This paper discusses Sfard’s commognitive approach and provides an empirical study as an example to illustrate the theory as method. Traditionally, research in mathematics education focused on the acquisition of mathematical knowledge and the didactic process of knowledge transfer. Through attending to a distinctive form of language in mathematics, as well as mathematics as a discursive subject, alternative views of making meaning in mathematics have emerged; these views are therefore “critical,” as in critical discourse analysis. The commognitive discourse analysis method has the potential to bring more clarity to our understanding of students’ mathematical thinking and the process through which students are socialized into school mathematics.
We present a framework of researcher knowledge development in conducting a study in mathematics education. The key components of the framework are: knowledge germane to conducting a particular study, processes of knowledge accumulation, and catalyzing filters that influence a researcher decision making. The components of the framework originated from a confluence between constructs and theories in Mathematics Education, Higher Education and Sociology. Drawing on a self-reflective interview with a leading researcher in mathematics education, Professor Michèle Artigue, we illustrate how the framework can be utilized in data analysis. Criteria for framework evaluation are discussed.
In this article, we discuss project-based learning in the context of a wheel garden as an instructional tool in science and mathematics education. A wheel garden provides multiple opportunities to teach across the curriculum, to integrate disciplines, and to promote community involvement. Grounded in the theoretical framework of constructivism, the wheel garden provides a multidisciplined educational tool that provides a hands-on, non-traditional arena for learning. We will examine some of the cultural, art, science, and mathematics connections made with this project.