## Questions 1

My students sit at tables instead of individual desks. To reduce the incidence of cheating, I create two versions for each test. I’ve learned in the process that similar looking problems actually can vary quite a bit in their effectiveness.

Here’s my first example:

-4 – 9 =

-9 – 4 =

Similar problems, same answer, yet about 20-30% of my students will answer one correctly, and the other incorrectly.

I’ll leave the which is which and why as exercises to the reader.

## { 7 } Comments

More students would get the second one correct, I believe.

Mentally I could “see” -9-4 but I had to calculate -4-9. This is essentially the same “number instinct” effect as how people can tell there are 4 things in a set without counting, but 9 requires at the least some sort of mental grouping. (It also explains how animals can count up to 4 or 5.) I never thought about it in this context, though.

I’m going to say because -9 – 4 looks like a regular subtraction problem, so they will probably answer with -5.

But to make similar problems, why would you switch the order when you could just use two numbers other than 9 and 4?

What am I missing? They both look the same to me as well as my students. I teach a class of struggling learners and I use these words to “Row, Row, Row, Your Boat’ ( although now we just say it out loud instead of singing when we review work together in class). “Same sign add and Keep, Different signs subtract. Keep the sign of the biggest number, Then you’ll be exact.”

Well, I’d say that’s a typical problem. My students usually answer this one correctly:

(-5)+(-4)

and they answer this one incorrectly:

-5-4

But when we start calculating with polynomials, they tend to do p(x)-q(x) like p(x)+ [-q(x)]

That’s kind of non-sense, but they keep on doing that way.

(By the way, I’m a Spanish high-school teacher)

Yowza.

I ask a simple question that I think I know the answer to, and I get back a whole messload of food for thought.

I’m going to leave my analysis of the question for a bit still, to see if any other insights pop up.

Don’t try to make sense of it. I once gave a quiz with the answers listed upside down on the bottom of the page. I still had people fail!

I believe that some kids will see -9 – 4 as – (9 – 4) = -5. (I used to see this problem commonly in -9 + 4 = -13, because their rote memorization of “PEMDAS” makes them falsely believe that addition comes BEFORE subtraction.)