WARREN D. HICKMAN
WARREN D. HICKMANProfessor of Mathematics
Westminster College
I teach mathematics in the Department of Mathematics & Computer Science. Currently, I am doing research in the characteristics of an excellent teacher, particularly a teacher of mathematics. This has taken me into the areas of conflict resolution and the working alliance. I teach two courses for the preservice teachers; something I enjoy very much. Actually, I have worked with the preservice teachers for twenty years and have great interest in mathematics education. Tennis, chess, bridge, biking, and reading are high priority interests. (A glimpse of why I teach. I share it with you.)
THE BRIDGE BUILDER An old man going a lone highway Came at the evening cold and gray To a chasm vast and deep and wide. The old man crossed in the twilight dim. The sullen stream had no fears for him; But he turned when safe on the other side And built a bridge to span the tide. "Old man," said a pilgrim near, You are wasting your strength building here; Your journey will end at the ending day, You never again will pass this way; You’ve crossed the chasm deep and wide, Why build this bridge at evening tide?" The builder lifted his old gray head- "Good friend, in the path I have come," he said, "There followeth after me today A youth whose feet must pass this way, This chasm that has been as naught to me To that fair-headed youth may a pitfall be, He too, must cross in the twilight dim, Good friend, I am building this bridge for him." Will Allen Dromgoole
A View of Learning Mathematics
Educational research findings from cognitive psychology and mathematics education indicate that learning does not occur by passive absorption and imitation (Davis, 1984; Case & Bereiter 1984; Cobb & Steffe, 1983; Hiebert, 1986; Lampert, 1986; Lesh, 1983; Schoenfeld, 1987). Rather, learning occurs as students actively assimilate new information and experiences and construct their own meanings. This is a major shift from learning mathematics as accumulating facts and procedures to learning mathematics as an integrated set of intellectual tools for making sense of mathematical situations (Resnick, 1987). This view of learning is summarized in Everybody Counts (Mathematical Science Education Board 1989, pp. 58-59).
In reality, no one can teach mathematics. Effective teachers are those who can stimulate students to learn mathematics. Educational research offers compelling evidence that students learn mathematics well only when they construct their own mathematical understanding. To understand what they learn, they must enact for themselves verbs that permeate the mathematics curriculum: "examine," "represent," "transform," "solve," "apply," "prove," "communicate." This happens most readily when students work in groups, engage in discussion, make presentations, and in other ways take charge of their own learning.
All students engage in a great deal of invention as they learn mathematics; they impose their own interpretation on what is presented to create a theory that makes sense to them. Students do not learn simply a subset of what they have been shown. Instead, they use new information to modify their prior beliefs. As a consequence, each student’s knowledge of mathematics is uniquely person