This report details a set of three tasks used in an exploratory study of pre-service teachers' (PSTs) experiences of task design for the mathematics classroom. The three tasks, which I call the "Orange Dot Tasks," were constructed in Desmos, a dynamic geometry environment (DGE), and participants engaged each task through manipulating…

In this case study we explored how a mathematician's teaching of the Cauchy-Riemann (CR) equations actualized the virtual aspects of the equations. Using videotaped classroom data, we found that in a three-day period, this mathematician used embodiment to animate and bind formal aspects of the CR equations (including conformality), metaphors,…

Although research highlights the importance of analyzing the geometric work of teachers, there are few validated instruments in this line. This study presents the processes of design and validation of a forced-choice questionnaire that allows the characterization, from a theoretical basis, of how geometry teachers organize their teaching practice.…

This mixed-methods study examined the factors contributing to teachers' self-efficacy in teaching for conceptual understanding and investigated the impacts of a targeted intervention on their self-efficacy to work toward all students having equitable access to teaching that builds their conceptual understanding. This three-manuscript dissertation…

On the basis of a substantial, robust, and well-replicated cognitive science research literature, interleaving has been recommended across a range of professional pedagogical works as an evidence-based strategy for mathematics teachers. This report first notes the conflation of interleaving and spacing effects underpinning those recommendations…

Using origami in the classroom, this study examines the experiences of pre-service middle school mathematics teachers. A case study model was employed in this study as a qualitative research approach. The study involved 39 senior pre-service mathematics teachers. Document analysis, semi-structured interviews, and observation techniques were used…

A qualitative research design comprising of open-ended questionnaires and focus group discussions was used to investigate learner-related variables that impede the integration of ethnomathematics approaches into the teaching and learning of geometry. Proportional stratified sampling and recruitment based sampling were used to select the 40…

For both first-year teachers and veterans, closing a lesson and assessing whether students met learning goals is a persistent challenge. This article explores how teachers using demanding, discourse-rich tasks can make informed decisions about when to move on in a lesson. Specifically, the author considers a "launch-explore-share and…

This article describes an instructional sequence used with inservice secondary mathematics teachers as part of a graduate course. The instructional sequence focused on designing tasks using Interactive Geometry Software (IGS). This study answers a call for replication studies to investigate the use of an established instructional sequence. Results…

Background/purpose. Geometric reasoning is essential for students' cognitive development, yet middle school learners in Morocco face major difficulties in this area. This study investigates the challenges perceived by teachers and aims to identify effective pedagogical strategies to enhance students' geometric reasoning skills. Materials/methods.…

We conducted a multimedia survey experiment with a nationally representative sample (n = 405) of secondary geometry teachers. Participants were shown storyboard depictions of instructional episodes and asked to rate the appropriateness of the (hypothetical) teacher's actions using a Likert-like response format. We analyzed participants responses…

The investigation at scale of the tensions that teachers need to manage when deciding to follow recommendations for practice has been hampered by the problem of occurrence: The conditions in which those decisions could be made need to occur during an observation in order for observers to document how teachers handle them. Simulations have been…

In this paper, we analyse a grade 8 (age 13-14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully planned board work to support a rich and extensive plenary discussion (neriage) in…

We report on an effort to vet a list of 10 student learning objectives (SLOs) for geometry courses taken by prospective geometry teachers. Members of a faculty online learning community, including mathematicians and mathematics educators who teach college geometry courses taken by prospective secondary teachers developed this list in an effort to…

Variance and invariance are two powerful mathematical ideas to support geometrical and spatial thinking, yet there is limited research about teachers' knowledge of variance and invariance. In this paper, we examined how high school teachers deal with the task of looking for invariant properties in a dynamic geometry environment (DGE) setting.…