A continuing series on the things I encouter while grading. I'm not sure what's been so special about it this year. I've had a harder time making myself do it, for one. But everytime I sit down to grade something, I have to make a decision "what am I looking for?" and "what proves there was a knowledge transfer?" Take this example:

It's a two-step polynomial multiplication problem. The first step is executed perfectly. In the next step the student made a typo. The result from part 1 should have been multiplied by (x + 10) but for some reason (x - 9) appeared. A little careless or they made a minor visual error when looking for the next item to use, possibly pulling the -9 at the end of the third binomial there. I suspect it results from not multiplying the binomials from left to right in the first place. There are people that would see this, mark a little "-2" or in the hardcore mindset mark the whole thing wrong because *technically* the student did not answer the given question, they answered an incorrect version of the question. But look at the work. Despite having the wrong term, the operation continues flawlessly even with the misplaced (x - 9) being used.

In a points world, this student does not receive full (or possibly any) credit. And yet it's very clear they understand the concept. One would argue they are fluent in the concept since they essentially made up a problem that demonstrates the mechanics of polynomial multiplication.

I gave the student full credit. What would you do?