If you have been homeschooling your children during the past few months, you will have noticed that mathematics has become very wordy and visual, rather than mostly being an array of digits.

A natural question to ask as a result is: when we say we are teaching maths, is it really just a pupil’s mathematical proficiency that we are testing?

For the Programme for International Student Assessment (Pisa) global education rankings, it is, strictly speaking, “mathematical literacy” that is being assessed and not just mathematics alone.

Another popular international study on mathematics, the Trends in International Mathematics and Science Study (Timss), focuses more on mathematics in the curriculum and distinguishes questions on “knowing” (for example, basic addition skills), “applying” (which often involve a context) and “reasoning”. So, in some question types, language again plays an important role.

The picture in schools is likely to be similar.

Being aware of this is one thing, but it also is important to understand the consequences of such language-heavy mathematics.

In 2013, the organisation that publishes Timss released an interesting report for which it combined mathematics and science scores from primary school level with scores from its sister study on reading called the Progress in International Reading Literacy Study (Pirls). It developed measures that calculated the “reading demand” of assessment items, taking into account the number of words, specific mathematical terminology, symbolic language (eg, numerals and operations) and visual displays such as graphs.

It then analysed the achievement data for both mathematics and reading in light of the assessment items’ reading demand. In nearly all countries, the difference in achievement between poor and good readers was larger on items with high reading demand than on items with low reading demand. In short, making things more wordy has a negative impact on how a weak reader scores in maths.

Images often accompany language-heavy tasks to assist the pupil, but do they help? Verschaffel and colleagues say that images or graphics used in word problem solving have mixed results depending on the nature and function of the graphics. Mathematics textbooks might make ample use of decorative pictures but, unfortunately, empirical evidence for their effectiveness is non-existent. Even for more representational and organisational diagrams, they found that the results are mixed.

So, what should we do? Representations don’t have to always be given by the instruction - sometimes they can be “self made”. Verschaffel describes an approach with “self-made” representations: learners are taught to solve a well-defined set of word problems by identifying, drawing and completing a teacher-imposed schematic diagram. The Bar Model Method, popular through Singapore Maths, is an example of such an approach.

As for word problems, the review highlights important factors to consider. It states that word problem-solving performance is significantly associated with several cognitive resources such as working memory capacity and inhibitory skills.

For example, individual differences in working memory account for variance in word problem solving even after controlling for other cognitive variables. Unfortunately, working memory is hard to train.

Meanwhile, inhibitory control - the ability to ignore salient but unhelpful stimuli and responses - is increasingly considered to be important for mathematical word problem solving. Can a student inhibit distraction by an irrelevant, decorative picture?

Unfortunately, there are no easy answers to the challenges in maths becoming more word and picture orientated. I do, however, think that one key characteristic of mathematics - its abstract nature - should not simply be replaced by language.

We need to be aware that mathematics nowadays asks much more of a pupil than just numerical skills. At the very least, acknowledging that can help us to have a better conversation about whether that is what we want, and what impact it might have on our pupils.

This article originally appeared in the 10 July 2020 issue under the headline “The language of maths? I’m lost for words”