Vicki Zhang

image: Vicki Zhang headshot

COURSE: ACT247 Introduction to Life Contingency Models
DEPARTMENT: Statistical Sciences and Actuarial Science

This second-year, large-classroom course is the first in a series of three courses on life contingency models, which are crucial for actuarial science students who aspire to become actuaries in the life insurance industry. It is a required core course for all actuarial major and specialist students. This course is highly mathematical and perhaps the first opportunity for students to apply the knowledge from various courses they have taken in the first year (probability theory, statistics, calculus) in the context of life insurance. The course will cover survival distributions, life tables, and pricing insurance with both continuous and discrete distributions for mortality assumption. It also lays the important foundation for advanced studies in life contingency models in the third and fourth year.

As this course is a required core course and students will need to achieve a minimum grade in order to continue their study in the actuarial science program, students in the past were frequently overwhelmed, stressed and even burnt-out. The traditional course material and structure did not help either. There are scores of small mathematical topics that students need to master and those topics were delivered sequentially. Although there is an internal logic to much of those topics and to some extent, the order of delivery, the logic remained purely mathematical and non-intuitive, especially for entry-level students.

Moreover, in general the topics in this core course are among the least popular with second year students, who are primarily nineteen or twenty years of age, and may have little motivation in learning the mortality models, especially through math question drilling. Students from the past had expressed to me that they found the course material dry and irrelevant to their lives. Traditionally, course assessments were multiple-choice exams, and students routinely resorted to rote learning to pass the exams.

On a personal note, I have taught this course once, during my first year of teaching at UofT. Although new and inexperienced on the job, I made a concerted effort to shift students’ focus from memorizing materials to pass multiple-choice exams, to genuinely understanding the theories and applications. I spent numerous hours writing new questions that I thought would better assess students’ true level of conceptual understanding, compared to the traditional test bank I was given. The end result of my effort was mixed. I believe my exams did a good job differentiating between students who truly “got it” (i.e. being able to clearly explain the myriad of concepts and the rationale of formulas and draw connections among them) and those who were only good at rote learning and regurgitating formulas. However, the average class grade was lower than previous years and as a result, many students complained about my exams. As I reflected on that experience, I recognized that although I put much effort into writing quality exam questions, I did not do enough to challenge the way the materials were ordered and taught. Student energy in the classroom was low as usual, and that is what I want to focus on this time around.

My lecture redesign focuses on two main areas: what I call “narrative mathematics” and using mix-media to engage students in and out of the classroom. I drew inspiration from arts-based and narrative-based pedagogy in fields like medicine as well as the gamification idea in secondary education and higher education. I created an overarching story script which presents itself as a central character’s obstacle course that ties together the numerous mathematical concepts covered in this course. In many ways, it is similar to a “concept map” pedagogical approach but with a crafted storyline and character building. To reflect the predominantly international profile of our student body, I chose to create a central character who is an Asian-Canadian woman, an immigrants’ child, who at times feels caught in between worlds. A small sample of students who had a preview of this script had told me that they could relate to this character at a personal level. The chief goal is to provide students with a clear sense of relevance and an intrinsic purpose of learning, namely, to assist a character who they can relate to and who is in need of expertise acquired in this course. Another key objective is to provide students with an intuitive and memorable concept map that links a large number of mathematical concepts that would seem daunting to lower-level undergraduate students.

To help deliver the narrative I have written, I contacted UofT’s Digital Dramaturgy Lab (DDL). We will be developing a mix of video clips, podcasts, still photos to tell the sub-stories in the big narrative. The mix media platform was chosen to recognize that students have distinctively different learning styles – even more pronounced in a large classroom setting – and instructors need to be conscientious about presenting the materials in ways that accommodate different students (“a choreography of attention”). In-class response system (PollEverywhere) as well as a course website will be used to allow active instructor-student interactions throughout the course.

Along with lecture redesign, the learning and assessment activities are also redesigned to promote active, student-centered learning, as well as combining formative and summative assessments. Instead of the traditional assessments for this course – multiple choice, numeric question exams, I will add a frequent quiz component, as well as in-class Q&As through the PollEverywhere platform. I will also ask students to apply their newfound knowledge in mini-case studies where they need to use Excel for calculations and write a brief report for their findings. These bite-sized Excel-integrated mini-assessments are part of the scaffolding process that will lead to their final project where students will analyze and recommend a real life insurance policy for the central character in the story. Students are encouraged to write for the general public in their report, and I plan on curating some of the best analysis papers on the course website. In terms of summative assessment (i.e. mid-term and final), I will include written answer questions that can test students’ conceptual understanding of the material in a more direct way (e.g. to derive a formula from scratch using first-principle reasoning). This will help students focus on meaningful concepts in their learning, in order to battle a long-held emphasis on pattern recognition and rote learning for the purpose of passing multiple-choice exams.

The CDI has offered me a wide range of ideas and inspiration. Although I was aware of active learning before coming to the CDI, the various activities modeled during the CDI really drove home to me the importance of always putting students in the center of learning during my course design. That is why instead of lecturing one math topic at a time, I wanted to create a narrative-based pedagogy that students can relate to personally. That is why I want to help students find an intrinsic purpose in learning the course materials (e.g. helping the central character through her challenges, write for the general audience in the final report, etc.). The CDI also taught me to always start “backwards”, from the “big ideas”, the core goals of the course. I was then able to cluster concepts and sub-ideas around the core goals in building my narrative.

During assessment design, I learned from the CDI the importance of combining frequent, formative assessments and summative ones. CDI’s student-centered approach again shifted my focus from testing knowledge recall to helping students succeed in higher level learning – through scaffolding all the main assessment components (e.g. small quizzes and in-class responses leading to formal exams, mini-cases leading to final project).

I have been an avid participant at many CTSI’s workshops over the years and I have always learned something new at each of the workshops. What’s equally important was that I met many like-minded, passionate educators through these gatherings. From those interactions, I learned how others across the university use various teaching strategies in their classrooms and even received personal help from various colleagues in developing grading rubrics and managing project assignments. I found CTSI a welcoming and much-needed “watering hole” for peer-based learning and support across campus. I have also consulted many written and video materials under the Teaching Support menu on CTSI’s website. There is a great collection of tips and strategies there, written by experienced educators, many of whom are teaching academy members. It is a wonderful forum for a relatively new faculty member like myself to pick the brains of acclaimed educators. I borrowed many of the techniques I learned in those pages – concept map, virtual office hour, using rubrics, lecturing style, etc – in my own classroom.

I am still in the process of finalizing the narrative “script” for this course. The media production is also ongoing. I will give the first redesigned version of the course in Winter 2017 semester. How to help TAs transition to the new design will be my next challenge. I will need to clearly communicate to them my teaching philosophy, my focus on conceptual understanding and purpose of learning, and the grading rubrics for case studies and final project. I still need to design the activities TAs may employ in their tutorials and those activities will have to be consistent with the rest of the course redesign.