Learning to calculate the area of composite shapes is an important application of area measurement but evidence suggests that many middle school students struggle to calculate the area of even simple composite shapes. In this article, I report the findings of a classroom design study conducted to investigate the collective development of…

Coordination of theoretical probability and relative frequency estimates is challenging in probability teaching and learning. Modeling is one of the ways of teaching and learning that facilitates inquiry between these two perspectives. Given that, we designed a modeling activity to support fifteen secondary students in investigating theoretical…

Sampling distributions are fundamental for statistical inference, yet their abstract nature poses challenges for students. This research investigates the development of high school students' conceptions of sampling distribution through informal significance tests with the aid of digital technology. The study focuses on how technological tools…

We discuss a teaching experiment that explored two pre-service secondary teachers' meanings for the unit circle. Our analyses suggest that the participants' initial unit circle meanings predominantly consisted of calculational strategies for relating a given circle to what they called "the unit circle." These strategies did not entail…

This paper uses a multilevel analysis of mathematical reasoning rooted in Cultural Historical Activity Theory to examine how mathematical discourse and student reasoning about linear functions developed across 3 weeks in a ninth grade bilingual algebra class. Despite the teacher's expertise teaching with a conceptual focus, and her stated…

Based on insights into the nature of vocational mathematical knowledge, we designed a computer tool with which students in laboratory schools at senior secondary vocational school level could develop a better proficiency in the proportional reasoning involved in dilution. We did so because we had identified computations of concentrations of…