I am going to switch gears to physics education for awhile. This is still very relevant to Math-Teach because David Bressoud of the MAA is currently writing a series of articles promoting the adoption of ?research proven? physics education strategies in mathematics curriculums. An ironic proposal since the modus operandi of these strategies is to remove the math from physics. The inspiration of Bressoud?s series of articles (and a planned MAA study) is a report from the ?President's Council of Advisors on Science and Technology?, otherwise known as PCAST.
For the goal of increasing the number of STEM undergraduates by one million students, the report recommends that colleges start using ?research proven? physics education strategies because the research says they work so darn good. The report makes no mention of the quality of the STEM graduates, just that there needs to be one million of them. The thought did cross my mind of sending PCAST all of the resumes I have rejected in the last few years. I wager that if everyone in the position of hiring STEM graduates did the same, PCAST would get their one million bodies. In any event, this report references several of the studies that support those darn good conclusions and includes one in the appendix.
In Bressoud?s July article, ?Learning from the Physicists?
he talks about the lack of widespread adoption of these ?research proven? strategies. Specifically, he writes...
?Unfortunately, the experience of the physicists demonstrates that the existence of research based instructional strategies together with documentation of their effectiveness is not sufficient to guarantee their widespread adoption. Why not??
I answer Bressoud?s ?Why not?? with a four point response (thanks to Hake?s paraphrasing) that is as follows...
The CURRICULUMS resulting from this research and associated with these strategies ARE...
1. Compromised and designed for academically uninterested terminal students.
2. Lack the essential elements for academically interested students: rigor, detail, development and challenge.
3. Claim to be PROVEN but only in their terms, not in the traditional terms we expect.
4. Doomed because they don't produce STUDENT advocates.
Of these 4 points, points 1 and 3 are the easiest to prove repeatedly and convincingly. Thus, I will go through all of the research referenced in the PCAST report and in Bressoud?s articles and prove either point 1 or point 3, or in some instances, both.
Point 1, the ?terminal case? is the easiest to prove. If the study references an introductory course meant for non engineering majors then it is a study of a terminal curriculum and the point is proven. Several studies are in this ?terminal by definition? category. Several more studies are terminal in nature but do not state this explicitly. In those cases I will display the quizzes and exams associated with the study and make the prima facia case that they are terminal curriculums.
Point 3, the ?bogus proof case? is also very easy to prove. Generally, point 3 comes into play when a study is not of the terminal case. For example, one of the studies I reference below is with regards to an advanced Quantum Mechanics class. Obviously, this is not a terminal class. So what is a ?bogus proof?? A bogus proof is one in which I tell you that students perform better in class B than A, except I define ?better? by using a specific and partial test that I have developed. For example, in class A we might be doing a full and detailed development of the material, including derivations, while class B will focus primarily on the highlights (which my ?proof? test covers). Naturally, if I give class B an actual physics exam (the highlights in the context of all the detail) they will fail entirely. But if I give class B a test of just the highlights they will do much better, since that was their main focus. It turns out that class A will often not do as well on the highlight-only test, although they certainly don?t fail it. While class B?s focus is mainly on the highlights, class A?s focus is on the highlights in a functional context. In short, these proofs are bogus because they are comparing the outcomes of two very different classes. They are changing the curriculum to include MUCH less physics and then proving that it is better via a test designed for MUCH less physics. This problem could easily be avoided if the researchers would compare like to like. For example, I would take two AP Physics classes, teach one the traditional way and the other the ?research proven? way and then compare results on the AP Physics exam. This isn?t a difficult concept to understand. As I go through study after study you will begin to ask yourself ?Why are they not doing this??
Just to start off with, the following is the study included in the PCAST report referenced above. This is the new and improved way to teach our alleged future one million STEM graduates we need to remain competitive.
Source: Deslauriers, L., E. Schelew, and C. Wieman. (2011). ?Improved learning in a largeenrollment physics class.? Science 332: 862864.?
If you have a subscription to Science (a free subscription will work), you can read the study here...
This was a one week study involving two large classes, Both classes were taught traditionally, up to week 12, at which point, one class continued to be taught traditionally and the other class was taught using an interactive approach. A multiple choice test was prepared at the end of week 12 by the researchers (from previous test material that they had already prepared) and It was agreed on by the instructors of both classes. The test covered that week?s worth of material, was given to the students and the results showed that the interactive students did much better.
1. This was a terminal class by definition. This was an introductory physics class that all students must take.
2. This was a terminal class by the nature of the questions. If you can?t view the test questions above then I will describe the questions as being a mix of fact and concept questions. For example, if two lasers both emit 1 watt of power, but one laser has a higher photon frequency than the other, does it emit more photons (per second) than the other or less?
3. It appears that the authors of the study (and the instructors of the interactive class) were familiar with the test prior to the beginning of the week while the instructor of the traditional class was not.
4. Finally, a one week study? That doesn?t necessarily have to do with my points but how did a one week study get chosen as the example study in the PCAST report. I would have chosen something more substantial.
This second study is by the same authors and represents a case of bogus proof (point 3). This is a study of two sections of an advanced physics class, namely, Quantum Mechanics. This is a full term study. I am still seeking the actual course materials and exams but the description of the two classes, C1 and C2 below (in the authors words) tells us most of the story.
?The general structure of the course was the same in both years. The class met twice a week for 1 hour and 50 minutes and once per week for 1.5 hours, for a period of 11 weeks. There were two in-class midterm exams and a final exam, as well as weekly homework assignments. The homework assignments for C1 were typically four to five substantial word problems that encompassed both conceptual ideas and quantitative calculations, whereas for C2 the problems tended to be more broken up into a number of smaller pieces that would have a specific conceptual or quantitative focus, but the total amount of time required to do the homework was similar for both groups. Both cohorts had similar weekly optional problem-solving sessions where students would gather in a room with teaching assistants to work on homework problems. The material covered was quite similar in the two years, except C2 covered some additional material, primarily on applications of quantum mechanics. Standard widely used but different textbooks were used for both courses. The lecture notes were posted online for C2 but were not for C1.?
In short, two very different QM classes. Different homework, different quizzes, different exams and naturally, a different focus. The test of proof was (of course) not a full quantum mechanics test, just a quantum mechanics inventory. I will hold off saying too much until I get the actual course work and tests. But I will end with pointing out that the authors were very "careful" in their descriptions of C1 and C2. I don't mean careful as in being careful to make sure that the reader fully understood what made up C1 and C2. I mean "careful" like in a deposition.