This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory
identifying and characterizing middle grade students' initial and developing understanding …

This article presents the results of a teaching experiment with middle school students who
explored exponential growth by reasoning with the quantities height (y) and time (x) as they …

The purpose of this paper is to argue that attention to students' ways of thinking should
complement a focus on students' understanding of specific mathematical content, and that …

This paper addresses the role of learning progressions in informing many international
standards documents, discussing the affordances and limitations of building standards and …

The topic of rational numbers in mathematics has an ample research base that illustrates, in
some cases meticulously, how children's thinNing about fractions could progress. TaNen …

Researchers have recommended using tasks that support students in reasoning
covariationally to build productive meanings for graphs, rates of change, exponential growth …

This study characterizes children's understandings of quadratic function from a variation
perspective in the context of a quantitatively rich instructional setting. We studied middle …

My titular question (Where is the line?) mainly elicits discomfort among my friends and
colleagues who work in the area of teacher education and professional development:“Is …

This chapter explores the influence of psychology on Mathematics Education research,
which is motivated by a desire to improve mathematical thinking and learning and …

This study characterizes s of quadratic function from a variation perspective in the context of
a quantitatively rich instructional setting. We studied middle grade (ages 12-13) ceptions …