Last week a journalist got in touch to ask me what I thought about the use of calculators in A-Level mathematics – the two-year ‘gold standard’ exam in England and Wales that many students choose as they build to go to university.
The question was put like this:
To what extent did you find students were reluctant to learn how to problem-solve themselves because they know that their calculators can do a lot of maths for them? I’m looking for a comment about how this plays out in the classroom: when you were a teacher, did you have many students asking “why are we learning to do this by hand when the calculator can do it faster?”
This kind of left my jaw heading floor-wards.
First up, there is actually very little in the mathematics A-Level that can be done ‘just with a calculator.’ These aren’t the kind of problems that can be attempted with immediate access to a tool like that. By way of example, from a recent paper:
So I was a bit confused that debates around calculator use were still a thing. But this isn’t a blog post about issues around the changing demands of the mathematics syllabus. What it is about it the artificialising of intelligence.
Because the real coming problem – as I explained in my response to the journalist – is not about tools to take on the cognitive load of computation, but those that are now able to problem solve, end to end. So the question is not ‘why are we learning to do this by hand…’ but ‘why are we doing any mathematics at all…’
The calculator is – mostly – an arithmetic machine. It can offer values of trigonometric ratios, but it cannot process the text of a question and offer an answer.
Large Language Models now can. In fact, the latest release of ChatGPT has shown greater abilities in being able to break problems down into smaller chunks and thus solve much more sophisticated questions thrown at it. This piece in the Japan Times outlines it quite well.
But the deeper question – the one I constantly used to get from my students – is why. Why study this? Why learn this?
For many, the single reason was to able to get over the hurdle of a formal assessment – like the A-Level. And if this is the purpose of studying a topic – to be able to pass an assessment in that topic – then being able to ‘hack’ that assessment is a logical – if corrupt – step.
So it’s no surprise that someone has managed to hack a standard(ish) calculator to be able to run ChatGPT. As they call it, ‘the ultimate cheating device’:
We might call this ‘artificialising’ intelligence. It is projecting a level of skill and knowledge in order to be able to access… a particular job? a particular university?
As I explain in God-like, this is tapping into very ancient desires. We want to know everything… or at least be seen to know everything.
This drives at the heart of the purpose of AI. Is its purpose to increase our knowledge, or to artificialise our intelligence? Is it a ‘hack’ to allow us to leapfrog others, or a genuine augmentation of our ability to act in the world?
These are questions not yet settled, and ones that will take some discipline for us to consider as we look at how we are going to live alongside this extraordinary invention. If everyone at the pub quiz has Google open on their phone, the quiz becomes about something else – people’s ability to search quickly, rather than to enjoy discussion around obtuse trivia. And if everyone has access to an AI… what will this say about intelligence? What will that then mean? Will an artificial intelligence necessarily be a bad thing?
Though I won’t be in the classroom as these questions are worked out in schools, I will be helping schools and education policy leads think about them as the very foundational ideas about the purpose of education and learning are shaken. It’s not going to be an easy one to answer…
Well, I asked ‘Claude‘ – which I use quite a bit – and it offered up this:
Prompt: What will the purpose of learning be if we all have access to advanced AI?
Response: That’s an interesting and complex question about the role of learning in a future with advanced AI. Here are a few key points to consider:
- Access to advanced AI does not necessarily eliminate the need for human learning and skill development. Even with powerful AI assistants, people will still need to learn critical thinking, problem-solving, creativity, and other uniquely human skills to thrive.
- The purpose of learning may shift more towards developing the ability to effectively leverage AI tools and systems, rather than solely focusing on memorizing facts or procedures that AI can handle. Learning will be about understanding how to apply AI capabilities to solve problems.
- Education may evolve to emphasize learning how to learn, collaborate with AI, and continuously adapt to technological change. The focus could be on cultivating lifelong learning skills rather than static knowledge.
- Certain types of learning, like deep exploration of academic disciplines, artistic expression, and philosophical inquiry, may retain importance even in an AI-enhanced world. These forms of learning may serve to expand human potential beyond what AI alone can provide.
- There is also the possibility that advanced AI could make certain types of learning obsolete or vastly more efficient. However, this could free up time and resources for people to pursue other forms of learning and growth.
Ultimately, the purpose of learning is likely to evolve rather than disappear in an AI-rich future. The key will be adapting educational models to capitalize on the strengths of both human and artificial intelligence.
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