Sep 12 2008
Four Beliefs that Impede Education: Part 5
Part 5 (of 5) Problematic Belief #4: Numbers Are Mere Exclamation Points
To review a chapter of textbook material, I sometimes use an activity I call the “Psychic Quiz.” Not only is it fun and different, but through it I gain another means of drawing students into “doing science,” informal as the case may be. Here’s how it works: I advance around the room, posing a true/false question to each student. But before I read their question, I ask them to give me the answer. They must use “psychic” powers to read my mind, or consult a spirit looking over my shoulder, or what have you, to intuit the correct response. Then I read the question. After hearing it, the students can change answers if their intellectual mind has come up with an answer that conflicts with what they attempted to divine via paranormal means. As I go about the room, I keep a running blackboard tally of all the hits and misses.
Only once have the results caused me to pause, searching for words. In that case, roughly ¾ of the students displayed negative psychic abilities (which, to me, makes as much sense as positive psychic abilities). The class displayed the noteworthy – yet ultimately meaningless – ability to guess wrong. Otherwise the results have been clearly unimpressive. Correction, the results have been clearly unimpressive to me. Thanks to one student, however, I have realized that even after giving a brief talk about probability and chance, not all students grasp the meaning.
The student – a middle-aged woman returning to school, an individual who boasted to the class that she was a former professional psychic – had asked me bluntly why I was giving no credit to those few students who had “gotten it right.” A hit is always a hit, isn’t it?
How can students ignorant of basic mathematical and statistical concepts truly understand science? Thanks to that episode and a number of similar experiences, I have been motivated to set aside precious class time to give my students a brush-up on such things as the meaning of average differences, change expressed as percentages, and the concept of statistical significance.
At the beginning of one class I will mention research that found a 30% increased chance that a man will be homosexual for every older brother he has. I ask the class, “Say I have 3 older brothers – what is the chance I am a homosexual?” Invariably, I hear the response, 90%. And so I explain that we need to know the original rate to understand the meaning of a percentage increase or decrease. In the case of my being homosexual, the original rate is roughly 2%. So with three older brothers, my chances of being homosexual increase to not 90%, but shy of 5%.
I drive the point home by asking how many students would pay $100 for my secret to increasing their chances of winning the lottery by 50%. Hands fly. I then admit I have no secret, but the point is they would be forking over $100 to increase their chances from about 1 in 28 million, to 1.5 in 28 million. Not what you’d call a steal of a deal.
I wish I had a dime for all the times I saw or heard a news report announcing a new scientific finding about something associated with an increased risk of cancer, and the amount of the increase was never mentioned. When they are used, numbers seem to be employed only to impress. A 30% increase? Holy smokes, that’s big!
When doing real science, we don’t use numbers to make a point. By and large, the numbers are the point. Any captivating rhetoric should be viewed not as the proverbial cake, but as the thin layer of icing spread above and around the substance of science. Until our culture becomes more mathematically literate, its ability to understand science will be handicapped.
Coupled with our culture’s innumeracy is its near total focus on reasoning. Any data gets overshadowed by the relatively dazzling language we use to deliver it. A widespread sentiment undoubtedly worthy of an entire essay, but here something I will address as a tangent, might be expressed this way: “what is reasonable is right.”
Students fall prey to this sentiment far too readily, as do American consumers by the score. How else do you explain the great wealth generated by sham treatments? Magnets to increase gas efficiency by aligning the fuel molecules — sure, sounds reasonable. Crystals to cleanse your personal energy field by canceling negative vibrations — sure, sounds reasonable. What goes MIA is the evidence supporting the claims. The same often goes for theories. Many perfectly reasonable-sounding psychological theories, to put my field under a spotlight, simple don’t hold up under scientific scrutiny. As a defense mechanism, do people habitually repress traumatic memories? Do responses to abstract stimuli, such as inkblots, provide us with reliable information about a person’s unconscious mind? The apparent reasonableness of an argument and any evidence in support of it can be two completely separate things.
As a corollary, there are also those tremendously robust theories that hardly seem reasonably, even to well-educated minds. Consider relativity and quantum theories: these are not reasonable ideas in an everyday sense. It is only thanks to scientific measurements that we are confident of their value.
An important and indispensable part of science is the language we use to explain and argue and theorize. But if the language part is not firmly tethered to data (to observation and measurement, to what I am here calling “numbers”), then our level of confidence in the explanation must reflect this.
Concluding Thought: The Authority of My Hunches
Turning my scientific inclinations back upon the workings of my own mind, I fully realize that what I have explored in this series of posts is emphatically not science. Pre- or para-scientific journalism, perhaps. What I have written may strike a number of you as reasonable, but that certainly doesn’t make it valid. To support my words, I have only my own bias-prone observations, without more weighty numbers to back up these observations. However, I am open and receptive to outside information and correction. If any of you skeptical readers have information pertaining to what I have discussed, please share it. Or if you have thoughts about how I might test the above, ditto.
