Speaking to teachers in London earlier this year, prime minister Rishi Sunak claimed that an “anti-maths mindset” in the UK was an impediment to the development of numeracy, and that the idea it was “OK to be bad at maths” was putting children at a disadvantage.

“We’ve got to start prizing numeracy for what it is: a key skill every bit as essential as reading,” Sunak said.

You don’t have to look very far to find examples of this “anti-maths” rhetoric. Last year, London headteacher Katharine Birbalsingh - then the government’s social mobility tsar - told a group of MPs that one of the reasons why a disproportionately small number of girls study physics was that they don’t like “hard maths”.

“That’s not to say there isn’t hard stuff to do in biology and chemistry - there is,” Birbalsingh said. “But it’s not mathematical.”

What is it about maths that leads people to believe that it’s OK not to excel at it? And what can schools do to dispel those ideas?

In our book I Can’t Do Maths! we look at why children believe that the subject is too hard and, more importantly, how to change their minds.

We’ve identified five “dogmas” that plague maths teaching. You have likely heard them before in some form or other. We aren’t proposing that these are the only five dogmas, or myths if you like. But we think they’re pretty major ones.

Busting the myths about maths

If the aim is to shift attitudes towards maths, we believe that tackling these misconceptions is where schools really need to start.

Myth 1: maths is a “building block” subject

Considering maths as simply a “building block” subject - something that has to be learned methodically and in a particular order - is probably the most deeply embedded of our five dogmas.

The idea that in order to learn something you need to start with the simplest ideas and slowly build upwards seems to be common sense, and the primary maths curriculum in most countries in the West is designed with this in mind.

However, while it might seem counterintuitive, there will be some children for whom algebra will make more sense than times tables.

When the idea of moving from simple to complicated becomes embedded, it can lead to some students being cut off from parts of the curriculum that are wrongly deemed to be too complex for them. It can also inadvertently serve to make mathematics seem inaccessible and authoritative.

‘There will be some children for whom algebra will make more sense than times tables’

So, what can schools do to counteract this?

We need to recognise that there are different ways of sequencing maths - and that the most logical sequence is not necessarily the most productive for learning.

For example, the UK’s National Centre for Excellence in the Teaching of Mathematics (NCETM) suggests teaching numbers 20-99 before 11-19, since 11-19 are the irregularly named ones and, by focusing on 20-99 first, we can help children appreciate the structure of number naming before working on the exceptions.

Psychologist and mathematician Caleb Gattegno, meanwhile, proposes something more radical: sequencing the curriculum in terms of awareness, placing awarenesses of algebra before awarenesses of number.

That’s not to say that Gattegno’s model is the “best” model, or even that there is a “best” way to organise the maths curriculum. But it does show that there are many possible routes to understanding maths.

We should therefore be cautious about denying students the opportunity to work on more complex ideas just because they have not understood a supposedly simpler concept that those ideas make use of.

Myth 2: maths is all about right and wrong answers

Of course, there is an element of maths that is all about solutions; you get them right or you get them wrong.

This can actually be a source of relief and comfort for some people, bringing some welcome dependability in such a chaotic world. It can also be satisfying to know, after working on a problem for a while and arriving at a solution, that you were right.

But there is a problem in treating maths as if it is always a matter of getting to the correct answer.

For a start, students who keep getting 90 per cent of the way to a solution and falling just short might start to feel alienated, even though they are doing lots right. This can lead to them being completely turned off the subject.

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On the other hand, some students who keep getting things right can develop anxiety. They get worried about the perceived need to keep on getting the correct solution. At both ends of the spectrum, this is a really unhelpful way to treat maths.

Thankfully, there’s a very simple way that teachers can get out of the “right or wrong” paradigm, which is to focus on methods rather than answers.

People approach even very simple problems - such as 8 x 7, for example - in all sorts of different ways. If you ask someone what they did in their head when working it out, you will get different approaches, all of which are correct in their own way.

This shift in focus from answers to methods really opens up the classroom in a way that is more democratic and more interesting. Students can discuss and debate, and they actually benefit from hearing the different methods. They can get into deep questions about mathematical structure, which are really important.

While some children may enjoy maths always being right or wrong, we know that there are many more who are turned off by this, perhaps sensing that, in real life, things aren’t always so easy. The key here is emphasising the journey rather than just the final destination.

Myth 3: maths is “culture free”

Wherever you are in the world, 2 + 2 will always equal 4. There’s a universal agreement about this - and many other mathematical “facts” - which can give the impression that mathematics is not about opinions or fads, and that it stays the same regardless of where you are.

Also, if you look at many maths curricula, they tend to focus on theories that are at least 400 years old. It is easy to conclude, therefore, that the subject is pretty set in stone; that it is stable, established and immune to cultural influence.

However, that simply isn’t true, and this perception can blind us to the human choices that are made around mathematics.

An obvious example of this is the number base that we use. We have 10 symbols and then they start repeating, but other cultures have 12, while computers use just ones and zeros. While it’s common across almost all cultures that people use their hands to count, different cultures do so differently.

In England, counting often begins by extending first the thumb and then each of the fingers in order; in Iran, it’s more common to start with the little finger and work through the fingers first.

‘Maths is certainly not devoid of subjectivity or humanity’

These are literal examples of cultural differences, but perhaps more important for teachers is how mathematics can be used in a way that is specific to its locale. Maths can become more culturally relevant to students if it is presented through topics like climate modelling or how we approach social issues.

It’s a mathematical algorithm that dishes out social care benefits, for example, or deems whether the NHS should be funding a particular treatment.

These interfaces of human decision making, powered by mathematical processes, are subject to significant cultural influence and can show how different groups can implement maths to fulfil all manner of different purposes.

In a classroom, it is all about looking for ways in which mathematics is used practically in different locations and highlighting the human nature of decisions behind some of the big ethical choices that we face.

Ultimately, maths is full of values, and not just numerical ones. It is certainly not devoid of subjectivity or humanity. Furthermore, in the maths classroom, questioning what is valued, and why, can be a great starting point for building deeper understanding.

Myth 4: maths is for some but not for others

It’s still very common for people to think about maths in terms of “ability”; perhaps they do this more than in other subjects. One mistake here can be an overreliance on past performance as an indicator of future attainment.

A direct consequence of this is the prevalence of setting in UK schools. In primary maths lessons, for example, it is still common to group the “highers” together on a table and then children of similar ability on tables all the way down to the “lowers”, who, despite attempts to mask their group name, always know who they are. In secondary schools, too, setting and streaming are common.

Once children are placed in lower sets, or lower groups within a class, there is rarely any movement out of that position, and we know that such placements have a high degree of error, even when judged with an independent attainment test.

We also know that “lower” groups tend to be given more routine and repetitive work than their peers, with less opportunity for creative thinking or problem solving.

We would always advocate strongly for mixed attainment teaching because there’s a lot of research from around the world that suggests that, broadly speaking, this approach is better for everyone.

In England, the recent introduction of “mastery” approaches to mathematics may actually be helping here, as they have encouraged a push towards mixed-attainment teaching.

In addition, practices where the teaching and learning of mathematics is not always focused on individuals - incorporating communal chanting, for example - can help to get away from the idea that maths is not for everyone. Small-group activities can also help to bust the perception that maths is an individual pursuit.

Myth 5: maths is hard because it is abstract

Maths is seen by many as being cut off or distanced from our everyday experiences of the world; it is abstract, and therefore complicated. But where does this perception come from?

The idea that understanding abstract concepts is something we develop over time, after developing our understanding of the tangible world, appeared in the mid-20th century, largely thanks to the work of the Swiss psychologist Jean Piaget.

Whether or not Piaget was correct (and there is significant doubt), abstract thinking came to be seen as something that only older children could accomplish and was associated with theoretical or hypothetical thinking.

The idea seeped into school that you have to start with concrete materials, then maybe you draw pictures of them, and only then can you think about them in a more abstract way.

‘The shift in focus from answers to methods really opens up the classroom’

But, in reality, children are doing abstract thinking all the time. Take language acquisition, for example. Understanding that the sound “pen” refers to a writing implement is an abstract concept, but we know that children can learn language by spotting patterns like this.

There are other examples, too. Even very young children like to spend time in imaginative worlds, and what are they if not abstract?

That’s why we believe that opportunities for concrete, pictorial and abstract thinking should be on offer in maths from the earliest stages of learning.

A lovely example is how one primary school teacher mobilises the idea of abstract mathematical thinking in her classroom by treating each day of the month as a focus of investigation. For example, by saying: “Today it’s 7 October. What do we know about 7?” This is a question that encourages children to build connections - it invites new thinking about 7 that doesn’t depend on a single, central idea.

Pupils might get to a particular understanding that the teacher has in mind, like the idea that 7 comes after 6 on the calendar. But they might get to other understandings as well - that under 7, we find 14; that there are three 7s on the calendar for the month of October; that 7 is also the number of days in a week.

It’s all these connections that give 7 its “personality”, that make 7 worth getting to know. Some connections will be very powerful for some students and others for other students.

We feel that this sense of excitement and wonder is crucial to developing connections with maths. The subject needs to include emotion, as well as just being something intellectual or cognitive.

The exact solutions given in this article may not work in your classroom. They will need to be adapted according to the particular opportunities and constraints that you have, which might include the time of the year, the topic, classroom dynamics and so on.

But our aim in showing these possibilities is to stress that there is not just one way of doing things. If we can open students’ minds to that fact, we have a better chance of breaking down stubborn misconceptions - and that will go a long way in turning fewer learners away from maths.

Alf Coles is professor of mathematics education at the University of Bristol, and Nathalie Sinclair is a professor in the faculty of education at Simon Fraser University in Vancouver, Canada. They were speaking to Chris Parr. Their book, I Can’t Do Maths!, is published by Bloomsbury