Pascal's Triangle is, without question, the most well-known triangular array of numbers in all of mathematics. A well-known algorithm for constructing Pascal's Triangle is based on the following two observations. The outer edges of the triangle consist of all 1's. Each number not lying on the outer edges is the sum of the two numbers above it in…

This article describes explorations using The Geometer's Sketchpad for algebra and calculus content.

The purpose of this report is to examine results in mathematics for the ACT Educational Planning and Assessment System (EPAS) in schools nationwide. EPAS consists of three programs: EXPLORE[R] (for students in grade 8 or 9), PLAN[R] (for students in grade 10), and the ACT[R] test (for students in grade 11 or 12). The following questions are…

Students mainly perceive the transition to secondary school as an opportunity to start their school career anew. Reality often proves them wrong, especially in the case of mathematics. In our paper, we briefly discuss children's transition to secondary school as both an opportunity and a problem, with reference to the Greek context. In discussions…

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)

The geometry textbooks of the new system of secondary education in Iran differed dramatically from the old ones considering the aims, the visions, the content, the approach, and the educational purposes. Four hundred eighty mathematics teachers participated in a nationwide professional development program conducted by the author to facilitate the…

This article begins with a comparison of two groups of teachers, working on the same tasks in Analytic Geometry. One group has only basic experience in CAS-assisted problem solving, and the other group has extensive experience. The comparison is discussed in terms of the interplay between reflection, operative knowledge and execution. The findings…

The interpretive framework for the study of learning introduced in this article and called "commognitive" is grounded in the assumption that thinking is a form of communication and that learning mathematics is tantamount to modifying and extending one's discourse. These basic tenets lead to the conclusion that substantial discursive change, rather…

In this article, the author describes a 200-year-old ladder problem that can carry learners to high levels of mathematical thinking and activity. This problem requires learners to go from a word problem to an equation to a graph and from there to a solution. As this problem of specifics is turned into a problem using variables, technology,…

Mathematics is both a beautiful language and the simplest systematic discipline men ever created. The simplicity of mathematical concepts almost guarantees that the facts it establishes about those concepts will also be elemental. Despite this simplicity, most people complain about the difficulty of mastering the subject and shun the study of…

High school students in the United States have been taking more challenging courses in recent years, but academic achievement has been stagnant. At the heart of the matter is the quality of curriculum, instruction, and assessment. Some courses tend to be more challenging in name than in practice. High schools also have a history of autonomy that…

In this study, I present an analysis of high school geometry curricula regarding mathematical proof opportunities. I examined eight U.S. high school level geometry textbooks, which were categorized into three main groups: technology-intensive, standards-based, and traditional curricula. I conceptualized "ideal" proving activity combining…

Because of the educational importance of mathematics and science, IEA's (International Association for the Evaluation of Educational Achievement) Trends in International Mathematics and Science Study, widely known as TIMSS, is dedicated to providing countries with information to improve teaching and learning in these curriculum areas. Conducted…

This paper was prepared in response to the Conference Board of Mathematical Sciences recommendations for the preparation of secondary teachers. It shows how using trigonometry as a conceptual tool in spreadsheet-based applications enables one to develop mathematical understanding in the context of constructing geometric representations of unit…

Presented are practical activities relevant to teaching mathematics in the American Indian culture that can be used in the non-Indian classroom. Discussed are tessellations, exercises that allow for artistic creativity and geometric exploration. The use of Pascal's triangle is included. (KR)