Message from NCSM President, Paul Gray
Generalizability
The word of the month for February was intentionality where we are conscious of being intentional about making decisions that are in the best interest of our teachers and students. Particularly with respect to equity. Equity is on my mind so much that it’s just become a part of how we do things in mathematics leadership. Sort of like problem solving…it’s not something we only do on Fridays but is a way of doing mathematics all the time.
April’s word of the month is generalizability. Research and better practices can tell us so much about powerful and effective mathematics teaching and learning. Every researcher learns in Research 101 that they should be cautious when taking something that they learn from one group of people and generalizing that finding to a larger more general group. That only works if the smaller group is representative of the larger group. That’s what I mean about generalizability. When it comes to research and better practices, are we wise consumers of this information?
Picture it. Houston, 1999. I’m sitting in a meeting with local schools participating in a regional school reform project. I teach at what is affectionately known as a comprehensive high school meaning that we have an attendance zone (i.e., we accept all students who reside in a particular geographic area) and have instructional programs that are designed to meet the needs of a variety of students. We served about 2,500 students, over 95% Black and brown, in grades 10-12. The year before, we built a separate 9th grade campus for our 1000 freshmen.
In this meeting, the presenter spoke about the wonderful things that another high school was doing that we should consider doing on other campuses. The school being showcased was a public school that was a “school of choice” (i.e., students must apply and be accepted to attend). It also served about 400 mostly white students in grades 9-12.
How in the heck are we supposed to apply ideas from one context to a completely different one? I just couldn’t shake the feeling that the presenter must’ve thought I just fell off the turnip truck.
I didn’t know it then, but I had encountered a generalizability problem. The presenter was telling us about some pretty snazzy ideas that teachers in one school were doing well. Where I got stuck was taking an idea from a small school of choice and applying it as-is to my classes in a large comprehensive school. Those terrific ideas and practices worked well in one setting that wasn’t representative of a larger more general population. Hence, they didn’t generalize to that larger population very well.
When considering research or better practices, you have to keep in mind the context and whether or not the idea will generalize to yours. It’s disingenuous to take something that research shows works for 5th grade students and use it to build a program for 10th grade students. It doesn’t generalize from 5th grade to 10th grade. Likewise, it’s disingenuous to take instructional strategies that are shown to work for a small, nonrepresentative population of students and generalize them to a large population.
I am all for learning from the experiences of others. And if someone is doing something that works well for their students, I want to learn from it and see how I might get it to work for my kids. But before I jump on that bandwagon, I’m going to sit with my colleagues and carefully consider the context where the idea comes from and how that compares to the context in which I am teaching. We’re going to think carefully about how well the idea generalizes to our district, school, and students.
Y’all be careful. We’ll touch base again in May just before I wrap up my 50th lap around the sun!
Paul
