The investigators of the project Measurement, Modeling, and Methods Category are studying how science and engineering students build towards problem solving expertise throughout a major part of their academic careers and how they transfer their knowledge and skills across undergraduate STEM courses. They are observing students' problem across 3 years of courses starting with mathematics and continuing through introduction to physics to engineering courses.
The three year research plan consists of longitudinal and cross-sectional studies that take place both in-class and out-of-class and involve 3000 students through seven classes at Kansas State University. The research team is studying the following variables associated with problem solving: the problem features of structuredness, complexity, domain specificity, and dynamicity; problem representation of form, organization, and sequencing; and individual differences of domain knowledge, problem solving experience, reasoning skills, and epistemological maturity. Quantitative data and qualitative evidence are being used to study the variables. An on-line homework system created with previous NSF funding (DUE 0206923) will enable quantitative analysis of the variables with large numbers of students.
The data of subjects from underrepresented groups will be analyzed and compared to the larger groups of students. Results of this project are expected to advance the knowledge and understanding of STEM teaching and learning in undergraduate education.
courses in the undergraduate curriculum. Our results indicate that in all three disciplines students are able to master procedural knowledge. However, they do not necessarily develop a deep conceptual understanding. In mathematics, the students have difficulty gaining conceptual understanding beyond the action and process levels of a mathematical concept. In other words, students, even after three semester of calculus, do not develop an ‘object’ or ‘schema’ level understanding of mathematical concepts, as per the APOS (Action Process Object Schema) framework (Dubinsky & McDonald, 2002). Students may pass the courses by mastering the procedures without mastering the concepts of mathematics and learning how to transfer them to different situations (Bennett, Moore, & Nguyen, 2011). In physics, students can ‘crunch through’ the math, but they have difficulty with the physical interpretations of mathematical notations and operations. In particular, we see improvement in students’ understandings of integral as an area underneath a curve, however few students display an understanding of integral as a process of accumulation (Nguyen & Rebello, 2011a, 2011b). Similarly, students also struggle with the use of graphs in physics sense making (Gire, et al., 2011). When students move into engineering they appear to have a misdirected understanding of ‘area under the curve,’ properties of functions, time shifts and other concepts that they appear to have had a clear understanding of in their mathematics class (Chen, Warren, Nguyen, Rebello, & Bennett, 2011). One key issue is that students seem to be much more adept at applying graphical information to accumulation problems posed during mathematical interviews than they are during physics or engineering interviews. In particular, we have found problems that are mathematically identical where students can do the problem in the context of mathematics but are unable to solve the same problem when posed in the context of physics or engineering. The issue however, is not that students have difficulty recalling concepts. Our interviews indicate that they can recall the mathematical concepts quite easily. The issue is deeper; they have difficulty activating the right conceptual resources within the contexts of the physics or engineering problem. In othe rwords, they appear to have learned the math concepts insofar as applying them to problems in a math course, but later when they transition to a physics or engineering course, they need considerable scaffolding to do so. In addition to investigating students’ difficulties with problem solving and transfer in thesethree courses, we have also investigated the use of instructional strategies to address students’ difficulties with activating the mathematical concept in the context of physics and engineering. In focus group interviews in physics, we have created several collections of problems and hints that show some preliminary success in helping students solve problems in multiple representations. Each collection combines abstract mathematical scaffolding, student evaluation of different lines of reasoning and student creation of complex problems. Using a treatment group, control group and pre-post quasi-experimental design we have shown robust improvements in students’ skills of transferring mathematical concepts to physics problems (Nguyen, Gire, & Rebello, 2010). We have also developed online learning modules in engineering to help students with their conceptual difficulties. For the online learning modules we find, significant correlations between module scores, grades on written examinations and performance in previous mathematics courses have demonstrated variable clarity, but qualitative assessments of the technology-facilitated environment point to a clear increase in student learning (Chen & Warren, 2011). Overall, the project has advanced the state of knowledge of conceptual difficulties that students face as they attempt to transfer their knowledge of mathematics to problem solving in physics and engineering. The project has led to 20 peer reviewed publications and about 35 talks and posters at conferences. Three graduate students have completed Ph.D.s in Mathematics Education or Physics Education based on their work completed on this project. Three post-doctoral research associates (one in mathematics and two in physics) were supported on the grant during the course of this project. All of them have secured tenure-track positions in which they continue their discipline-based educational research work.
