Damaging short cuts

Yesterday, my year ten class were doing Standard Form (Why did we drop the word index? Standard Index Form is much better!) During the lesson it became very apparent that they were nowhere near fluent in the use of negative numbers, so today I taught a lesson on directed number to fill in the gaps.

The first few examples were of the form – a + b, or a- b, and were easily dealt with, but then I gave them an example which blew their minds. The example in question was:

“-7 – 4”

I talked through it to nods of agreement but then I got this:

“It can’t be -11, there are two negatives and Miss so and so said that two negatives always make a positive”

AAAAAAAAARRRRRRRRGGGGGGGHHHHHHHHHHH!!!!!  went my internal monologue. Others in the class murmured agreement. A long discussion ensued, about where this fallacy comes from and why it’s entirely wrong. We got there, and now the class have a deeper understanding of negative numbers and how to deal with them, however,  I think this could have been entirely avoided if this short cut just wasn’t taught. If they had just been taught how to handle negatives in the first place.

This isn’t the only topic that falls foul of this. I’ve written before about “BIDMAS“, Tina Cardone (@crstn85) has put together a superb book on a variety of similar things and just yesterday Michael Tidd (@michaelt1979) tweeted “Can we all just agree to stop using the crocodile inequalities analogy”.

This is one that infuriates me. Every year I have to unteach this because a number of pupils have quite understandably changed the story in the head to “the big number eats the little number”. This seems sensible, as a big crocodile would certainly be more likely to eat a smaller crocodile than the other way round.

Why can’t we just teach the concepts and forget about the shortcuts? They are more of a hindrance than a help!

Nix the Tricks – A Book Review

A little while ago I wrote a piece around BIDMAS and the problems it can cause just teaching mnemonics without bothering to fully explain the underlying concepts. It was borne of the frustration of many conversations along the lines of

“Sir, you’ve got that wrong 9 – 3 + 2 is 4 because you do addition first.” 

“No, addition and subtraction are inverse operations, they are of the same order you we perform them left to right.”

“No, Mr so and so taught me that you always follow BIDMAS”

“AAAAAAAAARRRRRRRRGGGGGGGHHHHHHHHHHH”

Someone responded to my post with a tweet which linked to “Nix The Tricks“, which is freely available as an ebook, and I downloaded and read it.

The book itself is great, it is a collaborative effort by many maths teachers who share my frustration with the problems that teaching this sort of “trick”, rather than deeper understanding, can cause. The book has been put together by Tina Cardone (@crstn85). Tina and her collaborators go one step further that venting about the tricks and offer some brilliant alternative methods to help teachers who haven’t thought in detail about how to teach certain topics.

Its a fantastic book and I would advise any maths teacher to download a copy, especially those new to the profession.