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Teaching Math and Science Requires Talent, Not Just Assigning Homework
As an educator, I have strong concerns when teachers fail to provide clear and simple explanations to students struggling with concepts in math and science. The rare and gifted student will always be able to connect the dots, but less talented students are often short-changed. The concern is not just that the student may not understand a particular problem that is poorly explained, but that chronic exposure to poor teaching may have the permanent effect of distracting students from math and science, a very big problem for the United States.
I see bad explanations all the time, and not just in class. A recent example came from an article I was reading in Scientific American, a popular and highly regarded science magazine. The author was talking about the “Monty Hall” problem, in which a contestant on a game show is shown three doors. Two doors hide donkeys, while one door hides a brand new car. The writer went on to explain that the contestant chooses door number one, but before that door is opened, door number two is opened to reveal a donkey. Next, the contestant is asked if they would like to proceed to gate number three. For most of us, it seems like there would be a 50/50 chance of getting the car with either of the two doors left closed, so a switch wouldn’t improve his chances of winning. . It turns out, against all intuition, that your chances improve if you change. Originally with three doors to choose from, there was a 1/3 chance that door number one hid the new car. Passing through door number three after the second door opens (revealing a donkey), you will have a 2/3 chance of getting the car, twice as favorable as at the start of the game. How is it possible?
At this point, most students are intrigued, but it’s the explanation that will get them interested in probabilities or turn them off, maybe for good. The author begins his explanation by saying that there are three possible door configurations:
1. donkey, donkey, new car
2. donkey, new car, donkey
3. new car, donkey, donkey
Goofing forward, he says that in the first two cases the change brings you to a favorable outcome, while the change in the third case leads to an unfavorable outcome, so the change offers a 2/3 chance of winning.
Based on this explanation, most students look at the second configuration and wonder how going through gate number three leads to a favorable outcome, since there is a donkey behind gate number three. Also, most students will say that the second configuration is impossible because a donkey was shown behind the second door, so the “donkey, new car, donkey” configuration is illegitimate. Between the first and third legitimate configurations, one is good for switching and the other is bad for switching, so it doesn’t matter if the competitor changes or not.
The student is not responsible for the confusion here. Instead, the failure lies squarely with the author who didn’t explain things clearly enough. In fact, all the author needed to say was this: for the second configuration, the contestant would have been shown the donkey behind gate number three, leaving the contestant the choice of moving on to gate number two, and thus a favorable outcome. By omitting this simple statement, the problem is nearly impossible to understand, with the result that student interest fades and the light becomes dim.
We need to think more carefully about how we explain the intricacies of math and science to students, who make up a significant proportion of Scientific American readers. Doing it right opens the minds of young people to the beauty of these subjects, but doing it wrong destroys their interest. Like it or not, the future of the United States is tied to the intimate exchange of ideas between teacher and student that takes place every day in classrooms across the country. If students don’t like math and science, we won’t have enough mathematicians and scientists, which in turn leads to our country’s inability to maintain a competitive position in the world. It also leads to a society that has stopped trying to unveil the secrets of the universe, which I have always considered part of being human.
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