What's the problem?
In my experience, if there is one rule that pupils of all ages and abilities remember (and can recall proudly when prompted), it is that two minuses make a plus. This, of course, is all well and good when multiplying and dividing, but can lead to a whole world of problems when applied, without prejudice, to addition and subtraction problems. Hence, the answer to the question pictured above is often given as 9, with the logic being that those two nasty minus signs turn themselves into a lovely little plus.
What's the solution?
Rules, without understanding, can be a very dangerous thing in mathematics, and are the root cause of many of the misconceptions that students possess. The difficulty is that, once rules are ingrained, they are very hard to weed out. To solve this nasty problem, you have to get pupils early and get them thinking about the questions themselves. I have found that young pupils respond quite positively to thinking about a bowl of soup.
Imagine you have a lovely bowl of soup that has a current temperature of 10 degrees. We also have ice cubes, each of which takes 1 degree off the temperature, and we have fire cubes (bear with me here!), each of which adds 1 degree to the temperature. Now, what happens if we add 3 ice cubes to our soup? Well, our soup gets 3 degrees colder, and we have 10 + -3 = 7. And if we now dip our hand in and take out 4 fire cubes, we have 7 - +4, which must equal 3 degrees. Once pupils have got their heads around this concept, it is time to progress to the likes of 4 - -5 (a temperate soup of 4 degrees, has 5 ice cubes removed, so the temperature goes up to 9 degrees), and the potentially deadly -4 + -5 (a chilly soup of temperature -4 degrees has a further 5 ice cubes added and goes down to -9 degrees).
I have heard similar techniques involving money, sandcastles and even witches. I know the scenarios lack a certain degree of credibility, but I personally prefer that to a rule that can be mercilessly misapplied by pupils left, right and centre.
Craig Barton is an advanced skills teacher from the Bolton area. He is also the creator of www.mrbartonmaths.com and can be found on Twitter @mrbartonmaths
Check out these resources and collections on the TES website, which may help to tackle the problem:
- Secondary maths collection: Tarsia - number resources
- Negative numbers
- N8 - using directed numbers in context
- Negative numbers (MEP, Year 7, unit 15)
- Tarsia - negative numbers (level 5)
In the forums
Read about common maths misconceptions compiled by primary teachers.
Find all resources and links at www.tes.co.ukresources012.