Discusses a number of Theo van Doesburg's paintings concerning arithmetic composition. (KHR)

Describes episodes from work with a small group of 8th grade students who were working independently on a geometry course. Uses Geometer's Sketchpad for the tasks. Discusses students' reasoning skills and their interpretation of the painting in terms of the mathematical properties and relationships. (KHR)

Discusses the mathematics of Theo van Doesburg's painting, Arithmetic Composition 1. Investigates ratios and symmetries as well as relationships among geometrical forms in the painting. (MM)

Introduces a metaphor for conceptually-oriented mathematics teachers and discusses possible implications for mathematics teacher preparation and professional development. (MM)

Discusses the role of play in the learning of mathematics. Describes a play for the third grade mathematics classroom that focuses on negative numbers and number concepts, and revisits Vygotsky from this point of view. Concludes that mathematically imaginative play can contribute greatly to mathematics learning in elementary school. (Contains 20…

Addresses the definitions of several mathematical concepts and the relationships between them based on a theoretical framework presented in the first part. Presents two examples of mathematical activities on equivalent and non-equivalent definitions constructed in the context of professional development workshops for mathematics teachers.…

Explores some of the issues behind mathematical modeling for technology with reference to undergraduate teaching and professional practice. Discusses theory and practice in mathematical modeling and its place and uses of modeling in engineering. (ASK)

Critical mathematics education cannot be translated into principles. Aims to search for a working philosophy of mathematics for critical mathematics education. Concludes that aporism attempts to consider mathematics in its social, cultural, and political complexities, and to express uncertainties about mathematics' possible role as an educational…

Addresses the concept of mathematical definition as well as the definitions of different mathematics concepts. Focuses on the possibility of defining a mathematical concept in several ways based on logical relationships between different mathematical statements related to the concept. The choice of one of these statements as definitional plays a…

Investigates magical mathematical moments in order to seek to understand what they are and how they happen, to look for examples, and to reflect on their impact on students' mathematics learning. Describes magical moments as they appear in references in the literature and characterizes those moments. Provides examples from classrooms. (Contains 27…

Describes the different types of reasoning in scientific research activity. Outlines three different but complementary ways to integrate history into the presentation of science. Considers and illustrates the close historical relationship between mathematics and physics. (Contains 50 references.) (ASK)

Discusses Brousseau's work on the theory of didactical situations in mathematics and its applications in mathematics classrooms which do not address the collection of obvious components, but instead discuss phenomena by analyzing knowledge in given situations. Meanings emerge in situations engineered by analyzing a situation and developing an…

Discusses the gap between educational theories and practice and focuses on constructivism in mathematics classrooms. Contains 12 references. (ASK)

Focuses on books by Brown, Dowling, and Davis that constitute significant and substantial attempts to broaden and deepen the nature of discourse about, and activities in, the field of mathematics education. (ASK)

Word problems have several purposes in mathematics education. Concentrates on two of these purposes--word problems as applications and word problems as mental manipulatives--and compares them with each other. (ASK)