Monday, October 25, 2010

Phantom Variables in Education - class size, for example

There is no doubt that one-to-one tutelage with a highly qualified instructor is a very effective way to learn something difficult. After all, there is no reason to believe that Plato’s education via the Socratic method took place among the rabble of the agora. When it comes time for graduate students to become polished researchers, they find one person to sponsor their dissertation and take leave of group classes until the hard work is finally done.

There is also very little doubt that those very small, prestigious schools with exalted reputations frequently tout those small class sizes associated with fine results. The question becomes, is it actually the size of the class that makes the educational experience high-quality? If it is the size of the class that matters, then why do efforts to reduce mean class size for larger schools tends not to impact test scores and metrics used to estimate disciplinary troubles?

My answer is that class SIZE is a phantom variable, one that is easy to measure but is irrelevant to most educational questions. Because counting the number of people in a room is easy to do, it is frequently done. It’s a metric that is used as a stand-in for educational quality, as a substitute for something more meaningful, something to do with the “amount of attention” each teacher can give to each student.

I have another “favorite” phantom variable, another common psychometric and educational distraction. It’s INSTRUCTIONAL TIME. Number of school days available, length of the school day, minutes assigned to each subject; these, too, are easy to measure and also substitute for something more meaningful, something to do with the “amount of instruction” the children can receive in total, or on each subject in the curriculum.

My contention is that, barring unsafe or ridiculous circumstances, class size can seldom be an actual barrier to instruction (notable exceptions being situations such as one teacher overseeing hundreds of students or children packed into spaces so that fire codes are violated); similarly, neither are questions of instructional time (except in exigencies such as those brought on by natural disasters, such as when Hurricane Katrina dramatically shortened the school year for children along the Gulf Coast).

What actually matters, and what is seldom measured directly, is HOW MUCH ACTUAL INSTRUCTION learners receive. Not hypothetical “attention” as a division of students-per-adult; not “time per subject matter.” How many interactions with the teacher occur? How many interactions with instructional materials occur? This is a very old-fashioned idea in education and in industry – it has variously been called “total quality management” and “behaviorism” and “evidence-based practice.”

What it looks like is smart students, working hard. They are engaged in “ASR” or active student responding. In a group lesson, the students may be participating simultaneously using choral responding, response cards, or guided notes. Individual students may be working at a computer that has a program that gives them many response opportunities with feedback; or they may be receiving tutoring from a peer or from an adult (e.g., classwide peer tutoring).

Are all of these tactics easier to do in a classroom with a favorable student-to-teacher ratio? Absolutely. Will the effectiveness of any instructional tactic that works be enhanced with additional time to deliver more of an effective educational practice? Certainly. But is the ACTUAL variable of interest the size of the class or the amount of time? Not the way I see it. The ACTUAL variable of interest is WHAT IS BEING DONE in that class, regardless of “for how long?” or “with how many students present?”

Perhaps the studies that fail to show systematic effects of reducing class size or increasing instructional time, have problems with their outcome variables because they failed to take into control for variability in WHAT THE TEACHERS ARE DOING in those classes of varying size and duration.

Archimedes famously said: “Give me a place to stand and a lever long enough and I will move the world.” 220 BC

I think I know where I stand on measurement issues and research questions. What I don’t have is a lever (a pry-bar?) to move the world of educational administration & policy, so that the measured outcomes are variables that are actually relevant dimensions of the phenomena of interest. That Eureka moment has still not come, for me, or for American education.

Heward, W. L. (1994). Three "low-tech" strategies for increasing the frequency of Active Student Responding.


  1. We agree that absolute number of students is of questionable importance when measuring effectiveness. We've always felt, for example, that we can teach a class of 35 as effectively as a class of 25. Of course, what happens in those prestigious private schools with small student-teacher ratios is that the schools are probably wealthy enough to provide all kinds of other goodies as well as more "individualized attention": Up-to-date technology, nutritious lunches, full-body massages (OK, maybe not that last one). Conversely, schools in poorer neighborhoods may be overwhelmed by students (and also staffed by the least experienced teachers). Class size may impact education--the question is, What impacts class size?

  2. Wonder what happens when a public school actually does start offering full body massages? Is the best metric "time to Supreme Court filing" or "time to firing?"