Cognitive and Metacognitive Abilities Involved in the Solution of Mathematical Word Problems: Validation of a Comprehensive Model.

With this investigation we tried to validate an economic model of the cognitive and metacognitive abilities involved in Mathematical Word Problems. From the literature we chose seven abilities: text comprehension, problem representation, problem categorization, solution estimate, planning the solution, procedure self-evaluation, calculus self-evaluation. In order to measure these abilities, we devised a series of mathematical word problems (partitioned problem) where, for each ability, subjects have to answer a multiple choice question. A hierarchical regression model with only five variables (excluding solution estimate and calculus self-evaluation) explained more than 50% of the variance of the solution scores of the Partitioned Problems, and 40% of the variance of the solution of a series of problems presented with only the text. The model was validated with five different samples of subjects of different school grade and with a bootstrap procedure. Furthermore the relationship of the variables was tested using a path analysis. The discrimination validity of three different levels of problem solving efficiency give further support to the validity of the model. The model obtained may be utilized in order to devise practical instruments for the analysis of mathematical word problem difficulties. Copyright 1998 Academic Press.