J. Layman & G. Shama, Presented at the Research Conference in Collegiate Mathematics Education, Central Michigan University (Sept 1997). (html version)
Abstract: The University of Maryland offers a physics course as part of the Maryland collaborative for teachers' preparation [MCTP] project. One of the course aims is to promote the learning of the concept of a function through the learning of physics. The students learn in small groups, through problem solving and with the aid of microcomputer based laboratories. Students are asked to examine and find connections between experiments, stories, graphs and algebraic representations. Analysis of observations of students' group work in the course revealed that experiments differed from stories in many characteristics as graphs differed from algebraic expressions. Similarities were found among the translation process from an experiment or a graph to a story or an algebraic representation. Similarities were also found between the opposing direction translations. These translations differed in many characteristics from translations between graphs to experiments and from translations between algebraic equations to stories. According to the above analysis the four situations -- experiment, story, graphical and algebraic representations -- can be presented has vertexes of a parallelogram. Each edge and diagonal of the parallelogram represents a bi-directional arrow of possible translations. Between parallel edges there are many similarities.
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