To accompany the release of Free Practice on TUTOR, our Maths team have put together this piece exploring the impact of practice.
Allow me to introduce you to two brothers, Peter and Paul. Both want to exercise to lose weight and improve their aerobic fitness but both have very different ideas about how to meet their respective goals. They begin their fitness journey from the same starting point, eat the same meals and get the same amount of sleep but this is where the similarities end.
Peter decides that he is going to run a lot in one session. So he decides to run 24 km on day one and rest for the remainder of the month. This is somewhat wise because it sounds like he’ll need the rest. Paul, understanding a little more about his body works, chooses to run 2 km, three times a week, across the month. Both will have covered the same distance at the end of the month but who is likely to be fitter as a result of their exercise routine?
You may be asking what this has to do with mathematics but we can take the central message in this story and use it as a lens through which to view the act of learning. The work of Professors Robert and Elizabeth Bjork, as well as countless collaborators, demonstrates very clearly that knowledge stored in our long-term memory has both a retrieval and a storage strength. Meaning that disuse has a degrading effect on that which we (or our pupils) believe we (they) know.
This sounds quite bleak but we should not be disheartened because the mere act of retrieving information makes memories stronger, increasing both the retrieval and storage strength at the same time. In fact, every time we retrieve information stored in long-term memory, a new, stronger memory is formed. So if Peter decided to cram 12 hours of study into one day and Paul, being the creature of habit that he is, decided to spread it out into 3, 1-hour sessions a week, across the month, it would once again be Paul who saw the greatest improvement at the end.
In his book, Atomic Habits, James Clear talks about the impact a 1% improvement made every day, over the course of a year, can potentially have. He uses the example of the meteoric rise of British Cycling (who put this hypothesis to the test at the turn of the 21st Century) to exemplify his point but we, as teachers of mathematics, should also take heed of this advice.
Mathematics isn’t learned in large chunks of study. We don’t give our pupils one behemoth 6-hour lesson at the start of the week and expect them to retain what has been taught 7 days later. Yet, so many of them develop study habits which can only be described as cramming, despite a plethora of research that demonstrates its inefficacy as an approach to study. Our messaging to our pupils should be clear. Practise regularly, be consistent, aim for 1% improvements, form slightly stronger memories each day and you will meet your goals.
As misguided as he was, Peter’s exercise regime was not born of a unique condition to which only he was susceptible. Humans are, by their very nature, always looking for the path of least resistance and the existence of countless fad diets and exercise plans stands as a testament to the prevalence of this trait across our species. In much the same way that Peter is in desperate need of sound advice on how to meet his fitness goals, our pupils look to us for advice on how to meet their individual learning goals. We need to expose our pupils to the habits and routines which are most conducive to the formation of meaningful connections between the areas of mathematics they study and which can provide them with access to the relevant knowledge for any given task at the drop of a hat. By and large, we all have the same cognitive architecture. It is how we put it to work that counts and which distinguishes those who can from those who have not yet.
To find out more about Free Practice on TUTOR, head here: https://completemaths.com/blog/free-practice-now-on-tutor