Section 3.2 Goals of “Math Bits” sessions in Paradigms in Physics junior year courses
The PI described the dilemma that the new “math bits” sessions were designed to address:
Most physics departments face a question of whether to teach math methods either as a separate course or embedded in the upper division physics courses, and neither one is particularly a good solution. When it (math methods) is taught as a separate course, it tends to be too math-y and too separated in time for some students to be able to understand how it (the math) is going to be implemented. When it's embedded in the courses, when time gets tight, it tends to get ignored or it's taught so much in context that the students don't know how to abstract, how the math works in general in cases other than in the particular context in which it is being described, so they don't know how to generalize it to other situations.
The intent of the “math bits” sessions in the junior-year physics courses is to blend these two approaches, to provide “just-in-time” mathematics instruction within a physics course but presented by a separate instructor. Having a separate instructor responsible for the “just-in-time” mathematics instruction is intended to ensure that not only does such math instruction occur but also that the students will have access to the type of generalized understandings that a separate mathematical methods course would encourage. The PI described this intent as follows:
The idea is that it will be just the week of math methods that is relevant to that particular course, so it's like embedding it in a course, but we're having me teach each of those “bits” along side of whoever is teaching that paradigm (course), so that it's a separate voice, so that it can't be allowed to disappear. And so that I can attend to helping the students generalize the mathematics and to see how it might apply to another situation, or it might already have applied to another paradigm (topic), things like that. So that's what the intent is.
The embedding of mathematics instruction within the physics courses, but taught by a separate instructor, is this physics department's current approach to making sure that students understand the mathematics they need to succeed in doing the physics they are currently learning.