Commentary on Theories of Mathematics Education

300 A. Zollman
vancing problem-solving research and curriculum development, specifically mathematical
modeling and data modeling at the primary level.
Forward to the Past?
The beginning of this chapter is a disparaging reflection of the research, namely
classroom teaching of problem solving strategies and heuristics does little to improve
students’ problem-solving abilities. But this is a piece on “problem solving
for the 21 st century” and is optimistic for the future. It makes a strong case for mathematical
modeling in the elementary grades, proposing problem solving to develop
conceptual development.
There are caveats that need to be remembered. Twenty-five years ago, Bank
Street College of Education created a thirteen episodic educational video program
called The Voyage of the Mimi. This was an interdisciplinary problem-solving unit
for middle grade students, first aired on Public Broadcasting Service (PBS), then
marketed by Sunburst Software. Throughout the voyage, an oceanographer, marine
biologist, teenage assistants, a deaf college student, and the captain’s grandson
construct hypotheses, make measurements, collect and analyze data. Students were
shown video scenarios and then asked to solve various problem situations (counting
whales or procuring enough fresh water for the trip) that occurred on board
the Mimi. The Voyage of the Mimi was a slickly-produced television series—now
remembered as a young Ben Affleck’s first starring role as the captain’s grandson
(http://www.bankstreetcorner.com/voyages_of_mimi.shtml).
In 1990, the Cognition and Technology Group at Vanderbilt University created
the Jasper Woodbury Problem Solving Series videodiscs. The 12 interdisciplinary
videodisc adventures were also for middle-grade students. Each adventure was designed
like a detective novel, ending in a complex challenge. The videodisc series
was to research the relationships between cognition, learning and anchored instruction
(i.e., situated instruction in the context of information-rich environments to
encourage students to pose and solve complex, realistic problems) (http://peabody.
vanderbilt.edu/projects/funded/jasper/).
Both of the above instructional programs were alternative mathematical modeling
approaches to traditional teaching of problem solving. Each had good problemsolving
results. Neither had significant standard mathematics test results above, or
below, the normal student population.
Neither programs are used today in schools. Why? No single instructional
method directly affects learning (Zollman in press). Specifically, more attention
must be paid to the classroom teacher, who is the single most important influence
on student achievement and motivation (Darling-Harmon 1999). Indeed, improving
teaching quality is the “mechanism for improving students’ academic performance”
(Wenglinsky 2000, p. 9). The cost, instruction time required, expertise needed, implementation
training, plus many more variables (social, cognitive, and political)
pressure the classroom teacher “to stay the course” in problem-solving instruction.