CURRICULUM, DELIVERY, ASSESSMENT
I have a long history of interest in new developments in delivery and assessment. As a PhD student I was involved in “calculus reform”, co-developing interactive computer algebra system (Mathematica) notebooks for student assignments. At the University of Auckland I was a member of the Academic Committee involved in formalizing learning outcomes and overall curriculum for the algorithms courses. I have developed lecture notes and syllabus from scratch for several courses. I taught sections of about 50 lecture courses at University of Auckland since 2002. At UMass (Math & Stat) since Fall 2019 I taught Mathematical Writing (4 times), Mathematical Modeling, and a graduate math course, designing my offerings from the ground up. In that department, class sections are all around 30 students, but at Auckland I frequently dealt with 300 students in one lecture. I prefer the smaller classes, but developed a lot of skill in dealing with the larger ones. Since switching to CS at UMass, I have twice taught a large sophomore probability course for CS majors, taught discrete math for non-majors, and am currently teaching an upper-level combinatorics course.
Video lectures. In 2018-19 I planned, performed and edited over 20 video lectures for an algorithms and data structures course (see https://www.youtube.com/c/MarkCWilson). I used them as part of a flipped classroom approach when teaching in the first half of 2019. Student responses showed that the lectures were popular (but my plan of replacing traditional lectures with them was less popular – students seem to see them as a useful extra especially for revision). They have received over 42000 views so far and are being used by people worldwide.
Undergraduate research. While in Auckland I supervised honors projects and summer research projects by 8 UoA students, along with REU-style projects by visiting undergraduates from Union College and IIT Kharagpur. This was not usual in the traditional research university department at UoA. I have since supervised two REU projects at UMass. Three of my summer students have gone on to complete a PhD in computer science or mathematics (Oxford, Queensland, Auckland) and four projects led directly to CS conference papers. The other students are all working in software-related industries. A main reason for the diversification of research interests over my career has been to find topics that are more accessible to students. In 2024-25 I am supervising 4 undergraduate minority students in CS through the ERSP.
Textbook. With M. Dinneen and G. Gimelfarb, I wrote in 2004 the 260-page textbook for COMPSCI220 at UoA (subsequently used also as a supplementary reference for several other COMPSCI and SOFTENG courses), “Introduction to Algorithms, Data Structures and Formal Languages” (Pearson NZ, ISBN 1-877258-79-2). Specifically, I chose the publisher and conducted all negotiations; organized the writing overall and edited and wrote two of the three main sections; contributed equally to the second, substantially revised, edition published in 2009; negotiated the reversion of rights from the publisher, so we could produce a free e-book version from 2013; maintained an online up-to-date list of errata and gave students incentives to report new errors.
Assessment. After much reflection on consistency of marking and grading, in 2007 I introduced multiple choice assessment for several courses, and this included overseeing development of multiple choice examination preparation software (written by then PhD-student Christof Lutteroth) which was used by at least 5 departmental colleagues. This frees time to allow teaching staff to concentrate on developing a high-quality question bank focused on learning objectives. I updated my own question bank every semester and shared it with UoA colleagues.
Automarker. With M.Dinneen I oversaw development from scratch of the “automarker” submission/feedback/marking system for programming assignments. In this major ongoing project, I played a major role in supervising the hired programmers, discussing required features; successfully applied with colleagues for two local Teaching Improvement Grants to develop the system; assisted several staff members to use the system, and was the main conduit for user feedback from faculty.
We gradually developed the system into a much more user-friendly and robust piece of software, which has been used in at least 6 courses so far, by at least 8 lecturing colleagues. We surveyed students on their user experience. The system gives feedback on common deficiencies, such as compiler errors, runtime errors, and resource inefficiency, allows students to refine their program by repeated submission, and can also be used for grading. It allows for personalized feedback and also whole-class competition via scoreboards, giving students a taste of the environment of a programming competition. The project started in 2008 and improvements are still being made, although I am no longer associated with it.
TEACHING PHILOSOPHY
The diversification of student motivations, backgrounds, and abilities that has taken place in the last few decades makes university teaching ever more challenging. Despite this, my key goals in teaching have not changed much since I began to teach. I see my role mainly as a coach, guiding and motivating students to carry out research themselves, and to set their own goals for performance. I believe in using technology and educational research to make teaching more efficient and effective. Below I expand on my main goals.
Help develop a research attitude in all students
Everything that is now smoothly presented in textbooks was at some time in the past newly discovered and exciting, at the forefront of research. In order to assimilate a concept, students must follow much the same process of discovery that previous researchers have done (albeit accelerated and shorn of most of the dead ends and false starts). Thus it is an obvious goal to develop the “research attitude” in students.
I aim to assist students in posing their own questions and answering them as far as practical. Of course, in lower level courses I will usually know the answer, but I see no great dividing line between beginners and professional researchers. There should be a difference in knowledge but not much of a difference in the basic methods. Practice at analysing complex problems, thinking logically and systematically, generating and testing hypotheses, and communicating one’s findings clearly to one’s peers are very useful for all students no matter what their future goals.
Unfortunately it is easy to slip into the habit of teaching (and learning) by lazily appealing to authority and memorization rather than adopting the correct attitude. The process of acquiring new knowledge is not smooth, as we all know, but too often new ideas are presented to students in a way that makes them appear soporifically inevitable. A quotation from Paul Halmos expresses how I want students to learn (and how I want to teach), and what I hope that they will themselves want after taking my class:
Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
As far as practical teaching goes, I don’t go as far as running a class completely along Socratic lines – this has been tried by some but seems to be practical only for very small classes of very strong students. I do try to include in all assignments some element of discovery, where the answer to the question is not clear and there are many ways to approach it. I try in lectures to ask a lot of questions, and restrain myself from answering them too quickly (this is one of my hardest jobs as a lecturer).
Create a safe learning environment for all students
In the last few years, issues such as micro-aggressions and more overt discrimination have become increasingly recognized. I joined a discussion group at UMass on antiracist teaching practices, and am trying to learn more about the kinds of barriers to learning that someone with my background has not faced, but which do affect a substantial number of students. I aim for a relaxed classroom atmosphere. I use flexible grading practices that allow students to present their best “k out of n” assessments for the final grade. This reduces unhealthy anxiety over grades and students know they do not need to worry about missing an assignment owing to illness, for example. I aim to create a classroom space and community where all students participate. To model for students the fact that everyone makes mistakes and the aim is to learn from them, I intend to try live coding and other forms of presentation where I need to work out answers on the fly.
Provide opportunities for the best students to excel
Healthy competition is a powerful motivating force in learning, as I can attest from personal experience. The most able students naturally seek each other out in any class, and usually enjoy a friendly rivalry. It is my job to ensure that these instincts are expressed in a positive way. Students who delight in learning (and showing off their knowledge) make teaching really worthwhile for me — without them, I would do a competent job, but without any passion. I try to allow for a component in all assignments, tests, and even lectures in which the most able students can show what they can do. For example in CS courses involving programming I have often asked students to write a program to solve a particular problem – bonuses are achieved by beating the performance of my own answer to the question (which happens surprisingly often).
Ensure that every student achieves something worthwhile in the class
Motivations and abilities of students vary widely. Some students have a distinct lack of intensity in the way they approach their study, and some have poor study skills and inefficient learning styles (I certainly do not believe that all learning styles are equally valid in every course).
I aim to challenge them very early in the course to clarify their thinking about their learning as related to the course. This includes their performance goals, learning objectives and styles, and misconceptions of the subject material. I aim still to convince these less excited students of the benefits of working in research mode. But in any case, I want every student to learn at least one thing well, rather than have a confused mass of knowledge on a variety of disconnected topics. I try to get them to clarify what their learning goals actually are in the course and then achieve to the best of their ability.
Teaching theoretical/mathematical courses as I mostly have in my career so far poses some challenges. To quote Claude Chevalley, “mathematics is to some extent an exercise in rectitude of thought, of which it would be futile to disguise the austerity”. It is the instructor’s job to soften the “austerity” as much as possible. I try to communicate my enjoyment of the subject to the students, while maintaining good humour and not trivializing the difficulties they face.
In practical teaching terms, this means using simple but key motivating examples, being available for discussion (I often have an open door policy for office hours), balancing the competitive and nurturing impulses of me and my students, and trying very hard to practice what I preach at all times. All assignments, tests and exams have some routine, confidence-building component. I have worked hard on aligning my assessment more clearly to the learning objectives of the course, and on ensuring a good range of difficulty in questions. Depending on resources, I am considering trialing some sort of course delivery and assessment that encourages students to set their own goals, and take more responsibility for their own learning. My own experience as a student with a “Keller plan” course was positive.
Use technology and educational research to teach more efficiently and effectively
I have always been interested in using advances in technology or educational research to approach as closely as possible the ideal of personalized instruction by an experienced tutor for every student. Resource constraints have made this very difficult in the past. In recent years such ideas as clickers, flipped classrooms, and student peer review have been widely discussed. I have followed this discussion with interest but without being fully convinced, although I have tried a flipped classroom approach. I have still mostly concentrated on modelling good technique and habits of thought, communicated via traditional lectures supplemented by high quality lecture notes. I was an enthusiastic adopter of the PeerWise (developed at UoA and now used worldwide) multiple choice question system as a tool for student learning.
Formal listing of learning objectives and designing assessments that reflect these objectives (constructive alignment) can make a large improvement in many courses. I have been trying to upskill as a teacher by learning about this and intend to continue this process. I attend teaching-related local workshops every year.