This is an important piece of research. It shows that children’s brain activity changes as they make the transition from basic counting skills to automatic fact retrieval. Moreover, automatic retrieval of single digit arithmetic tasks has been shown to correlate with performance in advanced, high school level maths skills. (See comment below.)
This transition should take place around 8 to 9 years old, but it won’t happen unless children PRACTISE. And what better way to practise single digit arithmetic than learning the column-based methods! Children get faster at single-digit arithmetic whilst learning to operate with larger numbers at the same time. It’s a double win! And let’s not forget how much it improves their confidence and enjoyment of maths, at that age, when they realise they can handle working with larger numbers.
It’s pretty clear why a strategy-based approach at such an early age is catastrophic for developing young mathematical minds. Anyone who claims that the Numeracy Project was based on the work of Jean Piaget uses his name in vain. Piaget’s stages of cognitive development would place the strategies at the Formal Operational Stage (aged 11 to 16 or higher).
It’s reassuring to see cognitive neuroscience supporting a common sense approach to learning maths.
This is a reproduction of a table in Prof. John Hattie’s book, Visible Learning (2009). The “d” numbers are effect sizes; they measure the effectiveness of teaching practices. It turns out, surprisingly, that d is almost always greater than 0. “When teachers claim that they are having a positive effect on achievement or when a policy improves achievement this is almost a trivial claim: virtually everything works. One only needs a pulse and we can improve achievement.”
After synthesising over 800 meta-analyses representing tens of thousands of studies, Hattie concluded that we should be aiming for an effect size of 0.40 (the overall average) or higher.
The results speak for themselves. Teachers as activators are more effective than teachers as facilitators. On the left, we have Direct Instruction and Mastery learning. On the right, we have Inquiry-based teaching and Problem-based learning.
On which side is the Numeracy Project?