Identifies and describes three steps where connections between written symbols and understandings can be made: (1) developing meaning for symbols; (2) developing meaning for rules; and (3) checking the reasonableness of solutions. (YP)

Discusses a calculation method to approximate pi. Describes how to get an approximation to the circumscribed and inscribed perimeters of regular polygons of n sides. Presents the computer program and result of the approximation. (YP)

Suggests activities involving the use of indices. Provides five activities with examples for routine practice, pattern recognition, prediction, conjecture, generalization, factorization, and limit concept. (YP)

The problem of finding all topological spaces is considered. Two characterizations are presented whose proofs involve only elementary notions and techniques. The problem is appropriate for students in a beginning topology course after they have been presented with the Embedding Lemma. (DC)

Investigates the development of understanding of quantity in 36 children with Down's Syndrome. Findings confirmed similarities in sequence of development between Down's Syndrome children and nonretarded children. Down's children who received training recognized conservation of continuous and discontinuous quantity. (RJC)

Provides an overview of a course, "Applied Linear Algebra," for teaching the concepts and the physical and geometric interpretations of some linear algebra topics. Describes the philosophy of the course, the computer project assignments, and student feedback. Major topics of the course are listed. (YP)

Certain misunderstandings in science, mathematics, and computer programing reflect analogous underlying difficulties. These misunderstandings are examined through four knowledge levels: (1) content; (2) problem-solving; (3) epistemic; and (4) inquiry. Analysis of several examples shows that misunderstandings have causes at multiple levels, and…

Presents strategies for teaching elementary students about ratio and measurement. Primary students read and discuss a story that involves measurement, then write letters of advice to one of the characters. Intermediate students read the story, write and share letters of advice, discuss the benefits of standard measures, and measure themselves. (SM)

Four experiments investigated under which conditions and at which age level children in grades four through six would become aware of the conflict between practical and theoretical considerations in mathematics. Students in grades four and five did not indicate an awareness of this conflict, while about half the sixth graders did, indicating a…

Presents exploration activities and problems related to the concept of linear function which can be performed using Parallel Axes Representation. (PR)

Activities in this article are a practical response to the philosophical debate about the use of technology in mathematics classes. Shows how technology can help students understand the sophisticated mathematics embedded in r, the correlation coefficient. Includes reproducible student worksheets. (MKR)

Shows how to model Newton's method for approximating roots on a spreadsheet. (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)

Describes the use of a graphic organizer--webs--to help students learn to connect concepts in mathematics. (MKR)

Discusses past research involving Piagetian conservation concepts in Native American students; the relation of language to mathematics education; holism in mathematics learning; mathematics and culture; the Outdoor World Science and Mathematics Project, which developed learning modules involving Native Americans; and mentorship in an atmosphere of…