By Nariankadu D. Shyamalkumar

Many universities in the past decade have invested in technologically well-equipped classrooms that facilitate active learning, and faculty across disciplines have successfully embraced instructional strategies that leverage upon such facilities. In such an environment, it behooves actuarial faculty to consider alternative pedagogical paradigms that incorporate peer instruction and an active learning environment to not only improve the learning experience of future actuaries but also to enhance their learning outcomes.

Flipped Classroom is an alternative teaching paradigm that reverses the terms of the location where activities related to learning occur. In the traditional approach, information delivery happens in the classroom and assimilation of concepts—through working on assignments—happens at home. Under
the flipped classroom approach, students are responsible for gaining the information at home and arriving in class ready to work on problems. The instructor can facilitate gaining of information at home by providing reading materials, instructional videos, etc. The instructor can encourage students to
come prepared for class by providing online-quizzes that students need to take before class starts. Some instructors have used responses on these quizzes to address any areas of difficulty in class, a strategy referred to as “just‑in‑time teaching.” The two main advantages of the *flip *are that it allows the instructor
to play a larger role in the assimilation process, and that it greatly facilitates guided peer learning.

Notably, flipped classroom approaches don’t require the use of technology, but computing is an indispensable tool to enhance conceptual understanding in actuarial science. An instructor could choose to flip only a part of his course—hence, each instructor can adopt their own variant of this paradigm, taking into account their audience, to maximize their role in the assimilation process and opportunities for guided peer learning.

My interest in changing my instructional style originated from my experience in teaching Life Contingencies, which I have taught for about 14 years. I have always reinforced the importance of recurrence relations, especially in relation to life insurance/pension computing on a spreadsheet platform. I would derive non-standard recurrence relations—for example, those related to variance of present value random variables—as well as work out a few examples using MS Excel in class. Despite being of the view that computing can be a very important tool in building insight, I was largely unsuccessful in raising the computing literacy of my actuarial students to a level where it could become this potent tool. This was even after planting some computational problems as part of my assignments; many students ignored these as they were deemed time consuming and perhaps less SOA exam oriented. So when I became aware of the TILE (Transform Interact Learn Engage) classrooms at the University of Iowa about three years back, I was very interested in trying a new strategy. However, in my opinion it is very important to have a set of specific goals before one embarks on trying an alternative methodology.

At Iowa, access to such classrooms requires one to complete a training course, and as part of this I got to listen to faculty from various disciplines who discussed their methodologies—what worked for them and what did not. This was very useful to me. I strongly recommend engaging with others on campus who have tried an alternative teaching methodology. This is where I was initially exposed to the paradigm of flipping a classroom. One thing that was apparent to me while listening to their experiences was that, with actuarial students predominantly being highly motivated and possessing a strong work ethic, many of the challenges that these faculty faced would not be faced by actuarial faculty—and my experience tells me now that I was right!

I twice taught Life Contingencies in this format—in the spring of 2014 and 2015. I taught the first of a two course Life Contingencies sequence, with three 50-minute lectures and a discussion. The classroom I used consists of circular tables (see http://tile.uiowa.edu/technology#L1022) seating nine students, with groups of three sharing a laptop computer. There are whiteboards on all the walls of the room for groups to discuss their ideas, flat screen TVs for students to project their laptops, and all of the instructional technology found in most classrooms these days. I allowed for self-formation of the groups, and there are arguments in support of this in pedagogical research. I started the course by recording instructional videos using a tablet PC and screen capture technology, and making them available on ICON (our course management site). Partly due to some technological challenges in video delivery across platforms (especially tablets, smart-phones, various browsers etc.) I moved away from it after a few weeks. Another important reason was a personal barrier that another faculty had mentioned—when making videos, one should be able to live with it not being perfect, otherwise the time it takes to record the video can quickly balloon. From then on, off‑class instructional support remained mainly through class notes, other documents and worksheets available on ICON.

In my course, I retained regular assignments instead of online quizzes. These assignments helped me gain a sense of students’ development of problem solving skills—skills akin to those tested on exam MLC. The questions in class were conceptual, and mostly involving the use of MS Excel. The first group work with in-class discussion involved a product description of a mortgage conversion to biweekly payments. The groups were asked to make a case as to why the business model works, what (if any) are the risks the business assumes, what cost and risks does the mortgagee assume, etc. This served both as a way to get students to recollect interest theory and as an icebreaker to get students interacting within their groups. Below are two examples of conceptual questions, both involving computing.

- Assuming that mortality rates are increasing beyond a certain age, what would be the behavior of the Actuarial Present Value (APV) of insurance and annuity products as a function of age? Can this be generalized, and what would be an argument to prove such a generalization? In particular, will this behavior transfer to the variance of the Present Value of the benefits paid? What would be a converse and would it hold true?
- Overlap theory is an argument that has been used by opponents of sex distinct mortality (see a study note titled
*U.S. Gender Discrimination Regulations As They Affect Financial Security Programs*, by Patricia L. Scahill, FSA). Given two sets of mortality rates, calculate the overlap. What do 100% overlap and zero overlap mean? What are the typical values of inter-risk class overlap, and how do these compare to intra-risk class but across age overlaps? How would you argue against the overlap theory as an actuary? A recent article for assigned reading is "The Actuarial Argument for Gender-Distinct LTC*Long-Term Care News*, April 2014, pg. 20-21.

Both times I taught using the above approach, it was an enjoyable and rewarding experience for me. And judging by comments from students and anonymous course‑end evaluations, I believe that it was an enjoyable experience for the students as well. This course is taken by juniors in the spring semester and for many, just before their first summer internships. Many students have told me that in-class computing experience substantially helped them during their internships, and recently an international graduate student told me of a similar experience interning back in China.

This semester, I am teaching two courses dealing with the material for Exam C, and I am teaching both of these using the above approach. It is very enjoyable to teach using R, a popular open-source statistical software environment. In fact, there is a ten-minute gap between the two
classes (as they are scheduled back to back), and the students unanimously voted for me to use this time as well. I am using a similar classroom, the teaching style is less flipped, and the software is R instead of MS Excel. On a side note, I hope to introduce students to parallel programming before the end
of the course as well, so I will focus on providing some of the conceptual problems that we did in the class so far. Below, I refer to *Loss Models *by Klugman, Panjer and Willmot, fourth edition.

- What do we desire from a measure of skewness? Can we construct alternate measures of skewness, and how do they compare with the standard measure? Why should we expect the skewness of a gamma distribution to be a decreasing function of the shape parameter?
- After stating a precise version of Theorem 3.7, the students were asked, through simulation, to look at a class of counterexamples where the convergence to normality fails to take hold.
- That a gamma mixture of exponentials (example 5.4) is a Pareto and a gamma mixture of a Poisson is a negative-binomial have a common underlying argument using the memoryless property (Poisson process). The groups simulated a Poisson process to see this happening, apart from thinking it through probabilistically.
- The students gained insight into kernel density estimation using various kernels, bandwidths, and distributions generating the sample. Also, they were asked to show that consistency fails with non-diminishing bandwidths, using the law of large numbers and simulation.
- We interactively showed—using the law of large numbers—that a four parameter transformed gamma can be made to converge to a transformed gamma. Also, we showed using the central limit theorem that a transformed gamma can be made to converge to a log-normal. These lead naturally to the required conditions, and simulations help them see the speed at which these convergences take hold.

While I do not provide any statistics to test for improved learning outcomes, such data can be found in the literature (even though they would not be from teaching to actuarial students). Eric Mazur is a Harvard physics professor who has written much about peer learning, and I highly recommend viewing a video of his lecture on the peer learning methodology. He has statistics supporting its efficacy as well.

While I adopt a teaching style somewhere between traditional and fully flipped, where I depart from the traditional approach is by engaging students in active learning and guided peer learning in class and by playing a more direct role in assimilation. The examples of conceptual questions hopefully give an idea of what can be attained by a tweak away from the traditional approach. I very much enjoy the experience, and I believe that so do most of the students!

Nariankadu D. Shyamalkumar, ASA, Ph.D., is assistant professor at the University of Iowa in Iowa City. He can be reached at shyamal-kumar@uiowa.edu.