PDEs Course Design (Part 5): Inclusion and Excellence

This post is part of a series (previous parts 1, 2, 3, and 4) in which I am blogging my way through a new course on partial differential equations (PDEs) that I am about to teach… OMG… tomorrow since it’s past midnight now. What am I doing still blogging instead of getting ready for class?

Anyway, I’m guessing that most people reading my blog are positively disposed to the idea that we should work toward an educational system that provides all students with access to high-quality instruction, resources, expectations, and support so that we can achieve more equitable and excellent outcomes for all.

That last part is the part that we sometimes quibble over, even those who are in the “diversity camp”. Sometimes we pit inclusion and excellence against each other, when we should be spending more time figuring out ways to structure our system so that inclusion and excellence go hand in hand.

Here’s my crude illustration of the difference between these two perspectives.

inclusion and excellence

Diagram A on the left shows what happens when you try to create equitable outcomes without raising the bar for everyone: you end up improving outcomes for some and degrading them for others so it can seem like inclusion and excellence are pitted against each other. Diagram B on the right shows what happens when equity and excellence goals come into alignment. Everyone gets better outcomes. And though some might benefit more than others, the outcome is more equitable.

That’s why I’m really intrigued by studies describing interventions that improve outcomes for all and produce more equitable outcomes at the same time, like this, this, or this. (If you know of more studies like this, please let me know!)


During dinner last week, my dear friend Bill Thill (@roughlynormal) got me thinking about all of these issues. That led me to wonder, am I designing a class that pursues both equitable and excellent outcomes for all?

I’ve spent a few hours trying to sketch out a “theory of action” that links the different design elements of my course (proficiency assessments, active learning, video lectures, application project, etc.) to plausible student outcomes. I didn’t come up with much, but I assuaged myself by remembering that I was struggling to do something that the three studies linked above didn’t do either: they don’t really explain why students did better, they only observed that it happened.

So, I am about to start teaching this course with a strong reminder that it’s an experiment. I don’t know what the outcome will be, but I will try to be attentive and look for signs of trouble and success.


My conversation with Bill also reminded me that I also need to convey to my class this notion that inclusion and excellence don’t have to be at odds with each others. For example, inclusive teaching practices won’t result in a less rigorous class. I don’t intend to “cover” fewer topics than my predecessors did in previous versions of the class. In fact, my hope is for every student to achieve high levels of mathematical proficiency.

Here we go! Wheeeeeee!

One thought on “PDEs Course Design (Part 5): Inclusion and Excellence

  1. Great diagram. This is a key topic. Even putting aside equity (even your top students need to learn something!) you’d never be able to sustain approach A, because you’d lose the good will of your key allies: the top students. (And in the case of pre-college math, their parents.)

    I’m not very familiar with math ed research, but I recommend Peter Liljedahl’s work. See http://blog.mathedpage.org/2015/05/random-groups.html and http://blog.mathedpage.org/2015/05/the-thinking-classroom.html.

    Also see my posts on extending exposure (http://blog.mathedpage.org/2013/08/extending-exposure.html and follow the links therein.) It’s not research but it’s a practice honed over decades of teaching heterogeneous classes: lag homework, separate related topics, use multiple representations, make tests cumulative, “count” test corrections. Some less actionable thoughts are here: http://www.mathedpage.org/teaching/heterogeneous.pdf

    No idea if any of this will apply to your situation.

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