About 1/3 of my kids got got through the subtraction. About 1/3 thought they remembered the rules from 7th grade, and bypassed the algebra tiles, and got most of the questions wrong.[1] The final third did pretty well on addition, and then got confused on how to do the subtraction.

I can’t get frustrated, because I knew going in that this was conceptually difficult. I think i just need to hit them with multiple representations. Multiple, as in lots, as in way more than two or three.

Fortunately, I’ve got a good resource. I was a dumbass for forgetting about it, but I literally stumbled across it yesterday morning in my office.

Big shout out to Ms R. whose mom works for AIMS and who turned me on to their books. These aren’t just worksheets – they’re lessons that address multiple conceptual models at the different levels of Bloom’s taxonomy. In this case, they have one book that completely deals with positives and negatives. For those interested, the first lesson I’m using from the book is also available online.

^{1} There’s a scene in *Stand and Deliver* where the Jaime Escalante character has his kids chanting “A negative times a negative makes a positive”. It seems to me that every 6th grader has gone through that, and then remembered it as “A negative *and* a negative makes a positive”, and then tries to apply the rule to addition. This then screws up the whole model for addition, and they get even more confused than they already were. There has to be a better way.

## { 3 } Comments

Oh my. I never, ever thought about them remembering the “times” as “and”. Let us know how the AIMS books work out.

Ok i teach at highschool but I see to many student who dont get negative numbers. In my veiw the best way to clear things up is to start talking about the two diffrent minus signs…

you have the operator (to take away) and you have the value (debt, less the zero) and work and work and work from there…. and always make them think… and when they ask about a problem (like 12-2*(-3)) you force them to do a word problem about money that would give that calculation. They hate me for the last part but it gives result…

/Per

you actually have 3 different minus signs: there is the one that indicates a negative value, the unary operator, and the binary operator.

I think you’re right that the differences need to be addressed – I’m not sure you you want to approach it from a functional aspect, or a lexical one.