I teach high school science (including algebra-based “honors” physics) and I never fail to be surprised by the poor math skills of some of my students. Most are taking the honors-level Precalculus class concurrently with physics, and yet some of them have difficulty with even the most basic algebraic manipulations–like simple rearranging of equations to solve for an unknown.
What really floors me is the following scenario that happens pretty much every year:
A student who is struggling comes in for tutorials to get help with some homework. I have him work a few of the problems with my assistance–nudging him in the right direction if he gets stuck. I can see that he is mostly ‘getting’ the physics of the problems. He has a decent conceptual grasp of what is happening. It’s just the math that is holding him back. Atrocious algebra skills. Deep-rooted misconceptions about basic algebraic relationships. (Common examples: 7x - 5 = 80 becomes 2x = 80 and so x = 40. Or 12y = 56 becomes y = 56 - 12. Gah! And even when I explain the mistakes, they still don’t understand what they did incorrectly!)
Usually, I end up gently pointing out to the student that he has some big flaws in his understanding of math, so that he will know where to focus his efforts. Invariably the response is, “But I’m good at math! It’s physics that I don’t get!”
And that’s the sad part of this–most of these students don’t understand how bad their math skills are. They actually believe that they are “good at math.” The truth is that they are “good at math class.” They get high grades in their math classes, which makes me wonder just what the hell is going on in those classes?! They are failing physics because of their obviously poor math skills, but they are “good at math.” :smack:
Do you mean they actually had you doing Archimedes, or some other rigorous proof of the volumes/areas? IIRC some of the proofs related to areas aren’t that hard to grasp, but the volume proofs are more difficult.
In my experience you might be told the volume formulas in the fourth grade, but nobody would be taught rigorous proofs of the formulas at that age, at least not in the public schools.
This sounds more like analytical geometry than plain old Euclidean plane geometry. Usually we don’t get any kind of geometry in detail until high school, at which point there’s usually a whole semester devoted to it. Exactly when that happens varies depending on how much of a struggle first year algebra was, because the algebra usually comes first. For most of us, high school geometry is our first exposure to the kind of math that’s driven by proofs rather than by rote memorization, or by pages full of the same type of arithmetic problem. Before high school, any geometry we had was nothing more than a few days of an entire semester otherwise devoted to arithmetic drills of one kind or another.
I suspect they intended to reply to the OP of this thread.
(Just sayin’ when you discuss math, you ought to be more precise… And maybe a little less condescending in the face of clearly understood informal terminology. Not that the points you note aren’t worth noting; they just don’t have to be made with that tone.)
I’m not sure whether the proving processes we followed were Archimedes’ or not, if it was it probably wasn’t mentioned. It was the year I missed half the classes due to recurring tonsillitis, and a long time ago: I basically learned from the book, and yes it involved volumes and it involved going through the steps to find the formula, only the formulas still weren’t presented as “math with letters” (that was 6th grade). You’d end up knowing that the volume of a parallelepiped (sp? - early in the morning and feelin’ lazy) was “height times width times depth” and that you got the same value no matter in what position it was and this somehow was used to teach/reinforce that “in multiplication, ab is the same as ba”…
We did have the proofs in the book and I vaguely remember MA explaining some of them in class; I know we didn’t have to go over the proof in exams. At that level, the proofs were presented as a series of logical steps where you knew how and why each followed from the prior one; they were tools that we could use if we got stuck remembering the formula.
Then we got to 6th grade (5th was a repeat of 4th minus the geometry), and we got “math with letters” and proofs that we had to “just memorize” for the first time, and for the first time the regurgitation of the proof was part of the exam. That’s also the first one of my math teachers that I’m sure did not understand or like the subject at all, I got in trouble for asking “how do I know which step to do next? I can’t see the logic to follow it” when I tried to understand the proof of the solution of quadratic equations: her answer, “math isn’t logical.” :smack:
