Maths curricula around the world are not fit for purpose in the age of “ubiquitous computation” and artificial intelligence (AI).
This was the provocative argument put forward by the technologist Conrad Wolfram at the Council of British International Schools conference in London this week.
Speaking to a room full of international school leaders, Wolfram, the European co-founder and CEO of the computational technology company Wolfram Research, described the rapid development of digital technologies over the past few decades as “the fastest-changing industrial revolution that the world has ever experienced”.
For example, he noted that most people in the developed world now typically have at least one computer (such as a smartphone) on them at all times and that these devices can perform calculations far more efficiently than humans.
As such, he asked, why does the mainstream maths curriculum still insist on teaching children hand calculation?
Wolfram said he believes that by ignoring the reality of the power of computing, the maths that students learn at school by the time they reach the end of their secondary education is “pretty much totally divergent from what you actually need” in life.
“Maths education has done a terrible job of adapting to the real world,” he said.
A maths revolution
For the maths we teach to be useful in the modern world, Wolfram argued that the curriculum should be revolutionised in terms of how most maths problems are approached.
Specifically, he said that when using maths, typically, a four-step process is followed:
- First, you define the question you want answered.
- Second, you pose that question in mathematical terms, perhaps as an equation.
- Third, you calculate the answer to the equation.
- Finally, you interpret the answer.
“In educational core curricula, we’re spending almost all our time doing hand calculations on step three,” Wolfram said. “Yet computers do that billions and billions of times better than we do.”
Instead, he said we need to focus on steps one, two and four: “That’s what we need humans for: pose the problems, use a system to come out with better answers. Don’t get fooled by the answers.”
However, because the current curriculum asks students to do calculations by hand, it can only ask so much from them before the maths becomes too difficult.
This means students are asked to solve what Wolfram calls “toy problems”, which they are typically unenthused by because they are so abstract.
By inserting computers into the curriculum, Wolfram believes maths will have more practical usage, as it will become about learning real problems and their link to the world. This may be welcome news to any maths teacher faced with students asking: “Why do I need to learn this?”
If this approach was taken, Wolfram continued, the curriculum could be focused not on the computational ability of pupils but on conceptual understanding.
“Why don’t we teach calculus to 10-year-olds?” Wolfram posited to surprised, if agreeable, murmurs from the audience.
He used the example of the water glass on the lectern in front of him, which was thinner at the bottom than it was at the top. The concept of how you would calculate its volume - by slicing the shape up into little discs and adding the volume of those together - is not difficult to understand, he said.
“That concept, I think, is amenable to many - probably to 10-year-olds and below.”
But, he said, “the algebra is hard”, and so a maths problem like this is not taught until later in the curriculum, even though anyone with an “integrate” function on their calculator could solve it if a teacher showed them how.
Taking this further, Wolfram said that the power of machines is now such that pupils need to be taught not just how to use computation but how it works - citing machine learning as something that he has not seen “on a single maths curriculum around the world”, but that he believes “should be [taught] at primary level”.
This is work that Wolfram and his team are trying to deliver through resources on his website, Computer-Based Math, which aims to give teachers and students computational maths exercises that centre on “real-life problem solving”, not “historical hand-calculating”.
Teaching for the future
Doing this is vital, he argued, because as computation becomes more embedded in our society, we must teach young people how to use technology for real-world purposes so that - in light of so many fears about AI taking jobs - we can future-proof their career possibilities.
“We’ve got to work up a level from the machines,” he said.
“Don’t get students competing with what machines do best - they will be subjugated by the AIs rather than managing them. We need to optimise the human-computer decision making.”
He admitted that changing curricula in light of all this would be hard, but the time had come to recognise that maths education needs to evolve in light of a reality where computational power is everywhere. As such, we need to “reinvent and rewrite our entire curriculum on the assumption computers exist”.
Ellen Peirson-Hagger is a senior writer at Tes
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