## The great calculator debate

Back in December I posted this blogpost about calculators. It caused quite a stir and prompted many responses. Dave Gale, aka reflective maths, tweeted back with this video, Colin Beveridge, of flying colours maths, responded with this blogpost and there was a much wider debate on twitter with tons of people getting involved on each side. It was brilliant to see. I thought though, that I needed to write a further post to clarify and review what had been said.

In the first instance, I selected a sensationalist title which was intended to catch the eye. I do think, though, that the title may have led people to think my stance was a little more hardline than it actually was. And having seen the views set forward by the alternate position, I think my view has softened further still.

When I wrote the original post I was certainly advocating the banning of calculators in primary classrooms, and I would stick by this now. The opposing case to this was that an inability to subtract two and three digit numbers from 360 was causing a barrier to teaching angles. I would counter this with the statement that subtracting two and three digit numbers from a three digit number is such a basic skill that it needs to be mastered either before moving on to angles, or with angles providing a great opportunity to hone this skill. The other argument was that the government were banning calculators from KS2 tests, but using the same test. On the face of it, this is silly, but I don’t think it is a valid argument for keeping calculators. Rather it is valid argument for altering the tests.

Colin wrote in his post that calculators are not the enemy, but rather it is their misuse. I can see his point here, but I wasn’t advocating we destroy them all, I was advocating that we eliminate their use in primaries and cut it down radically in secondaries. He questioned the necessity of adding 4 or 5 numbers with 5 or more digits together, and this is a point I will concede. My hard line of only using it for trigonometry was perhaps too hard. But I still feel a vast reduction in their use would produce better mathematicians in the long run.

The video Dave sent was of Conrad Wolfram talking about why the future of maths should basically be entirely computational. Conrad feels that we need to stop teaching hand calculation and start teaching only computational mathematics. I feel that this would be an entirely wrong move. Computers can only do as they are told. If we are looking to prove a theorem generally, then we need to be able to hand calculate. Computers can check case after case, but this is not enough for a “proof”, as it is impossible to check an infinite amount of cases. A computer would not have been able to come up with mathematical induction or infinite decent.

A number of people responded along the lines of “What’s the point in learning how to do this when you can use a calculator?” This seems to me to be a ridiculous argument, like saying “Why learn to write when you can use a word processor?” or “Why learn to walk when you can use a mobility scooter?” If we head down that path is won’t be long before we are like the fat oafs in “Wall.E” (see this video) or even completely plugged in, a la “The Matrix”.

When teaching my further maths class numerical methods, I often have to field questions as to why we are doing this when if it were needed in the research world a computer would just do it. My answer is always simple, and always the same. “If no-one learns the theory, it will be forgotten, and no-one will be able to programme the computers to do it.”

No, calculators are not the enemy. But if the world becomes too reliant on them then we lose the skills we have built up over the centuries, we lose the ability to construct proofs for general cases, and we lose the beauty and the satisfaction one can get from solving a problem with nothing more than a pencil and paper.

Since the original post, I have realised that this is a wider issue than just calculators. Discussions with colleagues have highlighted that this problem occurs in other subjects when scaffolds are used. Thesauruses can lead to nonsensical sentences in English, for example. Scaffolds can also just mask a problem, pupils can get round something they cant do in lesson (ie subtract 197 from 360), but if it comes up on a non-calculator exam then they will not be able to obtain the correct answer.

Further reading:

From Mark Miller: Removing the cues

and Revision before redrafting (which includes the “greatest” sentence known to man: “a quantity of the most evil inscription is fashioned subsequently to a lexicon”.)

Seems like a rational conclusion, and one I’d largely agree with.

Worth noting that just today DfE confirmed that the KS2 test has been re-written to remove questions which would have implied calculator use in the old format. So no need even for those issues to arise!

Superb news!

Reblogged this on The Echo Chamber.