I am starting to think about planning for Calculus I for next year, and there is an idea I would like to try: I want to stop labelling problems according to the corresponding standard, and put the burden on the student to determine which standards they met. I have tried this before (as have other people), but I would implement it different from how I did it last time.
So each quiz would go like this: I give them several (unlabelled) quiz problems. The students do what they can. When they are done, they submit their work. However, when they submit, we make some sort of a copy (perhaps a paper copy, perhaps just take a picture with the smart phone), and then the student takes one copy home.
At home, the student tries to figure out which standards she met on the quiz. For each standard, she writes up an argument as to why she met that standard. Specificity is key—the student would need to explicitly say where and how she met the standard. She submits this at the next class period, and this is graded as I usually do.
Here are the things I like about this idea:
- Students have to reflect on their work in order to get credit. This could lead to higher quality writing.
- Students would have to take ownership of their learning. They need to be aware of the standards they are missing, and make a concerted attempt to learn it well enough to be able to apply it on a quiz (including recognizing where it makes sense to apply it).
- Students can solve problems any way they like. As long as they can solve the problem using a standard, it counts. For instance, a linear algebra student might get “eigenvalue” and “determinant” credit for finding the eigenvalues of a matrix.
- Students are forced to really think about what the standards are and mean. There could be metacognitive benefits.
- I can ask more synthesis questions on quizzes; I do not need to isolate ideas for each question.
- Students no longer get the hint that the label provides (if the quiz question is labelled as corresponding to the “Tangent line” standard, then the student has a pretty good idea that he should find a tangent line at some point).
- It might give me room to have more standards (and more specific standards of the “I can do this” variety, rather than standards that are really topics, as in “Tangent lines.” David Clark encouraged me to make this transition last weekend).
Here are some potential problems:
- If the problems are too synthesis-y, then students won’t be able to do very many on each quiz. This might be fine, but it would be bad for a student who gets stuck and does not know where to start (on the other hand, maybe it would help teach students to start with something?).
- Students may try to shoehorn standards where they do not belong. This is what I would do if I were missing a small subset of standards.
- I am not certain I can write quiz problems that will give everyone the opportunities they need at the end of the semester. Students need different things, so I would have to have a lot of questions (note: this actually doesn’t need to be any different than how it is now; I can just provide straightforward, say, “Tangent lines” problems to quizzes if I need to. So this actually isn’t much of a problem).
- It forces students to be aware of what they have not yet demonstrated; this might be asking too much of some first-years.
I am on the fence about this, although I would really like to try it. Perhaps I could do both: keep the old way (with the labels) and do the new way. I could make that work.
What am I missing? What other advantages, disadvantages, and difficulties would this have?