THE PRODUCTIVITY OF TRANSFORMATIONAL REASONING: STUDENTS’ WAYS OF UNDERSTANDING CONGRUENCE BASED ON LEARNING EXPERIENCES.

This study explores how students reason about congruence based on their high school learning experiences. We developed an online survey to characterize how students understand congruence and gather their recollections about high school geometry coursework. Three ways students understood congruence emerged from data analysis: pictorial, measurement-based, and transformational. Our results indicate that (1) transformational reasoning was the most productive among students’ meanings but was exhibited by less than one-fifth of participants and (2) that diverse contexts encourage critical and productive thinking about congruence. In this paper, we discuss the implications of our findings to research and teaching of congruence. [ABSTRACT FROM AUTHOR]