Examining the use of conceptual frameworks such as the instructional hierarchy (IH) to drive academic interventions represents an important area of inquiry in order to understand why an intervention was effective. However, to date, the IH has only been examined retroactively to explain the effectiveness of math interventions and has not been used…

The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

Students' opportunities to struggle with mathematical ideas have long been considered paramount to learning. However, there's little research on how teachers; (1) draw on and make sense of the discourses of perseverance; (2) enact it in classroom; and (3) develop an expansive view of perseverance. To contribute to these lines of research, we build…

Language plays a key role in statistics and, by extension, in statistics education. Enculturating students into the practice of statistics requires preparing them to communicate results of data analysis. Statistical argumentation is one way of providing structure to facilitate discourse in the statistics classroom. In this study, a teaching…

Forty 4th and 9th grade students participated individually in tutorial interviews centered on a problem-solving activity designed for learning basic algebra mechanics through diagrammatic modeling of an engaging narrative about a buccaneering giant burying and unearthing her treasure on a desert island. Participants were randomly assigned to…

The pedagogical and design considerations for the use of a virtual reality (VR) learning environment are important for prospective and current teachers. However, empirical research investigating how preservice teachers interact with transformative content representation, facilitation, and learning activities in a VR educational simulation is still…

In this article, we address the methodological implications of analysing online discussion boards with a focus on participants' changing identities. More specifically, we propose the use of a Communities of Practice framework as a heuristic method for considering how participants' contributions to online discussion play a role in changing who they…

Major revision in the U.S. mathematics curriculum since the 1960s have led to significant differences between the mathematics curriculum of the United States and those of many other countries. This study explored how eight Chinese immigrant students, with different cultural backgrounds, mathematics knowledge, and learning styles, learned in an…