How should we teach mathematics in school?

Years ago, I lived next to an artist. We have often talked about our two disciplines, visual arts and mathematics, and we have decided that in both cases, creativity comes from the same impulse: the pleasure of patterns, the joy of problem solving, general curiosity and open-mindedness.

Turns out we were right. Also, STEAM has now become a thing – it’s STEM with an A for Arts – although in Australia the focus is still primarily on STEM (Science, Technology, Engineering and Mathematics.)

We certainly need a STEM-literate workforce if we are to be players in a digital and clean energy world. The problem is that we are not attracting enough students. According to the Australian Department of Education, Skills and Employment (DESE), the number of students in grades 11 and 12 studying STEM has stabilized at around 10%. A recent report gave the US figure at 20%, also a worryingly low level.

Because math underpins so much of STEM, one response to these disturbing numbers is an increased emphasis in math education on computation and utility rather than beauty and creativity.

Math is incredibly useful – it underpins everything from weather reports and GPS to bridges, buildings, cars and planes, from the internet and cell phones to our supply chains, banks, medical techniques, and much more. Yet the president of the Australian Mathematical Society, Ole Warnaar, reported in the Society’s Gazette last year on member feedback on proposed revisions to Australia’s mathematics curriculum – and a key concern was its overly utilitarian approach.

Because math underpins so much of STEM, one response to these disturbing numbers is an increased emphasis in math education on computation and utility rather than beauty and creativity.

Warnaar certainly supports teaching students to apply mathematics in meaningful ways, but he also laments that in our curricula, current and draft, “not enough effort has been made to try to convey the intrinsic beauty of mathematics and the fun that can be gained from learning and understanding”. new mathematical concepts”.

“not enough effort has been made to try to convey the intrinsic beauty of mathematics and the enjoyment one can derive from learning and understanding new mathematical concepts”.

Ole Warnaar, President of the Australian Mathematical Society

I am okay. To begin with, in the historical development of mathematics, the desire to solve practical problems and the desire to explore logic, patterns, and curiosity-driven research for themselves, often went hand in hand, each inspiring the other. . I also fear that an overemphasis on usefulness may blind students to the ethical and other issues associated with technology, such as its ownership and scope, and its political role as a purported panacea against climate change and growth for growth. – the economy of sake.

Even at a purely practical, STEM-focused level with an overly utilitarian curriculum, students are likely to see math as a bewildering black box of tools, rather than a creative and challenging language that can help them to innovate in the field of their choice. Already half of our students dislike math, compared to 38% internationally – although we also have one of the highest proportions of off-screen math and science teaching in the world..

In Victoria – and the situation is similar across Australia, the UK, US and elsewhere – less than 10% of year 12 students studied the most advanced maths subject in 2019; just under a third have studied intermediate-level mathematics, and almost two-thirds have taken a general mathematics course that does not include differential calculus. Boys outnumbered girls in all three subjects, with the gap reaching a ratio of almost two to one in the most advanced mathematics.

The gap is even wider for Aboriginal and Torres Strait Islander people, who hold STEM degrees at one-tenth the rate of working-age non-Aboriginals, according to Australia 2020 STEM Workforce Report; for women, the figure is one-third that of men.

Of course, an obvious question is: does it matter that few students study the most advanced math in grade 12?

Most research-based universities, including the Group of Eight in Australia and Oxford in the UK, expect students to achieve good grades in at least the second most advanced mathematics subject if they wish. obtain degrees such as biomedicine, commerce, science, engineering. , and IT. Universities have had to respond to the downward trend in the number of advanced math (and physics) students by offering remedial subjects – but these come at the expense of taking other subjects that deepen knowledge and engagement with the course. So there are good career reasons to choose advanced math (and science) in high school.

Additionally, advanced math also offers the most opportunity for intellectual challenge and satisfaction. If you know how to read it, an elegant proof or a beautiful meaningful equation can be as impressive as a beautiful work of art or music.

In this context, I remember a recent study This suggests that one reason fewer girls are choosing STEM careers is that, while they generally do as well as boys in math and science, they do better than boys in the humanities. Which suggests that we could attract more girls if we embrace STEAM and include in our math the teaching of beauty, history, and intellectual enjoyment of the subject.

Offering a wide range of math subjects is important – not just to prepare students for STEM careers, but also to navigate today’s increasingly complex world.

Trying to play around with the ATAR system is another apparent reason students are increasingly choosing easier math and avoiding physics. It is telling that Estonian schools – whose students performed well in mathematics in the recent PISA rankings (2018) – have hardly any “high-stakes” tests. PISA’s methodology is disputed, but interestingly, Estonia ranks first in mathematics after China, Singapore, Japan and Korea – and these five countries are all countries with highly based on technology. Australia came in at 29th, just behind New Zealand and Portugal, and just ahead of the United States, which on the face of it manages to maintain its technological lead only because its high-end education is so good. .

It is a difficult task to design the best programs for the wide range of students taking mathematics courses in 12th grade. Not everyone cares about technology, business or other practical applications, and not everyone cares about “elegance” and “beauty”. Yet the role of education is to encourage engagement with new ideas – and the challenge for educators is to find the right balance. Clearly, it’s important to offer a wide range of math subjects – and not just to prepare students for STEM careers, but also to navigate today’s increasingly complex world.

We saw it during the height of the COVID-19 pandemic, when the media published major stories about exponential growth rates and the spread of the virus, and we were all eagerly awaiting the latest modeling update. mathematics of the pandemic.

We also saw how ignorance of statistics fueled anti-vax claims about hospital admissions that were just plain wrong.

Ease with this type of baseline data analysis is also important for understanding the effects of climate change. Relatively few students will go on to play a significant role in discovering solutions to this and other pressing problems, although many will help implement them. But we all need to know how to interpret data on key issues, so that we can make informed decisions in our lives and in our politics.

All of this raises the question of whether or not certain forms of math should be required throughout high school, such as English. Some countries have already taken this step, including Estonia, Sweden, Japan, Finland, Korea, Taiwan and Russia. New South Wales plans to make maths compulsory by 2024, while from 2023 Victoria will encourage more pupils by offering a second more basic general maths subject in Year 12.

New South Wales plans to make maths compulsory by 2024, while from 2023 Victoria will encourage more pupils by offering a second more basic general maths subject in Year 12.

Around 80% of grade 12 students in Australia already take a maths subject, and I fear that making it compulsory will be counterproductive if we don’t also up our game in terms of school funding, salaries and teacher training. teachers – and if we don’t address inappropriate cultural attitudes towards math, such as ‘math is too hard’ or ‘boys are better at math’. Then there’s ‘we’ll never use this stuff, so what’s the point’, something students rarely say about English or the arts.

We need to solve these problems, because mathematics should play an educational role as important as English. Both of these topics focus on how to use language in order to think carefully and critically. Both also aim to build a rich and empowering vocabulary, whether to express our feelings, build logical arguments, make sound financial decisions or understand the numerical terms needed to engage with – and interpret the research reported in – the medicine, technology, the environment, and other aspects of daily life.

There are similarities even at the literary level, like understanding how to make and decipher metaphors. In the study of gravity, for example, it’s a deeper (and more relevant) experience to understand the inverse square law as a metaphor rather than just a memorized formula – and more such treats. are proposed to the university, as the multifaceted metaphors of the wave equation and gravitomagnetism. Conversely, it says a lot about our culture that English curricula rarely include literary mathematics and scientific writing in their selected texts. Our magazines and newspapers rarely review this genre either. It looks like we really need STEAM! And I bet we will be richer, individually and as a country, for a culture that understands and embraces math rather than fearing it.

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