Resource description:
It seemed to me that the reason students often struggled with this topic was an over emphasis on the rules that underpin the process of adding and subtracting negative numbers. Even though my teaching of this topic had always generalised from an initial discussion of the reasons behind the rules, students frequently misapplied the rules, chanting (almost as a mantra) two minuses make a plus and going on to make -3 – 7 = 10.

Although students invariably understood the rule at the time they were taught it, that subtraction of a negative number was the equivalent of addition, it was never long before their understanding began to weaken and they reverted to a half remembered and not fully understood rule. It occurred to me, partly through conversations I had had with students, that the problems were caused not from a lack of initial understanding of the concepts but from a more basic misunderstanding of negativity being a property of a number. I wanted students to understand that a number is either positive or negative and that a negative sign is part of that number. The misconception that minus means the same thing as negative is regularly reinforced both in school and beyond (weather reporting for example) and I believe that students struggle to answer questions involving directed number (and for that matter algebra) because they are not aware of the difference between the two terms.

I went on to develop a very simple resource that aimed to ensure students understanding of negativity being a property of number was sound.
The resource was a SMART board based resource and consists of a series of ‘number tablets’. Crucially the tablets can be dragged around the screen, thus ensuring that students realise that the sign belongs to the number.

Teacher comment: Having read ‘Teaching Negativity’, Chris Haynes’ fascinating account of how he ensures that his students gain a good understanding of adding and subtracting negative number, I realised that this was a topic for which I was guilty of not thinking deeply enough when I came to teach it. My approach had not altered significantly since I had started teaching and yet I had never felt totally happy with my students’ understanding.

What I did: I set the students a target value that they had to achieve by using combinations of numbers from the number tablets. Initially, I directed the students by suggesting the calculation’s structure:
Students had to find as many answers as they could in a given time. However, as their confidence grew I reduced the number of restrictions so that they could use any amount of tablets and subtraction as well as addition signs. In the first lesson I refrained from introducing subtraction of negative numbers. However students were so keen to produce as many combinations as possible during that lesson that some of them intuitively experimented correctly to produce correct combinations involving subtraction of negative numbers, e.g. 1 - -5 = 6.

In the second lesson, I formally introduced the topic of subtraction of negative numbers to the class using the excellent Excel macro available from this site before continuing with the number tablets.

Other questions covered included:

What is the largest/smallest total using the number tablet?

What is the largest/smallest total using the number tablet?

What about cases involving three possibilities and combinations of negative and positive numbers?

Reflection: I feel as though despite, or perhaps, because of its simplicity this resource offers a subtle but crucial element to my teaching of this topic; one that was definitely missing beforehand. I hope that when my class moves on to look at algebraic manipulation involving negative numbers, for example

^{-}3x - 12x

they will be able to apply their understanding from this exercise and be able to concentrate on the algebraic aspects of the question rather than getting tangled up dealing with the direction of the calculation. I believe that providing a student has a mental image of the calculation:

^{-}3 – 12

on the number line (ie the calculation starts at -3 and moves 12 spaces to the left), they will be much more successful and confident when dealing with this topic. Hopefully, the number tablets provide a foundation on which to build this imagery.