Hello! Welcome to my blog on pedagogy at Brix. This is my first ever blog post, and I’m not really sure how to write a blog. So, starting with the subject of ‘a desirable difficulty’– a task that is outside your comfort zone and requires a substantial amount of effort to complete – seems appropriate.
When studying I have always found that I understand maths better if I have been really forced to think about it – working out how and where to apply information, rather than doing repetitive questions. During my degree I was set weekly problem sheets on lectures and invariably found that the sheets which helped me learn the most were the ones which were pitched slightly above my ability. In having to work to understand what was happening in questions, choosing which parts of lectures to apply to a problem, as well as getting things wrong, I was forced to think more about the material. This helped me to remember it better later on, giving me a deeper understanding of the maths I was learning.
It turns out that this isn’t just my experience: there’s loads of research  which shows that you learn better when you are given tasks which are at the edge of your ability- tasks which are hard, but doable. These tasks are called desirable difficulties. They initially slow down learning, but in the long term increase understanding and the amount you remember- a more ‘thorough’ way of learning. I am struck by the contrast of setting desirable difficulties with other ways of teaching – for example giving repetitive and similar questions (e.g. 50 sets of simultaneous equations) to a student to reinforce what they have learnt. Although this improves short term performance, it doesn’t have much of an impact on information and skills retained in the long term . There is even some evidence that getting questions wrong is good for long term learning, because the attempt to retrieve the information (albeit incorrectly) reinforces the correct information better than simply seeing it again .
This ties into what I’ve noticed when teaching. A couple of years ago I was teaching a small group Foundation GCSE maths. One thing they really struggled with was shapes, so I began to give my group 10 circles to find the areas of as a warm up at the start of every session, hoping they would learn to use A = r2 fluently. After each session I would come back a week later to find that they had forgotten how to find the area of a circle again.
Rather sceptically I took the advice of a fellow tutor, and gave the group much harder shapes to find the areas of – like rectangles with semicircles attached and triangles with circles cut out – questions much harder than those they would see in their exams. As I expected, they really struggled with the problems, becoming frustrated with how difficult they were and reaching answers much more slowly than they could for easier questions. I wrote the experiment off as a failure and moved on. I was completely taken aback when a week later the students could still remember that A = r2. Somehow the added challenge they had to overcome (and perhaps the added fun) fixed the information in their brains much better than repetition.
I’ve been thinking about how to include more desirable difficulty into my work. I found loads of helpful resources online  , detailing ways of increasing difficulty which have been shown to be effective- some as simple as making the font harder to read. Some methods which I think are particularly relevant for maths include:
- Quizzing students more often, even on material they don’t know.
- Allowing students to be confused and encouraging them to work out hard questions themselves, with minimal help.
- Waiting for an answer – encouraging students to think about a question you’ve asked them before they answer.
- Giving students the answer to a hard question and asking them to explain why it is the answer.
At the moment I am writing materials to teach probability for S1. This has been really fun to do because probability is a topic where you can ask quite hard questions which require a relatively low level of knowledge. The aim of my questions has been to force students to think further about the probability rules they have been learning, and work out which rules to use and how to use them. Some things I’ve included are:
- Presenting students with a rule (e.g. P(A) + P(A’) = 1), then asking them to use this themselves without an example. It’s a simple jump to notice that P(A’) = 1 – P(A), but one which a student will now have to make themselves.
- Writing more questions which use previous material, so that students have to work out what is relevant. This will reinforce what they have learnt before, and tie ideas together.
- Providing unnecessary information for questions which the students have to sort through, working out what is and isn’t relevant.
That’s the end of this post – thank you for reading!
For more academic research into desirable difficulties, check out the website for the Bjork Learning and Forgetting Lab – it’s run by Robert Bjork , who invented the term desirable difficulty in 1994. Also have a look at this great article by William Emeny, who spent a week at the real learning and forgetting lab in UCLA.
I would also recommend checking out:
- Suggestions of how to make learning harder
- This discussion of desirable difficulties in the classroom by Psychology in Action
- Ideas for introducing desirable difficulties into maths lessons
|||16 08 2016. [Online]. Available: https://bjorklab.psych.ucla.edu/.|
|||C. B. Parker, “phys.org,” [Online]. Available: http://phys.org/news/2015-01-students-effectively-math-problems-drills.html. [Accessed 16 08 2016].|
|||H. L. Roediger, “Scientific American,” [Online]. Available: http://www.scientificamerican.com/article/getting-it-wrong/. [Accessed 16 08 2016].|
|||“Tomorrow’s Professor Postings,” Stanford University, [Online]. Available: https://tomprof.stanford.edu/posting/1419.|
|||W. R. Speer, “directorymathsed,” [Online]. Available: http://directorymathsed.net/download/Speer.pdf. [Accessed 16 08 2016].|