Section 3.4 Surprises encountered while integrating math bits into the junior-level physics courses
The PI had taught the mathematical methods course for many years and had initiated the integration of mathematics instruction into several of the Paradigms in Physics courses previously, so the plan to expand this process to all the junior-level physics courses had seemed desirable and feasible. What was personally surprising was “how hard it is to do this.” The PI also reflected upon what surprised the students.
Personally surprising: How hard it is to do this.
In reviewing the rationale for eliminating the mathematical methods course and integrating the mathematics instruction into every junior-level physics course, the PI expressed the following:
I for years described the problem of math methods as if you take it out and teach it separately then the students, because it's separated in time from when the students are going to use it, they don't see what its useful for, and particularly there's a set of students who if they don't immediately see what it's useful for, they just won't remember it but when you integrate it into the courses, then when time gets tight, it tends to disappear, and the physics faculty end up only doing the one example and not talking about it generally and not talking about where the students will see it in other parts of physics, and not helping to make those other connections, and so we explicitly decided in Paradigms 2.0 to have the math bits taught by a different faculty member so that they could protect that space, and...I'm still astonished at how hard it is to do so I'm just finding, I'm taking a much more different approach to it than I thought I would, in very interesting ways...using context independent and probably more clear math notation and teaching the math names for things as well as the physics names for things.
The challenges noted above contributed to this sense of surprise as well as a renewed commitment to the importance of generalizing the mathematics that the students encounter.
Surprising for students.
The PI also commented upon the students' surprise in how much math is required to do physics:
I think that the students are stunned in the junior year about how much mathematics is actually required to do physics, and the fact that each different paradigm (course) has a whole set of new mathematics that they have to master is still surprising them but maybe the dividing it up into a week here and a week there is turning it from like one huge surprise into a bunch of smaller surprises, “oh! I have to learn some new mathematics”, I am hoping that it feels more accessible to them.
Addressing this surprise for the students and easing its effects has been the motivation for undertaking the extensive effort that integrating mathematics instruction in all the courses has required this year.