We build on mathematicians' descriptions of their work and conceptualize mathematics as an aesthetic endeavor. Invoking the anthropological meaning of practice, we claim that mathematical aesthetic practices shape meanings of and appreciation (or distaste) for particular manifestations of mathematics. To see learners' spontaneous mathematical…

Tailoring workshop (TW), a school-based teacher training program, has been developed in China on the basis of the Teaching Research Groups (TRGs) to better focus on teacher's genuine needs, improve their problem-solving ability, and inter-subject collaboration. Literature on teacher workshops predominately roots in western settings whereas scant…

Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their "explicit" models are accessible -- those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its…

In our technological age, many technologies and real-world objects communicate with each other or partly merge. However, this combination of technologies and real-world objects has not yet found its way into everyday teaching practices in schools to any great extent. To investigate the possibilities of combining technologies and real-world objects…

This study used a machine learning framework in conjunction with a large battery of measures from 9,718 school-age children (ages 9-11) from the Adolescent Brain Cognitive Development[superscript SM] (ABCD) Study to identify factors associated with fluid cognitive functioning (FCF), or the capacity to learn, solve problems, and adapt to novel…

International comparative studies on mathematics teaching and learning often provide unitary and harmonious images of classroom practices. This paper aims to complement those studies by describing the complex aspects of those practices. Adopting activity theory as a framework, this paper considers classroom teaching and learning of mathematics as…

Lines and angles are essential for students because of geometry and its many applications in daily life. However, there are still many students who have difficulty grasping the material. Therefore, it is necessary to design learning using the right approach, context, and media. This study aims to produce a learning trajectory that can assist…

The students' perception of how they are positioned by their teachers offer valuable insights into how teachers might engage students in the act of learning, construct themselves and acts in ways desirable to students, and how they might make the learning process a more enjoyable one for students. Teacher positioning is an important factor in…

Representation is widely viewed as central to mathematical problem solving, while online scaffolding is considered helpful in supporting learners' progress from actual to potential developmental levels of mathematics understanding. Therefore, this study investigated the effectiveness of employing online single vs. multiple representational…

The folklorist Vladímir Propp identified a curious phenomenon in his study of 100 Russian fairy tales: despite their tremendous surface variety, they followed a single narrative structure or morphology. This article argues that the same phenomenon applies to SoTL articles: despite the tremendous variety of content and methods that SoTL articles…

Mathematics instruction can work to open or constrain children's opportunities to learn, and the busy, interactive nature of instruction makes it challenging for researchers to identify patterns in high-quality opportunities to learn. While researchers have documented how whole-group discussions and small-group work can contribute to such…

We have the ability to capture data from students' interactions with digital environments as they engage in learning activity. This provides the potential for a reimagining of assessment to one in which assessment become part of our natural education activity and can be used to support learning. These new data allow us to more closely examine the…

Background: Programming a computer is an increasingly valuable skill, but dropout and failure rates in introductory programming courses are regularly as high as 50%. Like many fields, programming requires students to learn complex problem-solving procedures from instructors who tend to have tacit knowledge about low-level procedures that they have…

In this reflective methodological paper we focus on affordances and challenges of video data. We compare and analyze two research settings that use the latest video technology to capture classroom interactions in mathematics education, namely, The Social Unit of Learning (SUL) project of the University of Melbourne and the MathTrack project of the…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…