A few days ago, CFED (Corporation for Enterprise Development) and the Institute for Policy Studies recently published a report entitled The Ever-Growing Gap: Without Change, African-American and Latino Families Won’t Match White Wealth for Centuries. It’s a worth-while read, both illuminating and depressing at the same time. The authors argue that the growing wealth divide in our nation is not an accident but the result of past and present policies that widened the difference between the wealth of White households and households of color. They then advocate for an audit of current Federal policies to determine their impact on the racial wealth divide.

This got me thinking about teaching and equity. What can I do in the context of where I work and teach? I believe that the racial gap in educational outcomes (in all forms: degree attainment, participation in advanced courses, productive disposition toward learning mathematics, learning outcomes, test scores) is not an accident but the result of past and present injustice. The fact that there is a growing wealth divide also means that there are deep divides in educational outcomes along class lines as well. And of course, there are clear correlations between class and race in the United States.

At the same time, I am also moved by Rochelle Gutiérrez’s (and others) writings about our gap-gazing fetish in education. (See this and this.) We need to walk a fine line of advocating for more equitable outcomes but at the same time avoid privileging the performance of White and Asian students as the standard to aspire to, propagating a culture of deficit when referring to other students of color, and having only school-based conceptions of what it means to do mathematics.

All of these things were swirling in my head and that got my wondering…

Imagine if instructors were equity-minded and routinely made instructional decisions taking into account the potential impact of those decisions on any patterns of difference in educational outcomes across groups of students. Imagine what would happen if measures of educational outcome differences were a regular part of all teaching evaluations at your institution.

What would it take to get there? In this post I am mostly thinking about how this would play out in my own teaching. That seems like the natural place to start.

I would need a range of measures of educational outcomes (not necessarily standardized tests) that I could use a the beginning and end of each of our courses. These could include measures of disposition toward mathematics, metacognitive skills, problem-solving skills, or pre-/post-assessments of mathematics content knowledge and skills. I could then use these measures to look for preexisting patterns of difference in outcomes for students entering a course, and the same or similar measures used at the end of course could show whether those patterns of difference were bigger, smaller, or stayed the same. Or, I could use the same instruments for different courses over time to so whether there are any systematic patterns. All of our instructional decisions could then be analyzed over time so as to reveal the instructional strategies that hit that sweet spot where educational outcomes are high and differences between groups of students is lowered or even eliminated.

Here are three paired histograms showing the distribution of men and women’s performance in my introductory differential equations course over the last three years. The course content and assessment stayed almost exactly the same, though between 2015 and 2016 we went from a flipped/unflipped experimental design to a uniform treatment (a hybrid course) for all students. (For more details see http://invertedclassroomstudy.g.hmc.edu.)

What do these data reveal? I’m not sure. The differences in means are not statistically significant, but I wonder whether there is more that the shapes of the distributions can reveal. The means are heavily influenced by students in the tail of the distribution. It seems that the mode for men is the same as or slightly higher than that for women in each case. That doesn’t seem good to me. A similar analysis for the pre-test assessment scores shows no difference in performance between men and women going into the course. My conclusions are that (1) I didn’t do any harm (whew!) in creating any gender difference through my course, and (2) moving to a hybrid design had no impact on gender equality in my courses.

(Note #1: I did a really bad thing by manually coding each student as male or female based on what I knew of them instead using self-report data. I classified any transgender students according to their gender expression at the time of the course. Note #2: I didn’t have access to the metacognitive and attitudinal survey data that was collected in these courses. That would also be interesting to analyze in this way. The assessment that was used here consisted of five multi-part questions that address both computational skills, conceptual understanding, and ability to apply knowledge to model physical situations.)

Some practical problems to consider: (1) Norm-referenced assessments won’t work here and we would need criterion-referenced assessments instead. We want to make sure to encourage a growth mindset and to give students clear learning targets. (2) In most cases there are too few students in my courses to allow for meaningful statistical analysis. And there are all kinds of privacy and FERPA regulations to worry about if I want to get detailed demographic information about my students. (3) Sometimes we over-assess our students. How do we avoid that? (4) If I am at all a decent teacher and I use the same instrument as pre- and post-assessment of content knowledge, I should expect the distribution to narrow after a whole course-full of learning. That means that unless I have access to a good measure of prior knowledge, the comparison can only be made from course to course. (5) If I only use instruments once per course, results would be difficult to compare across courses unless there were some way to know that the groups of students are consistent in meaningful ways over time.

Clearly there a lot of problems to the ideas I’ve mentioned above, which is probably why people don’t do this more regularly. And all of this takes time and effort to do. (The analysis that I did above took me a few hours.) The key is to find ways to reduce the barriers so that it becomes easier to gather the right kinds of data and use those data to promote equity in learning. I want to get to a place where we can make data-driven decisions in pursuit of equity-promoting instructional decisions and practices. Is this a good idea? And if so, what tools, practices, and systems do we need to develop to get there? I welcome your thoughts!