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## Teaching Math and Science Requires Talent, Not Just Assigning Homework

As an educator, I have great concern when teachers fail to provide clear and simple explanations to students who struggle with math and science concepts. The rare, gifted student will always be able to connect the dots, but less talented students often fall short. The concern is not only that the student may not understand a particular poorly explained problem, but that chronic exposure to poor teaching may have the permanent effect of turning students away from math and science, a very important problem for to the United States.

I see poor explanations all the time, and not just in the classroom. A recent example comes from an article I was reading in Scientific American, a popular and highly regarded science magazine. The author was discussing the “Monty Hall” problem, in which a game show contestant is shown three doors. Two doors hide donkeys, while one door hides a new car. The writer went on to explain that the contestant chooses door number one, but before that door opens, door number two opens to reveal a donkey. The contestant is then asked if they would like to switch to door number three. For most of us, it seems like there would be a 50-50 chance of getting the car with either door remaining closed, so a switch wouldn’t improve the chances of winning. It turns out, counterintuitively, that your chances improve if you switch. Originally, with three doors to choose from, there was a 1/3 chance that door number one would hide the new car. By switching to door number three after opening the second door (revealing a donkey), you’ll have a 2/3 chance of getting the car, twice as favorable as when the game started. How is it possible?

At this point, most students are intrigued, but it is the explanation that will either turn them on to the topic of probability or turn them off, perhaps 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

Sticking forward, it says that in the first two cases, the trade leads you to a favorable outcome, while the trade in the third case leads to an unfavorable outcome, so the trade gives a 2/3 chance of winning .

Based on this explanation, most students look at the second configuration and wonder how switching to door number three has a favorable outcome since there is a donkey behind door number three. Also, most students will say that the second configuration is impossible because a donkey was shown to be behind the second gate, so the configuration “donkey, new car, donkey” is illegitimate. Between the first and third legitimate setups, one is good to switch and one is bad to switch, so it shouldn’t matter if the contestant switches or not.

The student is not to blame for the confusion here. Instead, the failure lies squarely with the author who did not explain things clearly enough. In fact, the author only needed to say this: For the second configuration, *the contestant would have been shown the donkey behind door number three, leaving the contestant with the option of switching to door number two and thus a favorable outcome.*. By omitting this simple statement, the problem is virtually 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 complexities of math and science to students, who by the way make up a significant proportion of Scientific American’s readership. Doing it right opens young minds to the beauty of these subjects, but doing it wrong destroys their interest. Like it or not, America’s future is tied to the intimate exchange of ideas between teacher and student that takes place every day in classrooms across the country. If students do not like math and science, we will not have an adequate supply of 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 reveal the secrets of the universe, which I have always considered a part of being human.

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