"But Miss, I've got a calculator, why do I need to learn how to do this?"
- By Devon Francis
For several years, students have been asking the same question: why do they need to learn maths if they can just use their calculator? Thankfully, what previously separated us from machines is our ability to problem solve; we can use mathematical tools during individual steps to solve a larger problem. But in an age where AI is rapidly improving and can now solve many multi-step problems, a new question is emerging: what purpose do humans have in solving problems? Is there any point in learning how to problem solve at all?
In our second CPD session of the day, Dr Katie Chicot (CEO of MathsWorldUK) presented how to use hands-on maths to spark curiosity amongst students (when used in the classroom) and wider society (when exposed to maths in family exhibitions and workshops). She discussed how, although technology can have a huge impact in what we are capable of doing, an understanding of maths is vital in knowing what questions to ask in the first place. Therefore, the most important skill that we want our students to leave with is the curiosity to jump into problems and to want to ask more questions beyond what we already know.
A particular highlight of the session was creating mobius strips out of strips of paper and
then testing what happened when we cut them. Initially, we created the mobius strip by sticking two ends of a strip of paper together, where one end was twisted. We then cut a line along the centre of the strip. What was initially fascinating was that, although there was a twist in the paper, you could follow one surface along the entire shape. When we had cut it, we then had the surprise that, despite feeling like you would end up with two strips of paper, the cuts actually unravelled to reveal one longer mobius strip! Next, we were asked to make a new mobius strip, but this time to cut a third of the way from the edge all the way around. This time, we passed the initial starting point (but on the other length) and went round the surface twice. When we got back to our original cut and the paper fell open, we were left with two loops: one locked inside the other! The purpose of this exercise was not just to feel the surprise of the results, but to also question what next? What other questions could we ask, or tests could we perform? Our table decided to find out what would happen if we started closer and closer to the edge – would we go round more than twice or would it be similar to our second experiment?
At the end of the session we reflected on how we could incorporate this kind of activity into our everyday teaching: could this be used as a lesson before Christmas to make “maths Christmas decorations”; or maybe a more advanced lesson on geometry and surfaces? Either way, it has definitely inspired me to think about including exercises where I can ask the students to do the hard work: what do you want to learn next and how can you investigate it?
By Devon Francis
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