## Difficulty Learning Negative Numbers.

The difficulty with learning *negative numbers *is widely acknowledged in the *teaching* profession. In *Making Sense of Negative Numbers *by Cecelia Kilhamn (2011) the goal of the research is ‘*to better understand why the topic of negative numbers is so difficult to teach and to learn.’*

This difficulty does not mean that there is something wrong with the subject. However, it is recognised children do have more difficulty with *learning* the *mathematical concept* of negative numbers than other concepts such as positive numbers, addition, subtraction and multiplication. These concepts exist in the natural world.

Children are great learners. See how they pick up language so easily. I started studying Italian during the lockdown and struggle. I will never develop as good an understanding or accent as a child would.

The question is why do our children struggle so much with the concept of negative numbers.

## Metaphors.

Many teachers use metaphors to help with the teaching of negative numbers. These include apples and negative apples, money transactions, motion along a path, arrows on a number line, different coloured beads, stairs and thermometers. These are problematic. For instance if the temperature is -3^{o} and gets -8^{o} colder, then the temperature would be -11^{o} or would it be 5^{o} because in arithmetic -3 – (-8) = 5. Explain that to children.

The idea of using metaphors is a good one. The metaphors mentioned earlier work fine for addition and subtraction but not as well for negative numbers. Metaphors are based on the real world, so it is unlikely an adequate metaphor will ever be found to properly represent a concept that is impossible in the real world.

Ask any child which of the following lines A and B is bigger and they will quickly identify A as the biggest.

Now show them the number line and ask them which number is bigger -5 or 3. It is not surprising that children find the concept of negative numbers hard to deal with.

We expect children to understand that in some ways -5 is smaller than 3 and in other ways -5 is bigger than 3.

## Negative Numbers Cause Cognitive Dissonance.

*Cognitive dissonance* is described as *‘The mental discomfort that results from holding two conflicting beliefs, values, or attitudes. People tend to seek consistency in their attitudes and perceptions, so this conflict causes feelings of unease or discomfort.*’ The use of negative numbers requires our children to hold two *conflicting beliefs*.

Teachers and children are not the only ones to find difficulty with negative numbers.

Negative numbers are difficult to learn and require us to overcome conflicting beliefs. Are they really *fit for purpose* or could we come up with a better system?

Check out the Quora discussion on Negative Numbers at

Quora Link