The Composition Effect in Symbolizing: The Role of Symbol Production vs. Text Comprehension

A person's ability to translate a mathematical problem into symbols is an increasingly important skill as computational devices play an increasing role in academia and the workplace. Thus it is important to better understand this "symbolization" skill and how it develops. We are working toward a model of the acquisition of skill at symbolizing and scaffolding strategies for assisting that acquisition. We are using a difficulties factors assessment as an efficient methodology for identifying the critical cognitive factors that distinguish competent from less competent symbolizers. The current study indicates there is more to symbolizing than translating individual phrases into symbols and using longterm schematic knowledge to fill in implied information. In particular, students must be able to compose these individual translation operations into a complete symbolic sentence. We provide evidence that in contrast to many prior models of word problem solving which address story comprehension skills, a critical element of student competence is symbolic production skills.