A paper I keep returning to is by Carol Bryan and colleagues. They surveyed the attitudes of maths teachers in the US, Australia and Mainland China and Hong Kong. The most notable finding relates views on the relationship between memorisation and understanding:
Though they all agree that memorization plays an important role in mathematical understanding, teachers from the four regions do not fully agree on what that role is or to what degree memorization is important. Furthermore, there was a re-occurring concern of whether or not memorization should come before or after understanding. For teachers from Mainland China and Hong Kong, memorization can come before or after understanding. However, for Australia and US teachers, memorization can only come after understanding. Nevertheless, memorization after understanding is held in higher regard than memorization before understanding (or ‘‘rote’’ memorization), though some of the teachers from Mainland China say that perhaps the latter could be an intermediate or transitional step towards understanding the mathematics.
I was reminded of this when I saw the comments following a tweet by Pritesh Raichura, Head of Science at Michaela Community School in London.
Michaela is an independent, government-funded school known as a ‘Free School’, similar to Charter Schools in the US. Last year, its first students completed GCSE examinations and the results were phenomenal. It is important for those who are unfamiliar with GCSEs to realise that these assessments involve essay questions and structured answers, not just factual recall. So Michaela students are capable of far more than simply recalling facts.
Michaela serves a diverse community and is open to all. Its students are not wealthy. I used to teach similar students in nearby Greenford and so I find Michaela’s achievements particularly impressive. You may think education academics would be interested in how they achieved their success.
The objections to Raichura’s tweet seemed to centre on the idea that understanding should come before memorisation and so drilling students is inappropriate. Even if you truly believe that this is what the research shows, would Michaela’s success not at least give you some reason to pause? Science is not the process of dismissing anomalous results because they do not fit your preconceived ideas. Science is about actively seeking anomalous results.
And we know there is often a disconnect between the small-scale studies of researchers and large-scale implementation in schools. Dismissing meaningful, large-scale success on the basis that it conflicts with smaller research studies – if such a conflict existed – would seem to have things entirely the wrong way around.
What does research actually say about memorisation and understanding? Well, as far as it goes, it seems to support a two-way, iterative relationship. So the East Asian teachers probably have this right.
Perhaps the US commentators are suffering from being locked into a ‘WEIRD’ perspective – western, educated, industrialised, rich and democratic. They may do well to seek more diverse viewpoints.