In beginning this chapter we immediately faced a dilemma. There is nothing that can be
called “the concept of function.” The phrase “concept of function,” regardless of its meaning …

A growing body of literature has identified quantitative and covariational reasoning as critical
for secondary and undergraduate student learning, particularly for topics that require …

Angle instruction often begins with familiar, real-world examples of angles, but the transition
to more abstract ideas can be challenging. In this study, we examine 20 third and fourth …

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

Abstract Mathematics educators and writers of mathematics education policy documents
continue to emphasize the importance of teachers focusing on and using student thinking to …

Abstract The Calculus Concept Readiness (CCR) instrument assesses foundational
understandings and reasoning abilities that have been documented to be essential for …

Researchers have argued that covariational reasoning is foundational for learning a variety
of mathematics topics. We extend prior research by examining two students' covariational …

Trigonometry is integral to mathematics education. The field of trigonometry plays a crucial
role in the study of mathematics and its applications. Despite the importance of the subject …

This paper investigates the implications of three students' fraction and measure schemes for
their understanding of rate of change functions. Steffe and Olive's (2010) descriptions of …

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