In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

In this dissertation I explore instructors' work with instructional tasks as they plan to introduce various representations of derivatives. Drawing on the notion of "framing" from sociology, I adopt a situative lens to study calculus instructors' planning of instructional tasks. I rely on Herbst and Chazan's (2012) notion of…

This study aims to analyze the problem-posing skills of primary school mathematics teacher candidates with problem-posing experience and their views on problem posing. The case study, one of the qualitative studies, was used in the study. The study group is ten prospective elementary mathematics teachers who were selected using the purposive…

This dissertation explores the intricate dynamics between the self-perceptions of undergraduate mathematics (UM) educators and their conceptions of excellent teaching practices conducive to student learning. Employing a sequential mixed methods approach, the study addresses two primary research questions. First, it investigates educators'…

We present a case of one teacher's engagement in project-based learning for algebra I students. This teacher was a member of a cohort of mathematics teachers and career technical educators who participated in a two-week intensive summer institute investigating autonomous vehicles. During the academic year, the follow up support for these educators…

"Vicarious learning" research is a burgeoning area of inquiry, which examines the learning of students who observe and are engaged with video- or audio-taped presentations of other people engaged in learning (Chi et al., 2008). In such studies, the students or "vicarious learners" (VLs) are positioned as indirect participants…

"Vicarious learning" research is a burgeoning area of inquiry, which examines the learning of students who observe and are engaged with video- or audio-taped presentations of other people engaged in learning (Chi et al., 2008). In such studies, the students or "vicarious learners" (VLs) are positioned as indirect participants…

This paper describes the evolution of "recognition of need for data" and "strategical thinking", two types of thinking identified by Wild and Pfannkuch in their Framework for Statistical Thinking in Empirical Enquiry, as well as its relevance for math teacher professional development. The research was carried out with ten…

Recommendations for preparing teachers of mathematics have been published by multiple professional organizations in the United States; however, there is limited research on whether student course perceptions affirm the instructor-identified alignment of mathematics content courses for prospective secondary mathematics teachers (PSMTs) to these…

Too often, high school algebra students encounter topics in a discrete, disconnected fashion. In the authors' first years of teaching, they found students to be adept at solving problems they were currently studying; for instance, they could solve quadratics during a quadratics unit. Too often, however, students struggled with that same content…

Justification skills should be fostered in teaching mathematics as they are highly related to effectiveness in problem solving. However, pre-service mathematics teachers do not always have the necessary skills in using mathematically convincing language and justifying their solutions. Thus, they should be introduced to a variety of instructional…

In this paper we present the results of a study which was carried out in an inquiry-based teaching and learning environment with the use of 'what if not' methodology coupled with the integration of dynamic geometry software. The vast majority of the students reported that they perceived themselves as participants rather than spectators. Most of…

Inquiry-based instruction is a student-centered approach to teaching that focuses on active learning (Barron and Darling-Hammond 2008) in which students engage with "tasks that promote reasoning and problem solving" (NCTM 2014). Specifically, such tasks encourage a variety of solution strategies and stimulate use of the NCTM Process…

As mathematics educators we want our students to develop a natural curiosity that will lead them on the path toward solving problems in a changing world, in fields that perhaps do not even exist today. Here we present student projects, adaptable for several mid- and upper-level mathematics courses, that require students to formulate their own…

Have you ever considered how technology could facilitate reasoning and sense making of systems of linear inequalities? In this article, the authors share how to use Google® Maps® and Desmos to achieve this and provide students with opportunities to access mathematics as they build a more formalized understanding. Using an inquiry-based approach,…