RUME 26
2024
Omaha, Nebraska
Student Thinking and Challenges when Representing Distance in the Cartesian Plane
Page: 1377
The purpose of this poster presentation is to highlight the variations in student thinking when working with difference expressions in the Cartesian plane — a fundamental skill crucial for grasping numerous Calculus concepts. Despite its pivotal role, previous research has shown students often struggle to conceptualize and express distances. We surveyed n=169 undergraduate math students to evaluate their ability to represent distances within the Cartesian plane using expressions in terms of both x and y. Through analysis of the responses, we identified two crucial components for completing the tasks: a) using a magnitude interpretation of subtraction and b) establishing the Cartesian connection. We found a significant proportion of students did not use either of these components appropriately, leading them to incorrect responses. Our findings show a need for instruction on the skills foundational to understanding distances in the Cartesian plane within Calculus education.