How do textbook authors and professors cook up homework/assignment questions?

Question

I was looking around on the internet and I found some notes with homework appended to them (for those interested, it is math). What struck me is that these questions are not only lengthy, notationally challenging, but also appears to be quite complicated. For a biology course no less.

Can any authors or professors illuminate as to how (i.e. the process) these assignment questions are developed? I thought about this and found several scenarios which are quite interesting to think about, but at the same time, ridiculous to me.

For professors/authors:

scenario a: the professor/author goes home and quietly sits in front of a fireplace and starts brain storming weird scenarios and writes down these random thoughts

scenario b: the professor/author demands his graduate students to pump out 10 questions on a weekly basis, the rest is history

scenario c: the professor/author picks up another book and make adjustments to questions that looks interesting and then puts into his own book. But then this sort of becomes a chicken-egg problem. What about a completely new field that no one has touched before?

scenario d: there exist a large central depository of problems that professors submit to it, and draws question from it, a massive database out of reach of any students. This is some fringe conspiracy theory.

scenario e: The Hamilton approach. Ideas just flies out at random say when you are taking a shower, or buying some groceries and then you jog them down very quickly and then send it to a depository. Kind of like scenario a but much more random.

What about people who are cross discipline and working on their own field? Are there dedicated personnel who is neither an author, nor a professor, but just works on developing these assignments all day? This question just opens up a can of worms.

Please feed my curiosity, I would love to know how they are developed because maybe I will also develop my own someday. I know there exist some distinction between authors and professors (although the two coincides on a great degree), let me know if things done differently between different professions.

Answer 1

I have been teaching university courses, as well as authored books and booklets for students, in computer science. I have therefore created assignment questions for these books, exams, and term papers. I always found two qualities of an assignment to be the most important one: It must contribute to the understanding of the topic the textbook or term was about. Additionally, it must be fair, i.e., solvable in the allotted time frame without the student/reader having to be a genius. I usually create questions in this way:

1. I identify the essential topics for the textbook's chapter, or the term. These topics constitute the "general topic area" any question must reside in. I usually write these down on paper and put the back in front of me every time I need to create a new assignment.
2. For each topic:
   1. I identify the most common concepts one is required to understand in order to master the topic. Basically, the building blocks of a topic.
   2. I formulate a problem that requires the student to correctly apply this "building block" in order to solve the problem.
3. When I have created a set of questions for a a chapter of textbook, I save them and close the file for at least 2 days, sometimes a week. I create a usually calendar entry to look at them again.
4. When the calendar alarm fires, I open the file with the assignments and print it. Then I set a timer and begin answering my own questions. For textbooks, one needs the answers anyways, typically. I set a timer and, for each question answered, note how much time I needed for answering the question. I take care to only use the tools the student will also have at hand. I then multiply the time by 2.5 (roughly --- your mileage may vary, but see below). This gives me a rough idea on how long a student might need to answer my question.
5. I check the timespans against the allotted time for the student. Typically, there is some sort of time boundary for students: In an exam, obviously, but also for term papers and textbook chapters.
6. Refinement.

Note that the estimation of how much time your students may need to answer your question depends very much on how fast you answer your own questions, and is also a question of experience. I usually take my time and try to do them "extra-neat." Especially when creating textbook or lecture notes, this pays off quickly. This is how I arrived at the factor 2.5. As @scaahu pointed out in his comment, a higher factor might be sensible. In general, I'd recommend starting with a higher factor --- for example, the mentioned 5.0 --- and reduce it only if your students consistently have much time left after an exam, or are finishing their term papers very quickly, over a number of terms (this is important!). Forcing students to come up with answers quicker and quicker does not necessarily mean that your assignments will have made them smarter. More often, it creates a lot of frustration among the students without any benefits, and, in my experience, rather leads them to present (generic) answers they memorized beforehand from, e.g., your lecture notes or other textbooks, rather then come up with their own answers.

Answer 2

You missed scenario f, which I suspect is the most common: The professor has been teaching this class and refining the textbook/notes for years, and developed homework questions out of problems that have come up over the course of that extended period of time of engaging with this material.

Answer 3

Actually, none of your scenarios describes my workflow. I use two approaches:

1. For every chapter/section/topic/… (let stick to section) I think about what concepts the students should master. To figure this out I collect all definitions, results and techniques from that section and design questions around these. For example, I think about questions that make the students understand a definition (and a definition is best understood while working with it). I am from mathematics, so here is a mathematical example: The concept are continuous functions. Problems for this concept could be "Show that this function is continuous!" with a concrete function or "Let f be some continuous function. Show that f has this or that property!". For results the approach to design problems would be to think about why you teach this result. It certainly is good for something. Find that and ask a question for you can use the result. For techniques it is even simpler: Give a problem that can be solved with this technique.

2. There are things that could be explained in the lectures but for some reason I prefer to have them in the homework. This could be a corollary/side result/additional result that is useful and simple enough to derive but too much for the lectures. It could also be a core result for which the proof is simple and the idea of proof is obvious or the proof is just very illuminating.

I should add that when I decided what kind of homework I want to give, I usually look at textbook and see if I find problems in the respective categories and only if I can't find problems that fit, I start to derive my own problems. (So you may say that after I decided which kind of problem I want, I follow scenario c…)

Answer 4

Another case is where you've worked on a more complex form of a problem in the past -- perhaps as part of a larger research project. Perhaps the answer had an interesting or elegant 'core' to it. You try to write a more simplified version of the same problem, while preserve the interesting essence of the more complex problem. Relevance to a current 'real world' problem helps to make assignment/tutorial problems more interesting, and they stimulate more thought and discussion.

Answer 5

To be honest, from my own experience and working with two different advisors of two different universities in two different countries (US and non-US), the professor will choose book A to include in the syllabus and choose book B (doesn't mention it to students) for homework and exams questions. For instance, for steel design, many professors like T. Segui's book to get examples and ask students to buy it because it is very simple and straightforward. However, most homework questions come from McCormac's book that is a bit more complicated. I have rarely seen anyone wrote their own exams except for very old professors who are "old school".

Answer 6

I've been amassing my own sort of "test bank" of question types and formula variations of my own design over the past several semesters, driven in large part by the desire to both create a pool of as many non-repeated question types as possible (to foil those amassing their own test files on the other side of the battlefield), as well as the interest in finding problem types that capture as much of the relevant core concepts as possible in a compact, relatively workable form (to reduce the number of students whose level of comprehension is buried under a tangled mess of bad algebra).

For example, as part of the calculus discussion on derivatives and their effects on the graph of a function, I've been slowly compiling a critical mass of equation types whose derivatives are reasonably straightforward (even if not always "easy") and which contain at least example of most of the key features (maxima, minima, inflection points, etc.), from which I can then pull my favorites (or favorites of the week) to craft a number of distinctive but reasonably equivalent versions of a test for a large section. In deference to the identify-key-details nature of my father-in-law's abiding hobby of birdwatching, I call it the "calculus field guide." Work now to accelerate for the summer, no pun intended.