Its the end of the school year. Ordinarily this doesn't mean much to grad students, but for the past few years i have been tutoring two of the most amazing high school students in whatever math or physics they were assigned or could imagine. They were both seniors this year, so i'm dipping back into the pool of sophomores and juniors to cover the gap between stipend and rent. The place where i work is good at attracting good kids, but i'm struck once again by how infrequently high school students are made to answer the question "Does this answer make sense?". I know students enter the college physics sequence with the (dis)ability to grind through an algorithm, get a ridiculous answer and circle it without blinking. They must be picking that up in high school, but it is sufficiently dis-incentivized that it usually doesn't last long. My previous students learned to anticipate the question long ago, so it caught me off guard last week when a new student wrote down a completely nonsensical answer and then waited calmly for my evaluation of his work. This amazes me every time i encounter it because the question "Does this make sense?" is at the heart of the process that turns students into scientists.
At first, when intuition is a pretty good guide to reality, the question forces a check on math skills which are too often subpar or merely misguided. If you calculate the speed of any ball to be in excess of Mach 1, you should realize immediately that you are wrong. This provides a good opportunity to re-examine your work before submitting it for a grade. On the flip side, routine reality-checking helps students anchor the numbers and units they are working with onto familiar things. Humans are 1-2 meters in size and 50-100 kg in weight. Less obviously, 10 seconds is too long for a ball to be in the air, humans can't fall faster than about 50 m/s (120 mph) and "1 g" of horizontal acceleration would take a car from 0 to 60 (mph) in 2.7 seconds, which is only achievable in a road car if you have quite a lot of money. These are the sorts of things students can find out by doing simple problems at home and using them to calibrate their reality-checker. They do what no amount of class time can achieve, pull the world of numbers and formulae down into the real world where they can be used in day-to-day life. Only then will they get into your head and change who you are.
As some point intuition runs out. For some students, magnetism is a completely foreign land. For others, its relativity. Routine, in-class questioning "Does this answer make sense?" is the only way to build up a feel for subjects with which the students can't possibly have any direct experience. They go from using intuition to check their math to building a sense of what reality ought to be using math. This process carries students straight through from the time physics starts to get confusing to the day they ask a question, realize that no one in the world knows the answer and use some combination of intuition, observation and math to push the boundary of knowledge a little bit further. And not just in physics. The whole of science education is based around the question "Does this make sense?".
Why is the single most important question needed to create scientists apparently never asked in the high schools of a nation which prides itself on its scientific excellence? I have to admit i have paid almost no attention to secondary education since i was its recipient. As much as i love teaching smart, motivated teenagers with supportive families as a side job, teaching mandatory classes every day for a career is something else entirely; and i have great respect for people who can do it well. That said, it strikes me as odd and mildly alarming that students coming from very good school systems make it into adulthood without ever coupling mathematics to reality. Maybe there is something about meeting a new tutor which causes students' common sense to shut down, so that i'm seeing a bunch of false negatives? Maybe my standards for common sense are unreasonably high? Normally these posts end with some sort of conclusion, but i am honestly stumped here. Anyone in high school want to comment?
