at GCSE (the qualifications taken at the end of compulsory education around the age of 16) to a top grade in A-level maths immediately before entry into university. The second area was the attitude to maths, and the issues of maths phobia and maths anxiety. This lead me on to the work of Dr Jo Boaler and her ‘How to Learn Maths‘ MOOC. Unfortunately, by the time I became aware of it the course was due to finish so I downloaded the videos and settled down for some offline viewing. Her book “The Elephant in the Classroom” is my current hometime reading on the commute home, and goes into the ideas in more detail.

Her premise is that the typical teaching of maths is strongly counterproductive and doesn’t equip students to actually use maths in the way they need to do in real life. This is because it relies on individual work using standardised methods with little creativity or active problem solving. Also, the (predominantly) UK and US practice of grouping students by ability leads to fixed expectations of both student and teacher. Her solution is to use a problem solving approach, involving group work, active discussion and explicit demonstration that there a variety of ways to reach the answer. She draws heavily on the work of Dr Carol Dweck around the concept of mindset, who distinguishes between fixed mindsets and growth mindsets. Fixed mindsets are where a person believes that people possess a fixed amount of a certain trait or talent (like mathematical ability) and that there is little that they can do to change it. This manifests itself as the self-fulfilling prophecy that there are those who are good at maths and those that aren’t. A person with a growth mindset believes that development comes through persistence and practice, and that anyone can improve their skill in a particular area. While these mindsets can apply to any area, I’d argue that Maths is one of the areas where the fixed mindset is particularly common and stated, and not only that, but that it’s culturally acceptable to be bad at maths. For example, while it’s not uncommon to hear people say that they’ve never been able to do maths you’d never see anyone smiling, shrugging their shoulders and saying *“Ah, that reading and writing stuff. Never could get the hang of it”*. Dweck’s work on mindset really resonates with me, and while I’m largely in the growth mindset there are a few areas where my mindset is more fixed. Now that I’m aware of those I can take steps to change them.

This concept of mindset links in to my earlier post on behaviour and reward because in addition to cultural and institutional barriers to innovation we now can add internal barriers. A fixed mindset leads to risk-averse behaviour because self-worth becomes connected to success. Failure doesn’t present a learning opportunity but passes sentence on the person as the failure. The failure or success at the task is the embodiment of the worth of the individual.

Growth mindsets on the other hand, allow ‘failures’ to be positive. A paper by Everingham *et al* (2013) describes the introduction of teaching quantitative skills through a new interdisciplinary course, looks at the effectiveness over two years and describes rescuing it “… from the ashes of disaster!” Evaluation at the end of the first year produced some worrying results. Maths anxiety for all students had increased. Female students were less confident in the computing areas of the course and male students were less engaged with the course overall. Significant changes were made to student support and assessment practices for the course and the second evaluation produced much better results. This is a great example of the growth mindset in action – they tried something and it went wrong. Rather than playing the ‘bail out and blame’ game they persisted. They redesigned and tried again, and then made public their initial failure through publication. When I worked as an IT trainer someone asked me how I ran my training room. I replied that I aimed for an atmosphere where people could screw up completely, feel comfortable and relaxed about it, and then get the support to put it right. What works for students works equally well, if permitted :-), for institutions.

## References

Etheringham, Y. , Gyuris, E. and Sexton, J. (2013). Using student feedback to improve student attitudes and mathematical confidence in a first year interdisciplinary quantitative course: from the ashes of disaster! *International Journal of Mathematical Education in Science and Technology*, **44(6)**, 877–892. DOI: http://dx.doi.org/10.1080/0020739X.2013.810786