A few weeks ago, as a homework assignment we were asses student work on transformations. The activity that the students completed is called Aaron’s Designs, which gave students the chance to draw reflections and rotations of a given figure on a grid, and to describe transformations needed to make a given pattern. We were given this sample of student’s work and this rubric to help with grading.

I was surprised by the amount of time that it took me to grade the work. I kept finding myself wanting to make changes to the rubric clearer. I found myself in a grey area where if a student didn’t answer completely correctly what type of partial credit should they get? Do I give them the benefit of the doubt that I might not be understanding what they were trying to say, or do I grade a little more harshly and follow the rubric letter by letter? More often than not I found myself wishing that I could talk to the student and ask them questions to get more insight into their thinking and reasoning. The following image is a sample of a student’s answer that made me want to have a conversation with them.

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I wanted to ask this student questions such as, How did he use the same design? What did he do to it? Both times of what? Could you describe what he did with pictures or arrows to help strengthen your answer? What thoughts did you have while thinking about and answering this question? That’s what I wanted to know for one student on one question, and there were 15 students, no wonder it took me so long to get through them!

I was pleasantly surprised by the fact that every student got the first question correct. The students were given one shape already drawn on a grid and were asked to reflect the shape over the y-axis, and then reflect those two shapes over the x-axis. The second question gave some students problems, only about half of the students earned full credit for this problem. The students were given one shape already drawn in and were asked to rotate the shape 1/4 of a turn 3 times. According to the rubric, each of the three shapes that was correctly drawn earned them one point. The problem with this was that the students who reflected the shape like they did in question one still earned one point because reflecting happened to put one shape in the correct spot. Although they earned a point, they did not show understanding. The third and final question posed to the students had all shapes already drawn in, and asked the students to describe the transformations that may have been used to draw the design. This is the question that produced the majority of my questions for the students. Out of 15 students only 6 received full credit for this question, many students used the wrong terminology or didn’t describe the transformations in a way that made sense. for many students I wrote down questions along the lines of could you describe it any other way? With pictures or using arrows? For the students who received full credit , I asked as an extension if there was more than one sequence of transformations, and how many there could be.

This exercise made it very clear that you can’t get a full picture of a student’s understanding based off of a short paper and pencil test. It also shows how valuable it is to go over test corrections with students is, that way you have dialogue happening and they might be able to better or further explain their thinking. One of the most important take-aways that I got from the activity was how important a well written rubric is. It is important for you to help while grading and to grade fairly and not go crazy, and also for the students to know hat is expected/ how they will be graded, and also to ensure that they are being graded fairly.