Postulates a form of mathematical reasoning that learners engage in spontaneously that is not inherently inductive or deductive. This transformational reasoning is generated through the learner's inquiry into how a mathematical system works. (Author/MKR)

The common goal of the empirical studies discussed in this analysis was to assist children in developing a meaningful understanding of the rational number construct, founded on durable fraction concepts. Some research has focused on partitioning; some on ratio and proportion. Contains 59 references. (Author/MKR)

Reports the results of a teaching experiment involving like terms and equations in algebra. Seventh-grade students (n=6) experienced difficulties in decomposing an additive term into a difference. (Author/MKR)

Data from (n=4) students in grades three through six showed a consistent parallel between the types of units constructed in a geometric setting with those in a numeric context. Students who constructed abstract composite units in tiling the plane also did so in adding and subtracting whole numbers. (Author/MKR)

To understand an individual student's learning in the complexity of the mathematics classroom, it is necessary to examine the events before, during, and after learning. To illustrate, the process by which two children each construct new mathematical meanings is examined from these perspectives. (Author/MKR)

Discusses the growing interest in and focus on the social and cultural context of the mathematics classroom in mathematics education research. (MKR)

Analyzes the functions of semiotic mediation in a long-term teaching experiment, Mathematical Discussion, on the plane representations of three-dimensional space by means of perspective drawing in grade two to five classrooms. (Author/MKR)

Explores the opportunities and challenges of learning and teaching mathematics in the information era from a Vygotskian perspective. A systemic approach is taken to investigate the ways in which information technologies have changed the contexts for and forms of mathematical activity in society, and the challenge that this change presents to…

This study examined the usefulness of selected aspects of Tharp and Gallimore's theory of assistance as a theoretical framework for describing and analyzing change efforts in a middle school mathematics reform project. One particular classroom assistance activity is presented and analyzed in terms of characteristics of assistance that should lead…

Constructivism has assumed a dominance with mathematics education but it ignores the social implications of the construction of meaning. It is argued that constructivism is a liberal discourse that valorizes the individual construction of meaning. In doing this, the social and political contexts in which mathematical knowledge is located is…

Describes the mathematics classroom from the perspective of social phenomenology. Introduces a framework through which mathematical work is seen as taking place in the imagined world through the filter of the world in immediate perception. (Author/MKR)

Discusses critical constructivism which addresses the sociocultural contexts of knowledge construction and serves as a powerful referent for cultural reform. Contains 75 references. (Author/MKR)

Examines and discusses the differences in mathematics learning and practice in and out of school maintaining the position that while some differences may be inherent, many differences can be narrowed so that mathematics learning and practice in school and out of school can build on each other and be connected. (Author/MKR)

Proposes a framework to review the literature of the culture of mathematics, specifically in the use of the term ethnomathematics. Derives a definition of ethnomathematics; reviews two examples as a test of the power of the definition and the resultant description of ethnomathematics. (Author/MKR)

Describes a research project whose major aim was to evaluate first-year teacher-education students' understanding of subject matter knowledge in the domain of area measurement. This study focuses on the student teachers' substantive knowledge, knowledge about the nature and discourse of mathematics, mathematics in society, and their disposition…