Complexity of Shapes and Quantitative Reasoning in Geometry

Abstract

ABSTRACT— We explored the effects of task‐related factors on reasoning processes in geometry focusing on a comparison‐of‐perimeters task in which the irrelevant feature area interferes with the reasoning process. We studied the effects of congruity, salience, and complexity on participants’ accuracy of responses and reaction times. The study shows that incongruent trials yield lower accuracy and longer reaction times than congruent ones. In addition, increasing the salience of the irrelevant feature results in a lower rate of success. Previous research suggested that a high cognitive load leads to higher interference in the incongruent condition. The current study shows that, in this condition, increasing the level of complexity of shapes associated with a higher cognitive load decreases the accuracy of responses and increases reaction times. Our findings can aid educators to select appropriate tasks and examples in their classrooms, taking into account how the level of difficulty is affected by complexity, salience, and congruity.