The Process of Constructing Speed-time Function from Distance-Time Function y=2χ by Students Using Different Reasoning Methods for Continuous Change

Abstract

This study investigates the way students perceive and express change in an exponential situation with different reasoning methods for continuous change - for example, students, who use chunky reasoning, construct a new function representing the change of exponential distance-time function. Using case study approach, the study presents the results of teaching experiments conducted on three high school freshmen students. It may be difficult to generalize the results since the sample size was limited; however, the findings have the potential to inform researchers in mathematics education about students’ conceptual knowledge of continuous change. The information about the process of constructing the speed-time function from the distance-time function based on the students' understanding of continuous change may also be helpful in interpreting student thinking in differential concept.

Keywords

• exponential function
• quadratic function
• distance-time function
• speed-time function
• chunky reasoning
• smooth reasoning