Online Math Numbers at Waterloo, and Comparative Judgments as a Teaching Strategy — Tonya Elliott, CEL

math equationOnline Math Numbers

If you weren’t already aware, here are a few numbers about online math at the University of Waterloo:

  • The Math Faculty has been offering fully online courses since Fall 2003 and, since that time, has offered 55 unique online courses to more than 21,000 students
  • The Centre for Education in Mathematics and Computing (CEMC), with support from the Centre for Extended Learning (CEL) and local software company Maplesoft, was the first group on campus to release a large set of open educational resources (OERs). Called CEMC courseware, the OERs include lessons, interactive worksheets, and unlimited opportunities for students to practice skills and receive feedback. At the time of this post, the resources have received over 1.8 million hits from 130,000 unique users in 181 different countries.
  • In 2015, the Canadian Network for Innovation and Excellence (CNIE) recognized CEMC, CEL, and Maplesoft for their OERs through an Award of Excellence and Innovation.
  • The Master for Mathematics for Teachers (MMT) program has the highest enrolment of all the fully online Masters programs offered at the University of Waterloo. MMT and CEL staff who work on the program were one of three teams from Waterloo who won a 2016 Canadian Association for University Continuing Education program award.
  • Maplesoft is using a focus group from Math, CEL, and CTE to develop a new authoring environment that will specifically target the needs of online STEM course authors. It is anticipated that this tool will be released in early 2017 and, over time, should save development costs by 50%.
  • The Math Faculty, together with the Provost’s office, has dedicated $1.2 Million over the next three years for additional work on online projects; over 90 course development slots allocated by CEL have already been filled.

These numbers are some of the reasons Waterloo is considered a leader in the area of online math education.

Comparative Judgments

From June 19 – 22, a small group from Waterloo and I joined an international team of mathematics educators to discuss digital open mathematics education (DOME) at the Field’s Institute in Toronto. Lots of great discussions happened including opportunities and limitations of automated STEM assessment tools, integrity-related concerns, and practical challenges like lowering the bar so that implementing fully online initiatives isn’t the “heroic efforts” for Faculty it’s often viewed as being today. Of all the discussion topics, however, the one that got me most excited – and that my brain has returned to a few times in the month since the conference – is using Comparative Judgement (CJ) in online math courses.

colour shadesThe notion behind CJ is that we are better at making comparisons than we are at making holistic judgments, and this includes judgments using a pre-determined marking scheme.  It doesn’t apply to all types of assessments, but take this test on colour shades to see an example of how using comparisons instead of holistic rankings makes a lot of sense. Proof writing and problem solving may also lend themselves well to CJ and three journal articles are listed at the end of this blog for those who would like to read more.

Here are some of the questions I’ve been pondering:

  • Are there questions we aren’t asking students because we can’t easily “measure” the quality of their responses using traditional grading techniques? How much/when could CJ improve the design of our assessments?
    • Example: Could CJ, combined with an online CJ tool similar to No More Marking, be used by students in algebra courses as a low-stakes peer assessment activity so students could see how different proofs compare to one another? Perhaps awarding bonus credit to students whose proofs were rated in the top X%.
  • Which Waterloo courses would see increases in reliability and validity if graders used CJ instead of traditional marking practices?
  • How much efficiency could Waterloo departments save if high-enrolment courses used CJ techniques instead of marking schemes to grade exam questions or entire exams? Could CEMC save resources while using CJ to do their yearly contest marking?

I don’t have answers to any of these questions yet, but my brain is definitely “on” and thinking about them. I encourage you to read the articles referenced below and send me an email (  If you like the idea of CJ, too, or have questions about anything I’ve written.  If you have questions about Waterloo’s online math initiatives, you’re welcome to email me or Steve Furino.


Jones, I., & Inglis, M. (2015). The problem of assessing problem solving: can comparative judgement help? Educational Studies in Mathematics, 89, 3, pp. 337 – 355.

Jones, I., Swan, M., & Pollitt, A. (2014). Assessing mathematical problem solving using comparative judgement. International Journal of Science and Mathematics Education, 13, pp. 151–177.

Pollitt, A. (2012). The method of Adaptive Comparative Judgement. Assessment in Education: Principles, Policy, & Practice. 19, 3, pp. 281 – 300.


Blackboard image courtesy of AJC1.




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Tonya Elliott

Tonya Elliott

In her role as an Online Learning Consultant (OLC) with the Centre for Extended Learning (CEL), Tonya Elliott provides instructional design and project management support to faculty and staff who wish to design, develop, and/or deliver fully online courses, programs, and resources. The majority of her projects are with members of the Faculty of Mathematics; however, she really enjoys working on a variety of online projects from faculty and staff from all areas of campus.

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