**By Mark M. Maxwell**

While on a job interview in Vermont, one faculty member from the hiring committee prefaced a question with the words, “I have been teaching for 25 years.” His colleague interrupted and corrected him by saying, “No Bob, you taught for one year and have been repeating for the past 24.”

I didn’t get that gig in Vermont and I have yet to find my most effective teaching method(s). I suspect my best teaching would differ dramatically from your best teaching. And I am convinced that student development and understanding is a function of what the student does—not what the instructor does or knows or says. Therefore my goals are to provide students opportunities to learn, to collaborate with each other, and to effectively communicate their solution methods.

During the 50 ^{th} Actuarial Research Conference (ARC) hosted this year by the University of Toronto, I solicited activities that promote active problem solving, collaboration, and communication within a classroom. Several suggestions are described below. Some techniques might better lend themselves to lecture-based classes, flipped classes, or classes where students do the content presentations. Some techniques are scalable to large class size. Maybe you will get excited to try something new this year.

**Math Relays: **Divide the class into teams of size three students. Teammate #1 is given the first question and is responsible for writing the solution with the input of the other two teammates. Once the first question is complete, teammate #2 receives the second question and is
responsible for writing the team solution. This process is repeated for a total of 6 questions. All three students receive the same score.

We like that all students are invested in solving all six problems. Each student must practice writing two solutions and gets feedback/suggestions from two peers. This format also decreases the amount of grading and commenting from the instructional staff.

**Students Present Review Problems: **Heekyung Youn of the University of St. Thomas (co-host of next years ARC) assigns a single review problem to a group of three students. In order to save time, the group writes its solution on the board prior to the beginning of the next class. One student from the
group is selected at random to explain the group solution to the class. Heekyung typically selects three to five problems/groups and is available to check solutions prior to class presentations.

Maxwell Comment: I will be stealing these techniques and especially appreciate that each student can be accountable for presenting the group solution.

**Actuarial Math-terpiece Theater: **Greg Wanner of the University of Wisconsin at Madison has devised skits to help students understand/comprehend some multi-step derivative material currently tested on the SOA Exam FM. Students assume the roles of the appropriate parties and carry out steps in the
transaction using props that represent dividends, interest payments, stock certificates, margins, and etcetera.

Maxwell Comment: gwanner@bus.wisc.edu

**Challenge Flags: **Jim Trimble of the University of Connecticut gives each student a challenge flag (modeled after the National Football League rule). When the instructor makes an error, the first student to throw the challenge flag is awarded extra credit. Challenge flags promote a
comfortable environment for students to question the professor. Student feedback implies that students pay more attention in an attempt to catch Jim in error.

Maxwell Comments: Jim claims that most errors are made intentionally and that he is not a replacement official. If a student correctly challenges Jim, does she get another challenge opportunity?

**Oral Exams: **Diana Skrzydlo of the University of Waterloo made a presentation during an ARC session on actuarial education regarding her experience using oral exams to improve and assess student learning. Oral exams are used in many professions and are common in several
educational systems. This Socratic method of asking questions, listening to student responses, and adjusting subsequent questions allows the professor to quickly assess the level of student understanding. Some students express themselves better with their verbal communication acumen while others benefit
from practicing this skill. Diana has created a bank of oral exam questions and randomly generates a subset of five questions for each 15-minute student interview. While preparing for the oral exam, students have the additional opportunity to benefit from creating sample questions and practicing with each
other.

Participants in this ARC session were impressed by (or feared) the amount of preparation and time commitment needed to implement this assessment activity.

Maxwell Comment: I am excited to experiment with oral exams this semester.

**Fermi Frenzy: **Stephen Camilli of Actex suggested that students create Fermi problems (e.g., How many piano tuners are there in Chicago?) and lead class discussion and solution. These problems can both challenge the best students and increase the participation of the least able
students because of the inexact nature of approximation and the uncertainty of correctness.

**Partial Summary of Teaching
Techniques:**

- R.L. Moore method—Students are given a list of definitions and theorems which they are to prove and present in class, leading them through the subject material
- Socratic method—Professor Kingsfield from
*The Paperchase* - Inquiry Based Learning (IBL)
- Lecture
- Entertainment/engagement: Stories, Singing, Dancing,
**Games** - Pictures. Foldables.
- Hands on (field trips, making mistakes, drop you in France)
- Reading, Homework, Research, Self Study
- Quizzes, Tests, Essays, or Oral Exams. “Exams should be learning experiences.” — Les Tanner
- Student explain to peers
- Math Relays
- Trial and error
- Think-pair-share. Round robin. Gallery walk.
- Jigsaw (brainstorm then add to prior group)
- Hull method: Rotate groups, keep one person as captain
- Create homework or exam problems
- By example
- Feedback on student work
- Stepp method: Have students score work of others based upon rubric
- Challenge Flags
- “I do not teach anyone. I only provide the environment in which they can learn.” ― Albert Einstein
- The Janine Stallings method: Groups of three or four. Brief pre-class assignment, first day group presentation, second day create and play a game, then assign homework from SOA, textbook and from group created problems

*Mark M Maxwell, ASA, is clinical professor &
program director at the University of Texas at Austin in Austin, Texas. He can
be reached at maxwell@math.utexas.edu.*