In these two companion papers, a learning activity is introduced that teaches students how mathematics works through the visual aid of picture grids. The picture grids are composed of 60 different acrylic stained-glass window overlays. Each fractional part is represented by a different color: fifths are green, quarters are yellow, etc. The square…

Mathematical norms are important cultural knowledge of mathematical activities. This paper reports an analysis of mathematical norms in ten consecutive lessons taught by an eighth-grade Japanese teacher. The lessons were located in the unit of simultaneous linear equations. The videotapes of the lessons, their transcripts, and the interview data…

This paper is based on research work carried out in the Foundation Course in Mathematics at Goldsmiths College, University of London. The theme of the investigation was to investigate the hidden faces of cubes placed on a table. In order to do this, the following investigational teaching styles and learning strategies were adopted: investigate…

These analyses form part of a three-year project looking at mathematical thinking as a socially organized activity. We revisit data from a University Calculus class using tools from two theoretical perspectives, used increasingly in mathematics education research: (1) semiotic mediation; and (2) discursive practices. We highlight how different…

This research offers empirical evidence of the importance of supplying diverse symbolic representations in order to support concept development in mathematics. Graphical representation can be a helpful symbolic tool for concept development in the conceptual field of additive structures. Nevertheless, this symbolic tool has specific difficulties…

We present results from a study which investigated the influence of dynamic geometry-based activities in the development of proving skills (in geometry) in high-school students (15-16 years of age). After a 12-week course on Cabri and the writing of conjectures and proofs, students were asked to write and prove conjectures based on their…

The concept of function is central in mathematics and grows in importance as one progresses in depth and breadth of understanding mathematics. Results from national assessment progress reports indicate that the majority of students do not comprehend the concepts of function and graphing. Technology has the potential to improve the understanding of…

One of the major goals of mathematics education reform efforts is for students to become more confident in their abilities. This paper suggests that computer conferencing provides a way to change classroom practice so that students can work together in a self-paced manner that builds self-esteem and confidence in mathematics. A pedagogical…

This study assessed parental attitudes toward early mathematics and examined the ways in which families initiate and support the development of young children's early mathematical concepts. Six families with preschool-aged children (4 girls and 2 boys) participated in this case study involving observation of family interactions, interviews with…

This paper describes an inquiry-based, student-centered mathematics, science, and technology curriculum guide. It features activities addressing such environmental science topics as groundwater modeling, water filtration, soil permeability and porosity, water temperature and salinity, and quadrant studies. Activities are organized so that the…

A collaborative action research project with preservice teachers built on Wood's (2003) paper on strategy reporting, inquiry and argumentation and the NSW Department of Education and Training documents called substantive communication. There is little research on argumentation about space mathematics in primary schools so this is the focus of the…

The physics learning problem that students usually regard equations and other symbols in physics as algebraic exercises rather than representations of real world phenomena is commonly known. This article discusses how the Web-based interactive instructional materials were used to help students connect the symbolic world and the real world. The…

This paper describes how a target group of seven students in a combined fourth and fifth grade mathematics class used structured representations to solve fraction problems situated within various realistic contexts. Emphasis is given to the ways in which students' thinking about rational number concepts influences and is influenced by the…

In this paper we report an analysis of a teaching sequence in which Grade 11 students were asked to produce some graphs corresponding to the relationship between time and distance of a cylinder moving up and down an inclined plane. The students were also asked to carry out the experience using a TI 83+ graphic calculator equipped with a sensor,…

This paper examines how self-evaluation strategies contribute to helping students take control over their own learning processes. In addition to examining the role of self-evaluation when a student takes on and exercises control over an activity in the classroom, this paper takes into account homework assignments and the role of parents. Subjects…