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Abstract: Traditional lecture settings are giving way to an expanding variety of instructional strategies, prompted by recommendations to increase active learning and the use of technology (among others). This paper explores the effect of this evolution in classroom practice on the task of classroom observation -- particularly considering the question, "What phenomena should an observer watch for?" In many cases, use of a protocol can guide an observer through the maze of classroom events. While such guides exist, they have tended thus far to focus the observer's attention on the instructor, with at most occasional attention shifts to student behavior. Yet under current efforts to involve students in active learning, focusing observation attention primarily on the instructor does not give a sufficient representation of classroom events. To establish this assertion, this paper offers examples of actual observations and comments on some classroom events that this kind of focusing misses. These comments lead to suggestions for additional focal points: student primary activity(s), student misbehaviors, primary media used by instructor and students, and physical setting. Although this paper uses mathematics as an example, many of the issues raised here transcend disciplinary boundaries.
Abstract: Research in Undergraduate Mathematics Education (RUME), the study of teaching and learning of college mathematics, is a new area of research in mathematics. Information to support this discipline is found in publications from all over the world, in the form of monographs, reports, research guidelines, resource manuals, as well as journal articles. Researchers in RUME require access to materials that are not only specific to their field but also to the broader literature of mathematics, education, learning theories, instructional strategies, alternate assessment techniques, cognitive development, and human behavior. This annotated bibliography is designed to be a template for a comprehensive and up-to-date collection of RUME resources. World Wide Web (Web) locations for many of the items are provided, as are descriptions of several Web sites that present information of interest to RUME researchers.
Abstract: As part of the reform movement in undergraduate mathematics education, instructors have been encouraged to take advantage of technology for teaching. At the University of Oklahoma, we chose multivariable calculus as the course in which to begin to increase the use of computers -- particularly to facilitate visualization of the three-dimensional objects studied in that course. In particular, this paper advocates use of the World Wide Web to disseminate multivariable calculus materials to students and to instructors. We begin by presenting an abbreviated example from the materials we have developed; we then offer a variety of options for using such materials. Results from faculty and student surveys provide context and an indication of the need for more extensive use of the web as a resource. We expect that, as appropriate materials are made available and promoted, use will increase and lead to enhanced student learning.
Abstract: The Department of Mathematics at the University of Oklahoma (OU) is developing technology-based materials for its engineering calculus sequence. In this report, we discuss the in-class use of Mathematica animations and sequences of overhead transparencies, and the out-of-class use of problem sets and the World Wide Web, with multivariable calculus. A goal of the ongoing project is to offer interested instructors a variety of materials that will enable them to incorporate technology at a level of integration that they deem appropriate.
Abstract: In 1989 members of the Department of Mathematics at the University of Illinois at Urbana-Champaign (UIUC) implemented the Merit Workshop Calculus Program. Based on Treisman-style workshop calculus, the UIUC program was intended to address the problems of low success rates of students from underrepresented populations and of failure to retain these students in mathematics- and science-based majors. The authors conducted investigation by examining transcript records for patterns of (a) performance in first-semester calculus; (b) performance in courses that require first-semester calculus as a prerequisite; and (c) persistence at the university, especially in majors requiring calculus. Analyses included gender and ethnicity effects. The results indicate that the Merit Workshop Calculus Program had a positive impact for both genders and for several ethnic groups (African-American, Caucasian, and Hispanic). Particularly dramatic results were noted for women and for Hispanic students. The results reported here are important because they are based on longitudinal data and distinguish differential effects for both well- and under-represented populations.
Committee:
Professor Lizanne DeStefano, Department of Educational Psychology
Professor Donald Sherbert, Department of Mathematics
Professor Kenneth J. Travers (chair), Office for Mathematics, Science, and Technology Education (MSTE)
Abstract: Historically, students from academically disadvantaged and minority populations have experienced disproportionately high dropout and failure rates in college mathematics. These students often place into courses considered remedial at the college level. This research examined the effort to make a college algebra course more effective for "at-risk" students, admitted to a research university through an academic support program. In particular, the study analyzed the extent of reform in this course and the impact of the course on student outcomes, and identified barriers and enhancers to implementing reform in this context.
The reform efforts included employing active learning and student collaboration strategies, and attempting to create a "Treisman-style" workshop environment. These strategies challenge instructors to check their impulse to show and tell, and instead learn to facilitate and coach; correspondingly, instructors design challenging activities that differ from the standard manipulation exercises found in textbooks. This study followed an instructor through her first semester of attempting to implement these strategies.
A combination of retrospective and prospective data was utilized. Admissions and transcript records enabled the calculation of background characteristics (demographic and academic) and persistence rates (university retention and course and career paths). Prospective data included classroom observations, instructor and researcher journals, a pre- and posttest, and student interviews.
The results indicated that (a) the academic support program itself provided a supportive, inclusive environment for both the students and the instructors; (b) the course employed active learning and student collaboration (but content remained at lower cognitive levels); (c) the instructor experienced frustrations in trying to balance content coverage with student involvement, in learning to release control to the students, and in discarding traditional notions of remediation; and (d) the treatment did not adversely affect student skills or attitude, and in fact the course enabled some students to pursue their chosen field.
Recommendations include upgrading the course content, providing instructor development opportunities, and -- most importantly -- strengthening the partnerships between the units (program, department, and instructor) involved in the management of the course.
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