This award supports a physics education project designed to help students learn ?generic expert skills? including sense-making of the answer (scaling and ratios, special and limiting cases, dimensions and units, exploiting symmetry, and especially estimation), as well as understanding that physics comes from a few principles. The project is based on three principles: a survey showing that professors very much want to teach these things, the use of online problems with embedded tutoring to help students learn, and plans to disseminate both the problems and a diagnostic test created from them to 200,000 students per year (which requires only one mouse click by their instructor). The plan is to distribute both the diagnostic test and the library of problems that tutor expertise in two ways: over the web to teachers (public domain) and through a commercial product (Mastering Physics) that currently reaches about 100,000 introductory physics students annually, but is expected to double this in the coming few years.
– Project Outcomes The title of this grant suggests that specially designed problems can help students learn to be experts. Our work has indeed collected such problems and made them available in LON-CAPA, an open source learning management system. However, we have also addressed the desirable outcome of teaching students to be more expert problem solvers by developing and implementing a new pedagogy, described immediately below. In addition, we have begun work developing two instruments that measure two important components of being an expert in Newtonian Mechanics: a Mechanics Reasoning Inventory, and a Procedures Test that involves simple procedures, like calculating the torque, the potential energy of a pendulum, or the kinetic energy of a rolling ball. (It is early in development, and is not described further here.) Teaching Problem Solving Most reformed physics courses and texts emphasize conceptual knowledge, and use a conceptual test such as the Force Concept Inventory to evaluate success. On the other hand, the large majority of physics courses nationwide evaluate students on their ability to solve problems. Unfortunately, there is no standard to assess this ability, and research has shown that standard introductory physics courses and teaching materials fail to help students approach unfamiliar physics problems involving the material that they have learned. This is largely because these courses emphasize declarative and procedural knowledge (e.g. that F=ma is a vector equation and how to draw force diagrams and get equations for each component), but not strategic knowledge – e.g. whether the problem at hand is best solved using energy concepts or F=ma. From this perspective the common student complaint "I understand the material, but I can’t start the problems" is a cry for help in gaining strategic knowledge. Professor David Pritchard’s RELATE education group (REsearch on Learning, Assessing, and Tutoring Effectively) has developed a new pedagogy for teaching Newtonian mechanics that is designed specifically to help students develop their strategic knowledge in an expert-like manner. It achieves this objective by helping students organize the course material into a hierarchy of models, and then approach solving of each problem as a similar model. All models specify the system, the interactions, and the model equation of change – SIM for short.) This approach is a simplification of the modeling physics approach that uses discovery-based laboratories to convince students that both physical laws and solutions to physics problems are models. This new pedagogy is called Modeling Applied to Problem Solving (MAPS). MAPS was implemented in a three-week ReView taught in IAP. This ReView was the basis for the Physics Department’s "Second Chance Program". At the end of the ReView, the 30 students who received a grade of D in the fall 2008 semester of 8.01 (Introductory NEwtonian Mechancis) were given an 8.01 final exam "calibrated" by an earlier 8.01 class. They scored only 0.1 standard deviations below the average (vs. 1.2 stdev below class average in December ‘08). The Colorado Learning Attitudes Survey about Science was administered before and after the ReView to see how expertlike their attitudes were. 8.01, like most introductory courses nationwide, reduces the expertise of student attitudes by about 10%. The CLASS showed that our ReView increased expertise by more than 10%, especially in the category "problem solving sophistication", a tremendous increase for such a short course. Figure 1 Here Mechanics Reasoning Instrument Most professors and all college presidents want their students to have better problem-solving and reasoning skills. Toward this end, we have written a Mechanics Reasoning Instrument designed to probe a student’s ability to identify which physical concept is involved in solving a problem as well as why they think this principle is relevant. Asking "Why?" is tremendously important: often students know a procedure for solving particular kinds of problems without understanding the underlying reason for this procedure or when it would no longer apply. Our instrument is similar to the format of the Lawson Test of Scientific Reasoning, asking a procedural question first, then a followup question asking why this procedure applies. We ask questions in two areas. One is to identify conserved quantities and/or to compare two quantities in a system (e.g. "is energy conserved?" "which force is greater?"). The other is to divide a situation into multiple parts, as one would during solution of a complex, multi-step problem (e.g. the ballistic pendulum). In both types students are then asked why they made the selections they did. This pairing of questions measures the ability of the student to reason from fundamental principles rather than superficial features of the problem. This exposes a fundamental difference between experts and novices. We have seen a strong correlation between a good postscore on this instrument and a student’s improvement in test scores over the semester.
