"Do fish ever sleep?" "Can snakes hear?" "Why do some trees stay green all year?" "When does a plant become a weed?" "Why do we have eyebrows?" Such questions as these often prompt some deep thinking, and quite a bit of conjecture among students. Almost everyone has an opinion. Some even have a plausible answer. Higher-order thinking involves processes that can not be settled with a simple statement of fact. Intriguing questions, styled after those above, often light the fire for an in-depth discussion of the topic at hand, and often on various other tangents as well!
In evaluating students' knowledge of a subject, I include oral tests. Students will sit next to me and respond to the written question that they have researched. They must also be prepared to answer any follow-up questions that I might ask, related to the topic. Many times questions beg other questions.
For example, one of my questions for physics asks the student to design a valid physics experiment, identifying what hypothesis they are trying to prove, and the steps involved in testing. One student responded that he wanted to determine if an arrow could really split another arrow when shot from a bow. I asked him what factor he would vary. He proposed using bows and arrows made of different materials. "How far away would you stand," I asked, "and what order would you shoot them?" He pondered for a moment and said, "I would set the distance constant for each shot, and use one bow at a time, and shoot each type of arrow; then I will change bows and repeat the process." Hmmmm. "Will you only shoot one of each type of arrow?" I mused. "Yeah, uh, well, maybe." "The problem with only one shot per combination is that you are basing your evaluation of your splitting question on just one sample," explained I. "Depending on the skill level of the shooter, you could hit the target 4 out of 5 times, but the first shot may be the one you missed!"
A thoughtful look gleamed from my student. I continued, "And that also brings up the question of the shooter. The results of your experiment are contingent upon the skill level of your marksman." I paused, allowing that potential pitfall to sink in, and then asked, "So how do we control that variable?" His face dimmed, and then suddenly brightened. "We would have to design an automatic shooter that would shoot with the same force in the same direction each time!" he exclaimed. "Congratulations," I told him, "You are now beginning to think scientifically.
If you could design an automatic, mechanical arrow shooting device, you would have established control of that variability in your experiment." We then took up the issue of only making one shot with each bow-arrow combination. "In the basketball playoffs, they play the best-out-of-five in most of the playoffs rounds," I said. "Why?" My ever-brightening and enlightened student answered quickly, "Because a team might have an off-night, and you don't base a champion on just one game!" Ah-hah! Light bulbs begin to flash. "So that's why we don't just shoot one combination!" he finished triumphantly. "Bingo!" I exclaimed. "So how many should we shoot?" The student had the number at hand: "Five." When asked "Why five?" he responded, "If it's good enough for the pros, then it's good enough for me." Alas! A brief bright moment of scientific reasoning, and then.. Not despairing yet, I accepted five as a decent number to start with, unless we got mixed results and no obvious trends.
Before leaving the subject, my student did reward me with one bit of sage awareness of the situation. "I just thought of something...if we hit the arrow the first time, we'll have to replace the target. So that means I would need a whole bunch of extra arrows." He banged his head. "But if I change the target, I have to make sure the wood grain and orientation is all turned the same way, otherwise the splitting may not happen at all, even if the arrow hits the same location. And since wood grains are all different, that means I will never have exactly the same target each time, so that is a variable I cannot control! Maybe I need to rethink this experiment."
My jaw slowly returned from its floor position and a smile blossomed on my face. A true scientist had been born right before my eyes. He had learned how to ask questions even after questions were answered, thinking logically about every detail of the experiment. I couldn't have been more pleased. Wait till the National Laboratories hear about him!