Technology & Model-Based Conceptual Assessment: Research in Students' Applications of Models in Physics & Mathematics

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To improve the communication between students and teachers, particularly in large classes, many universities have begun using technology-based response systems. These systems enable an instructor to pose questions and see, within a few minutes, the students' responses to those questions. Another similar approach is to assign homework that is submitted, graded and returned quickly via the World Wide Web. Both of these technology-based systems offer instructors the opportunity to record each student's responses in a database. Thus, the instructor can track students' understanding much more completely than with traditional homework and quizzes and can use the resulting data to investigate more deeply how students understand the scientific and mathematical concepts. In addition to seeing the present level of each students understanding the instructor can learn how the students change their thinking by making comparisons of responses throughout the learning process. A present, the analyses of these responses generally tell instructors when the students are obtaining the right answers. However, for students who are not answering correctly, the present systems do little more than indicate that the student is not applying the scientific theories and models correctly. Still missing is an analysis tool that is based on contemporary educational research and can provide robust quantitative information on the students' difficulties with the underlying scientific models and theories, and can track how the students' understandings of these models change during instruction. These tools must go beyond correct answer analysis and analyze students' incorrect answers by incorporating theories of learning into the systems. This project will begin with a model for students' conceptual learning processes and with existing work on assessing students' conceptual understanding in physics and mathematics. Then, research will be conducted on students' applications of scientific models and mathematical concepts, on how the students' thinking and applications change during instruction, and methods to present the results of these assessments to teaching faculty who are using in-class, real-time response or on-line homework systems. By constructing sets of questions in which incorrect answers provide insights into the scientific and mathematical models that students are applying, the project's results will lead to a deeper understanding of students' abilities to learn physics and mathematics and the contexts in which that learning occurs most effectively. The analysis will also provide insight into students' abilities to transfer knowledge between physics and mathematics courses. The major objectives of the project are to measure, with real-time feedback, students' understanding of fundamental concepts and the application of those concepts, trace changes in those understandings and applications during instruction, investigate how students' conceptual understanding depends on the context in which a new concept is studied, create analysis tools that can be used effectively in many educational environments, provide information about the transfer of knowledge between physics and mathematics, and investigate how students and instructors interact with this teaching environment.The result of reaching these goals will be a system that will have a large impact on the teaching of science and mathematics. The impact will be particularly great in large enrollment classes where instructors are often very detached from their students because, frequently, such information becomes available only after students take an exam. Of particular importance for the instructors is knowledge of when students have begun to change their thinking but still sometimes revert to pre-instructional applications of scientific or mathematical concepts-- a mixture of understanding and a lack of understanding. Such situations are recognized to be an important intermediate step in the learning process. By knowing the extent of this mixture the instructors can plan the next step in the learning process based on the students' present physical or mathematical understanding and the contexts which aid fundamental change in students' thinking. Thus, the project will provide both information and tools to help science and mathematics instructors learn about the present knowledge of their students and how to use that present knowledge constructively to improve the students' scientific and mathematical thinking skills.