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## Cognitive Issues in Upper-Level Physics Courses

The following notes were written by David Meltzer, as a presentation to the Round-Table Reporting Session regarding an invited poster session at PERC 09.

- In upper-level courses, instructors need to help students unpack a vast set of knowledge resources (physics and math concepts, math techniques, etc.) that are now coming to dominate the field of play.
- Students come into upper-level classes with lots of “baggage” including both potentially useful, and potentially harmful elements (physics ideas, ideas about how to learn physics, etc.). All of these will need to be addressed by instructors in some fashion.
- Instructors can not assume that upper-level students are “good to go” either from the standpoint of mastery of concepts or of techniques that were studied in lower-level courses. Instructors need to help get students into gear. To do this they must carefully explore their students’ thinking (to know where they are conceptually and in regards to technique), and then devise strategies that take into account what they have found.
- Additional work is needed to help students interpret math concepts and techniques and especially to connect them with physics ideas. Instructors must be cognizant of the existence of much “physics” math, that is, is math which is NOT taught in students’ math courses. (For example: how to factor out appropriate physical quantities to create small dimensionless parameters on which to base series expansions, in order to pull out leading-order terms.) This physics math MUST be addressed explicitly in physics courses if students are expected to master it.
- Students need to come to understand that when they reach the upper-level courses, the game is now becoming one of making sense of the material and of integrating diverse knowledge elements, not simply one of plugging and chugging as was often the case in introductory courses. This is a significant “cultural” shift that may entail substantial adjustment on the part of the students.
- Upper-level students may be more capable than introductory students of interpreting and applying arguments based on qualitative reasoning. However, they may at the same time tend to fall back on algebraic/quantitative reasoning and arguments (employing their more advanced math skills) when faced with problems that are unfamiliar or out of their comfort zone. This may or may not turn out to be a productive strategy for them.
- Instructors need to be on the lookout for and take note of student intuitions, (included among the “baggage” the students carry), and design instructional activities (e.g., tutorials) helping students to reason out the consequences of their intuitions.
- A diverse array of interactive activities, specifically including whole-class discussions, should be used to help students explore and focus on qualitative (“big-picture”) aspects of math procedures, etc. These big-picture issues may previously have been ignored or overlooked by the students, particularly as they focus on much longer and more complicated mathematical calculations than in their previous courses.
- A particular challenge may lie in quantum mechanics, where students may tend to give up on trying to make conceptual sense when problem solving. Students have an increased tendency to default to misleading intuitive or seat-of-the-pants ideas by answering questions in ways that are obviously wrong from a mathematics standpoint, which they could have realized had they focused on physical sense-making. Alternatively, in all upper-level courses, students may default to purely mathematical problem-solving strategies if they decide that qualitative sense-making (i.e., being able to justify their steps) is either not appropriate or not possible.
- Even in (or particularly in) upper-level courses it is desirable to assess students’ ability to communicate and explain their ideas, by using appropriate homework and assessment techniques. For example, instructors can compare and contrast students’ “correctness” in problem-solving with their performance in “reasoning and justification” of their ideas, employing separate scores for the two criteria. This is appropriate since both are important consensus instructor goals, and these types of assessments are very helpful in exploring details of students’ thinking and student difficulties. Traditionally, these broader goals have not been addressed in upper-level courses or valued on assessments. Specific examples of how to do this have been developed by the various PER groups doing research and development on upper-level courses.
- Engineering students in upper-level physics courses may tend to have a higher discomfort level with offering explanations of their reasoning, and may also have a greater tendency to favor “plug-and-chug” methods. They may also show a tendency to persist with familiar but inappropriate notational conventions and terminology that they learned in their engineering courses, but which are out of place or incorrect when used in their physics courses.