| Abstract: | This study was designed to examine open-ended assessment items which target conceptual, procedural, or strategic knowledge of the definite integral. Two research questions were considered. The first question was: To what extent does student performance on each item reflect the targeted knowledge type? The second question targeted student knowledge: What do students know about the definite integral? Students from both honors and engineering calculus classes were given open-ended assessment items, followed by interviews. It was found that at one point in students' growth in procedural knowledge over the semester, performance on procedural questions was masked by strategic concerns. By the end of the course, however, procedural knowledge was again displayed in response to procedural questions. Student responses to conceptual questions revealed not only the conceptual links which the students had formed but also the links which were missing. Because responses to open-ended questions are written in natural language form, care must be taken not to read more into an answer than is there. The strongest conceptual links were between integral and area, and between integral and antiderivative. The weakest conceptual link was between integral and limit of Riemann sum. Strategic items did yield a path to an answer, although students generally displayed only one path, and not all possible strategies were found. |
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