Applications of generalizations of both arithmetic and geometric progressions are presented. The first-order difference equation is used in solving seven examples from finance, business, and medicine. Detailed directions are included for each example. (KR)

Suggested are features which should be considered before selecting a specific interactive graphics package. Features that allow for accurate estimates of roots of functions and solutions to systems of equations are illustrated. Six graphics packages are compared including display, tabular options, misleading graphics, printing options, functions…

Describes three software packages: (1) "MacMendeleev"--database/graphic display for chemistry, grades 10-12, Macintosh; (2) "Geometry One: Foundations"--geometry tutorial, grades 7-12, IBM; (3) "Mathematics Exploration Toolkit"--algebra and calculus tutorial, grades 8-12, IBM. (MVL)

Discusses possible approaches to solving the problem of how many different triangles can be formed on an n x n geoboard and the different geometric concepts utilized to formulate a solution. Approaches include counting strategies, writing a computer program, and using difference equations. (MDH)

Presents two worksheets that ask students to count and classify the triangles that can be formed with a given total number of toothpicks or a given number of toothpicks for one side of the triangle. A third worksheet asks students to identify patterns observed during the investigations. Provides reproducible worksheets. (MDH)

Provided are student activities to introduce the geometric concepts of line symmetry and rotational symmetry as related to Hawaiian quilting patterns. Paper squares, scissors, and folding techniques afford the teacher the chance to stimulate class discussion about pattern recognition and to integrate mathematics with the cultural world outside the…

Describes one teacher's reflection concerning the quest to develop an understanding of school mathematics that promotes and sustains students' opportunities for exploration and conjecture. Recounts that a particular student's exploration of the features of parabolas eventually led to an understanding of the quadratic formula precisely because of…

Presented are four activities which allow students to work with rhombus patterns. These activities encourage students to search for, test, and verify patterns and to also practice computation and work with ratios. Diagrams needed for each activity are included. (KR)

Compares the content of geometry and measurement appearing in first- through eighth-grade textbooks in the United States and the Republic of Korea. American textbooks devoted a greater number of pages to measurement and geometry content, introduced the content earlier, presented concepts and skills more independently of each other, and presented…

Presented are three ideas for teaching mathematical concepts including "The Gymnasium- A Dynamic Classroom for Teaching Slope,""The Graphics Calculator: A Helpful Tool," and "The Point-Slope Equation Revisited." (CW)

Presents an argument for using dot paper rather than geoboards at postelementary levels to study perimeter, area, congruence, similarity, and other geometric ideas. Emphasizes need for students to be active learners. (GW)

There are two basic guiding referents in the present investigation: the teaching and learning of school-level geometry (basic concepts of Euclidian geometry and measure) and the analysis of the conceptions of prospective primary teachers in Spain. The work assumes that such conceptions appear and develop during school years, and that consequently,…

Implementing best practices like cooperative learning, using concrete manipulatives, problem solving, technology, active learning, multi-age grouping, and team teaching have shown benefits for students when learning mathematics concepts within the curriculum (Zemelman, Daniels & Hyde, 1998; NCTM, 2000). What started as a professional development…

The purpose of this article is to suggest ways of using research on children's reasoning and learning to elaborate on existing national standards and to improve large-scale and classroom assessments. The authors suggest that "learning progressions"--descriptions of successively more sophisticated ways of reasoning within a content domain based on…

The practice of students going to the boards to work problems has been a tradition in undergraduate education for over two hundred years. A study was conducted to determine what instructional techniques enabled students to better learn fundamental concepts in mathematics. This study identifies board work as a highly effective instructional…