In this article, the authors provide some insight into how teachers can potentially facilitate among students' representations and activities on mathematical tasks: between or among -- (1) student representations and the context; (2) multiple forms of student representations; and (3) processes in student representations. The authors use the…

Once teaching-learning events are conceptualized as inter-discursive encounters, it becomes clear that mathematics classroom talk is rife with invisible pitfalls. There are many types of unacknowledged discursive gaps, some of them necessary for learning and some potentially harmful. Such gaps may exist also between the teacher's intentions and…

In this paper, we propose a teaching approach centered on community and care, aimed at fostering a democratic classroom environment. We highlight the communal co-creation of the Rights of the Learner (RoTL) as the foundation for establishing a shared responsibility atmosphere. Our interpretation of the RoTL challenges traditional power dynamics,…

Traditionally, various meanings of "10" are systematically ignored in early childhood curriculum and children's understanding of numbers is restricted within the solitary mapping between the symbol "10" and quantity concept of "ten." This may be problematic for other ways that mathematics is used, both in modern life…

This article addresses why instructors choose to not use inquiry-oriented instructional practices (IO-IPs) even if they believe the practices are beneficial. A national sample of undergraduate mathematics instructors (N = 269) responded to questionnaires on their use of IO-IPs, beliefs on student learning, and recognition of professional…

This study focuses on the challenge of promoting significant mathematical discourse among preservice teachers. The study was conducted as part of an academic course that accompanies their practical training. Twenty-three math preservice teachers' learning process was examined as a result of using an analytic model designed for discourse protocols'…

Promoted action is an activity offered by the teacher to students so that they can develop new knowledge or experience. The promoted action chosen by the teacher will depend on the knowledge possessed by the teacher. It is commonly referred to as pedagogical content knowledge (PCK). In addition, to become a professional teacher with a…

There is a broad consensus that beginning teachers of mathematics need a strong foundation in mathematical knowledge for teaching (MKT), defined as the mathematical knowledge required to recognize, understand, and respond to the mathematical work of teaching one must engage in. One recurrent challenge in teacher education is how to provide support…

Research on non-cognitive factors has shown that persistence in the face of challenges plays an important role in learning. However, recent work on wheel-spinning, a type of unproductive persistence where students spend too much time struggling without achieving mastery of skills, show that not all persistence is uniformly beneficial for learning.…

This book provides a landscape of learning that helps teachers recognize, support, and celebrate their students' capacity to structure their worlds algebraically. It identifies the models, contexts, and landmarks that facilitate algebraic thinking in young students and provides insightful and practical methods for teachers, math supervisors, and…