Home Education Cracking the formula: how should Australia be teaching maths under the national curriculum? | Australian education

Cracking the formula: how should Australia be teaching maths under the national curriculum? | Australian education


Australia’s sliding mathematics ranking and disagreements around how the subject should be taught remain key sticking points preventing a consensus on the proposed national curriculum.

The nation’s eduction ministers met earlier this month to discuss the proposed curriculum and almost reached a consensus, but while most of the state and territories were happy with the latest revisions, the federal and Western Australian education ministers held out.

“The standards in mathematics and humanities and social sciences – they aren’t there yet,” said the acting minister for education and youth, Stuart Robert, last Friday. “We’d like to see mastery of mathematics for students to understand maths … not just an inquiry approach.”

Days later, Robert reiterated that an up-to-standard national curriculum would play a “key part” in arresting Australia’s falling rankings in the OECD’s Programme for International Student Assessment (PISA). The latest PISA results – which assess 15-year-olds’ maths, science and reading skills every three years – were released in 2019.

“Twenty years ago we were 11th in the world in mathematics, now we’re 29th,” Roberts said. “There’s only 38 countries in the OECD – so in terms of our performance, we have slipped substantially.”

Compared to Australia’s average scores from previous assessments, the country’s PISA performance in maths has been declining since 2003.

“You are, on average, 12 months behind now as an Australian student than where you were 20 years ago,” Robert said. “No one can consider that acceptable.”

How maths should be taught has been one of the key sticking points of the national curriculum, which is set to be finalised in April, and the first draft of which was released in 2010.

Last June, dozens of mathematicians, maths educators and educational psychologists took issue with revisions to the proposed curriculum. In an open letter to the Australian Curriculum, Assessment and Reporting Authority, they criticised the draft curriculum as having “little practical value as a guiding structure”, and took issue with “a push toward a central role for ‘problem-solving’ and inquiry-based learning”.

“We do not believe that a curriculum document should mandate a specific method of mathematics teaching, and it is especially concerning that the draft curriculum is extensively mandating learning through ‘exploring’ and ‘problem-solving’,” the letter said.

Two schools of thought

When it comes to maths pedagogy, experts disagree on what works best for student outcomes. Opinions are divided into one of two approaches: explicit teaching, in which teachers explicitly introduce and instruct on new concepts, and inquiry-led learning.

Inquiry-led learning – which is also referred to as structured inquiry, discovery learning, constructivist learning or problem-based learning – focuses more on students discovering information for themselves, without having it presented directly to them.

“With inquiry learning, from the outset, you withhold some information,” says Greg Ashman, who is a deputy principal at Ballarat Clarendon college in Victoria and a PhD candidate at the University of New South Wales.

Ashman, who played a key role in the open letter, is a proponent of explicit teaching, an approach he says is backed by educational psychology and cognitive science research.

In his classroom, he takes a teacher-led, “I do, we do, you do,” approach to introducing new mathematical concepts. “We don’t expect students to be able to do things that they don’t know how to do,” he says.

Peter Sullivan, an emeritus professor of STEM education at Monash University, favours structured inquiry. “The mainstream view among mathematics educators is that student-centred structured inquiry helps to develop in students their agency, in terms of thinking for themselves rather than following recipes,” he says.

“If, for example, we wanted the students to know how to add 132 to 99, there’s at least four different ways you can do it. The students will choose whichever way suits their knowledge and … where they happen to be in their development.

“So why would we say: ‘Here’s the one way in which you should add 99 to 132’,” Sullivan says. “Telling the students what to do isn’t going to be the optimal way to engage them in thinking.”

Sullivan cites 2012 research that surveyed students on whether their maths teachers used inquiry-based approaches that PISA termed “cognitive activation” strategies. PISA participants were asked whether their teacher “presents problems for which there is no immediately obvious method of solution”, “asks us to decide on our own procedures for solving complex problems” and “helps us to learn from mistakes we have made”.

“The more often that the teacher used those sorts of strategies … the more mathematics the students learned,” Sullivan says. “The results of the 2012 study were so clear that they haven’t bothered asking the questions again.

Ashman concedes that cognitive activation is “mildly associated … with some better outcomes”, but points out that so was teacher-directed learning.

The 2012 analysis found that across OECD countries, students whose teachers used cognitive-activation strategies and also those who experienced teacher-directed instruction had “particularly high levels of perseverance and openness to problem solving”, and were more likely to favour maths over other subjects.

“The more teacher-directed learning, the better the maths outcomes, until you get to very high levels of teacher-direction at which point it becomes a negative,” Ashman says.

Some, like educational psychologist John Sweller, who is an emeritus professor at UNSW, have argued that Australia’s falling PISA scores have been “concurrent with an increased emphasis on inquiry learning … and critical thinking in Australian curricula”.

“Inquiry learning was conceived six decades ago based on assumptions that flowed from our understanding of human cognition at that time,” Sweller has written. “Subsequently, it became increasingly popular despite very limited empirical evidence for its efficacy.”

A November analysis paper from the Centre for Independent Studies found that Australian maths classrooms were much more likely to use an inquiry-led approach compared to PISA high-performers such as Singapore, Hong Kong, Shanghai, and Taiwan.

The analysis found that “a lack of teacher-led instruction in Australia has contributed to declining student achievement”. “It’s estimated that the average 15-year-old would be about 10 months ahead of where they currently are if they received mostly teacher-led instruction, with only occasional student-led practice,” the report said.

“Effective teaching doesn’t employ explicit instruction alone, but a great deal of explicit instruction is often necessary before students have sufficient expertise for constructivist approaches to be introduced.”

The director of the Australian Mathematical Sciences Institute (AMSI) at the University of Melbourne, Prof Timothy Marchant, says both approaches are useful – explicit teaching to build up mastery and fluency of basic concepts, as well as student-centred complex problem solving.

“Having a balance there between those two different approaches is important in the classroom,” he says. “I think well-trained teachers can find that right balance.”

Marchant cites supply shortages of secondary maths teachers, as well as high rates of “out-of-field” teaching as other potential factors for Australia’s declining PISA performance.

A fresh start

It hasn’t been all bad news – results from the 2019 Trends in International Mathematics and Science Study (TIMSS) found a rise in the performance of Australian students in year 8 mathematics.

TIMSS has been conducted every four years since 1995, making it the longest running large-scale international assessment of maths and science.

More than 580,000 students from 64 countries – including 14,950 Australian students – took part in the 2019 study, in which Australia ranked seventh in year eight maths and science.

There was, however, no improvement in mean scores for year four maths, in which Australia ranked 23rd in the world, with no changes in achievement since 2007.

Last year, AMSI expressed “considerable concern” that the draft curriculum’s stronger emphasis on problem solving and inquiry would come “at the expense of mastery and fluency”.

The institute welcomes changes in the latest iteration that reverse proposed delays in introducing new concepts – times tables will be introduced in year three, instead of being pushed back to year four and linear equations will remain as a year seven topic instead of year eight.

However, Marchant says: “Our position is still that we would still like a fresh start, really, and that the new curriculum be prepared with consultation from all parties in the sector.”

“The curriculum should be pedagogically neutral – it shouldn’t force us to use a particular teaching style,” says Ashman. “It should tell us what it is we want the students to know and let us teach us the way we do.”


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