In this article, the author shares two investigations that relate the variables of height and volume using different contexts. Each of the investigations surfaced unfinished learning for students, regardless of their starting place, and facilitated growth in understanding of measurement and algebra. The Functions and Volume of Vases task…

Teacher gestures support mathematics learning and promote student collaboration. Aligned with speech, gestures can help students to notice the important visual information of geometry tasks. However, students' visual attention to the teacher's gestural cues during collaborative problem solving remains a largely unexplored field in mathematics…

We use Action-Process-Object-Schema (APOS) theory to study students' geometric understanding of partial derivatives of functions of two variables. This study contributes to research on the teaching and learning of differential multivariable calculus and its didactics. This is an important area due to its multiple applications in science,…

While there are many documented approaches to using technological tools to support collaboration in remote environments, studies related to proof-based courses are overwhelmingly situated in the context of geometry. This study uses instrumental genesis theory to study how students in an introduction to proofs course operationalize the…

Augmented Reality (AR) technologies allow for holograms to be layered over the real-world, "augmenting" human vision by adding technical information or illustrations onto 3D space. Although AR-based applications are showing positive effects in many systematic reviews and meta-analyses, well-designed, rigorous studies with strong control…

Productive talk is structured talk designed to support students in developing a deep understanding of the content (Michaels et al., 2008): a characteristic of high-quality mathematics instruction (National Council of Teachers of Mathematics, 2014). Students who engage in talk during mathematics class have opportunities to make sense of the…

Augmented Reality (AR) technologies allow for holograms to be layered over the real-world, "augmenting" human vision by overlaying illustrations onto 3D space. Here we explore the question: What affordances does AR in a collaborative environment have for the future of mathematics education in uncertain times? We conducted a study where…

The aim of this study is to show how the GeoGebra software-supported collaborative learning environment contributes to a group of students using multiple representations and reaching generalisations while solving problems collectively. Blending individual and collaborative learning activities were carried out with a learning method called ACODESA…

Students showed poor performance in applying higher-order thinking skills (HOTS) in solving Additional Mathematics problems. Therefore, this study examined the effects of Problem-Based Learning (PBL) and Collaborative Learning (CL) assisted by Geometer's Sketch Pad on the four levels of HOTS of Form Four students, namely Applying, Analysing,…

The current research trend of metacognitive regulation has shifted from an individual to a social context. One such social context is collaborative problem-solving. Interaction between group members is an essential factor in completing collaborative problems. Metacognitive regulation is divided into four forms based on the interaction in…

Technology to support collaborative learning has come a long way. Interactive tabletops support collaboration when correctly integrated in activity design. While these devices can now, in principle, be purchased by the general public, wide adoption in schools is hindered by their high cost and lack of mobility. In this paper, we analyze the…

The research question studied in this paper is how teachers' task designing can be enhanced in professional development. We show that this can be done by scaffolding. Scaffolding is used in problem solving and we apply it by considering designing a task as a problem. In the paper, we describe a professional development of four teachers led by a…

Collaborative problem solving (CPS) is widely recognized as a prominent 21st-century skill to be mastered. Until recently, research on CPS has often focused on problem solution by the individual; the interest in investigating how the theorized problem-solving constructs function as broader social units, such as pairs or small groups, is relatively…

We introduce, motivate, and exemplify a proposed theoretical construct guiding the design and facilitation of collaborative geometry activities, conceptually generative perspectival complementarity (CGPC). Participants in CGPC activities learn content by negotiating their respective perceptions of situated features they manipulate to accomplish…

This study investigates how learners collaboratively construct embodied geometry knowledge in shared VR environments. Three groups of in-service teachers collaboratively explored six geometric conjectures with various virtual objects (geometric shapes) under the guidance of a facilitator. Although all the teachers were in different physical…