Discrete Math - Day 37

Today we began the review process for the mid-term exam at the end of the week. The process I use came from an article I read in The Teaching Professor Newsletter. The premise is to let students build their own review guide and problem set.

To start things off, I ask students to list the five big topics studied in the course so far. I provide a limited time as I want them to focus on top-of-mind awareness. Next, I have students partner or work in groups to come up with an ordered list. In this work I encourage students to look through their notes to assist in getting good coverage. We then share out the topics.

I'll start with one group's list and then go around the class having other groups add topics not already listed. I will then group topics using a colored marker, for example indicating that counting, permutations, and combinations are all connected topics.

The class provided good coverage of the topics we have worked on this semester:

Counting topics

• Counting
• Combinations and permutations
• Exponential powers

Figurate numbers and Patterns

• figurate numbers (pentagonal numbers)
• Gaussian summation
• Pascal's triangle

Prime numbers and Ciphers

• prime numbers
• Euclidean algorithm
• greatest common divisor
• ciphers

Probability

• probability
• conditional probability
• Bayes theorem

As the list grew, one student commented by saying, "Wow, we've covered a lot of math already." Yes, they have and there's still a lot more to come.

Students are then asked to develop three practice problems reflecting different topics and different difficulty levels. I circulate around and push students to consider the problem they are posing and the solution that results. The tendency is for students to create simple problems, but with a little push they respond to upping the complexity and requirements of the problems they create.

I then ask students to have their problems created in a format that can be shared with the class and that they should have the solution developed for their problem so they can check the work of their classmates.

The topic listing activity helps to focus the problems that are created. The problem creation activity actually requires students to think at a deeper level about the topic, the wording of a question, and the solution for the problem. This provides their first review practice.

In the next class we'll work through the problems created in class today. I have extra practice problems ready in case more are needed, though providing 15 to 20 problems from the students generally is enough practice for a single class.

Visit the class summary for a student's perspective and to view the lesson slides.