How to boost students’ maths learning in primary schools

Australia has a maths problem: one in three Australian school students fail to achieve proficiency in maths.

When maths is taught well, children and the nation benefit. But taught poorly, students are robbed of a core life skill. Adults with weaker maths skills have worse job prospects and are more likely to struggle with routine tasks such as managing budgets and understanding health guidance.

Join Amy Hayward, Education Deputy Program Director, in conversation with co-authors Nick Parkinson and Dan Petrie, about how to boost students’ maths proficiency in primary schools.

Read the report

^{Photo courtesy of Ballarat Clarendon College}

Transcript

Amy Haywood: Australia has a maths problem. One in three Australian students are failing to achieve proficiency in numeracy according to 2024 NAPLAN results. That is worrying because maths is essential for daily life. Calculating the impact of your interest rates on your mortgage or paying taxes or just budgeting for that next family holiday.

Maths is essential to all of those tasks. I’m Amy Hayward, the Deputy Program Director in Grattan’s Education Team, and I’m here today to talk about what this means for primary schools. So why primary schools? Maths is highly cumulative, so primary schools need to lay down strong foundations for future success in school and in life.

And while a lot of time and attention has been paid to literacy by us at the Grattan Institute and others, maths has often unfortunately played second fiddle. We’re hoping that will change. Today we’re exploring our new report, The Maths Guarantee: How to Boost Students’ Learning in Primary Schools.

It’s a partner report to our previous Reading Guarantee research. And with it we’re hoping to put maths on the map, revealing the extent of the problem and providing a clear roadmap for transforming how we teach maths in Australian primary schools.  

I’m today here with my two co-authors, Nick Parkinson and Dan Petrie, Senior Associates in the Grattan Education Team.

Let’s dive right into the detail. Dan, can you tell me what’s going on with Australia’s maths results?

Dan Petrie: To start with, as you mentioned, Amy Australia has a big problem with students’ proficiency in numeracy. So just to explain that a little bit, in Australia, students aren’t proficient if they’re in the two lowest NAPLAN proficiency bands out of the four, and that’s the needs additional support, and the developing proficiency bands. So, in terms of what that means in practice, for example, at year seven, students who aren’t proficient might struggle with adding and multiplying, and they might still be counting on their fingers to solve simple problems while their classmates race ahead to algebra. And that creates a learning gap that widens every school day.

And based on one third of students not reaching proficiency as Amy mentioned, we calculate, there’s currently around 1.3 million Australian students who are at risk of leaving school without the basic skills they need to succeed in life, which is obviously a massive problem.

This problem is bigger for disadvantaged students. For example, Indigenous students and students whose parents didn’t complete high school are around twice as likely to be non-proficient. But many advantaged students also struggle. So, for example, one in five students whose parents hold a bachelor’s degree will also not be proficient.

At the same time as we have these proficiency challenges, Australia is lagging behind international peers in the share of students achieving excellence. For example, in 2023, TIMSS tests, that’s the Trends in International Mathematics and Science Study. When we looked at the advanced proficiency level, only one in eight Australian Year 4s were advanced. That compares with one in two Singaporeans, one in three Japanese, and one in five English Year 4s. So, we are not keeping up.

Amy Haywood: Thanks, Dan. So, it’s great to get that picture into, what are our overall results and what do they look like? But it does beg the question, why does that matter and what’s the impact for individuals?

Dan Petrie: The reason all these matters is because of how low numeracy impacts on people’s lives. So individual students with poorer numeracy are likely to have lower incomes, lower employment prospects, and worse social and emotional outcomes, such as greater likelihood of homelessness. But in addition, low numeracy skills do also impact national prosperity. They reduce our productivity and economic growth as well as Australia’s pipeline of highly skilled mathematicians. And so, all of this is gonna make it a lot more difficult for Australia to keep up in a world that, as we know, is rapidly changing and highly competitive.

Amy Haywood: Great. So that is a worrying trend. Certainly, something that we should be concerned about. I know we think a lot about students’ results across primary and secondary, and we know the gaps get bigger in secondary. So why is it that we care about primary so much?

Dan Petrie: We know students who are behind tend to fall even further behind, and we can easily imagine why this is true in maths, which is such a cumulative subject with topics all building on one another. So, for example, students who struggle with addition and subtraction may go on to struggle with multiplication and division. These are fundamental to fractions, and that in turn is essential to algebra. And these are more complex, and abstract ideas can be very challenging for students that are still learning the basics, who are more likely to be left behind. And this is one of the main reasons why it’s so critical to intervene early in the primary school years. Getting the foundations right in primary also matters because student attitudes towards maths, whether good or bad, are largely established in primary school. And there’s some easy wins to be had in primary schooling, for example, by increasing the priority placed on maths and dispelling the myth that maths is easy to teach and doesn’t really require any real depth of expertise, which in fact, actually the reverse is true.

Amy Haywood: Okay, so you’ve convinced me maths is important, we should care about primary school students. The next question is, what does really great maths instruction look like? And I know, Nick, you’ve taken a look at the literature. Can you tell me what you found?

Nick Parkinson: I sure can. And Amy, if you’ll indulge me for a moment, I just want to take a step back. You said the word effective. What does effective maths teaching look like? And I think in primary schools it’s important to describe what we mean by this word. One thing that we can forget is that actually students have a really limited number of hours in which to go from learning to count on their fingers to learning really quite complex things.

We did the maths, it being a math report, and let’s imagine you were a primary school student, and you had an hour of maths every day. You’re not sick once. You don’t have a school camp. You go to class every single day. Chances are you have only about 1,400 hours between when you’re a bright-eyed four or five-year-old walking through those school gates on the first day of Prep right through to that Year 6 graduation day, where people draw in markers on your, on your polo shirt.

Now, that 1,400 hours, that’s equivalent to about nine months of full-time work for an employee. So, it’s really not much time. And what the upshot of this is, is that efficient math teaching will be thinking about the most effective ways to induct students into the specialized knowledge of maths that it’s really taken humanity millennia to accrue.

Now Amy, this is a really big task, but it’s made much easier if students understand the science about how humans, including young children, learn.

Amy Haywood: Can you give us an insight into, what does this mean for success in maths and for teaching?

Nick Parkinson: What it means for success in maths is that there is a clear body of evidence, which is found time and time again, that the best way to help students learn new material in maths is through what’s called explicit and systematic instruction. So, what does that actually mean? It means that teachers break up learning into small, manageable chunks.

They clearly explain math concepts to students. They model worked examples and explain their steps out loud. So, let’s say that we’re together in a class and we’re learning to add fractions, the teacher might first explain some key vocabulary and then they might model an example of how to add fractions on the board.

Perhaps using something like a number line to help students’ understanding. They would guide students through practice questions which look similar to the one they’ve modelled and provide immediate corrective or affirmative feedback, so students know if they’re on the right track. Often a way that this is done is using things like mini whiteboards, which are small whiteboards that students complete a question on and hold to their chest at the same time, so teachers can scan the room to see who’s got the question, right, identify any misconceptions and figure out if they might need to do another explanation or more questions, or if most of the students have got it and they’re ready to move on. Once students are nearly always responding accurately, so they’re nearly always adding fractions correctly, but it’s still laborious for them, they need more practice to build their fluency so they can get faster at adding fractions and start to do it automatically and effortlessly. Now, it’s important to remember this is just part of a whole sequence. We’d come back to adding fractions periodically so that students, get more opportunities to embed it in their long-term memory and retrieve it from their long-term memory.

And we also would have opportunities for students to apply that knowledge to novel and unfamiliar contexts, whether that be some more tricky application tasks or using adding fractions in more complex maths later down the line.

Amy Haywood: So, what we can see from that, that Nick, is that it’s quite complicated what we’re asking teachers to do.

They need to be able to know the maths, they need to know what students might find difficult, and they need to be able to respond in the moment and then give lots of opportunities for practice. We’ve done a new survey of 1,745 teachers and school leaders across Australia. I’m curious to know what did we find and is this great practice, common practice in Australian primary schools?

Nick Parkinson: Our research found wide variation in how maths is taught. Fewer than half of teachers said that at their school, teachers agree on the most effective way to teach maths. And our survey shows that indeed practices in schools are highly varied. So just 54% of teachers said that their school had lesson plans that cover the primary school curriculum, and only 42% said that they used agreed textbooks or lesson materials as part of a whole school approach.

This is worrying, ’cause what we know is that maths is highly cumulative, and students need to progress and be shepherded on a journey that’s well sequenced. It’s hard to do this without coordinated materials. We’ve also talked about the importance of a lot of practice. The worrying thing from our survey is that more than half of teachers said that maths is not a timetabled subject at their school.

Amy Haywood: And this can mean that it’s sometimes the first thing to go, particularly if a teacher might not feel confident with maths.

Talking about confidence, Nick. We did find some concerning results in our survey about primary teachers’ confidence with maths. Can you tell us about that?

Nick Parkinson: This may not be surprising given what we’ve talked about in terms of math teaching in primary schools not being as straightforward as it might seem.

Although most primary teachers are maths teachers, not all have the maths confidence, the skills, or the training to teach it well. So, while 72% of teachers felt confident teaching Year 6 maths topics, this leaves 28% who felt otherwise.

When we look at the Year 7 and 8 math curriculum, which might be being done by some students requiring extension, fewer than half of teachers felt they’d be confident teaching topics from this part of the curriculum. This is troubling because high quality research finds that there is a strong association between how teachers feel about maths and their own math skills and the learning progress that students make in maths.

When teachers have to stand in front of the class, if they’re uncertain about maths, it makes it harder for them to provide clear explanations, address misconceptions, do modelled answers on the fly, or work through students working out to figure out where they might have made an error. It’s not fair on the teachers to ask them to do this if they’re not confident or their students, and so this really makes the case for much more support.

Amy Haywood: That’s a really good point about support and we will get into what support we think is necessary in terms of our recommendations. But I wanna first touch on what we’ve also seen in terms of great practice happening in the case study schools that we profile in our report. Dan, can you tell me what we found when we got the chance to look inside these schools?

Dan Petrie: We visited seven schools, and they showed us that there are many schools that are using exceptional teaching practices across Australia, and they also showed us what it would take for every school to get there.

Our schools represented quite a diverse slice of Australia. Uh, the seven schools were across three states in government, Catholic and independent sectors. They were in metropolitan and regional areas, and they were in disadvantaged and advantaged communities. Despite those diverse contexts, the schools did have a lot of common systems that supported consistently high-quality teaching across the whole school.

They had dedicated time for maths teaching, generally timetable for at least an hour a day. The schools had buy-in from all the teachers to their explicit and systematic teaching of maths, and that was generally with a shared instructional model. They had appointed school leaders who were resourced and dedicated to improving teaching practice, usually with an equal focus on literacy and maths, and that might include, for example, coaching. Uh, they had well sequenced and comprehensive curriculum materials shared by all the teachers. Uh, in some cases, schools developed those materials themselves, but some schools adopted high quality materials that were available publicly or through school networks. They were part of.

Our schools also had rigorous assessments to monitor student learning progress and to screen for students who are at risk of falling behind and who would need extra support. And they were generally using external benchmark assessments as part of their overall schedule.

And lastly, they had systematic approaches to building teachers’ capability in teaching maths. So that variously included shared reading or professional learning, classroom feedback and coaching, and common planning time that was often used for detailed discussions about student data and specific teaching practices they might wanna adopt.

So, if you’re a teacher that’s used to planning on your own. All this coordination that these schools are using is a big shift in practice. And school leaders across the country are gonna need a lot of help to put these kinds of systems and practices in place. So that’s why we think there’s a lot more support that can be provided to schools by governments and their Catholic diocese also.

Amy Haywood: So, let’s talk about some of that support. Our report sets out a 10-year maths guarantee strategy and we recommend five specific areas that we think government should work on. The first is setting more ambitious targets for student learning in maths. The second is giving teachers specific and practical guidance on how to teach maths most effectively.

The third is giving them the tools of the trade, so that is high quality curriculum materials, catchup support programs, and assessments. The fourth is giving them the PD so that they’ve got that expertise in how to teach maths really well. And the fifth is closer monitoring and stronger school reviews.

So, it’s an ambitious reform agenda, but we think it’s achievable. Once fully established the cost of the reform package should be about $152 million per year, or about $67 per primary school student. So many of these reforms actually are inspired by two countries or systems Singapore and England, and we were lucky enough to visit both of them as part of this research. And what’s interesting is both of them have taken this coordinated approach to really thinking about how do we lift primary school maths instruction across the whole system. Now the report is long. There’s a lot of detail and we don’t have the time to get into it all.

But I just wanna focus on a couple of reform areas. And the first one I’m interested to talk to you about is guidance. So, Nick, can you talk to us in a bit more detail? What did we say about guidance in this report?

Nick Parkinson: We’re calling on governments to lift their game on guidance.

Just one quarter of leaders we surveyed said that the government provides them valuable advice on how their school can improve maths teaching. We did a scan of public facing guidance provided by governments to primary schools and how they can better teach maths. What we found is that sometimes this guidance is inconsistent, and it’s not aligned to the evidence base.

It’s easy to see how we got here. In maths teaching our goal is for students to apply maths flexibly to novel scenarios, but guidance has sometimes conflated the ends with the means. What this means is there’s been a tendency to encourage teachers to primarily teach maths through games and activities.

These can be fun at the end of term, but there’s a real risk that if games dominate class time for maths, students are not thinking sufficiently about the underlying maths nor getting the practice that they need to become accurate and fluent in the foundational math skills that they’ll need to apply maths through later parts of school and in life.

We are calling for detailed national guidance on how to teach primary maths. National guidance that’s based on high quality, rigorous research. This should be led by the Australian Education Research Organization with input from researchers and practitioners. This has been done in other countries. Both England and Singapore provide their teachers much more detailed guidance on how to teach different parts of the maths curriculum.

And importantly, the Australian guidance needs to be practical. So, it should include suggestions for how to teach gateway skills in primary mathematics, advice on prioritizing different parts of the maths curriculum, recommended assessment schedules, and do not do lists of ineffective practices.

Amy Haywood: Thank you, Nick. Now another big part of our recommendations is focused on teacher and school leader professional learning. We really want to dial up the investment through micro credentials and setting up something called maths hubs. Dan, can you tell us what both of these would involve?

Dan Petrie: Both of those initiatives you mentioned are based on existing initiatives in England at the moment. Micro-credentials are based on England’s set of courses called the National Professional Qualifications. So, in Australia, micro-credentials will give teachers access to high quality external professional learning to build their knowledge and expertise in evidence-based maths teaching practices and the micro credentials would be a significant step up from the professional learning currently offered to Australian teachers. So, we’re recommending three different micro credentials in specific areas. One, the first is for teachers and effective maths teaching course. The second is a leading maths teaching course for current and future school leaders. And the third is a course on intervention for lower achievers, for teachers and support staff.

These courses will be at least 12 months long and delivered through a mix of in-person live and on-demand sessions. They’d align to the national guidance on effective practice in maths, which Nick mentioned earlier.

Amy Haywood: Thanks for that detail, Dan on Micro credentials and that set that we’re recommending. The second initiative in professional development that we wanna talk about was maths hubs. What are maths hubs?

Dan Petrie: Maths hubs are at demonstration schools, which uh, would be working in local networks of schools. So, they provide the practical on the job training that we know is really important for teachers. Teachers in the network will be able to visit the maths hub to observe high quality practice firsthand at a school that excels. And also, the hub schools will partner with a smaller selection of schools in their local network who need more specific support to improve maths teaching and student learning at their schools.

Amy Haywood: One other area that I really wanted to talk about was assessment. So, we’re calling for new research on effective maths assessment, as well as a mandatory early years numeracy test. Nick, can you tell us about this?

Nick Parkinson: I sure can. Amy, and I’m so glad you asked. This was one of the most interesting parts of this project ’cause there’s such a wealth of high-quality research that’s been done about the importance of screening and assessing students in mathematics. Existing maths assessments in Australia, they give schools and school systems, so that’s governments and Catholic diocese, an incomplete picture of students’ learning progress in maths. Let’s take NAPLAN. It first occurs in the fourth year of primary school. Results aren’t available until semester two, so it’s simply too late to pick up and flag on any challenges students might have in maths.

The other thing about NAPLAN is it mainly tests students’ ability to solve worded problems. Now, this is a really important outcome to track, but it doesn’t specifically test the foundational sub skills that we know are really important predictors of students’ later success. So that’s things such as students’ ability to identify numerals or their fluency with counting. Now researchers recommend that schools supplement standardized tests of general outcomes like NAPLAN with periodic screening assessments in maths up to three times a year.

These screening assessments are assessments which tell you whether or not students are on track. The challenge in Australia is there are not any research validated maths screeners at the moment. What we’re doing in this report is we’re calling on governments to validate screeners by testing them with real students in real classrooms.

What we wanna know from these results is, are the tests reliable? Do they produce similar results no matter which student population they’re used on? And are they actually predictive? So are they flagging whether or not students are on track, or they may be having too many false negatives or false positives. This research is common overseas, and we should have it here in Australia too.

You mentioned that we’re also advocating for a mandatory early year screener. So once there is a research validated screener in Australia, one that’s been proven to be effective, we’re calling for this to be mandatory. It’s really pleasing to see that there’s an early commitment to rolling one out nationally in 2028 in the new school funding agreement.

But what needs to be clearer is that this should be mandatory for all students regardless of where they sit, be that in Catholic independent or government schools and that it should ideally be efficient to administer. So, taking no more than 10 minutes or so and possible to do with a group of students.

Amy Haywood: Thanks Nick, for letting us know about assessments. I think unfortunately our time is done for the podcast and we’ve only been able to really scratch the surface of the detail that’s in the report. If you are listening in and wanna see more of that detail, please go ahead to our website, grattan.edu.au, where you can download the report freely.

A huge thank you to you, Dan and Nick, for coming on and explaining uh, all that we’ve done in our research. And thank you to those that are listening. I hope you enjoy the rest of your day.