|Abstract||Students who are more comfortable with the mathematical underpinnings of steps required to solve physics problems or to derive physics formulas will need to devote less intellectual effort to the mathematical aspects of physics class and will be able to think about the physics concepts proportionally more. My question deals with the best way to get students up to speed with the mathematics, particularly students who have not encountered the relevant mathematics before (despite what course prerequisites might imply) or who struggled with those mathematical concepts when they were introduced. I hypothesize that beginning a physics class with a brief review of the mathematics necessary to solve the problems and follow the lectures in the class will help students, particularly students with less mathematical background than others, succeed better at learning the physics than would beginning directly by teaching the physics.
This would be most useful in classes where students are not expected to have as strong of a mathematical background as physics majors typically are (although a nonzero quantity of physics majors are mathematically underprepared for their first physics classes). Consequently, I'd like to target the project at general physics classes for non-science (and non-health professions) majors. I would prefer to treat this as an intervention in a class which comes in two or more sections taught by the same professor, thus providing a control group. For the control class, I'm considering asking the professor--if I can find one willing to go along with this--to teach it as usual during that time, which means my intervention class would have a little less total instruction time explicitly in physics. (My hypothesis is that a properly-tuned math review will help the students more than the equivalent amount of time spent diving directly into the physics.)
It is my hope that an initial review of relevant mathematics would serve as a refresher to students who are reasonably comfortable with the mathematical topics but may not have thought about them in the context of physics before (which I hope will avert some boredom during this review on the part of the more advanced students) and as an alert to students who are uncomfortable with those mathematical topics that they may wish to devote some study time to the math.
I would like to measure the effect of the mathematical intervention by seeing if it results in a smaller achievement gap among students--a narrower score distribution (as measured by the assessments typically given in a class such as this)--or perhaps in higher class average grades. Since, in my experience, there can be a wide scatter between identically-taught classes in terms of achievement, it could be somewhat difficult to quantify how much of any performance gap that appears is due to inherent differences between the classes and how much could be due to the mathematical intervention. From a more subjective standpoint, I'd like to begin and end the semester with a survey given to the students in the test and control classrooms asking them about their level of mathematical preparedness and how they think that (will have)/has affected them during the class, with particular interest given to their level of comfort with the mathematical aspects of the physics. Ideally, I'd also like to do an exit interview with the professor to see whether the professor noticed any differences in the types of questions asked by the students in class and during office hours.
It would be nice also to test whether the math review is more helpful when given up-front in the first week of class (this is the approach taken by many upper-level physics textbooks, which begin with a chapter reviewing the math useful for the book) or when parceled out in chunks every few weeks as topics requiring those math skills crop up. The chief difficulty I see with the second approach is that it's harder to predict when small topics using particular math skills will crop up. Another question would be whether beginning with an overview of the physics to be learned in the class would better help the students. |