Emphasizes the importance of proofs and offers examples and ideas that might help educators develop students' mathematical reasoning skills. (ASK)

Investigated development of turn and turn measurement concepts within a computer-based instructional unit. Written assessments, interviews, and interpretive case studies of third and fourth graders found that turns were less salient for children than forward and back motions; students evinced a progressive construction of imagery and concepts…

Discusses geometry and Dynamical Geometry Software (DGS). Analyses the way DGS-use influences traditional geometry. Highlights changes in the interactions between geometry, computers, and DGS and human users, focusing on changes in the teaching and learning of geometry. Concludes that DGS deeply changes geometry if it is taken as a human activity…

Background: Since the early 1980s, there has been a growing interest in the potentiality of computers as facilitators of students' learning. The importance of using technology effectively as a learning tool has been emphasized by many researchers. However, finding good software that encourages pupils to explore and express mathematical ideas is…

This article describes an activity in which students plot collections of ordered pairs according to prescribed set conditions. The coordinate plane sets can have rich variety, and their construction fosters critical thinking, attention to detail, and algebraic reasoning. (Contains 3 figures.)

This article describes geometry-oriented problem-solving tasks that can encourage students to develop a positive attitude toward mathematics. The tasks concern working with polyominoes, two-dimensional shapes that consist of squares joined fully at the edges. (Contains 7 figures.)

This article is the sequel to the use of "Flatland" with beginning algebra students reported in Sriraman (2003). The use of "Flatland" with beginning algebra students resulted in the positive outcomes of cultivating critical thinking in the students as well as providing the teacher with the context necessary to introduce sophisticated mathematical…

In this paper we consider geometrical construction problems and their role in mathematical education. Owing to the main features of construction problems (accuracy in making conclusions, strict structure, rigorous language and constructivistic nature), they can be fruitfully used in teaching mathematics and computer science. We shall try to shed…

Good early mathematics is broader and deeper than early practice on "school skills." High-quality mathematics should be a joy--not a pressure. It can emerge from children's play, their curiosity, and their natural ability to think. This article describes the areas of mathematics that young children can learn, and encourages elementary teachers to…

A case study, originally set up to identify and describe some benefits and limitations of using dynamic web-based geometry sketches, provided an opportunity to examine peer interactions in a lab. Since classes were held in a computer lab, teachers and pairs faced the challenges of working and communicating in a lab environment. Research has shown…

In teaching a course without a textbook, we introduce a project in which students develop their own text. Details of the project, student reactions, benefits to students, and more are discussed. (Contains 2 footnotes.)

Many counting problems can be modeled as "colorings" and solved by considering symmetries and Polya's cycle index polynomial. This paper presents a "Maple 7" program link http://users.tamuk.edu/kfdrc00/ that, given Polya's cycle index polynomial, determines all possible associated colorings and their partitioning into equivalence classes. These…

The introduction of quilt pattern consisting of many quilt blocks formed by congruent triangles, for writing by the students in the geometry classrooms, is studied. It is found that the students enjoyed this method and writing also helped in understanding the geometric concepts expanding their vocabulary in geometry.

Montgomery County Public Schools (MCPS) "Special Education at a Glance." which includes a copy of the "Guide to Planning and Assessing School-Based Special Education Programs." provides in a single document, information about the special education population at each Montgomery County (Maryland) public school, including…

This article examines students' development of levels of understanding for measurement by describing the coordination of geometric reasoning with measurement and numerical strategies. In analyzing the reasoning and argumentation of 38 Grade 2 through Grade 10 students on linear measure tasks, we found support for the application and elaboration of…