Authors of calculus texts often include graphs in the text with the intent that the graph depicts relationships described in theorems and formulas. Similarly, graphs are often utilized in classroom lectures and discussions for the same purpose. The author or instructor includes function graphs to represent quantitative relationships and how a pair…

This work is an exploration of upper elementary students' sense making around four conventional representations of function: equations with algebraic notation, Cartesian graphs, function tables, and natural language. The cornerstone to the empirical work is a task called the Function Puzzle, where students are given 16 cards representing four…

The mathematical concept of function has been revisited and further developed with regularity since its introduction in ancient Babylonia (Kleiner, 1989). The difficulty of the concept of a function contributes to complications when students learn of functions and their graphs (Leinhardt, Zaslavsky, & Stein, 1990). To understand the concept of…

The goal of this study is to explore and characterize the effects of using a dynamic graphing utility (DGU) on conceptual understanding and attitudes toward mathematics, measured by the responses of college algebra students to an attitude survey and concepts assessment. Two sections of college algebra taught by the primary researcher are included…

Social networks have become more complex, in particular considering the fact that elements in social networks are not only abstract topological nodes and links, but contain rich social attributes and reflecting diverse social relationships. For example, in a co-authorship social network in a scientific community, nodes in the social network, which…

This concurrent embedded mixed methods study investigates the influence of the computer program Tinkerplots™ on 34 preservice elementary teachers' understanding of measures of center and graphical representations of data. Participants' opinions and beliefs about the effectiveness of the program were also explored. At the beginning of the…

The purpose of this study was to determine (1) strategies students use when solving composition problems and the difficulties they encounter; (2) conceptions and/or misconceptions students have with respect to composition of functions; and (3) the effect of using dynamic visualization during instruction on students' understanding of composition of…