It’s a half moon out. How long before the next full moon?
A good measure of the American educational system’s utter failure is the inability of most Harvard physics majors to answer these questions. I have been testing them episodically for 7 years. This failure is perfectly consistent with the results of Philip Sadler’s testing of the knowledge of the reasons for the seasons among Harvard and MIT graduates back in 1989. Sadler’s findings were the basis of a film called the Private Universe. It is also consistent with the testing of knowledge of the most fundamental concepts of physics by Harvard Professor of Physics Eric Mazur.
The most common answer among physics and non-physics majors to the half moon to full moon queston is the same: two weeks. The next most common answer is: “I have no idea.” One reason given for the second response is “I don’t know how long the lunar cycle is.” Wow! The third is: “it depends if it is waxing or waning.” The typical answer to the follow up question of what is it in each case is: well if it’s waxing two weeks, if it’s waning 6 weeks. Wow, again.
Why two weeks? Well, half moon suggests half a cycle and if a full cycle is a month. a half moon must be half that. Another reason might be the experience is that the shape of the moon changes only very gradually and the intuition is that it can’t possibly go from half to full in less than two weeks.
But two weeks is wrong. the answer is either 1 week or 3 weeks depending if it is waxing or waning. The rule of thumb answer how to tell waxing from waning is whether or not the C shape is backwards or not. The most common and wrong answer to the relative position question is that the New Moon (eg. no visible moon) is when the earth casts a shadow on the moon. No, that is called an eclipse.
Three Points: the scientific method is all about observing, asking, guessing, testing, and telling. This little case study shows that students are not being taught to observe, ask, guess, test, and tell. The best way to teach the scientific method and the joy of science is to start where humanity started: with the sun, the moon, and stars.
The best algorithm for ranking the power of experiments to teach the young is that they be easily repeatable and low cost. Turning the sky into a laboratory makes sense on both counts.