This study sought to explore whether access to definitions and general representations influences the construction of general direct arguments. Data was collected in college mathematics courses for prospective elementary school teachers. Participant arguments were analyzed along two variables: the generality of the representations and the…

Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that…

This study aims to analyze how the Mathematics Teacher Candidates (MTCs) define the "prism" and "pyramid" concepts in geometry. The research was carried out in 2017-2018 academic year with 92 MTCs. This test consists of 3 open-ended questions that MTCs can answer conceptually. The first openended question was as "Define a…

This article presents a new approach to generalizing the definition of means. By this approach we easily obtain generalized means which are quite different from standard arithmetic, geometric and harmonic means.