by Aaron Lee, Astronomy
Teaching Effectiveness Award Essay, 2010
Astronomy is an exhaustive subject, tackling scales from the grandiose to the minute, the massive to the massless, eternity to the seemingly instantaneous. This totality makes introductory astronomy courses like Astronomy C10 inherently difficult for non-science majors; the speeds, sizes, and masses introduced do not compare with students’ everyday notions of “quick,” “big,” or “heavy.” As a C10 GSI during the fall semester of 2008, I noted that this lack of intuitive understanding often made students view astronomy merely as a set of disparate definitions. Additionally, I found that students were far too trusting of their calculators, possibly due to a fear of math, and they blindly accepted whatever the calculator returned. My solution, implemented in my fall 2009 Astronomy C10 discussion sections, was to include weekly activities that taught students how to relate new concepts to familiar experiences to develop their intuition about the subject matter.
The first step was to get the students comfortable thinking about astronomy quantitatively rather than solely qualitatively. I began every discussion section by introducing an imprecise fact, such as “the speed of light is fast” or “the Sun emits a lot of energy each second through photons.” Students then critiqued the statement by assembling a list of questions it failed to answer (e.g., “How fast is fast,” “A lot compared to what,” “How many photons?”). The next step was to answer these questions in a way that helped develop intuition.
My strategy was simple: get the students to think of the material in terms of familiar experiences. For example, while some students knew the speed of light to be 300,000 kilometers per second, no one had an intuitive grasp for its units. We decided to convert kilometers per second to the more familiar units of miles per hour. I asked students to first guess the answer and write it on the board. By putting your intuition on the spot you learn more from your mistakes, especially when you cannot blame an external resource such as a calculator. Students then worked in groups to figure out the exact answer, and we took note of how far off (within factors of ten) our intuition led us astray. In this case, the answer (671 million miles per hour) was just as non-intuitive as the original value, so students came up with new questions that brought the speed of light closer to everyday reality, answering, “How long does it take light to travel the circumference of the Earth?” (0.13 seconds), which instigated the question, “How many times do you have to drive from Berkeley to Los Angeles in order to travel the circumference of the Earth?” (62 times). We now had successfully recast the speed of light in terms of more palpable numbers and units: “light travels from Berkeley to Los Angeles ~475 times a second.” After this exercise, students shared with me that they were better able to grasp the fact that light takes 8.31 minutes to travel from the Sun to the Earth. They now had more insight concerning the distances involved in our solar system and, by extension, our galaxy, whereas before they had viewed these points as unrelated facts. Other exercises extended beyond dimensional analysis and required students to assess what concepts from lecture would be relevant to answer these questions. This gave students a stronger understanding of how all the various ideas tied together.
Another benefit of these exercises is that they helped students become comfortable with unit conversions, scientific notation, and ratios — the same mathematical skills expected of them on the homework and exams. I was pleased to find consistent improvement with my students’ exam scores for questions that required math or critical thinking beyond mere regurgitation. Mid-semester evaluations also indicated that such exercises had made some students less trusting of their calculators; they now stopped to ask, “Does this make sense?” before committing to the answer. More importantly, students’ assessment of the method on mid-semester and course evaluations were 95% positive, often stating that this strategy — one they could now take and apply to other scientific subjects — had given them the confidence to approach science with a critical eye, which helped them to understand “how everything fit together” and allowed them to see “bigger picture ideas without math getting in the way.”