Prospective middle school mathematics teachers’ conceptualizations of slope

Abstract

In this study, the conceptualizations used by prospective middle school mathematics teachers when defining, representing, and exemplifying the slope concept and relating it with other mathematical situations were examined. Participants’ conceptualizations were identified by Nagle, C., Moore-Russo, D., Viglietti, J., & Martin, K. [(2013). Calculus students’ and instructors’ conceptualizations of slope: A comparison across academic levels. International Journal of Science and Mathematics Education, 11(6), 1491–1515. https://doi.org/10.1007/s10763-013-9411-2] framework. The findings showed the prospective teachers mostly used trigonometric and parametric conceptions. Real-world situation, calculus conception, geometric ratio, and determining property were other common conceptualizations used by the participants. On the other hand, algebraic ratio, behaviour indicator, physical property, and functional property conceptualizations were seldom used and linear constant conceptualization was never used by them. The implications for mathematics teacher educators and mathematics education researchers on how to remedy prospective teachers’ possible difficulties and errors about slope are discussed.