I am considering a new HW policy that I haven't seen elsewhere. Each week the student must turn in $n$ problems, of her choosing. There will be no HW score beyond documenting whether the student is turning in honest attempts at these $n$ problems. (
my general thought would be to make each HW contain $n$ challenging problems, a few medium problems, and $n-1$ easy problems)
If the student chooses to do so, they circle one of their solutions and the "grader" reviews it and gives the student very detailed feedback, including comments on the correctness and clarity of each step, the writing, and one take home message they should work on. No numerical grade would be assigned here, it is purely for feedback purposes, and it is optional (although there is no reason not to choose this option).
What is my desired outcome
- students do the problems that will allow them to learn the most. Struggling students can work on the easier problems and get feedback on them before moving to harder ones.
- stronger students can turn in the hardest $n$ problems and choose to get feedback on the one they found most challenging (but still had a solution for), without wasting time on the problems they found trivial.
- the lack of a numerical grade tied to the HW (beyond completion) seems to increase learning. See the answer to: Is it worth grading calculus homework?
- by choosing the problems that they will receive feedback on, they are learning how to identify when they aren't sure about a solution and when they are confident in it. Being able to identify you don't know something or when you think your argument is shaky is one of the most important skills in mathematics.
- students will see the value in HW as a learning tool rather than something they need to do just to get a grade.
- students are learning to own and take pride in their struggle. By circling the question they most want feedback on, I think it reinforces them to constantly be trying to learn more and not focus on the things they already know well.
What I want to avoid (possible drawbacks)
- non-struggling students doing easy problems just to quickly turn in the assignment. They end up learning less than in the traditional HW setting and do poorly on the tests because they haven't gotten feedback on problems of the appropriate difficulty level.
The goal is to make HW purely a learning experience that everyone can get the most out of but to also move away from a grade obsessed classroom culture. What are the advantages and disadvantages of this HW policy? and what changed to overcome some of the disadvantages?
Edit: another way of breaking down the questions (instead of easy/hard) is to use standards based grading as in this question Standards-based grading in calculus. So I'd mark a question as
- computation - applying formulas and rules used in this class,
- application - abstracting a concrete problem and figuring out which mathematical tools are most useful to solve it,
- adaptation - changing a formula or rule to fit a new, but similar type of problem
- theory - demonstrating a deep, theoretical, understanding of a concept presented in this class
And I might have a requirement that they must do problems from of at least 3/4 types and not tell them which ones are the hardest.