Our math department offers a class that our principal thinks is unnecessary. I truly don't understand his logic, which seems (to me) to be that students' doing well in this class is evidence that the class is unnecessary. If I'm misstating his position, it's only because he hasn't communicated it in a way that I can understand. To be clear, I think he's doing a fine job as principal and in general I support what he does, but on this one topic I just do not understand where he's coming from.
So I'm going to do a little statistical analysis. The course is a "prep for the follow-on course", so I've asked the district for the following data:
-Students who took both this course and the follow-on course at our school in the last three years
-Grades for those students in the follow-on course
-Students who took only the follow-on course at our school in the last three years
-Grades for those students
My goal is to be see if the prep course students do at least as well in
the follow-on course as do students who did not need the extra
preparation. It seems to me a chi-square test would be appropriate, looking at the proportions of students who "succeeded" in the follow-on course (grade of A or B) and whether or not they took the "prep" course. The true measure would be to compare the grades students would have gotten in the follow-on course had they not taken the prep course, but obviously that information is unavailable to us mere mortals. Any thoughts on the validity of the analysis as described above?
There's nothing wrong with doing that, but then I thought about the following: what if we were to do an analysis of standardized test results, by teacher, for different courses? Oh, I wouldn't need to know the teachers' names; the data could be given to me as Teacher A, Teacher B, etc. Would an ANCOVA analysis (using last year's test score as a covariate) be mathematically appropriate? And would it be "appropriate", for lack of a better term, to compare, say, all the geometry teachers?
I was thinking about this because we have some teachers who are all into Common Core, into group work, into all that stuff that I'm not; I'm a direct instruction kinda guy. Currently, though, my students' results can't be compared to anyone else's, as I'm our school's only statistics teacher and the other class I teach doesn't have a specific standardized test associated with it. We do, however, have several geometry teachers, and they use varying methods to teach the subject matter. My thought was that we could use standardized test scores as a proxy for the teaching methods and analyze to see which results are better. We have lots of geometry classes.
If I could see some evidence that so-called discovery learning and group work, which we're being pushed by the district to implement, is valid, I'd give it a shot, but until then I'm going to stick with direct instruction.
In any other field, a valid statistical test would be considered not only reasonable but obvious; in the unionized, we-are-all-one world of education, though, even the mere suggestion that some teachers (or their methods) are not as effective as others could ignite a firestorm.
What do you think?