Improving maths in primary schools starts by changing teachers’ beliefs

Ingrained ideas can be tough to shift — but not impossible. And when it comes to learning, a new study suggests that teachers’ beliefs can play a significant part in improving their classroom practice.

In their research study, Mastery mathematics: Changing teacher beliefs around in-class grouping and mindset, Professor Pete Boyd and Maths Specialist Andy Ash looked at the importance of teachers’ beliefs when implementing a maths mastery approach.

The self-reported beliefs of the study’s participants show support for a change in practice and uncover three key reasons why the maths mastery approach benefits teachers.

1. Textbooks take away the dull parts of lesson planning and let teachers focus on subject knowledge expertise

There can be a stigma around teaching with textbooks. Educators avoid textbook programmes for lots of reasons; maybe they think they’re too prescriptive, or they restrict student learning, or the overall quality of textbooks is just not up to scratch.

While in some cases this may be true, a high-quality maths textbook can do a lot of good for you and your school.

The study showed that primary teachers using Maths — No Problem! actually benefited from and were valuably challenged by the textbooks.

By saving teachers time on lesson planning

The textbooks helped teachers avoid the more tedious aspects of lesson planning — freeing them up to focus on developing their subject knowledge expertise instead.

“The structure provided by the textbooks seems to free teachers from more mundane aspects of lesson planning. The teachers argued that their lesson preparation is now focused on maths subject knowledge and working out the possible directions in which the children might go in trying to solve the anchor problem.”

By supporting teachers’ development of subject knowledge

A common misconception is that textbooks replace the role of the teacher. With a well-designed textbook scheme, this couldn’t be further from the truth.

“It’s revolutionised my teaching. My subject knowledge is beyond anything it ever was. I enjoy maths, I have an enthusiasm for maths and I think the depth of rehearsal I go through for my lessons, I would never, ever have had that freedom or time to do it if I didn’t have the textbooks.”

The study confirmed that teaching skills and subject knowledge are essential to delivering Maths — No Problem! textbook content.

“…the focus on exploring and on dialogue appears to keep the skill and subject knowledge of the teacher firmly at the heart of this mastery approach to maths. Therefore, the books in themselves are insufficient and only provide one element of the approach.”

Key takeaway: Teaching maths for mastery involves a big change in lesson preparation. Rather than spending time on maths activities, teachers can prepare and improve their subject knowledge to get the most out of the programme.

2. Textbooks shift teachers’ mindsets and remove the stress of making mistakes in the classroom

Teachers encourage their class to see mistakes as rich learning opportunities, but so often they don’t extend themselves the same courtesy.

Interestingly, the study pointed out that one benefit of teaching with Maths — No Problem! was that teachers began to shift their mindset alongside their learners, especially when it came to mistake-making.

By encouraging a growth mindset

The positives of making mistakes can be found in the work of Carol Dweck. According to her, children who have a ‘growth mindset’ see that intelligence isn’t fixed — it’s built through hard work, deep focus and, most importantly, resilience.

But do teachers maintain a growth mindset in their own practice? In the study, teachers reported that their attitudes towards mistakes and struggling had changed.

“In some ways the attitude [towards] struggle and mistakes goes beyond the children’s activity and attitudes and influences [to] the next layer up of the teacher’s practice. This allows the teacher to model being a learner at the level of Maths problems but also at the level of teaching Maths.”

By taking a collaborative approach to problem solving

Textbooks ease the stress of always having to be right. This could be especially useful for Newly Qualified Teachers (NQTs) or teachers who are new to the maths mastery approach. In the study, one primary teacher said:

“I’m far happier to be the person making mistakes at the front or not getting things right and I’m less frightened about mistakes in the lesson. It doesn’t worry me now if things aren’t going the right way. They’re not going the right way and we use that within the lesson… Talk to each other. Why isn’t this going in the right way? Why can’t we get this? What’s not right here?”

Rather than call out or label mistakes as needing pedagogical intervention, teachers involve the whole class to work collaboratively. They ask questions and help the class come to a consensus.

Key takeaway: Teachers who use a textbook programme like Maths — No Problem! worry less about being the person with the ‘right’ answer. Seeing their teacher struggle gives children reassurance that everyone makes mistakes, and that it doesn’t say anything about a person’s intelligence.

3. Textbooks open up more possibilities for classroom management and help teachers build a positive learning environment

The maths mastery approach goes against a certain view of learner attainment. Instead of grouping children by ‘ability’ (a term that we don’t like to use at Maths — No Problem!) all learners are given the same mathematical tasks and work through the textbook at the same pace.

You may be wondering, “how will struggling learners get the support they need? What about advanced learners? They need to be challenged too.”

Maths — No Problem! textbook questions are cleverly designed to be ‘low floor–high ceiling.’ Meaning they’re accessible to all learners and have built-in opportunities for challenge.

This benefits teachers in a few ways.

By helping teachers see the positives of mixed-ability grouping

Teachers who used Maths — No Problem! textbooks in this study no longer felt they needed to group students by attainment level. Instead, they’ve seen the benefits that accumulate at all levels of attainment when learners are seated together based on other criteria.

“…now I feel like the ‘high or middle ability’ children can help the other children by showing them the equipment and talking to them about it and also I think the reasoning and the talking from the ‘high or middle ability’ children, helps them as well to distil what they’re thinking by explaining it to somebody else.”

By giving teachers freedom and autonomy

An unexpected upside was that teachers now had the freedom and autonomy to decide what grouping looked like. Some teachers paired low-attainers with high-attainers. Others organised their classroom by temperament, or by how well they cooperated together.

By taking a ‘no-size-fits-all’ approach to classroom organisation, teachers were able to focus on facilitating learning outcomes for everyone.

Seeing success by changing group dynamics in their maths classrooms has led teachers to apply this new philosophy of pairing learners in other subjects. Outside the scope of this study as well, teachers have said they’ve seen similar benefits when able to try this strategy elsewhere.

Key takeaway: You don’t need to group learners by attainment to see all children succeed. Plus, Maths — No Problem! gives teachers the freedom to mix things up and see how different groupings affect learning outcomes.

By instilling a growth mindset, shifting teachers’ mindsets and abandoning in-class grouping by prior attainment, teachers have been able to transform their practice while seeing increased learner self esteem and efficacy.

References

Boyd, P. and Ash, A. (2018) ‘Mastery Mathematics: Changing teacher beliefs around in-class grouping and mindset’, Teaching and Teacher Education, 75: 214-223.