A while ago I watched an interesting youtube video that dealt with student misconceptions specifically in physics.  It resonated with me so much I just spent a few minutes trying to find it to share on this blog.   The point of Derek Muller’s research  is that students often think that they already know what they are learning.  I have done many lessons where I start with a class discussion of what students know about a particular topic.  Especially teaching 9th through 11th graders, many student have had Algebra I multiple times which unfortunately can reinforce certain misconceptions.  Last year, I had an 11th grader who regularly announced that this was her fourth time and she was going to “pass it.”

So I just erased my 2nd paragraph, and I am starting again, so it will be shorter!

One misconception that I noticed every year with my students was subtracting integers and whether adding negative integers were positive.  I have vacillated about how to deal with the misconception over the years.  At this point, I usually have two responses depending on the student.  If the student seems ready for the concept of subtraction, then I will use money or  a vertical timeline with the student to solidify their understanding.  If the student is still struggling with the concept of subtraction, then I coach the student to change subtraction to adding the inverse.

For example A)  -5 -8 is the same as  B) -5 + -8

I avoided the above method for a while because it doesn’t really address the concept of subtraction.  However, most students can solve B) whereas many students have issues with A).  I think that “converting subtracting to addition” is a shortcut that is useful for some students.

I dealt with the misconception during whole class discussions by highlighting what operation was being used when combining integers.  When students were able to understand a negative and a negative is a positive was dependent on the mathematical operation, I could usually address the faulty understanding by asking them what operation they were using.

I’ve had many class discussions where students insisted that a “negative and a negative is a positive.” I try to have other students verbalize why this is sometimes true.  This is a case when memorization of a key concept that is missing the condition can lead students astray.

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