This article discusses two mechanisms through which understanding static mathematical concepts (basic and more advanced mathematical concepts) in terms of fictive motions or motion events enhance our understanding of these concepts. It is suggested that at least two mechanisms are involved in this enhancing process. The first mechanism enables us…

This design-based research project explored how various design features of AR-based learning environments (ARLE) influence students' mathematics self-efficacy and learning of kinematics. Specifically, five ARLEs with different design features were developed and implemented with 136 seventh-grade students in two rounds. Data were gathered from pre-…

In this article, we discuss the process of understanding continuity, which is one of the most fundamental concepts in mathematics. The continuity of mathematical functions is formally defined in terms of abstract symbols and operations. This representation of continuity is very abstract or dis-embodied. Therefore, it is difficult to acquire a…

This article looks at an interdisciplinary college movement and mathematics course from the perspectives of one of its co-creators and a mathematics education researcher. It suggests deep, embodied use of choreographic problem solving can form an effective path to mathematics learning through (a) conceptual overlap between mathematics and dance,…

This article reports on an exploratory study that engaged students in dynamic experiences of generating the area of a rectangle as a sweep of a line segment over a distance. A case study from a design experiment with one pair of third-grade students is presented to initiate a discussion around the forms of reasoning that students may exhibit as a…

In the same chapter of his book "Opera Geometrica," Torricelli published two discoveries: 1) initial velocity of a jet from a container increases with the square root of the depth of the hole; 2) he drew the pattern of jets from three openings at the wall of a container filled with water to constant level "H" and determined the…

In this article we review the impact the design and implementation of an intensive programme that explores mathematical concepts through voice and movement has, to complement the previous work carried out in the core area of mathematics in early childhood education. An extensive body of research related to nonmusical outcomes and the benefits of…

An awareness of pattern and structure (AMPS) is critical in young children's mathematical development (Mulligan & Mitchelmore, 2009). AMPS is formally assessed in the early years of school (K-3), in structured conditions using predetermined materials, requiring verbal and written responses. However, children also express mathematical thinking…

This paper approaches the concept of the circle through the framework of mathematics-as-becoming. This paper focuses specifically on how a concept can be thought of as a process, and on the implications that this might have for mathematics learning. Contrary to long-standing assumptions about mathematical concepts as ideal, inert, Platonic forms,…

Mathematics is a particularly notable domain in which to understand the role of body movement for improving reasoning, instruction, and learning. One reason is that mathematics ideas are often expressed and taught through disembodied formalisms--diagrams and symbols that are culturally designed to be abstract, amodal, and arbitrary (Glenberg et…

In this article, we examine how a sequence of modeling activities supported the development of students' interpretations and reasoning about phenomena with negative average rates of change in different physical phenomena. Research has shown that creating and interpreting models of changing physical phenomena is difficult, even for university level…

Embodied mathematics activities involve students engaging in physical actions to help them better understand mathematics concepts. Current research shows these types of activities have great potential to help students develop conceptual understanding. The authors present four principles for designing embodied mathematics activities and give…

By accessing creative portions of the brain through dance, Pre-K students can more easily learn math concepts like spatial awareness and critical math knowledge prior to formal assessment in elementary school. This early foundational learning creates educational equity by resulting in a month of additional math learning before ever stepping into…

In this article, the authors first present the Hands Together! task. The mathematics in this problem concerns the relationship of hour and minute durations as reflected in the oft-overlooked proportional movements of the two hands of an analog clock. The authors go on to discuss the importance of problem solving in general. They then consider…

In understanding upper secondary school students' interpretations of information in symbolic representations of a distance-time-relation, little attention has been paid to the analysis of the condition of the conceptual development related to utterances. Understanding this better can help improve the teaching of attribute and information in…