Exploring mathematical connections of preuniversity students through tasks involving rates of change

Abstract

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures, representations or meanings or with other disciplines or the real-world. Four tasks were proposed to the 33 pre-university students that participated in this research; the central concept of the first task is the slope, the last three tasks contain conceptslikevelocity,speedandacceleration.Task-basedinterviews were conducted to collect data and later analysed with thematic analysis. Results showed most of the students made mathematical connections of the procedural type, the mathematical connections ofthecommonfeaturestypearemadeinsmallerquantitiesandthe mathematicalconnectionofthegeneralizationtypeisscarcelymade. Furthermore, students considered slope as a concept disconnected fromvelocity,speedandacceleration.