Last year I applied for and received a LITE Seed Grant to add some new techniques to STAT 334. The three main things I added were interactive tutorials, a case study competition, and oral exams. I'll talk about each one in a different post.

Part 1: Interactive Tutorial Activities

Different instructors use tutorials in different ways, but for me the most effective way is to give the students essentially an in-class assignment. Open book, they can talk to each other, and the instructor and TA(s) walk around and actively help groups. I've long done this in ACTSC 232 and wanted to try to take it even further in STAT 334.

I had 10 tutorials in the term and varied the activities each week.

The first and last I used for a pre-test and post-test on the course material. That's giving the same test before and after the course so I (and the students!) can see how much they have learned.

The tutorial before the midterm I used as a review activity. I broke the class into 6 groups, and each group was responsible for two things: writing down summary notes of the concepts in a specific few lectures, and answering a midterm-like question on that material. For the second phase we re-shuffled so there were groups of 6 people (one from each of the original groups.) Then in the new groups, each member took turns explaining their summary notes and going through the solution to their question. (I rotated the pieces of paper with that information around the groups manually.) By the end of the class, each person had explained one question and had 5 others explained to them, providing essentially a complete practice midterm and set of study notes, which I then posted on the course website afterwards.

The tutorial after the midterm I used to "take up" the midterm in a non-traditional way. I made groups of 3 such that every group had someone who got each question right or mostly right, gave them their (unmarked) tests back along with a blank test, and had them collaborate on a set of "solutions." Revisiting the material with other people to help made the midterm much more of an active learning experience. If people's answers disagreed, they had to debate who was right. Almost all of the "solutions" were perfect. At the end I gave them marked copies of their own original papers.

The other six tutorials were used to do questions and activities relating to important threshold concepts in the course, which many students have struggled with in the past. These included:

1. Playing some games of chance and calculating probabilities and expected values related to them
2. A demonstration of the multinomial distribution (with a loaded die) and why its marginal, conditional, and convolution distributions are all Binomial
3. Transformations of joint continuous distributions (3 different examples to practice)
4. The idea of double averaging and conditional expectation
5. My personal favorite, exploring the basic properties and definitions of Markov Chains (discussed further below)
6. The properties of the Poisson process including conditional event times, number of events in a subinterval, and the compound poisson process

For the Markov Chain activity, in groups of 6, each person represented a "state" (1, 2, 3, 4, or 5) in a Markov Chain and was given a piece of paper with instructions for which state to go to next if a coin came up Heads or Tails. The students traced the path of the chain several times on a piece of paper until they got a sense of how the chain behaved, and then were given a set of questions to answer about the chain. They did this for 3 different chains. Through this activity, I was able to introduce the concepts of classes, communication and accessibility of states, periodicity, transient/recurrent states, and the transition matrix, all without any formal definitions. That helped make all these theoretical definitions more concrete and easy to remember when we then defined them in the next class.

The tutorials were a resounding success. 98% of the students reported in an anonymous post-course survey that they found the tutorials helpful in learning the course material, and they were a lot of fun to run!