Matt DeLong

An objective approach to student-centered instruction

ABSTRACT We describe an algorithm for planning lessons based on the identification and achievement of student learning objectives. We discuss ways in which this algorithm can help novice instructors to include opportunities for active learning in their lessons. Examples of mathematics lessons are included to illustrate the use of the algorithm. Reactions of novice instructors to the algorithm are described, and ideas for incorporating this algorithm into an instructor training program are offered.

A Teaching Polygon Makes Learning a Community Enterprise

Abstract In order to strengthen departmental collegiality and improve teaching, our mathematics department instituted a Teaching Polygon. Building on the faculty development idea of Teaching Squares, each member of our department visited one class taught by every other department member in a round-robin fashion during the school year. The visits were followed by structured reflection and conversations about our observations. We found that being in each other’s classrooms strengthened our sense of community as a department, re-energized our enthusiasm for teaching, and encouraged us to reflect on ways to improve our own teaching.

Learning to Teach and Teaching to Learn Mathematics: The Professional Development Program

Overview We believe that it is important for a mathematics department to be actively involved in the professional development of its faculty and graduate students. By professional development we mean the training, assessment, and improvement of teaching skills and practices. Professional development that comes from within the mathematics department, rather than through non-disciplinary channels, is more likely to be meaningful and credible to the instructors who are involved. For example, sensibilities about teaching mathematics are sometimes quite different from those in other disciplines. Compare what is meant by “read the textbook” in a mathematics class to what is meant by the same statement in a literature or history class. In addition, the types and standards of argumentation and precision are different in the mathematics department than they are elsewhere. Moreover, there are certain obstacles that are more prevalent in mathematics than elsewhere. For instance, innumeracy and mathematical illiteracy are far more socially acceptable, or even favored, than is an inability to read or write. For these and other reasons, we feel that the best place for training and supporting mathematics instructors is within the mathematics department. We believe that an effective way for a mathematics department to train its inexperienced instructors, and to support and develop its other faculty members and graduate students is through an integrated professional development program that includes four components.

Learning to Teach and Teaching to Learn Mathematics: Assessing and Evaluating Students' Work

The mathematics course that we envision utilizes a variety of assessment techniques, including team home- work, projects, student presentations and writing assignments. A common element of these assessment practices is the clear and precise communication of mathematical ideas. In many cases, students are expected to work cooperatively – to produce a single piece of work representing the collective efforts of three or four students. In order to provide sufficient challenge for a group of students and sufficient incentive for the students to work cooperatively (instead of simply dividing the work among themselves, and later compiling their individual contributions for submission) the problems assigned are more complicated, and are sometimes more “open-ended” than exercises typically assigned in traditional mathematics classes. The problems assigned typically require students to make appropriate assumptions, to try alternative avenues of inquiry, to try to understand the mathematics more thoroughly by recognizing its application to otherwise unfamiliar situations, etc. The work that students produce on these more complicated assignments is not simply pages of algebraic manipulations with boxed answers at the end. Instead, students are encouraged (and helped) to exhibit their understanding of the mathematics in multiple ways (such as graphs, written accounts of their assumptions and reasoning processes), instead of simply recording the algebraic steps that they performed. As may be expected, assessing and grading student work of this kind can be radically different from assessing and grading pages of algebraic manipulations with a conveniently highlighted answer at the end.