> > Hansen demonstrated > > that he had either not bothered to read or had not > > understood the > > recommended references. > > I am amazed that you're taking the time to respond to > him. I have gained only a bare familiarity with "your > side" of these issues over the past few weeks, and I > found Hansen's comments amusing, at best. Nearly > every point he makes is addressed in Mazur's > "Confessions of a Converted Lecturer," for example. > While Hansen may have valid objections to that and > your other references once he investigates even a few > of them, his comments make it clear that he has not > done so in the slightest. > > Personally, I would like to see some honest > discussion of these matters, because I would like > nothing more than to learn that the more-or-less > traditional lecture approach is most effective in the > sciences, since it is the format in which I am most > comfortable (as are probably most students), but > arguments and evidence I have seen so far in its > favor have been despairingly unconvincing.
Robert Hansen does make some good points in that the FCI and other conceptual approaches should focus on problem solving and the mathematics as well, at least for students who do need to learn some of the mathematics behind physics. Focusing just on concepts is not enough unless the course is meant to be a purely conceptual course for non-science majors.
But do those who focus on conceptual understanding ignore the math? Do they ignore problem solving in physics that involves the math? Are they content if students score well on the FCI, even if they cannot solve mathematical physics problems? I doubt that, but I'm no physics educator or physicist.
However, I do that, in the Math Wars, traditionalists often accused reformists of sucking the math out of math class.
When it comes to lecturing, I too wish I could say that it works effectively but not with lower-level students. In particular, lower-level students often need to change their study and thinking habits and their attitudes about mathematics, but these things lectures rarely address. Furthermore, by devoting most of the class time to lecturing or quiet work with students working alone (the latter does not happen much in college except during quizzes and tests but has happened a lot in my K-12 math classes), students do not get opportunities to get commentary and encouragement about the study and thinking habits they need to be successful mathematics learners. By relegating all such activity outside class, students rarely get any such help and encouragement and end up continuing with their poor study habits without a clue as to why they continue to struggle with learning math. In short, if lecturing helps at all, it helps only those students who *already* know how to learn mathematics by reading and studying on their own.