Definitions play an integral role in mathematics and mathematics classes. Yet, expectations for definitions and how they are intended to operate, i.e., mathematical norms for definitions, can remain hidden from students and conflict with other discursive norms, explaining differences in mathematicians' and students' understandings of the nature of…

This article presents an inquiry-oriented lesson for teaching Lagrange's theorem in abstract algebra. This lesson was developed and refined as part of a larger grant project focused on how to "Orchestrate Discussions Around Proof" (ODAP, the name of the project). The lesson components were developed and refined with attention to how well…

This paper is a practical how-to guide to help you start using active learning or to have greater success and more fun with it. We categorize active learning techniques as Think, Pair, Share, Composite, Group, Move, or Lead and discuss how to implement activities in each category, along with advice on creating engaging, effective, and equitable…

In this paper, we discuss mathematical modeling opportunities that can be included in an introductory Differential Equations course. In particular, we focus on the development of and extensions to the single salty tank model. Typically, salty tank models are included in course materials with matter-of-fact explanations. These explanations miss the…

Existing research has highlighted the key role of observation and reflection in teacher learning during lesson study interventions, and how challenging it can be for pre-service teachers. This study focuses on the post-lesson discussion phase and on the observation of the research lesson of a lesson study process. It is carried out with early…

In this case study, we investigate how an inquiry-oriented interactive calculus textbook supported one U.S. college instructor's classroom teaching. We utilized analytical inquiry-oriented frameworks on observation data from a small classroom to capture textbooks' influence on the instruction conceptualized by the Teacher-Mathematics-Student face…

Describing and analyzing teaching practice has been a focus of researchers interested in the interaction and connections between teachers' content knowledge and their pedagogical knowledge. This study described the role of a teacher's mathematical content and pedagogical content knowledge in involving students in learning and solving Science,…

Much important research on the learning of mathematics with technology-supported inquiry has been devoted to learning with multiple-linked representations (MLR) as a mode of feedback. Like a mirror, MLR feedback helps students see their actions in one representation "reflected" in another. Yet, research has followed learning episodes…

This study scrutinizes the influence of project-based learning (PBL) and inquiry-based learning (IBL) on fourth graders' teamwork skills and critical thinking in math classes. A historical review reveals that while they have positive effects in multiple fields, their sole use in elementary math teaching is yet to be explored. 55 fourth-grade…

A key challenge in implementing inquiry-based learning in mathematics has been raising teachers' confidence and skills with unfamiliar pedagogical practices. The nature of inquiry in particular challenges traditional notions of teaching mathematics that dominate the field. Few studies have explored how teachers' perceptions of the nature of…

Preservice elementary teachers' attitudes towards mathematics are often negatively influenced by their K-12 education. Accordingly, teacher educators must allow preservice elementary teachers to experience mathematical instruction differently to change their attitudes toward mathematics and their conceptions about what it means to teach and learn…

This study builds on previous studies that have examined guided project-based learning in undergraduate statistics courses to examine students' attitudes toward statistics after participating in a graduate-level statistics course that used guided project-based learning as an andragogical technique. This phenomenological qualitative case study…

I explore some facts about the area, position, etc. of the Steiner ellipse using GeoGebra and numerical analysis. Students can use these for mathematical inquiry.

This study aims to investigate the effect of inquiry-based learning and direct instruction in enhancing mathematical thinking abilities among secondary school students to examine students' attitudes towards inquiry-based learning as a method for improving mathematical thinking abilities. This study adopted the quantitative research method.…

The interplay between mathematics teachers' beliefs and practices has been widely investigated and research has examined how teachers' beliefs about mathematics, teaching and learning change when participating in continuing professional development (CPD). In this paper, I track teachers' self-reported beliefs and practice changes as they…