Resistance to the proposed changes has recently been rallied via an open letter signed by leading mathematicians and educators.

Chief among signatories' gripes is that the curriculum now gives the nod to evidence-free teaching approaches that favour students steering their own learning, with a lesser role for teachers' guidance.

For its part, the Australian Curriculum Assessment and Reporting Authority argues the proposed changes will better allow students to apply their knowledge to "real world" problems through greater emphasis on inquiry and exploration.

But nudging teachers to preference such "problem-based" approaches will worsen our educational woes, not solve them.

Australian students' achievement in the OECD-run Programme for International Student Assessment has declined faster than any other country in the world, barring Finland, with the decline steepest in maths. International comparisons of Australian adults' numeracy also point to it being a serious weak spot in our wider population.

It's not that problem-solving isn't important - quite the contrary.

A key marker of students' learning is that they can muster acquired knowledge to an applied problem, especially in maths. What's at issue is how to properly develop students' capability to become effective problem-solvers.

For decades, intellectually appealing but frequently debunked approaches have been popularised based on three flawed assumptions.

The first misconception is that since the best problem-solvers tend to enjoy the best outcomes, educators should prioritise class time to directly developing those capabilities, rather than fixating on allegedly tiresome maths "facts" and procedures.

After all, they say, we have calculators to do basic operations for us.

Second, because problem-solving is a skill common across a range of subjects, it's claimed it should be developed as a supposedly generic and transferrable skill.

And, third, since some students appear more engaged when doing applied problems, it's argued teachers could better "activate" learners by exploring concepts first in an applied context, and then work backwards to generalise that knowledge.

Sadly, most educators are mistakenly schooled that these assumptions - collectively under the umbrella of "problem-based learning" - are grounded in evidence. But the education science proves otherwise.

Unfortunately, there's no short-cut to problem-solving prowess. Students gain the tools needed to confidently solve problems through mastery of arithmetic and mathematical rules.

While it's true that practice leads students to become more accomplished in solving particular kinds of problems, by far the best predictor of success is what they know.

This means teachers' efforts are best placed in bedding down the basics, so students can more readily recall and apply what they know.

Despite concerted efforts to identify generic and transferrable problem-solving strategies, research has repeatedly come up empty-handed.

It would be convenient if being good at solving problems in one subject could transfer to others, but that's simply not the case.

By extension, as there are no generic problem-solving strategies, there's also no evidence-based teaching practice to promote such skills.

What is known to be effective is building subject-specific knowledge and regularly practicing a wide range of knowledge-appropriate problems.

Nonetheless, it's not uncommon for dedicated classes aimed at building so-called "inquiry" skills.

This is a costly waste of teachers' efforts and takes students' limited learning time away from building the knowledge they need to boost their problem-solving capability in relevant subjects.

And countless studies have debunked the "inquiry first, instruction later" approach.

Students who are introduced to new concepts through applied problems frequently fail to grasp the new concept, or learn the wrong lessons from the specific case.

It may well be that some students seem more engaged during applications rather than explanations, but that shouldn't be conflated with their actual learning.

Moreover, any motivation temporarily gained is soon lost when children fail to successfully grasp the concepts from the assigned problems.

The upshot from the research is that teachers' efforts are best directed at providing "worked examples" - sequentially and explicitly solving problems step by step.

It's through this process that students best acquire new knowledge and build confidence to replicate this in future problems.

Challenging the educational orthodoxy on problem-based learning promises to remain a key battleground as educators and stakeholders continue to mull over the curriculum - and teaching practice writ large - in the months and years ahead.

Warding off this, and other threats, to our education system is a must if we're to avoid sliding yet further down the world's maths leagues tables.

The solution to our students' problem-solving woes lies in looking to the evidence, not wishful thinking.

Glenn Fahey is education research fellow at the Centre for Independent Studies and former consultant in education governance at the OECD's Centre for Educational Research and Innovation.