One of my Algebra 2 students gave me absolutely no work on his quiz yesterday writing equations given two points on the line, a point and a slope of the line, or given a point and a line that is parallel or perpendicular to it. As I was walking around checking how students were doing with the problems they were to be working on, he had his head down and was visibly frustrated.
I asked him what was going on and he said that he had the right answers but got no credit for them.
I responded that I had no idea where his answers came from - if he figured them out in his head, or guessed, or looked off someone else's paper.
He replied that he's not a cheater.
"I'm pretty sure of that. So how did you come up with the answer?" was my response.
He started to explain that he used the graph and figured it out from there. He didn't have any work because he kept the grid clean so he could work out the four problems. I shared with him what I was looking for work wise and why it was important to understand how to work the problem that way (especially since problems won't always work out so neat and clean).
I told him to wait a minute and went to get some graph paper. When I came back I told him to use the graph paper and show me how he got his answers on the four problems. I left him to work through it and he came back up towards the end of the period.
He began by saying he explained it to another student and she followed so he thought he had it for me. He proceeded to explain very articulately how he arrived at the equations for the problems with 2 points and 1 point and slope given - and I should add, very accurately. He demonstrated he understood what it meant to be a point on the line and how to write the equation in slope-intercept form (which is what I had asked for). I revised his score from 0 to 5 on the spot - he demonstrated he understood it. At that point, the period was ending and we left it that he would come back tomorrow with explanations for the other two problems.
I am hopeful the student will come back with the explanations tomorrow. I am also hopeful that he will make a better effort in the future to demonstrate how he is arriving at his answers so that I can see he truly understands the concepts.
Winning here with one student, at least, I hope....