Half of Australian 15-year-olds are not meeting expected standards in mathematics according to the latest Programme for International Student Assessment (PISA), highlighting continuing fallout from the shortage of maths-trained teachers.

The share of students achieving the standard was lower for maths (51%), than science (58%) and reading (57%), according to the Australian Council for Educational Research which manages PISA nationally.

Every 3 years PISA compares student performance in maths, reading and science. The 2022 data released on 5 December, provides results for 81 countries including Australia.

While mathematical literacy in Australia was slightly higher than the OECD average, local students’ performance was significantly lower than leading country Singapore.

The latest data reveals a continuing decline in students achieving the national standard in maths, with a 16 percentage point fall between 2003 and 2022.

**Maths-trained teachers key to solving numeracy deficit**

In Australia, a quarter of maths educators in years 7 – 10 have no training in the field, according to the Australian Mathematical Sciences Institute (AMSI).

In its most recent report on the state of the mathematical sciences, AMSI argues the lack of teachers with maths training is contributing to the deepening of Australia’s maths deficit.

Australia is not alone facing a shortage of maths teachers. Educators, particularly those specialising in maths and science are also scarce in the United Kingdom and United States.

There are simply not enough trained maths teachers to go around.

But as countries grapple with the shortage, some offer possible solutions.

Professor Tim Marchant, Director of the AMSI says “you need well trained and motivated teachers to motivate students to keep going with the subject”.

He says this is especially important in the early to middle years of high school, a time when students are making decisions about whether to keep going in years 11 and 12.

Having qualified teachers is not just about understanding the material.

“Besides the maths skill set teachers have, I think it’s really important that teachers love the subject and make it fun and engaging for students,” Marchant says.

There are many factors driving the current shortage, he says: the overall number of school children is increasing; the number of teaching graduates is decreasing; as high salaries on offer to mathematicians in the private sector lure them away from education.

Besides the maths skill set teachers have, I think it’s really important that teachers love the subject and make it fun and engaging for students

Professor Tim Marchant, AMSI Director

It’s a challenging problem, but Marchant says an approach from Ireland’s might offer a solution.

Ireland’s national government fully funds out-of-field maths teachers to undertake a post-graduate mathematics teaching qualification, he says.

It is the only nationally consistent, government-funded, university-accredited programme available to out-of-field teachers according to a study published in *Irish Educational *Studies, which found that within a decade (2009 – 2018), the share of out-of-field maths teachers in Ireland fell from 48% to 25%.

Dr Margaret Marshman lectures in maths education at the University of the Sunshine Coast.

She agrees teachers with a passion and interest in maths are much better placed to teach maths in an engaging and inspiring way.

“Sometimes kids will tell you the best maths teachers are the ones that can explain it in 3 or 4 different ways,” she says. But this can be challenging for out-of-field teachers who are often learning new concepts just ahead of the students, she says.

Marshman says its often newly graduated teachers being asked to teach maths, instead of more experienced educators. This adds to the challenge.

Allan Dougan, agrees the way many teachers are introduced to the profession is far from ideal.

Dougan started his career as a secondary school maths teacher, and is now the Chief Executive Officer for the Australian Association of Mathematics Teachers.

Sometimes kids will tell you the best maths teachers are the ones that can explain it in 3 or 4 different ways

Dr Margaret Marshman, University of Sunshine Coast

He says: “We’ve got a shortage of teachers, so we send teachers out so quickly. In some cases, we send them out before they’ve finished their training. And we wonder why we see a decline in the number of teachers staying in the role.”

Other countries do things differently, he says.

Scotland, for example, changed its model for teacher education in the early 2000s to better mentor new teachers, he says.

Under the new model, every student learning to be a teacher was guaranteed a job following their initial teacher education for a year.

“That job became was an extension of their training,” Dougan says. The new graduates worked with a reduced load timetable, they were given a program of development and allocated a mentor.

At the end of the year, mentors sign off if the teacher was competent. Or, if not, the teacher undertakes a further 12 months in the extended development program.

A long term decline in the supply of specialist maths teachers appears to be worsening according to a recent report by Australian Academy of Science. Primary school enrolments are surging at the same time as an older-than-average maths teaching workforce moves into retirement.

The Academy’s objective is to give all Australian children access to outstanding mathematics teachers to: “inspire school students with an appreciation of the fundamental utility and beauty of mathematics”.

It’s recent review says actions are urgently needed, calling on governments, schools and universities to increase support for existing out-of-field teachers of mathematics.

The number of qualified maths teachers might not add up, but examples from other countries might provide some creative solutions.

**Maths methods **

Beyond the lack of maths-trained teachers, there remain underlying differences of opinion regarding the best way to teach maths.

The spectrum extends from explicit instruction to inquiry-based learning. Although in reality many teachers use a mix of approaches.

The NSW Education Department describes explicit teaching as ensuring “students have a clear understanding of why they are learning something, how it connects to what they already know, what is expected of them, and how to do it.”

Inquiry, or problem-based approaches encourage students to explore a problem first by themselves or in groups without being provided with a structure or method for solving it.

Maths teacher and researcher Dr Greg Ashman advocates for “explicit models of teaching where you always explain things fully before you ask students to do anything with those concepts, or apply those procedures. That way you’re not overloading their working memory.”

Ashman’s PhD research involved small-scale randomised control trials looking at the order of instruction, and whether problem solving before explicit teaching is better, or vice versa.

“I had students in a lecture theatre randomly assigned to rows, one group read an unrelated article, while the other half of them solved problems. Then I lectured all of the students together in the lecture theatre, so they all got the same explicit teaching at the same time.

And then the conditions swapped, so the ones that had the problem solving did the reading, the ones that had the reading, did the problem solving.”

“I was able to demonstrate that explicit teaching followed by problem-solving was more effective,” he says.

Dougan believes the most effective and successful teachers are skilled in all of these practices, and have the confidence and knowledge to know which approach to pull out at the right time.

“What I would advocate strongly for is teachers being equipped pedagogically, knowing a wide variety of pedagogical techniques, and knowing which techniques to pull out at the right time.”