How to (not) Think, Say, or Do the Worst Thing

Daniel Wegner’s review article (Science, 325, 48-50, 3 July 2009) of “ironic behavior”, thinking-saying-doing-feeling exactly the opposite of what we intend, sheds light on a host of mental and behavioral problems.

To begin with, why do I drive my bike directly into a fallen tree branch when I have already decided to go around the branch? Why do cheering baseball fans make it harder for me to avoid swinging at a wild pitch? Why do I kick a soccer ball directly into the goalie’s outstretched arms when the entire net is available? These are all “ironic” behaviors and Wegner describes a multitude of situations where ironic behavior appears.

As I understand it, the current theory of ironic behavior postulates two competing mental processes. When we are instructed “don’t do/think/say/feel X”, we begin a conscious mental process of distraction, looking for something “not X” to do/think/say/feel. At the same time, we also initiate an unconscious “monitor” process that begins looking for potential mistakes. This monitor checks to make sure we aren’t doing/thinking/saying X and it keeps the idea of X alive in our subconscious rather than letting it dissipate. Normally these two processes work well together, but things can go wrong, and since the monitor keeps the notion of X alive, X is ready to pop out whenever a suitable trigger arises.

A nice example of this, and the simplicity of ironic triggers (of which there are many), is shown in Figure 3, which shows the tracings a handheld pendulum makes on a piece of paper in four experimental scenarios. The scenarios are generated by telling the person with the pendulum to “hold it steady” or “keep it from swinging up and down”, and their ability to follow each of these instructions is tested first, without competing distractions, and second, by asking them to count backwards from 1000 by threes. The images graphically demonstrate our inability to follow instructions when overloaded with a second, unrelated task.

So how can we avoid ironic behavior and thoughts? One way “we can stop thinking of things” is to make “time to devote to the project [of not X] and become absorbed in our self-distractions”. In other words, we have to give the conscious project of distraction, of following instructions, a chance. Multi-tasking is not helpful. Another helpful approach may be to relax. Striving for tight control of our thoughts, etc., may keep the unwanted thought alive to a greater extent than simply accepting an unwanted thought’s existence whenever it appears. Does this sound like vipassana?

Learning Math: Symbols Beat the Real World

There is a widely held belief (don’t ask me who the Widely’s are, but they include students, their parents, and even most of their teachers) that certain inscrutable subjects are easier to learn if we replace inscrutable symbols with concrete stories and pictures. Take algebra. Those x’s and y’s will never click with kids because symbols are too abstract, so replace them with real-world objects and – bingo – connections get made.

Maybe this point is too abstract? Fine. Here’s what I mean, you could teach algebra to students the “dry robot” way by teaching them rules for setting up and solving equations like 40(t-1)=400-50t or you could teach algebra the “friendly humanistic” way by giving them concrete examples like “One train leaves Station A at 6 p.m. traveling at 40 miles per hour toward Station B. A second train leaves Station B at 7 p.m. traveling on parallel tracks at 50 m.p.h. toward Station A. The stations are 400 miles apart. When do the trains pass each other?” (Hint to reader: the formula and the story are equivalent.) OK, the friendly humanistic approach requires a bit of story-telling, but its engaging, it can be pictured, it can be made into a movie. The formula? Bleah.

Yet it turns out the the widely held belief ain’t so. When it comes to learning math, the dry robot approach produces better results than the friendly humanistic approach (the latter appears to produce no learning at all!). A story in the New York Times (“Study Suggests Math Teachers Scrap Balls and Slices,” April 25, 2008 by Kenneth Chang) describes how scientists went about testing students ability to learn using the two approaches. (The original research article appeared in the April 25, 2008 issue of Science magazine.) Students who were taught with the concrete approach tended to remember the story, not the abstract principle that the story was supposed to convey. Students who were taught to process symbols, on the other hand, were more likely to remember and use the abstract principles.

Surprised? I’m not. I’ve seen this debate play itself out for decades in chemistry, the subject I teach. A chemistry teacher could make an even stronger case for the use of concrete examples (there really is a concrete world of phenomena underlying all of those symbols), but I wouldn’t be surprised if symbol-based learning actually produced better outcomes.

Teaching Math

Most people assume that mathematicians know how to teach math, but how much expertise do the practitioners of a discipline have in the teaching and learning of that discipline? Certainly they have gone farther in their study of mathematics than the rest of us, but does that experience qualify them as experts on how the rest of us learn, or the best way to get us to learn?

I ask this out of genuine curiosity and concern. The mathematics teaching community has become highly polarized in recent decades over the “right” way to teach math (as if there could be just one “right” way). Each camp angrily challenges the ideas put forward by the other camp. And bystanders are forced to deal with an uncomfortable truth: if one camp of mathematicians is right, then the other camp, i.e., a large number of mathematicians, are necessarily wrong.

If you think I exaggerate, consider this quote from a recent interview in Science (21 March 2008, p. 1605), “Larry Faulkner has successfully steered the National Mathematics Advisory Panel through some of the roughest waters in education” (my emphasis). Getting mathematicians to agree on how and when algebra should be taught is apparently a very, very tough job.

If you would like to read the report they produced, go here. Here are a few highlights of Science magazine’s interview with Larry Faulkner:

• “The 19-member panel was supposed to rely on sound science …, but only a relative handful of the 16,000 studies it examined turned out to be useful. The vast majority, says Faulkner, were of insufficient quality, too narrow in scope, or lacked conclusive findings. The literature is especially thin on how to train teachers and how good teachers help students learn.”
• “Q (Science): Why do so many students have trouble with fractions? A (Larry Faulkner): Fractions have been downplayed. There’s been a tendency in recent decades to regard fractions to be operationally less important than numbers because you can express everything in decimals or in spreadsheets. But it’s important to have an instinctual sense of what a third of a pie is, or what 20% of something is, to understand the ratio of numbers involved and what happens as you manipulate it.”
• “Q: How could schools lose sight of that? A: Well, they did.”
• “Q: What’s the panel’s view on calculators? A: We feel strongly that they should not get in the way of acquiring automaticity [memorization of basic facts]. But the larger issue is the effectiveness of pedagogical software. At this stage, there’s no evidence of substantial benefit or damage, but we wouldn’t rule out products that could show a benefit. If a product could be demonstrated to be effective on a sizable scale under various conditions, the panel would be interested.”

Can you succeed in school without really trying?

The Premise. Many people subscribe to the idea that being successful in school, i.e., being ’smart’, is a gift. You might be lucky and be born with ’smarts’, but whether you were born this way or not, there’s no point in trying to do anything about it. Hard work. Applying yourself. These things are not going to help you succeed in school. In fact, hard work could hurt. Dozens of teachers have warned me about the horrible effects of “drill and kill”. Scores of teachers and parents have told me that a good school is one that nurtures self-esteem, discovery, and creativity, and avoids any activity that looks like work or effort or carries the least possibility of failure. In their minds, the ideal school is one where children learn without realizing that they are learning.

My Response. There may be something to the notion of being “born smart”. No two people are exactly the same, so it stands to reason that no two brains will perform exactly the same. However, the possible value of a good brain does not rule out the value of hard work. Effortless learning may be pleasurable, but learning that is entirely effortless is not ideal.

It is easy to find examples of learning that is based on work. Learning to walk. Learning to talk. To read. And count. All of these basic lessons require effort, by which I mean, the lessons involve repetition driven by a desire to succeed. Babies fall down when they try to walk the first time. Children practice singing the alphabet and sounding out words. If these activities aren’t forms of effort, what are they?

Mature learners rely on effort too. Thomas Edison did not discover a working light bulb under his pillow one morning. Watson and Crick endured strong criticism from their colleagues before they hit upon the structure of DNA. Einstein labored unsuccessfully for years to find a unified field theory.

There are, in fact, countless examples, large and small, linking learning with effort, and yet this link doesn’t seem to exist in the American mindset. I have met many financially successful, college-educated parents who reject any connection between learning and work as inappropriate for their children. Why?

Part of the problem may be that we do not reward ourselves for hard academic work. When we learn something easily in school, we feel wonderful. When we hit a difficult subject, however, even though we may ultimately overcome our difficulties, we frequently harbor some resentment about the experience and we turn our interests and appreciation towards other subjects. Worse still, we run down anyone who is still making an effort. “She’s such a grind.” “He isn’t that smart. He just gets good grades because he works so hard.” By failing to appreciate our hard-won successes, whether they be partial or complete, we encourage the growth of some screwy notions about what works in our own lives and then generalize these ideas to our children’s school environment.

The Antidote. It is time to recognize that hard work is valuable and important. Not just for building houses and hospitals, but also for learning. Schools should promote hard work as a tool that is available to everyone and should teach students to identify, enjoy, and take pride in accomplishments that are based on effort. To help inspire this point of view, I have created a list of news bulletins that testify to the value of hard work in an intellectual setting:

1. Science, Sept 21, 2007, 317 (5845), p. 1657 [Random Samples] – Chess for Drudges? Psychologists at Oxford tested the chess playing skills of youngsters, and looked for correlations between skill, IQ, and practice time. “Although years of experience and IQ correlated with chess skills, the researchers found that the highest correlation was with the number of hours a day the children spent playing or studying the game.” [DOI: 10.1126/science.317.5845.1657d]