We investigated covariational reasoning among 487 secondary mathematics teachers in the
United States and South Korea. We presented an animation showing values of two varying …

Researchers continue to emphasize the importance of covariational reasoning in the context
of students' function concept, particularly when graphing in the Cartesian coordinate system …

The objective of this research is to identify the effectiveness of the GeoGebra program in
developing academic achievement and ensuring survival of the learning impact of the …

This paper presents a conceptual analysis for students' images of graphs and their
extension to graphs of two-variable functions. We use the conceptual analysis, based on …

Quantitative reasoning is critical to developing understandings of function that are important
for sustained success in mathematics. Unfortunately, preservice teachers often do not …

The focus of this study in which the theoretical framework of APOS was used is students'
generalizing function notion from single variable to two-variable function concepts in …

In this paper, we use relevant literature and data to motivate a more detailed look into
relationships between what we perceive to be conventions common to United States (US) …

Function concept that mathematics educators has worked on importantly for years is still a
source of difficulties for students. Because the functional relationship is a prerequisite notion …

Researchers have emphasized the importance of characterizing students' abilities to
coordinate changes in covarying quantities. In this paper, we characterize three …

This paper reports on part of an investigation of fifteen second-semester calculus students'
understanding of the concept of parametric function. Employing APOS theory as our guiding …