Discusses the importance of inquiry and discovery in science and mathematics education. Presents three science problems for students to develop their own solutions. Concludes that curriculum materials must engage and support teachers in the process of integrating mathematics and science. (ASK)

Investiges the mathematical behavior of graduate students and the experiences that contributed to their mathematical development and success. Students reported that a mentor facilitated the development of their problem solving abilities and continued mathematical study. When confronted with an unfamiliar task, students exhibited exceptional…

Explores insights that may be provided by a situated perspective on learning. Considers the ways in which a focus on the classroom community and the behaviors and practices implicit within such communities may increase understanding of students' mathematical knowledge production and use. (Contains 22 references.) (Author/ASK)

This review of recent literature, focusing on the integration of mathematics and reading, highlights three reading stances within mathematics classrooms. The first stance, reading problems, highlights the scope-and-sequence, transmission approach to learning mathematics, where the purpose of reading is to figure out how to solve an immediate…

The fields of mathematics, science, and engineering are replete with diagrams of many varieties. They range in nature from the Venn diagrams of symbolic logic to the Periodic Chart of the Elements; and from the fault trees of risk assessment to the flow charts used to describe laboratory procedures, industrial processes, and computer programs. All…

Two questions are asked that concern the work of teaching high school geometry with problems and engaging students in building a reasoned conjecture: What kinds of negotiation are needed in order to engage students in such activity? How do those negotiations impact the mathematical activity in which students participate? A teacher's work is…

Computer algebra systems are frequently used for research. In addition, some instructors have based entire advanced courses around these systems. One benefit is that they allow students to become familiar with the methods of calculus by individual experimentation. However, instructors have generally seen computer algebra systems as unsuitable for…

In this article, I present a study in which 12 pairs of 8th-grade students solved problems about a physical device with algebra. The device, called a winch, instantiates motions that can be modeled by pairs of simultaneous linear functions. The following question motivated the study: How can students generate algebraic models without direct…

If a curriculum developer's goal is to create a single linear sequence of tasks that lead to the development of some important mathematical concept, then some researchers have suggested that these sequences should follow progressions similar to stages of development that have been identified in Piaget-like research on the relevant concept(s).…

Using the power series solution of a differential equation and the computation of a parametric integral, two elementary proofs are given for the power series expansion of (arcsin x)[squared], as well as some applications of this expansion.

In this paper we examine the roles that metonymy may play in student reasoning. To organize this discussion we use the lens of a structured derivative framework. The derivative framework consists of three layers of process-object pairs, one each for ratio, limit, and function. Each of the layers can then be illustrated in any appropriate context,…

Several developments during the last decades have provoked spectacular changes in both Mathematics Teaching and the Education of Mathematics Teachers. From this perspective of renovation, we wish to define a new context in mathematics teacher education in which we consider that "pedagogical content knowledge" (Shulman, 1993, Mellado,…

Given three points in the plane, interest is in the locus of all points for which the sum of the distances to the given points is a prescribed constant. These curves turn out to be sixth degree polynominals in x and y , and thus are complicated. However, it turns out that often there is a point, within the triangle formed by the three given…

This article outlines an engineering problem requiring the use of a specialized trigonometric formula, and offers an answer to that age-old classroom question, "When are we gonna have to use this"?

The results of an action research project in which young children in one classroom are encouraged to solve and pose their own problems in their first year at school are described. The progress of these children supports the finding that kindergarten children could solve a variety of quite difficult word problems on their own.