Threshold training is a common term in distance running. It’s one of the most productive types of training that an aspiring athlete can do. The proper pace for threshold training is about 90% of maximum heart rate, and training in this way can significantly improve a runner’s speed.
I sometimes like to think of maths, as a tree of increasingly difficult concepts. Every learner is at a different point in climbing the tree. Every learner has their own threshold, having made their way to a certain point up the tree. It’s vital they don’t forget what they learnt lower down the tree, else they’ll fall back down. And equally vital is that they learn what is next for them personally on the tree, so they are working at their own threshold.
If a runner took a light jog every day for 15 minutes, she’d never improve. But on the other hand, if she trained at 95% of maximum heart rate every day, she may suffer exhaustion, and injury or perhaps a crisis of confidence.
If our mission is to significantly raise an individual child’s standards in maths, the single most important task is to establish that child’s threshold. Set the work too easy and they won’t learn anything new. Set the work too hard, and they will be learning concepts that are not underpinned by the necessary pre-requisites, meaning there’s a danger of the child not fully understanding the concept and then forgetting it soon after. This is what made Kumon the most successful supplementary maths provider of the 20th century: every child entered the program at their threshold, and the curriculum was carefully constructed to ensure pre-requisites were always in place and never forgotten. Children learned through doing maths, always at their threshold.
We know what happens when a child isn’t working at their threshold. We’ve experienced it ourselves as either a teacher, a parent or from our own memories of school. A year spent in a maths group where a subject-enthusiast teaches to the top of the class with great enthusiasm but to the extent that most get left behind, or understand only in bursts and forget what they learned a few weeks later. Alternatively, perhaps less commonly, is the wasted term that a child might experience if they are placed in the bottom group by accident.
Finally, it’s worth noting that as maths branches out into different disciplines, children may have different thresholds for Algebra, Shape and Space, Number or Data Handling for example. It’s difficult for a teacher to keep track of these thresholds, let alone teach individual children at the right level for each. Luckily, that’s where technology can make a difference.