Karl asked about the math involved in the gas laws in chemistry. There are some simple conversions with gas laws and there are some substitution into equations and then the rearrangement of the equations to solve for the missing variable. Like P1V1=P2V2 this equation shows the inverse relationship between pressure of a gas and its volume. When the students have three variables they are asked for the fourth.
I do not like the way that this attempts to explain the situation. I think that the kids are learning how to plug in numbers and get an answer. I do not think that it explains the situation. What I would like the students to understand, for example, is that when volume goes down then pressure will go up. If they setup the math first and in the above example first multiply the smaller volume and then divide by the bigger volume. (This will give an answer where the final pressure is smaller than the new one.) The understanding of the material is more inportant than the answer to the math. However, it seems that the students want to knwo the equation and not the concept behind it. How do we get the students involved?
A lot of times the students can do the math with numbers but not with units. Lets say we need to get meters to concel out when we start with meters per second. The students do not seem to understand if meters is on top of the units we are starting with then they need to divide by meters to get it to cancel out. How do we help them see the math of words?
To answer Karl's other question all students need to be concurrently enrolled in advanced algebra.