Mathematical Tasks Chosen By A Prospective Teacher In
His Professional Semester
Lewis Walston
North Carolina State
University
The Professional
Standards for Teaching Mathematics (National
Council of Teachers of Mathematics, 1991) maintain that teachers must help students develop
conceptual and procedural understanding of mathematics. Conceptual knowledge is
characterized by Eisenhart et. al. (1993) as the knowledge of the underlying structure of
mathematics-the relationships and interconnections of ideas that explain and
give meaning to mathematical procedures.
Procedural knowledge is defined by Hiebert and Lefevre (1986) to be made up of two parts: the formal language of
mathematics and the rules, algorithms or procedures used to perform
mathematical tasks. Research findings show that procedural knowledge is
emphasized in most lessons. This study
examines the tasks chosen by a prospective teacher in his profession semester
in light of his belief system as revealed by his writings and categorized using
ideologies identified by Ernest(Ernest,
1991). These tasks
were studied to determine whether the focus of the task was conceptual or
procedural. Sources of data were audio and videotapes of teaching episodes, the
prospective teacher’s lesson plans and the researcher’s field notes. Data were analyzed using multiple sorts to
define which tasks were emphasized procedural knowledge and those that
emphasize conceptual knowledge. The
belief system was categorized using Ernest’s ideologies. The findings were that the prospective
teacher’s beliefs were consistent with those of an industrial trainer and the
tasks he chose were largely conducive to the student’s learning mathematical
procedures.
References
Eisenhart, M., et al.
(1993). Conceptual Knowledge Falls
through the Cracks: Complexities of Learning to Teach Mathematics for
Understanding. Journal for Research in Mathematics Education, 24(1), 8-40.
Ernest, P. (1991). The
philosophy of mathematics education.
London ; New York: Falmer Press.
Hiebert, J. (1986). Conceptual
and procedural knowledge: The case of mathematics. Hillsdale, NJ: L. Erlbaum Associates.
National Council of Teachers
of Mathematics. (1991). Professional standards for teaching
mathematics. Reston, VA: The
Council.