A colleague is teaching Year 12 maths methods next year for the first time since the introduction of the new course. As part of the process, I sent her through the materials that we had created for the 2017 course. She spotted a potential flaw. “There needs to be more examples with literal terms in them. The sooner students see these, the better, because they find them hard.” She was right and we have added in examples of this kind.
In discussing this issue, my colleague and I both implicitly grasped an important point; early exposure to these examples would ultimately lead to a more positive emotional response to these kinds of questions. I don’t think anyone has ever articulated this reasoning to me and so I’ve probably picked it up through experience, both as a teacher and a student. It seems obvious to me that being left to struggle with a new kind of problem could lead to anxiety.
This matters because those who promote the use of inquiry-learning and problem-based learning in maths lessons, methods that leave students to struggle with new kinds of problems, have latched onto a concept known as ‘maths anxiety’; a form of stress that is so consuming that it can even harm maths performance.
Jo Boaler, advocate of problem-based maths teaching and the closest maths education has to a rock star, has suggested that maths anxiety is induced when teachers use timed tests. This certainly seems plausible and you may intuitively agree with the idea of eliminating time limits. However, timed tests also have some advantages. For instance, we really want students to just know many maths facts, rather than have to work them out, because this will then free working memory resources to focus on higher level aspects of a maths problem. By timing students’ retrieval of maths facts, we can ensure they have reached this level of automaticity. So this is a great question to test with research; where does the balance of cost and benefit lie?
In her book, Mathematical Mindsets, Boaler alludes to research that demonstrates the harm of timed tests. And yet, when reviewer Victoria Simms of Ulster University attempted to trace this claim to its source, she drew a blank.
Which brings us back to those examples. In a new Canadian study, a group of university students were surveyed on their levels of maths anxiety and their school maths experiences. They found that a greater perceived level of support from teachers was associated with lower maths anxiety and they also found that, “…there was a significant decrease in [maths anxiety] when participants reported that their teachers provided plenty of examples and practice items, and this remained after controlling for general and test anxiety.”
This is, of course, a correlation. However, in this area, correlations could be the best kind of evidence we are likely to get because, in order to do experiments, we would need to manipulate the anxiety levels of test subjects and that might be hard to get past an ethics panel.
Given that the finding is supported by common sense and a plausible mechanism – familiarity with example types reduces anxiety – then I think it perhaps provides yet more evidence for the superiority of explicit teaching.