PRE-SERVICE TEACHERS' PROPORTIONAL REASONING
STRATEGIES
Juliana Utley
Oklahoma State University
Kathryn Reinke
Oklahoma State University
kreinke@okway.okstate.edu
Proportional
reasoning is basic to the middle school curriculum and is an issue in current
reform efforts. There have been few
research articles dealing with pre-service teacher's proportional reasoning
abilities. This study examines
solution strategies used by 71 pre-service elementary teachers, 5 male and 66
female enrolled in mathematics methods courses, to solve a proportional
reasoning problem. They were asked to
solve an application problem involving variation between slow and fast speeds
of videotapes.
A variety of strategies were found in their solutions
including the traditional proportion algorithm, diagrams, and arithmetic
reasoning. An analysis of these showed that approximately 82% of the students
used a strategy other than the proportion algorithm. Approximately 58% of the
pre-service elementary teachers gave a correct solution and of those giving an
incorrect solution the majority displayed incorrect conceptual reasoning,
whether they used proportions or basic arithmetic. For example, 8.5% of the
students responded with the same incorrect answer, ignoring the relationship
between tape speeds. None of the students with incorrect solutions attempted to
use a diagram and only 4% of those with correct solutions attempted to use a
diagram. The majority if not all students had completed a mathematics course
that dealt with proportions and ratios; however, almost half of these students
did not respond with a correct solution. The results of this study suggest a
change in the curriculum from a mainly procedural presentation to a more
conceptual presentation of proportions is needed to enhance pre-service
teachers' preparation.