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…

Informal Australian discussion suggests that calculators are still widely regarded as devices for calculation, consistent with their naming, and are rarely recognised as potentially helpful to support students learning mathematics. In this paper, Barry Kissane explores some of the ways in which modern calculators might support students learning…

Earlier approaches to sense-making in mathematics have looked at the ways students comprehend a mathematical concept. Recent research suggests that some students make sense not only of mathematical objects that have a being, but also of objects that have yet to become. In such cases, learning mathematics is not just an act of comprehending a given…

There is a plethora of textbooks to choose from. While most textbooks contain the same content, teachers need to understand the textbook they have chosen to support their students' learning, as textbooks can significantly impact student learning and teacher instruction. When searching for a way to understand the various textbooks, my research…

This paper argues for reconceptualising an educational curriculum that locates its primacy in "practices." The argument is framed around the core purpose of education: to help people 'live well in a world worth living in'. Living well and learning about what this means is typically guided by epistemologically based curricula, and…

Problem-based learning puts students in situations that suggest problems without providing instructions and available knowledge. Therefore, when using problem-based learning, students need to be flexible, self-disciplined, active and self-occupied with knowledge and turn the knowledge the teacher intends to impart into their knowledge. For locus…

Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…

In STEM education, the engineering design process serves as a pedagogical strategy to connect science and mathematics concepts. While STEM approaches are increasingly favored in science courses, the role of mathematics in integrated STEM activities is often overlooked, despite its foundational importance across STEM disciplines. This manuscript…

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 theoretical article, we explore the possibility that instead of a mathematical connection arising "in-between" two (or more) pre-existing ideas or objects, which have presumably been known or understood, that connection is itself the motor of understanding. The standard view of connection, in which two existing ideas or concepts…

Gestures play a role in perception, production, and comprehension of language and have been shown to differ cross-linguistically and cross-culturally in aspects of performance and form-meaning relationships. Furthermore, gestures can serve as analytical tools to access tacit embodied-imagistic mathematical meanings that add to verbal-linguistic…

The goal of our research program is to explicate the learning of mathematical concepts in ways that are useful for instructional design and to develop design principles based on those explications. I review one type of concept and our elaboration of reflective abstraction, coordination of actions (COA) that accounts for its construction. I then…

This paper problematizes the metaphors of unpacking, deconstructing, and decompressing mathematics that are prevalent in discourses about mathematics teacher knowledge. It is argued that the logic of these metaphors is based on the reversibility of packing, constructing, and compressing mathematics and seems to suggest the view that knowledge is…

Mulla Sadra's philosophy has an ontological approach. However, his explicit texts or philosophical foundations in social issues such as education and especially the curriculum and its relationship with learning methods can be extracted. Mulla Sadra's different approach to learning has distinguished his educational system from other educational…

Researchers have hypothesized and, in some cases, shown that hypothetical learning trajectories (LT)s can be effective tools in teaching, but implementation, across individual teachers, varies. From the literature base, we have identified six ways researchers have hypothesized teachers might be able to use LTs in their work as teachers:…