A look at a process of measuring students' quantitative skill
levels with respect to problem solving in introductory physics labs. What
can we actually measure and how can we measure it? Some of the approaches
and some of the obstacles involved will be discussed.

A report called Rising Above the Gathering Storm gathered an
unusual amount of attention when the National Academy released it in 2007, and its conclusions have guided discussion in Washington DC and elsewhere since. The report makes the case that the future of the country depends upon strengthening the national infrastructure for mathematics and science, and particularly emphasizes the importance of improving science and mathematics education in public schools.

I began working to improve teacher education in mathematics and science at UT Austin in 1997 with a program called UTeach. We were highlighted in the Gathering Storm report, and are now the nucleus of a national effort. I will describe data from across the nation indicating the scope of the problem we face if we wish to increase access of citizens from many economic and demographic groups to mathematics and science. Then I will describe the steps we took at UT Austin, the accomplishments that generated national attention, and some of the problems that are still
unsolved.

UTeach is a project at UT Austin to recruit, prepare, and retain secondary teachers in science, math, and computer science. This seminar is an opportunity to discuss UTeach and its implications with one of the project co-directors, Michael Marder. For more information about UTeach visit the Web site: http://www.uteach.utexas.edu/

Expert problems solvers are characterized by continuous evaluation of their progress towards a solution. Part of this evaluation includes reflection upon the problem’s solution, both from an ideal knowledge perspective as well as that of the solver’s knowledge per se. In order to facilitate this process, a deliberate and explicit prompt may be useful as part of cognitive apprenticeship in order to foster diagnostic behavior in novice problem solvers. Two experiments involving introductory students will be discussed. The first is based on an individual diagnostic behavior ("self-diagnosis") in which the student is prompted to diagnose errors on a quiz during recitation, and the second is based on a group diagnostic behavior ("peer reflection") in which groups in a recitation discuss their homework solutions together. In both cases, consideration will be given not just to physical content but also to elements of a preferred method of problem-solving strategy. I will also present a study on a section of upper-level undergraduates with regard to attempting the same problem twice in an exam situation. This is done in order to investigate the premise that as more advanced problem solvers, they will more readily take part in the reflection exercise without the explicit prompting that may be more necessary for introductory students.