Even though reflective symmetry is heavily embedded in the everyday, learners continue to experience challenges when they mathematize concepts from this informal/everyday context. In this article we argue that symmetry exists in nature, it can also be symbolized algebraically and it can be abstracted into the world of axioms and theorems. We…

This study investigated the effects of applying mathematical modeling on revising students' preconception of the process of optimizing area enclosed by a string of a fixed length. A group of 28 high school pre-calculus students were immersed in modeling activity that included direct measurements, data collecting, and formulating algebraic…

This paper explores student interactions from the Virtual Math Teams-With-GeoGebra Project, a computer-supported collaborative learning environment that allows individuals to interact, collaborate, and discuss user-created dynamic mathematics objects. Previous studies of virtual math teams have focused on the coconstruction of a joint problem…

Within the South African school curriculum, the section on graphical functional relationships consists of signs which include symbols, notation and imagery. In a previous article we explored the role visualisation played in the way learners understood mathematical concepts. That paper reported on the learners' fixation with the physical features…

The purpose of the study was to assess student achievement and motivation during a high school augmented reality mathematics activity focused on dimensional analysis. Included in this article is a review of the literature on the use of augmented reality in mathematics and the combination of print with augmented reality, also known as interactive…

This study examines high school students' views of mathematics as a tool for social inquiry in light of their classroom experiences using mathematics to explore social issues. A critical theoretical perspective on mathematics literacy is used to ascertain the ways in which their views challenge or affirm the dominant image of mathematics in…

This paper refers to the concept of semiotic and theoretic control describing resources to conduct decisions in epistemic processes. We consider an argumentation process from a complex problem-solving activity involving different conceptual frames related to parabolas. Using a micro-analytical interpretative lens, we will show that, in order to…

In this article we examine intuitions as they emerge in groupwork activities. We provide a framework and a methodology to code various aspects of the activity, social and mathematical. Focusing mostly on students' gazes, we explore how affective moves give rise to, and determine, students' interactions and thoughts. We argue that intuition does…

Getting students to think about the relationships between area and perimeter beyond the formulas for these measurements is never easy. An interesting, nonroutine, and accessible problem that will stimulate such thoughts is the Lattice Octagon problem. A "lattice polygon" is a polygon whose vertices are points of a regularly spaced array.…

In this paper, we explore an approach to understanding how multimodality works in a community of practice. Using a social learning framework, we show how a community of practice, involving a pair of high school students, engaged in perceptual, bodily, and imaginary experiences while discussing about calculus concepts in a dynamic geometry…

This article describes a project that focuses on numeracy in secondary school mathematics. During the course of the project a teacher had the chance to develop and trial new tasks and styles of teaching and learning numeracy. She became increasingly comfortable with using more extended tasks for learning mathematics. However, she believes that it…

This article will describe two activities in which students conduct experiments with random numbers so they can see that having at least one repeated birthday in a group of 40 is not unusual. The first empirical approach was conducted by author Cauto in a secondary school methods course. The second empirical approach was used by author Flores with…

We live our lives in three-dimensional space and encounter geometrical problems (equipment instructions, maps, etc.) every day. Yet there are not sufficient opportunities for high school students to learn geometry. New teaching methods can help remedy this. Specifically our experience indicates that there is great promise for use of geometry…

Queensland rural and remote schools have difficulty in attracting experienced, in-field mathematics teachers. Thus, when such teachers arrive, much is expected of them to increase the mathematics knowledge of students. This paper looks at one such teacher who, against the high expectations placed upon him as an in-field teacher, experienced…

This study examined teachers' use of student tasks involving dynamic geometry software, in which a figure is constructed then altered while maintaining its constructed properties. Although researchers, professional organizations, and policy makers generally have been proponents of dynamic geometry for instruction, there is little research about…