Chad and Rob have already noted this piece of news about soon-to-be-published research indicating that the order in which high school students are taught physics, chemistry, and biology makes very little difference to their performance in science classes at the college level, while a rigorous math curriculum in high school gives their college science performance a significant boost.
I have a few things to say about this.
Good math instruction is good for students.
As Chad points out, it helps you build problem solving skills and think systematically. To the extent that these skills are useful in understanding science, of course they’re going to help.
Indeed, it’s my feeling that math instruction could get more rigorous in middle school and grade school than it seems to now. Getting over the idea that algebra is a foreign language (really, you’re just doing the same kind of number handling you’ve been doing with 2s and 7s and 9s, except you don’t necessarily know the value of the number your handling) would probably result in fewer kids convinced that they just don’t get math. And, if you can tackle algebra earlier, you have better prospects for introducing calculus during high school — maybe a couple years of calculus.
Physics makes less sense when it’s taught without calculus.
(This is an amplification of Rob’s point that you might as well set up the science sequence so you start with the course that requires the least mathematical sophistication and end up with the course that requires the most.)
Who wants to memorize separate equations to figure out the displacement, velocity, and acceleration of a projectile? If you can take derivatives, you know how to get the formula for velocity from the formula for displacement, and the formula for acceleration from the formula for velocity. More importantly, if you understand what taking a derivative means, you can really grasp how displacement, velocity, and acceleration are related to each other.
Teaching physics without calculus, to my mind, makes it less intuitive. So, leaving physics for last in the sequence makes it more likely that the students have the math they need to do it right.
Engagement with science needn’t always build upward from the smallest pieces.
Part of the rationale for the “physics first” movement was that physics deals with the stuff that underlies chemical phenomena, and chemistry deals with the stuff that underlies biological phenomena — so, to get the best intuitive grasp, you should start with physics, then do chemistry, then do biology.
Which is a nice theory, but somehow inclined planes (frictionless or not) didn’t come up in my high school chemistry class.
The physics that underlies chemistry is some pretty hardcore physics — not necessarily the stuff you learn the best in a high school physics course — and the same can be said for some of the chemistry that really makes sense of biological phenomena (which we didn’t really get into ’til the two semesters of biochemistry I took my senior year of college).
Besides, it’s not clear that students really grok the smallest bits of matter from which they’d be building up their picture of the world by starting with physics. There’s something to be said for starting on a level of engagement that seems more natural to them — perhaps organisms — then working downwards to organs, to cells, to molecules, to atoms, to subatomic particles.
Even better might be what sometimes happens already, where you start with the picture of the world you get from the high school biology class, then revisit it in the light of what you’ve learned about chemical reactions or thermodynamics, gradually adding layers of complexity to the account. After all, the accounts were constructed gradually. Do they need to be learned all at once?
“indicating that the order in which high school students are taught physics, chemistry, and biology makes very little difference to their performance in science classes at the college level”
So it’s clear, I’d like to point out that the study didn’t look at the order of teaching; it looked at how much of which sciences the students had taken in high school and how this correlated with college performance. To this study, someone that took physics, then chemistry, then biology in high school would be lumped together with someone who took biology, then chemistry, then physics in high school.
The authors made clear that they felt that this implied things about the importance or lack thereof for the order of high school curriculum, but they didn’t actually study that.
You’re absolutely right that physics makes far more sense with calculus. In my own experience, I had two years of physics, one without calculus and one concurrent with calculus. The equations I had memorized all throughout the first year suddenly made intuitive sense the moment I knew what a derivative and an integral were. But I also found that having physics at the same time helped me understand the calculus, because I had real-world examples of the abstract concepts. I’d advocate doing exactly this–teaching calculus and physics concurrently.
And I will always and forever advocate better math education in elementary school and middle school. By the time students are in high school they’ve already learned that math is hard and boring, and that they’ll never be able to understand it. But I think part of the problem is that elementary school teachers can get away with understanding barely more math than they are teaching. As a result they have no ability to help students gain the intuition for math that they need, because the teachers themselves don’t really understand it. So the students just learn that here’s a number, here’s another number, and if they follow this arcane process they’ll get a third number that must be the correct answer because the teacher said so. Aaaargh.
math instruction could get more rigorous
Certainly. It would also help to lighten up on the rote drills and theory to show direct applications, aka “why are we learning this stuff?” For example, I was working on a math curriculum with my daughter. The repetition was boring her and boring me. One evening, I prepended the introduction to probability by using skittles as a prop. Once she could see an application beyond some number being operated on by another random number to arrive at a third number, it was interesting. This is why we do science.
Tonight was fun because the set of geology tests (scratch, streak, acid, color, weight, magnetism) we’ve done over the last two weeks let us identify the ten mystery rocks. She’s already expressed an interest in going out into the yard and trying to identify more. (We need to get a little further away from the basalt country.)
I have to admit, I am somewhat puzzled by this latest piece of scienceblog based information. That is mainly because I know very little about science education on that side of the Pond. Thus I have a few questions (for interest, I will answer them for the UK)
1) How old is “high school” in the USA?
[11-16 compulsory in the UK, 16-18 optional]
2) Are you taught the sciences in some sort of sequential order in the USA? So, you do physics, then Chemistry, then Biology?
[They are taught concurrently, but usually seperatly]
3) People are talking about courses in calculus, is that usually offered as an individual course in the US, and at what level?
[Calculus would be part of a general maths course, and (if I remember correctly) is for high level GCSE (at age 16) and A Level (taken at age 18)]
4) Could someone explain in general how the US science education system works?
[In the UK it works by being dumbed down to a staggering degree, but thats a whole other whinge]
1) High school usually has four grades in the US, approximately ages 15 – 18.
2) The usual sequence is biology, chemistry, physics.
3) Yes, calculus is a separate course.
4)The science curriculum in the states depends strongly on the instructor. As a chemistry professor, I see students who are supposedly well prepared (according to their High School transcripts), but are poor students, and I see students who are less well prepared, but had excellent instruction in the courses they did take who do well.
I agree that a stronger math background is more important than the physics first curriculum. In fact, I would like to see a more European curriculum in which all the subjects are taken separately, but at the same time.
Dr. Stemwedel,
I have been watching your Phil 160 “What is Science” lectures online and they are excellent. Your lucidity is inspiring. Lately, they seem to be offline. I won’t bother the university since I’m not a student, just an autodidact from Louisiana, but, on your personal page, might I ask if the lectures will again be offered or have they been restricted in some way?
Thanks for your help.
Now where I teach chemistry, the normal sequence is Physical Science (8th grade), Earth Science (9th), Biology (10th), Chemistry (11th), and Physics (12th). While I completely agree about increasing the rigor of middle school math, I’m not sure I agree that calculus-based physics in high school is desirable. Most high school students will never take calculus, even if/when they get to college. “Physics for poets” is better than no physics for the majority of students. The reason I am in favor of physics first is more practical. I have to teach a lot of physics when covering the structure of the atom. Time saved there could be used to do more organic, bio-, or environmental chemistry. During my planning period I also overheard a biology teacher spend a couple of days on hydrogen bonding, that I’m sure she would rather spend on something else.
It might be possible to have it all by switching the 8th and 9th grade curricula while making physical science more rigorous, and following this by chemistry, biology, and calculus-based physics, in that order.
My high school was highly sexist. Everyone had biology, then chemistry. The two subjects the girls were not allowed to take were geometry and physics for some reason. I did not have physics until the university. Luckily for me, I like science and I like to read and study. I can ask questions in theoretical physics that only people with a doctorate in that area are qualified to answer. Meanwhile, my old school just keeps serving up the state’s “approved” standard students. I hope the playing field is equal some day in my home town.
I believe pretty easily that the order of high school science education does not make a difference when it gets to college. I had physics in high school before I took calculus, and I’m taking it now in college with the benefit of derivatives. While some things make more sense now, having the basis of alegbraic physics first actually made calc-based physics much easier. To learn the equations and concepts before being able to understand them may sound counter-intuitive, but having them stored in your brain and then being able to retroactively take them apart and understand them, I think makes for a more effective, if unintentional, teaching strategy.
Granted, there are some concepts and ideas that just cannot be approached, in all scientific fields, without the tool of calculus, but otherwise, a good solid base of alebra level science in high school regardless of order makes perfect sense.
Along the same lines though, starting calculus in high school is definetly a major advangtage for learning it in college. Being exposed to the ideas and theorems of calc before getting it intensely allows students breathing room when they first get to college and allows them to start working on the corollaries to calc, i.e. science, on higher levels.
I’m a biology PhD student, product of a ‘physics for pre-meds’ course (trig but not calc based). I second Susan’s comment of teaching calc and physics concurrently. I had to take calc twice (once sorta at the high school level and once at college) and I didn’t truly grok it either time. I rather disliked it in fact. Then I got to physics and all of a sudden it *mattered*. I didn’t need it for computation (because of the sort of physics I was required to take) but the derivitive concept clicked once I got to acceleration and velocity, in a way it never did in math class.
Some students will truly feel that the only good reason to learn math is to do the science- delaying the science by requiring mathematical pre-reqs is unwise.