Mathematician; Executive Director, H-STAR Institute, Stanford; Author, The Man of Numbers: Fibonacci's Arithmetic Revolution
A Genuine Science Of Learning

The education field today is much like medicine was in the 19th century—a human practice, guided by intuition, experience, and occasionally inspiration. It took the development of modern biology and biochemistry in the early part of the 20th century to provide the solid underpinnings of today’s science of medicine.

To me—a mathematician who became interested in mathematics education in the second half of my career—it seems that we may at last be seeing the emergence of a genuine science of learning. Given the huge significance of education in human society, that would make it one of the most interesting and important of today’s science stories.

At the risk of raising the ire of many researchers, I should note that I am not basing my assessment on the rapid growth in educational neuroscience. You know, the kind of study where a subject is slid into an fMRI machine and asked to solve math puzzles. Those studies are valuable, but at the present stage, at best they provide at most tentative clues about how people learn, and little specific in terms of how to help people learn. (A good analogy would be trying to diagnose an engine fault in a car by moving a thermometer over the hood.) One day, educational neuroscience may provide a solid basis for education the way, say, the modern theory of genetics advanced medical practice. But not yet.

Rather, I think the emergence of a science of learning arises from the possibilities Internet technology brings to the familiar, experimental cognitive science approach.

The problem that has traditionally beset learning research has been its essential dependence on the individual teacher, which makes it near impossible to run the kinds of large scale, control group, intervention studies that are par-for-the-course in medicine. Classroom studies invariably end up as studies of the teacher as much as of the students, and often measure the effect of the students’ home environment rather than what goes on in the classroom.

For instance, news articles often cite the large number of successful people who as children attended a Montessori school, a figure hugely disproportionate to the relatively small number of such schools. Now, it may well be the case that the Montessori educational principles are good, but it’s also true that such schools are magnets for passionate, dedicated teachers and the pupils that attend them do so because they have parents who go out of their way to enroll their offspring in such a school, and already raise their children in a learning-rich home environment.

Internet technology offers an opportunity to carry out medical-research-like, large scale control group studies of classroom learning that can significantly mitigate the “teacher effect” and “home effect,” allowing useful studies of different educational techniques to be carried out. Provided you collect the right data, Big Data techniques can detect patterns that cut across the wide range of teacher-teacher and family-family variation, allowing useful educational conclusions to be drawn.

An important factor is that a sufficiently significant part of the actual learning is done in a digital environment, where every action can be captured. This is not easily achieved. The vast majority of educational software products operate around the edges of learning: providing the learner with information; asking questions and capturing their answers (in a machine-actionable, multiple-choice format); and handling course logistics with a learning management system.

What is missing is any insight into what is actually going on in the student’s mind—something that can be very different from what the evidence shows, as was dramatically illustrated for mathematics learning several decades ago by a study now famously referred to as “Benny’s Rules,” where a child who had aced a whole progressive battery of programmed learning cycles was found (by a lengthy, human–human working session) to have constructed an elaborate internal, rule-based “mathematics” that enabled him to pass all the tests with flying honors, but which was completely false, and bore no relation to actual mathematics.

But real-time, interactive software allows for much more than we have seen flooding out of tech hotbeds such as Silicon Valley. To date, some of the more effective uses from the viewpoint of running large-scale, comparative learning studies, have been by way of learning video games—so-called game-based learning. (It remains an open question how significant is the game element in terms of learning outcomes.)

In the case of elementary through middle school mathematics learning (the research I am familiar with), what has been discovered, by a number of teams, is that digital learning interventions of as little as ten minutes a day, over a course of as little as one month, can result in significant learning gains when measured by a standardized test—with improvements of as much as 20 percent in some key thinking skills.

That may sound like an educational magic pill. It almost certainly is not. It’s most likely an early sign that we know even less about learning than we thought we did.

For one thing, part of what is going on is that many earlier studies measured knowledge rather than thinking ability. The learning gains found in the studies I am referring to are not knowledge acquired or algorithmic procedures mastered, rather high-level problem solving ability.

What is exciting about these findings, is that in today’s information—and computation—rich environment, those very human problem-solving skills are the ones now at a premium.

Like any good science, and in particular any new science, this work has generated far more research questions than it has answered.

Indeed, it is too early to say it has answered any questions. Rather, as of now we have a scientifically sound method to conduct experiments at scale, some very suggestive early results, and a resulting long and growing list of research questions—all testable. Looks to me like we are about to see the final emergence of a genuine science of learning.