Transitioning from material to theoretical geometry is often considered a significant challenge in compulsory education. Over the last twenty years, research rooted in the Theory of Didactical Situations (TDS) has explored how material geometry can support the teaching and learning of theoretical geometry, promoting continuity in teaching. These…

Research in mathematics education constantly oscillates between theoretical or 'Is' questions and practical or 'Ought' questions: Researchers are not only pursuing theoretical questions by investigating what those involved in the teaching and learning of mathematics do, but they are also working on practical recommendations for what they ought to…

With the objective of identifying intrinsic forms of mathematical production in complex analysis (CA), this study presents an analysis of the mathematical activity of five original works that contributed to the development of Cauchy's integral theorem. The analysis of the mathematical activity was carried out through the identification of the…

"Micro-analysis of noticing" is introduced as a method to analyze prospective teacher noticing, one that privileges the high variation exhibited by novice learners. The intent was to understand how prospective teachers' noticing moments suggest trajectories within and across whole-class discussions. We also focused on how prospective…

This position paper examines the phenomenon of the McNamara Fallacy to analyse flawed conceptions of "success" in mathematics learning, normalised assessment structures and their implications for mathematics education. The established presence of the McNamara Fallacy and the ramifications of this statistical fallacy provide a foundation…

In this paper we present a collaborative 3D modeling and printing experience within a Project Based Learning (PBL) activity, carried out with two different groups of participants: pre-service teachers at the Universidad Autónoma de Madrid (Spain), and school students of Primary and Secondary level taking part in an extra-curricular activity.…

Coaching is a complex endeavor that blends a myriad of concepts and skills. Practical experience, content knowledge, and coaching knowledge are instrumental to becoming an effective math coach. In order to design a professional development system to best support and build the capacity of coaches, we must identify what specific content and coaching…

We consider designs for conceptual learning where students first engage in pre-symbolic problem solving and then articulate their solutions formally. An enduring problem in these designs has been to support students in accessing their pre-conceptual situated process, so that they can reflect on it and couch it in mathematical form. Contemplative…

The Research Committee focuses on several systemic barriers that have impeded the equitable development of students' mathematics knowledge, including school and school-system structures that foster the social reproduction of inequity. To develop an equitable context for all students to learn mathematics, the Research Committee posits that we need…

Although many scholars in the field of mathematics education are aware that identity discourses are highly political, research in the field usually lacks a framework theoretically and methodologically to address the political dimension of identity research. Based on Laclau and Mouffe's discourse theory and the case of a female secondary school…

According to humanistic psychology, human beings have the potential to shape and change their lives. People are self-determining creatures capable of making decisions about what their existence will be like and who they will become. We interpret this specifically human feature as an empowerment to design one's life and also to influence…

The new model of Polish education was designed by the Komisja Edukacji Narodowej (KEN). The Commission, established in 1773, was the first ministry of education in Europe. It dealt not only with problems related to the learning-teaching process, but also promoted scientific development. The present analysis is an attempt at examining the process…

The zone of proximal development (ZPD) is a well-known and frequently used notion in both educational research and practice with a wide and diverse range of interpretations. My aim in writing this theoretical article is not to provide a critical examination or an extensive literature review of the ZPD, but rather to highlight some significant…

In this conceptual piece, I explore complex and contradictory conversations during an idea mapping task in which prospective elementary teachers interrogated dominant discourses within mathematics education, such as "mathematics is everywhere" and "being a math person." I argue that this exercise of engaging with contradictions…

This article characterizes my use of video as a tool for research, design and development. I argue that videos, while a potentially overwhelming source of data, provide the kind of large bandwidth that enables one to capture phenomena that one might otherwise miss; and that although the act of taping is in itself an act of selection, there is…