TAR: a model for university instruction

I present here a simple idea for breaking down how I typically plan out courses.

I have three considerations: time (T), accessibility (A) and rigour (R).  Accessibility is the breadth of audience that I reach; basically, the number of students who will get value from a lecture or class.  Rigour is the completeness of the material.  Time is the time available to teach.

With this in mind, I propose the following.

1. Time is proportional to the product of accessibility and rigour (T = A*R)

Time increases as rigour and accessibility increase

2. Accessibility is proportional to time divided by rigour (A = T/R)

The idea here is that if infinite time were available, it would be possible to teach any student anything with as much rigour as required.

3. Rigour is proportional to time divided by accessibility (R = T/A)

For a fixed period of time, any increase in accessibility will reduce rigour.

With this in mind, we get the following visual model to help understand the relationship:

As a university professor I have some control over time, but not much.  I do have control over accessibility and rigour.  For courses in which I know the material must remain accessible to a broad audience, I generally have to lower rigour.   If a course needs to be rigorous, then I expect accessibility to decline.

While I have little control over classroom time, I have discovered that online tools can be useful for increasing the time of instruction.  Using readings, online quizzes, and video content, I can increase content without requiring more class time.  I use this extra time to delve into details I can’t cover in class–and add rigour.


This is all obvious to experienced instructors, however, my treatment here is a bit more rigorous than what one typically sees in discussions of teaching strategies.  Which, unfortunately, means I very likely lost your attention several paragraphs ago.