Dr Alan Finkel and Professor Asha Rao commentary, and the paper available from the .

“I’ve left my glasses at home,” the 30-year-old with perfect vision said.

Chisholm Institute of TAFE senior educator Margo Murphy had heard this lie many times before and knew it was an attempt to disguise innumeracy​.

“They’ve developed survival skills,” she explained.

Adults are heading back to the classroom to learn basic maths skills they failed to pick up in school.

Research shows around 20 per cent of Australian students do not reach a basic proficiency in maths that “will enable them to actively participate in the 21st century workforce and contribute as productive citizens.”

According to an OECD survey, Australia is ranked 13th out of 23 countries on adult numeracy, but ranked fourth in literacy.

Most of Ms Murphy’s students at Chisholm’s Foundation College need to upgrade their maths skills so they can function in everyday life, and compete for new jobs.

Josh Cawse, 24, recently started a certificate that is equivalent to year 10 at the TAFE and has been perfecting his decimals, fractions and multiplication skills.

He left school at the start of year nine because “it wasn’t for him” and started a career in construction. Now he wants to join the Defence Force.

“I found I struggled with maths in school. I was always trying to keep up with the fastest in the class. Here it is at my own pace. I am motivated and focused now.”

½ñÈÕ³Ô¹Ï schools manager Janine McIntosh said society’s poor attitude towards maths was fuelling adult innumeracy.

“It seems to be quite acceptable to say I’m not good at maths. There’s a tolerance towards being weaker mathematically. You wouldn’t say that about cricket, swimming or English and the ability to read.”

Teachers own insecurities about maths were also contributing to the problem, she said.

Ms McIntosh said around 30 per cent of secondary maths teachers were “out of field” – teaching a subject they had no specialised training in.

“The students may have had seven years in primary school and six years in secondary school with some wobbly teachers. If the kids can’t see maths as a valuable skill to have then they just won’t do it.”

Senior Research Fellow at the Australian Council for Educational Research Dave Tout, who has taught numeracy courses at VET providers, said many adult students took up maths courses after struggling with personal finances. Many new parents had trouble with medication doses, cooking and diet, he said.

Adults studying remedial maths programs were often reasonably successful, and could learn year seven to 10 maths within six months, Mr Tout said.

“That’s because they are motivated and have a purpose for learning maths. They see the reason for it and can engage with the material. If we could do that more in our secondary schools, we would have more students realising earlier on that maths is useful.”

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Mathematics is the basis of all science. And its importance is increasing as computers handle large amounts of data, and models are used to simulate almost everything in science and medicine. But paradoxically, the requirement for proficiency in mathematics for people beginning science degrees in Australia has lessened over recent years. Stephanie Pradier says universities should reinstate mathematics prerequisites for students beginning many science degrees.

Bruce Henry, the head of UNSW Australia’s School of Mathematics and Statistics laments that 70 per cent of students now finish high school without any knowledge of calculus.

Is this a problem? Definitely.

We hear enough about how appalling it is that students in schools and universities have a lack of grounding in our political, social and legal heritage; that they lack the historical context to understand why we are where we are today.

That’s exactly why calculus should also be part of a basic, broad education. Calculus was a signal advance in maths, invented separately by Isaac Newton and Gottfried Leibniz in the 17th century. For the first time people could write mathematical equations that were able to relate not just quantities to each other, but rates of changes of quantities.

It enabled Newton to calculate the orbits of the planets using his theory of gravity and it opened up a rich field of applications for mathematics. Understanding electricity and magnetism would be impossible without calculus. In fact, most of modern technology wouldn’t exist without it.

That’s why giving high school students an understanding of calculus is important. Surely more than 30 per cent of students are capable of studying it. And, for the others, it’s at least important to understand what it is.

Henry points to another reason why calculus is important to study today. Calculus is not only key to understanding our current technology, but to developing future technology. At the moment huge strides are being made in statistics, a field with the generic name of “big data”.

STATISTICS UNDERPINNED BY CALCULUS

“But really, modern statistics – which is where the future is going increasingly – is underpinned by calculus. It’s increasingly important that students are taught calculus,” Henry says.

In fact, statistics is another area in which mathematics teaching has badly let down school students. All of us are bombarded daily by statistical claims, many of them spurious or misleading, and too few of us are sufficiently knowledgeable to separate the truth from the fiction.

The fact that “97 per cent fat-free” is an effective, emotionally appealing slogan for food manufacturers speaks of the lack of critical thinking about statistics. Are we happy if our food contains 3 per cent pure fat?

Fortunately, in the changes to the national school curriculum being developed, statistics is being given more focus.

But this brings us back to the question. Should maths be a compulsory subject in year 12? Not everyone can do maths well. But shouldn’t maths at least be taught as a life skill and as an important foundation subject at that level?

Henry thinks so. “English is compulsory, and shouldn’t mathematics be compulsory as a companion instrument to understand the world,” he asks rhetorically.

Interestingly federal Education Minister Christopher Pyne, long an advocate of giving school students more foundational understanding of history and other humanities subjects, now appears to see the need for it in maths and science.

Earlier this year he put to state governments – which actually run public schools – a plan to make maths and science compulsory to year 12. The states, unfortunately, knocked him back.

SCHOOLS LAPSE AS UNI REQUIREMENTS REDUCE

But maths in schools needs to be bolstered at more than just the foundational level. Worryingly, year 12 students have been making a long-term shift away from intermediate and advanced maths – the very subjects that teach calculus.

In the past 20 years the proportions studying intermediate maths in year 12 has fallen from about 27 per cent to 19 per cent, and the number studying advanced maths (which builds on intermediate) has fallen from about 14 per cent to 10 per cent.

One reason that year 12 students see no need to do intermediate or advanced maths is that an increasing number of universities no longer require it to enter degrees such as science, engineering and commerce, for which mathematical knowledge is necessary.

In NSW no universities require maths to enter any of these degrees, even engineering. So if universities are not insisting that students study calculus in year 12, even to enter courses in which calculus features heavily, why should they do it?

It’s a crazy state of affairs, in which universities – the institutions we rely on to develop and preserve high level knowledge – happily sabotage their own standards in pursuit of student numbers.

Those universities that have dropped maths prerequisites argue they are offering an avenue for bright students who may have attended a poor school at which maths was taught badly.

Second chances are to be encouraged, but they should be the exception rather than the rule. Universities need to bring back maths as a prerequisite for degrees that need it.

Top educators have defended Australian universities’ move away from requiring maths as a prerequisite for science, engineering and commerce degrees in which mathematical knowledge plays a key part.

The chair of the Australian Council of Engineering Deans, Moses Tade, who is also engineering dean at Curtin University, said universities were using “many innovative ways” to teach maths to engineering students who were not up to the necessary standard.

He said his fellow engineering deans would “refute” the notion that “you can’t do engineering without having done intermediate maths”.

released last week show that 41 per cent of Australian universities which offer engineering do not require students to have studied intermediate maths year 12.

And, to the knowledge of the ½ñÈÕ³Ô¹Ï (½ñÈÕ³Ô¹Ï) which produced the study, no university engineering faculties require students to have studied advanced maths in year 12, even though engineering courses are highly mathematical.

President of the Australian Council of Deans of Science Stephen Walker, who is also University of Queensland science dean, said that his university required intermediate year 12 maths as a prerequisite to science degrees and would not alter that stance.

However, only 14 per cent of universities offering science degrees require students to have studied intermediate maths and, speaking in his council of deans role, Professor Walker said the faculties faced a “fairly stark choice” because of funding issues.

DRAWCARD FOR STUDENTS

“If there was a university, or science faculty, struggling and needing more students for financial reasons, they may see that easing prerequisites is one way to get more student load,” he said.

“Then they may back themselves to use the additional income to provide the bridging training in maths. And that might actually work.”

“Do you shrink and potentially have to shed staff? Or do you say ‘we will back ourselves to take more students and fill the gap?'” he asked.

Professor Walker also said that some students with high ATARs decided to study science because they missed out on their first choice and had not done maths at year-12 level.

“Do you turn away a high achieving student who’s got every chance of doing well, because they didn’t do maths?” he asked.

President of the Australian Business Deans Council Ian Palmer, who is also a pro vice chancellor at RMIT University, said the maths used in commerce degrees differed from other disciplines. “It’s not maths so much as it’s business statistics,” he said.

According to the ½ñÈÕ³Ô¹Ï paper, only 13 per cent of universities which offer commerce degrees require year-12 students to have studied intermediate maths. Professor Palmer said that business faculties were able to train students up to the required level.

The ½ñÈÕ³Ô¹Ï paper also revealed that none of the 10 NSW universities require intermediate maths for courses in science, engineering and commerce.

University of Sydney science dean Trevor Hambley said he applauded ½ñÈճԹϠ“for highlighting the need to ensure students are aware of the crucial importance of maths proficiency for undertaking study and future careers in STEM [science, technology, engineering and maths] and related areas such as medicine”.

He said that introducing maths as a prerequisite would be one way of contributing to this awareness. “If universities were to do so, we would need to have a long lead time to ensure that their introduction did not impact unfairly on students who have already made their choices,” he said.

The ½ñÈճԹϠhas called on universities to reverse an historic low in the number of institutions requiring maths as a prerequisite to studying science, commerce or engineering.

Some 86 per cent of universities do not require maths as a prerequisite for science degrees, 87 per cent don’t require it for commerce degrees and 41 per cent don’t require it for engineering degrees, a report by the institute finds.

And those universities that do require students to have studied maths in year 12 only ask for it at the intermediate level, not the advanced level.

“As far as we know advanced maths is not a prerequisite for any formal course,” said ½ñÈÕ³Ô¹Ï director Geoff Prince.

The share of year 12 students taking intermediate and advanced maths has continued its long downward slide; only 28.7 per cent of year 12 students took intermediate or advanced maths in 2013, down from 28.9 per cent the year before.

Over the last two decades, students have shifted away from the harder options of intermediate and advanced maths, instead favouring elementary maths at year 12 level.

Professor Prince said the 20-year decline in year 12 students studying intermediate or advanced maths had the potential to halt productivity growth and was “choking the country’s galloping demand for these skills”.

“Universities must phase in restoration of maths prerequisites; the lack of them sends a negative and misleading message to schools about the value of these subjects,” he said.

NSW UNIS THE WORST

Universities in NSW have the worst record on prerequisites with no institutions requiring intermediate or advanced maths as a prerequisite for courses in science, engineering or commerce according to the report. Instead they say that maths is “assumed knowledge” for a particular course.

Professor Prince said universities were under pressure not to require maths because otherwise the numbers of students in courses would drop because of the fall in numbers of school students taking intermediate or advanced maths in year 12.

“The number of kids taking maths dropped which choked numbers in engineering degrees,” he said.

Science dean at the UNSW, Merlin Crossley, said the reason the university had moved away from maths prerequisites was that maths teacher shortages meant not all students got the chance to do advanced maths in schools. But said he would support a trial of restoring maths prerequisites.

The report did contain some good news which was that the proportion of year 12 students nationwide taking advance maths rose slightly in 2013, up to 9.6 per cent compared to 9.4 per cent in the previous year. But the proportion taking intermediate maths fell to 19.1 per cent in 2013, down from 19.5 per cent a year earlier.

BOYS BETTER THAN GIRLS

Boys continue to outnumber girls in intermediate and advanced maths. In year 12 in 2013, only 17.6 per cent of girls took intermediate maths compared to 20.7 per cent of boys. At advanced level, only 6.7 per cent of girls studied maths, compared to 12.7 per cent of boys.

Professor Prince said it would be helpful for students in senior school to understand the consequences of not taking advanced maths if they intended to study a science, engineering or commerce at university.”The universities need to communicate to schools that if you don’t have advanced maths you might have to pick up an extra subject,” he said.