Investigating and representing inquiry in a college mathematics course

Recent calls by the National Research Council and the National Science Foundation have stressed the need for excellence in undergraduate mathematics and science education with emphasis placed on inquiry learning. The purposes of this qualitative study include (1) the examination of the pursuit of inquiry in two collegiate mathematics classrooms incorporating methods of mathematical modeling and (2) the generation of a quantitative representation of characteristics of an inquiry environment.; Instructors and students in two classes of laboratory-based calculus for life sciences majors were observed. To capture descriptions of the environments and students' mathematical modeling skills, the classes surrounding three science investigations were audio or video recorded; interviews were conducted with one instructor and six students in the researcher's class; and copies of students' lab reports were obtained. Transcripts were coded using various scales to produce graphical images of the classroom environments.; The data were used to describe and document the effects of both classroom environments. Instructors' goals and time factors influenced the development of inquiry, mathematical modeling, symbol and language use, and the amount of reflection. In both classes when time was of minimal concern, the class pursued students' questions, developed students' modeling methods and notation, and consistently and frequently linked the mathematics and science contexts. When pressured by time to cover specific mathematical topics, the class pursued instructors' questions and methods and less frequently linked the mathematics and science contexts. Most students in both classes retained a process conception of mathematical modeling as they could apply the developed methods but relied on instructor prompts to relate the mathematics and science contexts.; The pictorial representations of the classroom environments illustrated that both classes had periods reflecting a constructivist inquiry environment. The graphs highlighted the classes' implementation of multiple cycles of inquiry, periods of consistency and inconsistency in connecting the mathematics and science, and intervals in which students' or instructor's ideas dominated discussion. Class observations suggested that the pictures lacked clarity in identifying periods of agreement or disagreement of the resonating concepts of students and instructors. Recommendations are made for future examination and representation of inquiry environments.