- I gave a quiz not long ago with the following question adapted from the homework:

The value of 5 points for the problem came from the following rubric I had in my head while grading it:

- +1 point for a correct free body diagram
- +1 for writing the sum of forces in the y-direction and setting it equal to ma
_{y} - +2 for recognizing that gravity was the only force acting at the minimum speed
- +1 for the correct final answer with units

Since learning to grade Regents exams back in New York, I have always needed to have some sort of rubric like this to grade anything. Taking off random quantities of points without being able to consistently justify a reason for a 1 vs. 2 point deduction just doesn't seem fair or helpful in the long run for students trying to learn how to solve problems.

As I move ever more closely toward implementing a standards based grading system, using a clearly defined rubric in this way makes even more sense since, ideally, questions like this allow me to test student progress relative to standards. Each check-mark on this rubric is really a binary statement about a student relative to the following standards related questions:

- Does the student know how to properly draw a free body diagram for a given problem?
- Can a student properly apply Newton's 2nd law algebraically to solve for unknown quantities?
- Can a student recognize conditions for minimum or maximum speeds for an object traveling in a circle?
- Does a student provide answers to the question that are numerically consistent with the rest of the problem and including units?

It makes it easy to have the conversation with the student about what he/she does or does not understand about a problem. It becomes less of a conversation about 'not getting the problem' and more about not knowing how to draw a free body diagram in a particular situation.

The other thing I realize about doing things this way is that it changes the actual process of students taking quizzes when they are able to retake. Normally during a quiz, I answer no questions at all - it is supposed to be time for a student to answer a question completely on their own to give them a test-like situation. In the context of a formative assessment situation though, I can see how this philosophy can change. Today I had a student that had done the first two parts correctly but was stuck.

**Him: I don't know how to find the normal force. There's not enough information.**

**Me: All the information you need is on the paper. [Clearly this was before I flip-flopped a bit.]**

**Him: I can't figure it out.**

I decided, with this rubric in my head, that if I was really using this question to assess the student on these five things, that I could give the student what was missing, and still assess on the remaining 3 points. After telling the student about the normal force being zero, the student proceeded to finish the rest of the problem correctly. The student therefore received a score of 3/5 on this question. That seems to be a good representation about what the student knew in this particular case.

Why this seems slippery and slopey:

- In the long term, he doesn't get this sort of help. On a real test in college, he isn't getting this help. Am I hurting him in the long run by doing this now?
- Other students don't need this help. To what extent am I lowering my standards by giving him information that others don't need to ask for?
- I always talk about the real problem of students not truly seeing material on their own until the test. This is why there are so many students that say they get it during homework, but not during the test - in reality, these students usually have friends, the teacher, example problems, recently going over the concept in class on their side in the case of 'getting it' when they worked on homework.

Why this seems warm and fuzzy, and most importantly, a good idea in the battle to helping students learn:

- Since the quizzes are formative assessments anyway, it's a chance to see where he needs help. This quiz question gave me that information and I know what sort of thing we need to go over. He doesn't need help with FBDs. He needs help knowing what happens in situations where an object is on the verge of leaving uniform circular motion. This is not a summative assessment, and there is still time for him to learn how to do problems like this on his own.

- This is a perfect example of how a student can learn from his/her mistakes. It's also a perfect example of how targeted feedback helps a student improve.

- For a student stressed about assessments anyway (as many tend to be) this is an example of how we might work to change that view. Assessments can be additional sources of feedback if they are carefully and deliberately designed. If we are to ever change attitudes about getting points, showing students how assessments are designed to help them learn instead of being a one-shot deal is a really important part of this process.

To be clear, my students are given one-shot tests at the end of units. It's how I test retention and the ability to apply the individual skills when everything is on the table, which I think is a distinctly different animal than the small scale skills quizzes I give and that students can retake. I think those are important because I want students to be able to both apply the skills I give them and decide which skills are necessary for solving a particular problem.

That said, it seems like a move in the right direction to have tried this today. It is yet one more way to start a conversation with students to help them understand rather than to get them points. The more I think about it, the more I feel that this is how learning feels when you are an adult. You try things, get feedback and refine your understanding of the problem, and then use that information to improve. There's no reason learning has to be different for our students.