A New Tool for Assessing the Understanding of Calculus by Relying on Relational and Instrumental Understanding

Abstract

The changes in high school mathematics books in recent years have led to some changes in the concept of calculus, and majority of learners used to work hard on memorizing rather than understanding. In the early years after entering university, they will be challenged by the same concepts and their application in other sciences. Review of the previous studies have shown that no research instrument has been developed to address such challenges till now. Then, the researchers of the study developed and standardized an instrument. The population consisted of all first-year undergraduate students of engineering and basic sciences fields from of University in Tehran. Using purposeful sampling technique, 162 male and female students were selected. All of them selected had passed the course of calculus 1. The researchers considered some factors and developed an instrument and finally validated it based on those components. Moreover, since there were no available tools to measure the derivative’s relational and instrumental understanding, some questions regarding the concept of derivative definition were designed and added to the end of the questionnaire. Finally, after the investigations conducted through exploratory factor analysis, a research instrument was developed and introduced to measure the understanding of the concept of derivative and its instrumental and relational understanding.

Keywords

• Calculus
• derivative
• mathematical understanding
• instrumental understanding
• relational understanding