Chapter 5: Is drilling worth it?

Why Don't Students Like School? by Daniel T. Willingham (John Wiley & Sons, 2009).

Or, How do you get to Carnegie Hall?

We all know the old joke, and it turns out to hold true not just for the obvious fields of music, dance, art, and athletics, but also for more cerebral, academic pursuits such as reading, writing, mathematics, science, history, etc.

As I mentioned in the comments to the previous post, drilling is just a harsh, perjorative term for practice and Willingham says there is no way around it, no short-cuts to success. In order to be proficient in any activity one must practice. There are few things in life that can't be lost to some extent when practice wanes or stops all together, but some core elements can be retained practically forever given sufficient, sustained practice over time. As an example from my own experience, I lived in Munich for a while and met a man there once who had married a German woman and was living fully assimilated into German society and culture. He had little contact with English speakers. Although he had grown up speaking English into adulthood, after living in Munich for 7 years his spoken English was sometimes halting, he stumbled over words, and couldn't remember key vocabulary - he would occasionally stop mid-sentence and say, "oh man, what's that word..."

Obviously he was still what we would call "fluent" in English, but clearly he had been affected by the lack of practice speaking his native tongue. Now, compare his situation with mine vis-a-vis speaking German. I only began studying German in college, but I took many semesters and then lived in Munich for a couple of years. I spoke well enough to get around, I read the local newspapers and watched the local news and I could carry on a conversation in German to a certain extent, but I was never fluent. That was over 20 years ago, and I can assure you that if I returned to Germany today I would have trouble completing a full sentence, much less carrying on a conversation.

The key is practice. Tally up the number of hours the American living in Germany spent speaking English and compare it to the number of hours I spent speaking German, and the difference would be obvious. You might argue that the example is invalid because growing up speaking a language in the formative years may account for much of the difference, but Willingham provides evidence from many other fields that show the same pattern. Here's a math example that I found pretty compelling.

Take a group of college graduates and give them a basic algebra test some years after they have completed their schooling. Compare their scores on this test with how long ago they completed their math classes. One obvious, common-sense trend emerges. Scores drop dramatically the further in time they are removed from their last formal math class. This is true if they only took one semester of math or if they took more math up to calculus level.

(See the graph at Google Books here.)

The study went further, though, by looking at students who had taken advanced math courses, calculus and beyond, which required the continued practice of basic algebra skills. Given the same test, the students who took advanced math courses scored as a whole significantly higher on the algebra test. Furthermore, the drop-off in scores was not nearly as steep - 55 years later, students who took advanced math classes did better on the test than students who took only algebra and were tested just 1 month after completing the algebra course! For the group that took courses in math beyond calculus, there was in fact no drop off at all (over time).

Willingham attributes this to the continuing practice required to complete advanced math courses. He anticipates the argument that students who take advanced math classes are simply "smarter" by breaking down the data according to grades achieved in their respective classes (not shown in the simplified graph). According to Willingham, students who got low grades (C's) in calculus still outperformed students who got A's in algebra and then stopped taking math.

Implications for teaching

Practice is essential. But how one practices is also important. There is value in spacing out practice over time, and the conventional wisdom on 'cramming' turns out to hold up pretty well upon closer scrutiny. It is in fact true that studying a few minutes per day is better than studying several hours crammed together the night before a test. I may have to reconsider my homework policies in light of this. Incorporating review into every day of class should also be helpful. I frequently give Do Now assignments that are reviews of earlier topics that students may wish we could just forget about.

Basic skills can be folded into more advanced skills. Think of the algebra example - at the calculus level, algebra skills are embedded. In biology, I spend time at the beginning of the year teaching experimental design directly, after which I incorporate that skill into almost every lab we do. I don't expect all students to understand independent and dependent variables at the same pace - some kids get it now, others will still be asking me which is which in June. They still have 2 more years of science classes to work on it. For this reason alone students should be encouraged to take advanced courses.

One reason practice is so important is to make some mental processes automatic, which frees up working memory to focus on more complex tasks. Working memory seems to be pretty much fixed, and people with greater working memory capacity are generally "smarter" than people with lower working memory capacity. We can cheat the system, however, through practice.* Think of writing as an example. As I type I am also trying to pull together several ideas from different sections of this chapter and present a complex idea as succinctly as possible. To the extent that I am successful at this task, it is largely because the basic elements of writing are more or less automatic - I don't have to think too much about making sure my sentences have a subject and a verb, or what to capitalize, where to put the punctuation, and so on. Yes, I have to proofread and I make plenty of errors, but my main concern is synthesizing the ideas, rather than worrying if my subjects and verbs agree. If I had more experience with mathematics, and statistics specifically, I suspect that this task would be even simpler!

Next: Chapter 6: What's the secret to getting students to think like real scientists, mathematicians, and historians? (Hint - it has a lot to do with chapter 5...)

*Indeed, studies have shown repeatedly that the vast majority of successful people are the ones who work harder, not necessarily the ones who are "smarter!"