Recognizing the need to implement standards-based instructional materials with school-wide coherence led some Philadelphia schools to adopt whole-school reform (WSR) models during the late 1990s. The authors report on the relation between mathematics achievement growth for middle-grade students on the Pennsylvania System of School Assessments and…

Many difficulties surrounding mathematical induction have been described by researchers. In this paper, I describe several underlying causes for these difficulties. In particular, the symbolic nature of induction is discussed, along with student cognitive levels, validation abilities, and proof schemes.

This article offers some ideas about creating mathematical art based on number patterns. It includes a process for students that integrates number and geometry and results in attractive and useful patterned squares. Students may pursue the activity with paper and pencil or they may use computer software like The Geometer's Sketchpad to achieve…

Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…

In the 1970s, the movement to the metric system (which has still not completely occurred in the United States) and the advent of hand-held calculators led some to speculate that decimal representation of numbers would render fractions obsolete. This provocative proposition stimulated Zalman Usiskin to write "The Future of Fractions" in 1979. He…

In 3 experiments, the authors investigated learning of the value of money from product prices in an unfamiliar currency when the prices are proportional to quantity. In support of the second stage of a hypothesized 2-stage process of learning, Experiment 1, in which 32 undergraduates participated, shows that response times for inferences of…

The present study explores pupils' constructed definitions of the concept of function in relation to their abilities in dealing with tasks of functions involving different forms of representations and problem solving tasks. A major concern is also to examine the interrelations between these three ways of thinking about or dealing with the concept…

Concerns about the importance of variation in statistics education and a lack of research in this topic led to a preliminary study which explored pre-service teachers' ideas in this area. The teachers completed a written questionnaire about variation in sampling and distribution contexts. Responses were categorised in relation to a framework that…

Here we explore the educational implications of classroom activities related to the backgrounds and motivations of talented Hollywood comedy writers and the mathematical moments they created for the Emmy Award-winning animated sitcom "Futurama." (Contains 6 figures.)

Some simple modeling with Riemann sums can be used to develop Beer's Law, which describes the relationship between the absorbance of light and the concentration of the solution which the light is penetrating. A further application of the usefulness of Beer's Law in creating calibration curves is also presented. (Contains 3 figures.)

We suggest that different string pendulums are positioned at different locations on Earth and measure at each place the gravitational acceleration (accuracy [delta]g is approximately equal to 0.01 m s[superscript -2]). Each pendulum can be remotely controlled via the internet by a computer located somewhere on Earth. The theoretical part describes…

The use of discourse in the mathematics classroom can be difficult to implement and manage. The same students participate in every discussion while others contribute only when called on, and even then their contributions are sparse. Some students make comments that relate to procedure but never reach the deeper-level mathematical concepts. This…

Many science topics can naturally be integrated with a variety of mathematical concepts, including the study of light and optics. In the hands-on activities described here, students explore the properties of light energy while building their understanding of geometric concepts. (Contains 2 figures.)

The article describes the social and cultural roles of Mesopotamian mathematics and the interplay of these roles with such patterns of mathematical thought as can be traced through the sources; it covers the period from the first formation of a genuine state, shortly after the mid-fourth millennium b.c.e., until the end of the Old Babylonian…

This paper explores Mechanical Engineering students' conceptions of and preferences for conceptions of the derivative, and their views on mathematics. Data comes from pre-, post- and delayed post-tests, a preference test, interviews with students and an analysis of calculus courses. Data from Mathematics students is used to make comparisons with…