Some Misconceptions Associated With Negative Numbers

 

One of my Algebra students had trouble with solving two step equations with a negative coefficient on the variable.  He saw it as subtraction rather than a negative number so he was rather confused.  I spoke with him more and learned that due to Covid, he'd missed out on learning that x - 3 is the same as x + (-3).  This lead me to looking into some of the misconceptions associated with negative numbers.

One misconception has to do with the idea that any negative number is less than zero which they get from number lines that have the zero in the middle with positive numbers increasing in value from zero and negative numbers decreasing in value as you move left on the number line.  Although, most students are great with determining order of positive numbers, they are more shaky when it comes to determining whether -3 or -7 is more.

I don't know if this is a misconception or if it is something students do because they don't want to borrow but I've seen students do one of two things. First, they have 62 - 29 so rather than borrowing, they treat it as if the actual problem is 69 - 22 = 77.  The other one is if they have a problem like 29-62, they just can't do that and want to do it on a calculator.  I think it might be due to the type of problems they work with as they learn the concept.  Most textbooks keep the problems quite simple like 5 - 8 rather than throwing in some like 87-105.

In addition, I get students who hit middle school and high school who still have issues with the idea that subtraction is the same as adding a negative number or is indicating a direction on a number line.  If a student see a problem like 8 - 2, they will tell you that it is 6 but if you write 8 + (-2), they are confused and do not see the two problems as the same. The same applies to 5 - 8 being the same as 5 + (-8).  As far as directions on number lines, I've seen students find the 5 and when they applied the -8, the begin at zero and moved to the -8 on the number line rather than moving 8 in the negative direction to get -3.

Furthermore, they also have trouble with multiplication and division of signed numbers.  They know that a negative times a negative is a positive but they forget that a negative times a negative times a negative will yield a negative number.  The same applies to division.  Add to that, the issue of a slope with a single negative sign, they often try to apply the negative to both the change in y and the change in x rather than seeing it as applied to only one as in -1/2.  Then if that isn't enough, trying to explain that a slope of 2/3 is the same a -2/-3.

I'm sure there are more but these are the ones I've seen repeatedly in my classroom.  I'd love to hear of other misconceptions from you.  Let me know what you think, I'd love to hear.  Have a great weekend.