Why learning maths is like learning ballet.
My son is training to become a ballet dancer. We have been to watch many classes and one of the highlights of our year is watching the whole school take part in a series on ‘on-stage ballet classes’.
From year 7 through to 19 year old graduate year students they come on stage one group after another. In this way, we see the progress made over time. From tiny children standing at the barre pointing their toes and demi-plieing, through to adult performers leaping through the air, pirouetting and balancing with what sometimes seems effortlessness until you look closely see the effort that is being applied.
What is key during this time, and of course afterwards as the graduates embark on a career, is the daily class.
The same exercises done again and again and again. With the keen eye of a teacher providing ‘corrections’. Corrections that to our untrained eyes are often miniscule, but that can cause real problems — sometimes even career ending injury if not addressed.
The teacher stops the child, shows what the problem is, shows how to do it properly and then the child practices immediately. Practices properly. Not repeating the error.
And over time, the procedures become embedded. So that when the student is performing, is choreographing, is being choreographed, they do not need to think about how to plie, or how not to ‘sickle’. That all happens instinctively, through muscle memory. And so the performance and the creativity takes place.
So what are the parallels with learning maths?
Students learn procedures, techniques, methods. They do some exercises to practice, the exercises get marked, not often immediately, sometimes many days later and sometimes by those who don’t know why the error is there, just that it is wrong. Then they do their corrections… sometimes!
With online learning, the situation is often worse. Students get told something is wrong — but with no indication of what was wrong. Teachers who get told by the computer that there is a problem, then have to guess what the problem was. Or students have to write what they did (not showing the maths they did, writing about it). Imagine that happening in ballet! “so, my right leg was sort of there, and my left twisted a bit from the knee there, with my arm outstretched…”
Without the immediacy, the student might also have gone away to practice more, but repeating the same error. Putting THAT into muscle memory.
So when they get a multiple choice question with oh so cleverly designed ‘distractors’, even though they did get a correction when they first learned the particular technique, that memory is dredged up to confuse, just like some 50–50 choice on ‘Who wants to be a millionaire?’
In Shanghai (please don’t need to stop reading), teachers get a 30% teaching workload. The rest of the time they mark and prepare. So that students get as immediate feedback as possible. Work is done, marked and any misconceptions addressed the very next lesson. No waiting a week. No practising the wrong way. No casual ‘forgetting to do the corrections’.
Almost as quickly as with ballet teachers and their corrections in class.
And over time, students become proficient, so that when asked to perform (or solve problems), they can apply the techniques they have learned, quickly and easily. No faffing around trying to remember how to multiply out a bracket or whatever.
When we consider the use of technology to mark work, with most current technology, students get feedback quickly, but with no correction. No ‘try this’ or ‘place that there’. They could of course, play the whole lesson again!
With the newer technologies now available, students can get immediate correction. Not leaving it till later, but just when they need it. So that practice can be perfect. So that they don’t practice till they get it right, but practice till they don’t get it wrong.
Learning maths is like learning ballet.
But for many years — pretty much forever really! — the feedback has not been timely enough for everyone. Or with technology, not accurate enough and not provide the corrections appropriately.
Only now can technology actually provide feedback in maths that is faster than the teacher (meaning less work for the teacher) and provide the corrections.
And then MORE time can be spent on performance, on problem solving, on creativity and on teaching.
Which can only be better for both student and teacher.