Syntactic manipulations and semantic interpretations in algebra: The effect of graphic representation

This study examined the effect of graphic representation of algebraic functions on performance of tasks involving expressions' transformations. Twenty eight teachers, who received instruction and practice using multiple representation software, were tested on their ability to debug faulty transformed expressions, either with or without graphic feedback. Two main strategies were used while debugging - Syntactic Manipulation (SYM) and Semantic Interpretation (SEI). It was found that subjects who used the SEI strategy, improved their performance while using graphs, as compared to no use of graphs. Some positive effect of the graphic feedback was also manifested for those using the SYM strategy, who were assisted by the graphs but continued to syntactically manipulate the expressions. All subjects improved their performance after the treatment, as measured by paper-and-pencil traditional tasks.