New research looks at how differences in textbooks might affect pupils’ performance in maths, but we should be wary of reading too much into it, says Christian Bokhove
For a maths education specialist like me, some of the most interesting studies of the last couple of decades have been conducted by Robert Siegler.
His analyses of large, nationally representative longitudinal data sets from the United States and the United Kingdom have demonstrated how pupils’ knowledge of fractions and division in primary school is uniquely predictive of their attainment in maths at secondary school (Siegler et al., 2012).
So, I was immediately intrigued by a new piece of research by Siegler and Dake Zhang, in which they compared textbook coverage of fractions in high-achieving East-Asian countries and the United States (Zhang & Siegler, 2022).
The fact that the research focussed on textbooks was an extra bonus: I have long thought the UK could get far more out of textbooks by looking critically at how other countries use them to teach key maths topics.
In their study, Zhang and Siegler find that, in the US, fractions are studied earlier, over more grades. East-Asian textbooks, meanwhile, concentrate fractions content into fewer years and use more challenging fractions problems.
There are also some interesting differences in how textbooks represent fractions. US textbooks contextualise problems and emphasise part-whole and measurement models of fractions, while East-Asian textbooks emphasise fractions in the context of multiplicative reasoning and as extensions of whole-number operations.
The authors are suitably careful about making connections between the performance of East-Asian countries in international league tables and what the textbooks suggest about when fractions are taught, the number of grades in which they are taught, or the way they are taught.
They acknowledge that prior knowledge, motivation, teachers’ knowledge, and cultural differences also contribute.
Such disclaimers are important to add. Reading the paper, some might assume that simply adopting a similar curriculum, or textbooks, to those used in East-Asian countries might be the path to better maths education. But it’s certainly not that straightforward.
To start with, the research that underpins the new study is generally quite old. Several of the key studies referenced by Zhang and Siegler use data from the Third International Mathematics and Science Study (TIMSS) 1995 - already 27 years out of date.
There’s also the fact that curricula and textbooks are very much cultural projects, so it is not a given that conclusions drawn from them would still hold true now. If you look at TIMSS 2019 questions on fractions, East-Asian countries do tend to score highly on average, but the mix of countries at the top of the chart is more diverse - including Ireland and Northern Ireland.
Finally, we need to acknowledge that “East Asia” can’t really be thought of as one homogeneous region. Some differences between, for example, Hong Kong, Japan and Chinese Taipei might be even larger than the differences between Western and Eastern countries.
I looked at some of these differences myself in a recent study, in which I used TIMSS 2019 data to consider how instructional practices might predict attainment in maths (Bokhove, 2022).
One of the things I found was that there was no consistent pattern of instructional practices across countries, including among East-Asian countries.
Curriculum and textbook analyses are important and worthwhile - and I will probably always be excited to see a new one - but, with these analyses, as with all education research, we must be careful about making easy generalisations, no matter how appealing they might be.
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