While many aspects of the teaching and learning of specific advanced mathematics courses have been studied, limited work has examined mathematical themes like sameness or its instantiations across disciplines. In this paper, we explore algebraists' collective example space for mathematical sameness. We used qualitative methods to analyze survey…

Project Based Learning (PjBL) has emerged as a promising approach in mathematics education. This study aims to analyze the implementation of project-based learning (PjBL) internationally in mathematics education and to identify the underlying learning theories, such as the method of writing an article through SLR. A systematic literature review…

Researchers agree that both domain-general skills and domain-specific skills contribute to mathematics knowledge, but questions arise as to which skills can and should be trained to improve children's learning outcomes. In this article, we synthesize research on training three domain-general constructs in early childhood (patterning skills,…

David Clarke's research has shifted the focus of classroom research in mathematics education from study of cultural patterns to study of patterns of participation and the learning that can result in highly complex social environments. His Complementary Accounts Methodology which informed the Learner's Perspective Study design included multi-source…

The Learner's Perspective Study (LPS) offers an extremely rich source of data for analyses of classroom situations. In this paper we focus on events in mathematics classrooms through the lens of the Theory of Didactical Situations in Mathematics, namely, on the situation of institutionalization. During the phase of institutionalization, the…

Learning progressions have become increasingly prevalent in mathematics education as they offer a fine-grain map of possible learning pathways a child may take within a particular domain. However, there is an opportunity to build upon this research in ways that consider learning from multiple perspectives. Many current forms of learning…

Behaviourism proposes successful learning to be dependent on the performance of conditioned behaviours that are distinctly observable and objectively measurable. Over the past 100 years, various behaviourist concepts have been superseded by sociocultural and cognitive learning theories, but the entwined areas of assessment in mathematics education…

Identifying students' errors in solving cases of critical thinking skills from two variables of linear equation (TVLE). This was a qualitative study using a descriptive exploratory approach. The participants of the study were first-year students of mathematics education. The method used in this research is a test, interview, and triangulation. The…

The book provides an entry point for graduate students and other scholars interested in using the constructs of Piaget's genetic epistemology in mathematics education research. Constructs comprising genetic epistemology form the basis for some of the most well-developed theoretical frameworks available for characterizing learning, particularly in…

In this article, the goal is to describe students' mathematical reasoning in the context of different settings of problem-solving tasks. The core of the tasks are real objects, which are presented to the students with the help of photos, a 3D model or in the environment itself. With reference to the experiential learning theory and relations to…

This paper starts by addressing a complexity theory and then distinguishing complex systems from complicated systems. After that, the paper addresses a concept study by connecting it with complex systems because a class is considered as a complex system having many students with different constraints, experiences, and perspectives including…

Due to the embeddedness of digital technologies in mathematics education of today, we often see examples of students simultaneously using their mathematical competencies and digital competencies. In relevant literature, however, these are not seen as a connected whole. Based on reviewing existing competency frameworks, both mathematical and…

Generalization is critical to mathematical thought and to learning mathematics. However, students at all levels struggle to generalize. In this paper, I present a theoretical analysis connecting Piaget's assimilation and accommodation constructs to Harel and Tall's (1991) framework for generalization in advanced mathematics. I offer a theoretical…

This study presents a case of a problem that did not originate in theory but rather ended in theory. It addresses the issue of the prevalent, traditional public view of the nature of mathematics and that of its teaching and learning that might hamper mathematics reform. In this study, we present a five-day professional development programme that…

Constructivist learning theories have become the dominant ideology in educational circles, in part, because there is a primacy on the agential individual with its definite identity. However, precisely because "to construct" is a "transitive" verb, it occludes the fact that in learning and development, we come to know something…