This mini post is a follow on from my previous post Less great ways to introduce topics.
There are two topics that go against my advice because they can’t really be conceptualised. There is no understanding, only acceptance.
Anything to the power of 0 is 1.
It is true because it must be true. No, you can’t visualise 7 to the power of 0. Yes I have made something out of nothing, yes I do wield a power equal to that of a god.
Multiplying a negative by a negative is an awkward one. It feels like there should be a way to conceptualise it; we understand multiplication and we understand negatives so we should be able to combine them seamlessly. This however is another situation where you can only show that it must be true and make pupils remember it.
I have tried before to try to make it something that we can conceptualised, however it essentially made me invent my own bit of maths….
I made this up as I’ve never enjoyed the use of associativity with multiplying negatives, saying -4 x 3 must be -12 because it must be the same as 3 x -4 always felt a bit of a cop out. But I cannot condone inventing your own maths and have only tried it the once.
I would also say that discovery maths can be very useful when it comes to Statistics and Probability. These topics were invented when a real-life situation called for applying maths so that it could be understood. It is perfectly valid to start by giving meaning to these topics by creating a reason for them to be used.
I also have one guilty pleasure with using discovery, using the nRich task tilted squares to introduce Pythagoras’ theorem. It is absolutely not worth the time and effort that it takes but I LOVE IT. It seems like Pythagoras’ theorem just pops up out of nowhere and you can get a seamless transition from area into just looking at the lengths in right angled triangles. It definitely does help pupils to have strong links between Pythagoras’ theorem and area which is how I justify its use but really it’s just so I can just turn around to the pupils and wildly exclaim “you’ve just proven Pythagoras’ theorem!!!!” which mean nothing to them as they haven’t heard about it before :/