# Skill-Based Exam Study Guides

“Will this be on the exam?” Skill-based exam study guides make that question a relic of the past, while making both teachers and students happier.

*The following is a post that I wrote for the MTEI Teaching Tip blog during my term as MTEI’s associate director.*

**“Will this be on the exam?” **It’s a disheartening question to hear as a teacher — everything you teach is important, after all. Eventually you write up a bulleted list of exam topics and post it. “What do I have to know about *topic X*?” “What about the starred subsection on *advanced topic Y*?” “Do I need to memorize *fact Z?*” It starts to feel like there’s no way to answer all these questions without just publishing the exam in advance. You’re unhappy, but you learn to live with it.

**“Will this be on the exam?” **It’s a natural question to ask as a student — you have limited time to study, after all. You’re trying to keep up with all the topics that were covered, but it’s hard to make sense of which are really the most important. Your professor posted a list of topics, but *topic X* lasted for five lectures, and you aren’t sure whether *topic Y* is worth spending extra time studying — it was in the reading, and your TA mentioned in your discussion section as something good to know, but your professor didn’t mention it in lecture. It starts to feel like there’s no way to optimize your study time without seeing the exam in advance. You’re unhappy, but you have to live with it.

**If either of those perspectives feels familiar**, here’s an idea that might make everyone happier: as part of your exam study guide, **publish the ***algorithm*** you will use to generate the exam. **A very easy way to do that is with a statement like these:

- I will pick 8 out of the 40 problem set questions, and change the setup of the question while keeping the underlying methodology the same.
- Look at the exercises in chapters 3 and 4 of the textbook. I will write problems similar to those.

But an even better way is to augment the list of topics in your study guide with a **list of skills about those topics** that will be tested. For example, you could augment the topic “polynomials” with any of these skills:

- Given two polynomials each with two terms, multiply the polynomials and state the result. Your answer must simplify and combine like terms.
- Calculate, without the aid of a digital device, the characteristic polynomial of a 2×2 matrix of small integers. Label where in your answer you take the determinant of a matrix.
- Write the code for a Python class that represents polynomials of a single indeterminate. You are given the fields and the class invariant. You must define a method to convert the polynomial to a human-readable string in decreasing term order, omitting any terms with a zero coefficient.

(By the way, well-written skills take the form of *learning objectives*. You can read more about those here.)

Did any of those skills surprise you? **The vast difference in testable skills reveals the inadequacy of merely listing topics in a study guide. **Although in your own class it might be clear to you which skills are relevant, it is considerably less clear to your students — especially to those whose comprehension of the material is currently low. By identifying the skills that matter to you, you give students the study advice they need to improve their proficiency and do well on the exam. Your students will learn more!

You’ll likely write several skills for each of the topics in your study guide. **All of those skills become templates from which you can instantiate new exam problems, **semester after semester. There is an up-front cost to write the skill list, but thereafter you can more quickly write new exams (or makeup exams). With a little maintenance each offering of the course, you might even generate **the next 10, 20, or 30 exams in your course** out of the skills list. That will save you a lot of time over the years!