In my recent book, I discussed ‘ouroboric’ processes in education. I suggested that some relationships that people think are linear – that motivation leads to learning or that conceptual understanding must come before learning procedures – are actually cyclical.

The examples that I gave were of positive processes. However, a new paper by Cambridge University researchers suggests that the negative relationship between maths anxiety and maths achievement is also cyclical.

I have written about maths anxiety before. The model that I used would be called ‘the deficit theory’ by the Cambridge researchers. This basically posits that maths anxiety is caused by a lack of ability. The teaching implication of this is that we should teach maths in the most effective way possible in order to improve competence and reduce anxiety. We might also consider giving students experience of success with some relatively straightforward work rather than asking them to struggle for extended periods.

The alternative explanation for maths anxiety is ‘the debilitating anxiety theory’. People who worry about their maths performance have to devote some of their working memory to the worrying. They therefore have fewer working memory resources to devote to problems. Jo Boaler is a prominent populariser of the debilitating anxiety theory amongst maths teachers and she advises that we avoid timed tests because they have been shown to induce anxiety. However, she also advocates open-ended problem-solving which is likely to overload working memory and which would not provide the routine competence that the deficit theory implies students need.

There exists powerful evidence for both theories. Longitudinal studies support the idea that poor levels of achievement lead to future maths anxiety. A range of lab-based studies such as those that induce stereotype threat – reminding a group that there is a negative perception of that group’s mathematical ability – show that maths anxiety leads to poorer performance.

The Cambridge researchers propose that the interaction works both ways. They also point out that while the deficit theory is supported by long term studies, the debilitating anxiety theory is supported by short-term experiments. So the two interactions work at different scales.

Leah, Isn’t this result a lot less surprising if you treat it as calculating the probability to be exceptional as 1 – the probability of not being exceptional. So just 1 – 0.98^N. So the more independent ways you can be exceptional the more chance you are and as the number of ways goes to infinity the chance of not being exceptional goes to zero.

What makes the other way – looking at the volume of the shell verses volume of the inner part less intuitive is it looks a lot like comparing surface area to volume. That is a very different problem with the opposite result.

https://joiningthedebate.wordpress.com/2016/02/03/senior-staff-to-sit-mock-exams/
Sorry if this is off the point.
Senior staff who are also not too hot on maths can give students excuses. They do not do it deliberately but subconsciously in their routine criticisms of maths teachers who do not have enough teal life examples.

Reblogged this on The Echo Chamber.

On maths, this post came up today from a UK maths prof over in Stanford Uni I like to follow > http://devlinsangle.blogspot.de/2016/02/theorem-you-are-exceptional.html Fun post, fun maths, fun message.

Leah, Isn’t this result a lot less surprising if you treat it as calculating the probability to be exceptional as 1 – the probability of not being exceptional. So just 1 – 0.98^N. So the more independent ways you can be exceptional the more chance you are and as the number of ways goes to infinity the chance of not being exceptional goes to zero.

What makes the other way – looking at the volume of the shell verses volume of the inner part less intuitive is it looks a lot like comparing surface area to volume. That is a very different problem with the opposite result.

https://joiningthedebate.wordpress.com/2016/02/03/senior-staff-to-sit-mock-exams/

Sorry if this is off the point.

Senior staff who are also not too hot on maths can give students excuses. They do not do it deliberately but subconsciously in their routine criticisms of maths teachers who do not have enough teal life examples.

Real life