I left my life as a secondary school maths teacher behind more than 12 years ago, but there are themes that will never disappear from my life, it seems, even though I have moved countries and now work in higher education.
One of those themes is the debate about procedural knowledge and conceptual knowledge in maths. Put simply, this is about whether it is more important to practise the subject or to understand it. I think the answer is quite trivial - it’s both - but nevertheless, the heated discussion continues.
Another recurring theme is each education phase pointing to the previous one as not having prepared students well enough for the maths they are teaching, while also thinking that certain parts of the curriculum should be pushed to the next phase.
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Admittedly, as a maths teacher, I would sometimes argue that primary schools were not teaching fractions well enough, and that some students should wait until university to learn certain parts of maths, because curriculum time was too precious to waste on frivolous topics.
Such certainties seem to arise in particular when curriculum reforms are at play, with recommendations to “fix” things. I think we need to be calm and measured about this.
The first question is what needs to be “fixed”. What are the indications that something is wrong? And if something is wrong, what is it exactly? (Note that this is different from saying that things need to improve; you can always improve, but that is different to fixing something).
This means exploring where things are going wrong. And it is here where the certainty of pointing to other education phases can become problematic. You also have to have an idea of how you might improve it. And finally, you need to look at the side effects of doing that.
What does the data say?
This is a complex process. I applaud those who make the effort to comment on curriculum changes. I think it’s great that in a recent Tes piece on fixing the primary maths curriculum, the emphasis was on both conceptual and procedural knowledge. I also liked how taking pleasure in maths was mentioned. I disagree, though, that the primary maths curriculum necessarily needs to be fixed. Improvements can be made, but it’s the primary curriculum that previously was heralded as being pretty good in England.
Reducing the amount of content in the primary maths curriculum might be smart. This should not, however, simply be in service of preparing for secondary maths. Both conceptual and procedural knowledge should be covered as part of a wide variety of topics, to avoid giving a narrow impression of one of the most interesting and beautiful subjects around.
We also can’t ignore the diversity in prior mathematical proficiency. The whole breadth of that should be addressed, regardless of whether you find maths challenging or want to be stretched.
Empirical data from the 2019 Trends in International Mathematics and Science Study (TIMSS) previously has been used to wax lyrical about maths achievement in primary school.
In TIMSS 2011, about 19 per cent of primary pupils said they did not like learning mathematics, while 44 per cent liked it. For lower secondary students this was 42 per cent and 14 per cent respectively.
In TIMSS 2019, 23 per cent of primary students did not like learning maths and 44 per cent “very much” liked learning it, while this was 50 per cent and 12 per cent respectively for lower secondary students.
Evidently, saying that the problem lies in primary seems far-fetched, both from an achievement and enjoyment perspective. There is a lot to improve on in both primary and secondary maths education, but if focus is needed anywhere, it is perhaps in lower secondary mathematics, where too many students lose their appetite for the subject. But reforms should always be designed with all education phases in mind.
Christian Bokhove is professor of mathematics education at the University of Southampton and a specialist in research methodologies
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