Understanding Negative Numbers

 

I’ve noticed that many of my high school students have issues understanding that four minus five is the same as four plus a negative five.  To many students subtraction is a completely different problem from adding a negative number and they arrive in high school with that thought.

I wonder if it has to do with students in elementary school where subtraction is taught as a take away or removal such as in 43 - 12 = 31.  You started with 43 objects, took away 12 and are left with 31.  For this type of problem, students who are not fluent in  addition and subtraction facts will count on their fingers.

In addition, they are taught that we cannot subtract a larger number from a smaller one because they haven’t learned about negative numbers. This is because to take away a larger number of items from a smaller number means students have to learn about deficits and that can be a complex topic. 

So, once they are taught about negative numbers being on the left side of zero and positive numbers on the right, they have difficulty comprehending it.  Even when negative numbers are shown on a number line, students are not yet introduced to the idea that positive and negative signs indicate a direction.

In this situation a positive sign refers to one direction while the negative refers to the other direction.  If you look at a number line, positive has you moving right and a negative number has you going left.  This conflicts with the idea of taking away a certain number of items.

Then throw in the idea of subtracting a negative number turning into a positive value.  In this case, students often learn to change the double negative into a positive so they can add but they don’t know why.  I’ve heard it explained as the first minus sign says facing the negative direction, moving in the opposite direction or in the positive direction.  Other times, I’ve heard it explained as being the same thing as multiplying by a negative one.  

When you get up to more complex situations such as subtracting rational expressions.  In this situation, students treat the minus sign as a subtraction rather than the minus sign being applied to all terms that appear after it.

As far as the brain is concerned, much of the processing occurs in the Inferior Parietal Lobe for both positive and negative numbers.There appears to be increased activity in the area when the brain is working on subtraction problems.  In addition, schools do not seem to teach the use of negative numbers in the same way as with positive numbers.  They do not drill or have students practice problems using negative numbers in the same way they do with positive numbers.

It has been found the brain relies on procedural rules more often when working with a double negative such as 4 - (-4) and the brain often finds the bracketed negative sign confusing.  Furthermore, the brain tends to rewrite problems such as 7 + (-3) as 7-3 because it finds it easier to deal with.

Is there a way to help students become more fluent solving problems with negative numbers.  I don’t know but I do know the lack of fluidity slows students down and they find it harder to solve problems.  Let me know what you think, I’d love to hear.  Have a great day.