Zinemin has a great post on understanding physics (and math) in high school.
I started writing a comment, then it got so long-winded that I decided (for once) to not hog other people’s comment threads with my verbosity, but to put it all in a post. Here’s what the comment would have been (Zinemin is a physicist, so some of the verbiage is more physicist-friendly than entirely general).
I grew up and went to grade school and college in Europe, so my experience as a student is quite different from what I see that my kids and students experiencing.
I think I started falling in love with math sometime in primary school (we had grades 1-8 as primary school, then grades 9-12 as secondary/high school). I had a wonderful math teacher in grades 5-8 and I think that made a ton of difference. (By the way, all teaches in grades 1-4 were what would here be education majors, but to teach grades 5 and onward the teachers had to have a bachelor’s degree in the subject they were teaching.) My primary school math teacher made everything clear and I remember looking forward to practicing at home from the books of problems (we didn’t have homework in most subjects past grade 5, just collections of problems from which to work at home); I remember doing problems in algebra and proving congruence of triangles. I think this confidence that I gained in grades 5-8 never left me when it comes to math.
I started having physics as a separate subject in 6th grade. I remember one of the most appealing aspects was the fact that I got to use my beloved algebra; we did the basic mechanics stuff — motion with constant velocity or constant acceleration; ballistic motion. We must have done the concepts of force and energy, because I remember making my dad teach me some basic trigonometry during the summer after grade 6th because I wanted to do inclined-plane problems. The physics lab was beautiful, I still remember these posters with the basic SI units, derived SI units, common prefixes. The physics teacher was excellent.
In high school I had a great math teacher throughout, and a great physics teacher in grades 11 and 12. My physics teacher in grades 9 and 10 sucked, when we covered thermodynamics and much of electromagnetism, and I still feel like I don’t know them very well. This is of course ridiculous, since thereafter I won awards in all sorts of physics competitions, I went on to major in theoretical physics and get a PhD in a related discipline. Still, there is a faint visceral insecurity about those particular classical physics topics stemming from this wobbly initial exposure, even though I use thermodynamics and electrodynamics all the time in research and teaching.
I started loving chemistry in high school, because I had several excellent teachers who showed us what the underlying laws were and why. I even went to chemistry high school competitions (I could titer with the best of them). During high school, I developed a deep distaste for biology because all that my two high school biology teachers ever made me do is cram and regurgitate their lectures back to them; I still occasionally have nightmares about answering questions about the nervous systems of nematodes. I never particularly cared about the nature/outdoors (the kid of the concrete jungle and all that), so all the botany stuff was lost on me. I really enjoyed what falls under basic cell biology (e.g. what different organelle do, the role of RNA). At one point, in perhaps sophomore year, we were learning about neural synapses, and based on what she taught, it seemed to me like I could think of synapses as little capacitors that can get charged of discharged; I don’t remember the details other than that I came up with this simple circuit-level model of how information travels through a network of neurons based on how I understood what she had taught and based on what I knew of electrical circuits; the teacher was very rude and dismissive, she said something about not being interested in my silly ideas and to take the stuff to the physics teacher, and that she wanted me to learn the material exactly as she had lectured. So yeah. I don’t like biology because my fee-fees were hurt. Even though intellectually I recognize the importance and difficulty of problems in biomedical sciences, something deep inside me cringes and shrivels whenever someone proposes a collaborative project that veers anywhere towards bio.
These early exposures seem to have a pronounced effect on how much confidence we gain, and confidence appears critical for later achievement. But I digress…
My Eldest is like an education experiment for me and my husband, because the system is very different from what we are used to and we have no idea what comes next. Where I went to school, the system was challenging and very good for smart kids, while average and below-average kids were left to just get bad grades or flunk and generally never do well. The US does a much better job catering to the average future citizen, presumably because the above-average ones are expected to find a way to excel anyway; they sometimes do, but they rarely do if they are poor. (nicoleandmaggie write a lot about challenges in getting access to education for gifted kids).
In connection with Zinemin’s post, I am witnessing my Eldest in the US pre-college education system and it is appalling how little connection is made between math and any of the sciences. Eldest is a freshman in high school, and they have integrated science (won’t have physics separately till junior or senior year, and even so only as an elective). This year, so far he’s had a unit of physics here and there, but they do not use math at all. You should have seen how they covered light that we observe from different stars, and inferences about star temperature or distance from color and brightness; it made my skin crawl. The math needed for the Stefan-Boltzmann law or Wien’s displacement law is really not that hard, a high school student could understand the power emitted per unit area of what’s essentially a generalization of the heater on the stove goes as temperature to the fourth, or why the intensity decreases as inverse distance squared from a source (such as a lightbulb; or a star). But it was all very qualitative, completely hand-wavy, with vague concepts such as perceived brightness and actual brightness (no definition of either and no textbook; based on the problems assigned, I managed to decipher the two to be, respectively, the intensity of light here on Earth (power per unit area) and total power emitted from the entire surface of the star; the fact that one is called perceived brightness and one actual brightness and they don’t even have the same units makes me want to break something. Once I deciphered what was meant, I was able to help my son with the work, but you should have seen his resistance. He is very good at math and can definitely do the manipulations needed for the calculations (it was a problem with three stars and their perceived/actual brightnesses and sizes and distances from Earth, so very simple algebra was all that was needed). Eldest just didn’t understand why I would want to inflict this math on him when the science teacher didn’t do it, it wasn’t necessary, and everything could just be handwaved. This is the only physics unit I saw him have this year; he might have had more, he just didn’t need help (he has excellent grades overall). But from what he mentioned in passing, most of the integrated science focuses on biology, a little chemistry, some geology and some astronomy, but nothing with even with a little math.
When I try to show my kid what I do for research, he zones out within 20 seconds because it is boring, and cannot understand why I would want to work on the stuff I work on because boooooring. This attitude appears common and continues into college. My undergraduate students still seem to think that they can be taught things in our physical science discipline without using math, as if math were some cruel curiosity that has no real use or connection to the concepts. It pains me when I hear this. Math is the language of nature and the fact that we can speak it is nothing short of miraculous.