The Benefits of Learning the Hard Way – And How DCI Can Help

From time to time this page will post newsworthy items that are indirectly related to DCI, but nonetheless may be of sufficient interest to readers to know about. This post falls in that category.

So, in that spirit I recount here the following lesson about learning from Range by journalist David Epstein that I have been reading – one that may resonate with you, and if it does, pass it along to your children or grandchildren.

Epstein reports a study of Air Force Academy cadets who all had to take basic a calculus I course, were assigned randomly over the course of a decade to different instructors, each of whom used the same texts and exams (which left no discretion for teacher intervention), and who were all subject to the same post-course evaluation forms. The same process was repeated with the next level Calculus II course and with more advanced math, science, and engineering courses. The economists who conducted the study confirmed that the standardized tests scores and high school grades were spread evenly across sections, ruling out any variation in the quality of the students by instructor.

The point of the study was to determine not only whether there consistently were better teachers – which, of course, there were – but more importantly, whether the quality of the teachers in the initial course made a difference to the students’ later academic performance in the higher- level courses. Common sense intuition suggests “of course” it would make a difference: the stronger the foundation of learning one has at an entry level the better the performance in more difficult courses.

Now the surprise. It turns out the students who took Calculus I from the more highly rated instructors did worse in subsequent, higher-level courses than the students who took Calculus I from the lesser rated instructors. The economists advanced a reason for this: that the students’ ratings were based solely or primarily on how well they performed in the short-run, namely during that Calculus I course, and were not giving sufficient credit to the lesser-rated teachers in Calculus I who used “deep learning” methods that required the students to go beyond rote calculations and apply what they were learning to real world problems. That is why the students who were effectively required to struggle more in the first course did better in subsequent courses.

This finding was strengthened by the fact that students whose instructors who were more experienced, but who nevertheless received lower immediate evaluations than the less experienced, but more highly rated instructors, did better in their subsequent courses. The more experienced teachers were less likely to teach mechanistically than the less experienced teachers.

Epstein cites other studies that confirm the Air Force study findings, leading to this key lesson: If learning is too easy and too limited, it will be less likely to “stick,” and also less likely to be applied to real world problem solving outside the limited learning “blocks” of exercises that are repeated in class (and often in homework). The best results obtain when there is “interleaving,” that is when different examples of the same principle are discussed and analyzed, so that students learn how to think abstractly – take what they learn from one setting and apply it to another.

Another term for all this is “critical thinking,” which is what all workers need in the 21st century to thrive. Computer software can perform calculations faster and more accurately than humans. Software programs also can recognize patterns more quickly than humans, which is why we see more computerization of reading X-rays, providing medical diagnoses, and doing all kinds of “expert analyses,” which are fundamentally about pattern recognition. If something can be routinized and subjected to a given set of instructions, it has or will be automated.

What computers cannot replace, though they can augment, is humans’ ability to frame problems – to say that Problem A resembles a similar problem that is has been solved by biologists, engineers, or physicists, and how solution techniques from the latter can help solve the former. The phrase “neural networks,” for example, describes a fundamental feature of the burgeoning field of artificial intelligence (AI) – which seeks to identify patterns from masses of data – but rests on an analogy of how the human brain works. As ethereal as modern physics has become, one still sees physicists, in both their professional papers and in speaking to larger audiences, invoking real world analogies to describe their typically incomprehensible equations and theories. Johannes Kepler, whose revolutionary insights about planetary motion changed our thinking about the universe, was addicted to analogies, Epstein reports.

The people that will earn the most and have the greatest professional satisfactions going forward are and will be those who have mastered critical thinking and are able to express their thoughts to others in a cogent and persuasive matter. Reasoning by analogy is especially important in times of rapid technological change, when people are continuously confronted with challenges that reach beyond what is familiar, and therefore demand new thinking. Analogies from what people already know can be very helpful in meeting these new challenges. This is the kind of stuff our schools at all levels ought to be teaching — how to think, not reproduce in wrote fashion some formula and memorize some facts, all of which can now be done with software or using a web-based search engine.

To be clear, it is important not to over-generalize the findings from the study of the Air Force cadets to other settings, say K-12 public schools, or even to other college environments. In the Air Force, all the students presumably were equally motivated, and as much of the variation in environments – in texts, exams, and evaluations – was eliminated by the study design. In the real world, students who get poor instruction and/or who are not motivated in lower grades are likely to be permanently impaired as they take more difficult subjects, which presume understanding of the foundations (if you have difficulty multiplying and dividing, you’re at a big disadvantage when trying to learn algebra, trigonometry, and so forth).

Fortunately, there is one important way to instill critical thinking in students, as early as late elementary school, all the way through high school (and even in college): through DCI. As elsewhere documented on this site, DCI teaches and promotes critical thinking in a way that is fun at the time and engaging. It will also help level the educational playing field that today is tilted against too many students, especially those from low-income families.

More broadly, whatever one may think about DCI, the Air Force study, and others like it, still should strike a chord. Just because you find something difficult to learn doesn’t mean you’re stupid, or that to try to understand it isn’t worth the effort. To the contrary, we’re more likely to remember a lesson learned the hard way, and to apply that lesson in creative ways in other contexts throughout our lives.