Ay 300 - Writing Homework Assignments

Writing good homework assignments is arguably one of the hardest parts of teaching. It takes practice to write a good individual problem and to weave multiple problems together into a useful, fair assignment.

It may be helpful to you to consider why we assign homework at all. Some of the reasons are:

• To help students study and (hopefully) learn the course material before exam-time. This is the best reason, but also a tenuous one: how many students do you think would hand in problem sets if they didn't count towards their final grade?
• To help students practice their problem-solving skills. Note that this is not the same thing as learning the course material. But most GSIs would probably agree that these are important skills for all students to learn, whether they are future astronomers or not. Recall our “Goals of Ay 10” discussion from last week.
• To give GSIs feedback on their sections' understanding of the course material presented so far.
• To give the students feedback on their personal understanding of the course material.

Students, especially non-science majors, tend to be overwhelmed by a problem if they're presented too many details at once. While it's good to force students to think hard about a problem, you also want them to complete the assignment. Ay 10 students tend to get frustrated when faced with a difficult problem that isn't broken down into steps. Many leave such problems blank, even if they can do the individual parts of the problem, because they don't know where to start. It's generally best to split problems into multiple parts that walk students through the questions. However, in classes for science/astronomy majors (i.e. Ay 7A and 7B), this is done much less on homework assignments since those students will eventually need to be able to solve larger, more open-ended problems that don't give as much guidance on how to get to the right answer.

You may decide that one of your goals is to teach your students how to tackle larger, more complex problems. This is a fine thing to decide, and it's certainly a valuable skill to have. In that case, you may decide to “chunk” your problems less aggressively, perhaps breaking them down less over the course of the semester. Keep in mind, however, that the problem-solving skills that are emphasized in your problem sets should be the same ones that will be most important on your final.

You can make problems more manageable for your students by including hints. The difficulty here, of course, is that most students will use hints immediately without attempting to finish the problem without help. A way to avoid this is to use hints that refer students back to previous problems, e.g. “Hint: If you're stuck, see assignment 2, problem 4.”. This gives struggling students a way to proceed, but because they need to look up previous problems, doesn't immediately make the problem easier. As a result, students generally try to think about the problems at least a little bit before using the hints.

While it's smart to break up problems into “bite-size” chunks, don't make final parts of a problem depend completely on previous parts. For example, if completion of part (d) requires a mass estimate from part (b), include in your instructions something like, “If you do not have an answer for part (b), use M=10³³ kg.” Students who can't solve part (b) will have a chance to work on part (d) if you do this. The result that you suggest to struggling students should be somewhat close to the desired answer (so that students can apply the “does this make sense?” test) but, obviously, not the exact value.

It takes practice to assess the difficulty of a homework problem. Some factors that increase the difficulty of a problem are:

• Conceptual difficulty. Some problems just demand a more sophisticated grasp of a concept than others.
• Presence of equations. Questions that involve anything but the simplest mathematical manipulations will be very difficult for most of your students.
• Use of jargon. This also includes difficult nonscientific words – English is not the native language of many Ay 10 students.
• Ambiguous or confusing language.
• Mistakes in the problem.
• Larger discrete steps. As described above, students will generally have an easier time performing a task if you break it up into pieces for them.

It's perfectly fine to write problems that are conceptually difficult. You should, however, avoid making problems more difficult than they need to be: use clear language, proofread your writing, etc..

Homework problems should be more involved and difficult than quiz or test problems, because students have more time and more resources to work on them. Your homework questions, however, should be designed to help prepare students for their quizzes and tests, since the latter are where the bulk of their grades come from.

Because students have a range of abilities and interests, you should write some easy questions and some hard questions so that each student learns something from doing the homework. A problem that every student gets right with minimal effort doesn't tell you anything about how your students are doing and doesn't deepen your students' understanding much. A problem that only a few can get right, on the other hand, will be an exercise in frustration for the majority of your students. As mentioned above, students in a class such as Ay 10 tend to get frustrated and give up on difficult problems, rather than work heroically to finish them – so try to avoid them.

Breaking your problems up into parts can help make your questions clear, but it's still extremely important to carefully edit your assignments. Ambiguous questions upset students and make grading difficult. If possible, have a fellow GSI (probably in addition to the Head GSI) or perhaps an Ay 300 instructor read a draft of your problem set before assigning it. Other GSIs may have good suggestions for improving question wording.

You can sometimes make multiple problem sets over the course of the semester connect to each other. For example, in Ay 10, multiple homework problems throughout the semester can involve blackbody radiation or Newton's Law of Gravitation. Always try to use similar terminology and notation between problem sets so that students can refer to their previous work and keep it consistent with the rest of the course material (i.e. the notation from the textbook and lecture).

Your homework problems should ask students to perform a variety of different tasks. This keeps things interesting and makes things more fair since different students have different problem-solving strengths. Some tasks that your problems might involve are:

• Computation (actually calculating numbers)
• Algebraic manipulation (manipulating equations, not necessarily plugging in numbers)
• Reading and interpreting text, either included in the problem statement or an outside resource
• Reading and interpreting graphs or diagrams
• Writing text: explanations, definitions, vocab recall, fill-in-the-blank, etc.
• Creating and/or filling in graphs or diagrams
• Ordering of objects by some property (“ranking tasks”)

Homework problems can explore topics covered in lecture or introduce new topics not mentioned in lecture or even in section. That being said, they should still largely focus on the major course topics, especially those deemed the most important (i.e. the ones that will appear on exams and quizzes).

It helps to keep your students' interest if your questions are put in a context that relates to everyday life. Amusing problem statements also keep things interesting, but clarity is more important than entertainment. If you can come up with a funny context for a problem, that's great, but don't let that get in the way of making it clear what you're asking your students to do.

You should at least indicate how many points each problem is worth, and preferably you should indicate the point breakdown of subsections of problems. When asking for written responses, give some indication as to what will factor into the grading. Not only will the students appreciate it, but it'll be helpful to have consistent instructions for the graders about how to handle written responses.

Of course, not all of your course's assignments must be problem sets. As a GSI, it's probably not in your power to totally change the nature of the homeworks in your course, but you may want to keep in mind that there's no law that you have to have your students do problem sets every week. Some other possibilities are:

• Assigning students to do some reading or research on their own
• Having students practice the scientific method:
  • Ask them to evaluate scientific claims
  • Have them make a hypothesis about some phenomenon, test it, and comment on its validity
• Have students take a small amount of data. (This is pretty much what the Ay 10 observing labs do, however.)
• A longer written assignment, possibly a research type project.

This list is, of course, inexhaustible. Anything that gets your students to grapple with the concepts taught in lecture (or in astronomy or science in general) is a good assignment!