# Automatically creating homework worksheets from textbook problems

This semester I am a TA for a Calc 2 course. At my first meeting with my instructor, he mentioned in passing that "Homework is always easier than an exam, because homework questions come from the textbook, so they always know which section the problems are from.". It's just anecdotal, but that does align with my own experience taking calculus courses: each section covers a very specific technique, and the problems in that section are designed to be solved using that technique, and often very little else.

It occurred to me that, since we regularly have 2-3 sections due for a single homework assignment, this 'bug' could be worked around. The 'manual' way to do this would be to (1) type up every homework problem into LaTeX, (2) randomize their order into a document, and (3) hand them the worksheet as a homework assignment

[ I would probably say explicitly that they are taken from the textbook. The goal here isn't to hide the fact that they're textbook problems, merely to make the section numbers less visible so that the student has to pause to think about the tools they need to start a problem. ]

But of course step (1) is fairly labor-intensive, even if there isn't any TikZ work involved. If I am using a very common book, like Stewart, is there an online tool to, e.g. create worksheets by typing in a list of problem numbers?

• Just a short question: You mention that typing things into Latex would be rather time consuming, so how are you posing the questions right now (as in all math classes I took or worked in as a TA, Latex was always what we did)? Do you say "do numbers 1,5,7,18 in chapter 4 of the book"? In that case, also mixing them would not get you far, the students are intelligent enough to match them to the exact same text in the book (I assume...). – Dirk Liebhold Sep 3 '18 at 8:43
• Yes, that is how it is done now. As I said, the goal isn't to hide that they're textbook problems. The fact that they can match them up with the book text may, in fact, be a feature: it provides a built-in 'hint' system, that students can choose to use or not. Some may abuse this system, but that is really not my concern: the homework counts for 5% of their grade and the exams count for 85%, so the incentives are clear. But as it stands now, they're not even realistically given the choice to practice the 'What is my first step?' skill. – Eric Stucky Sep 4 '18 at 12:32

Easier than the proposed solution may be to use another book, or online worksheets, and look for one of the following features:

1. "Mixed practice" (a.k.a. varied practice) exercise sets, which are intended to solve precisely this problem.

2. End-of-chapter review exercises, which may generally have the same composition.

3. A test-generator program with premade testbank problems (e.g., Stewart links to "Cengage Learning Testing Powered by Cognero" see bottom here; my preferred choice is Pearson Testgen with some Pearson text's testbank).

There are lots of ways around this:

• As Daniel R. Collins has suggested, many textbooks feature end-of-chapter reviews or "mixed practice" problems. Indeed, my recollection is that Stewart's calculus features such review sections quite prominently at the end of each chapter. It might not be a bad idea to assign exercises from those sections, if only as review before an exam.
• If you use an online homework system, such as MyLab or WebAssign, you can create homework assignments which mix problems from various sections of a single book, or which include problems from multiple books. Alternatively, you can create assignments using these tools, then print them out and give them to the students as handouts. This may actually be the solution that you are looking for---I believe that ebook version of Stewart's calculus comes bundled with some online homework system which you could potentially use to construct assignments.
• Frankly, it isn't that difficult to $\TeX$ up a bunch of problems for homework---it just takes some practice. If you want to include images, that takes a little longer, but if you use \includegraphics or some such package to include .eps or .png images, you don't have to muck about with TikZ or pstricks.

That being said, I don't think that it is necessarily a bad thing to tell students which tools they are expected to use, at least not when they are first learning to use those tools. At the very least, I think that there should be a very clear distinction made between "These are the problems that you are doing in order to get a handle on this new tool introduced in section x.y," vs "These are the questions which could potentially use any tool you have ever learned, up to an including those introduced in section x.y."

If you have access to an online version of the textbook, you could take screenshots of each problem you want to use and compile them in a TeX document very quickly. It's also very easy to rearrange the order of the problems.

In university, you should be able to work out a deal with the prof and/or other TAs to say this to the students.

Your homework assignment is to make a compilation of the 10 most likely types of questions you expect on your next test. You must:

1. Give each question a descriptive title.
2. Include step-by-step solutions, with explanations, cues (how you would know what to do), diagrams, checks, comments/comparisons/contrasts, etc. as necessary.
3. Rate each question as easier, as hard as, or harder than you expect on the test. At least one question must be conceptually harder than what you expect on the test.
4. Compare your set of questions and solutions to those of 2 of your peers. Keep editing until everyone approves of everyone's work.
5. Hand in your 10 questions at least 2 weeks before the test.

You will receive feedback from your TA 1 week before the final exam, mostly to tell you if you are or are not on the right track. Needless to say, you should have mastered everything that you hand in.