The Blocks Task: Comparative Analyses of the Task With Other Proportion Tasks and Qualitative Reasoning Skills of Seventh-Grade Children in Solving the Task

Abstract

A nonnumeric task called the blocks task was developed to investigate children's understanding of the proportion concept. The first part of the article discusses this task through two cognitive task analyses: The first task analysis establishes an isomorphism between the blocks task and several real-world problem types; the second task compares and contrasts the blocks task with three other proportion-concept tasks-rate and mixture tasks, the balance scale task, and the fullness task. The second part of the article reports a study of three aspects of adolescents' solution of the blocks task: (a) the basic problem representation that the children constructed in response to the task presentation and the corresponding solution strategy they used, (b) relations between the problem representations and the strategies, and (c) differences among high-, middle-, and low-ability children in terms of problem representation and solution strategy. The investigation resulted in the identification of three categories of problem representations and three categories of solution strategies. A hierarchy of sophistication was evident among the problem representations and among the solution strategies, and a strong relation was observed between