Presents background information on the method used by Hipparchus to determine the distance between the earth and the moon. Describes student activities that employ Hipparchus's Method and Aristarchus's Method for determining the relative distance of the sun and the moon from the earth and Eratosthenes's Method for finding the circumference of the…

Explores the role of software tools in geometry problem solving and how these tools, in interaction with activities that embed the goals of teachers and students, mediate the problem solving process. Through analysis of successful student responses, shows how dynamic software tools can not only scaffold the solution process but also help students…

Chronicles a teacher's first year teaching geometry at the Hershey Montessori Farm School in Huntsburg, Ohio. Instructional methods relied on Euclid primary readings and combined pure abstract logic with practical applications of geometry on the land. The course included geometry background imparted by Montessori elementary materials as well as…

Sex-related differential studies on mathematical abilities have hardly taken into account the mediator role of the verbal factor, which contrasts with the interest shown in the mediator role of visuospatial aptitude. We predicted that if sex-related differences were found, mental rotation would mediate mathematical abilities typically favoring…

This study investigated the effect of students' ability and type of instructional program, structured and unstructured, on easy and difficult posttest items. Seventh-grade students worked through 14 instructional activities in The Geometer Sketchpad, a dynamic geometry program, and accessed a Geometry tutorial developed to parallel the state…

Proof and reasoning are fundamental aspects of mathematics. Yet, how to help students develop the skills they need to engage in this type of higher-order thinking remains elusive. In order to contribute to the dialogue on this subject, we share results from a classroom-based interpretive study of teaching and learning proof in geometry. The goal…

It is widely attested that university students face considerable difficulties with reasoning in analysis, especially when dealing with statements involving two different quantifiers. We focus in this paper on a specific mistake which appears in proofs where one applies twice or more a statement of the kind "for all X, there exists Y such that R(X,…

It is customary for engineering syllabuses to include a substantial amount of mathematics, a fact traditionally justified through their usefulness in the analysis and resolution of many technological problems. In other words, usually the role of mathematics in engineering is emphasized. Nevertheless, the opposite viewpoint could be considered as…

Given a conic section, the locus of a moving point in the plane of the conic section such that the two tangent lines drawn to the conic section from the moving point are all mutually perpendicular is a curve. In the case of an ellipse and hyperbola this curve is a circle referred to as the director circle. In the case of the parabola this curve…

A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…

A problem sometimes called Moser's circle problem where a circular region has to be partitioned with chords without any three chords intersecting at one point, is discussed. It is shown that Moser's circle problem makes the students to use a variety of mathematical tools to find correct solutions to problems and gives an opportunity to think about…

Faced with selecting a geometry curriculum for our preservice elementary teacher mathematics course, we used a mixed-methods study to investigate the effectiveness, with respect to student achievement and student perception, of three reform-oriented curricula. ANCOVA results indicate students using one of the curricula scored significantly higher…

In this article we describe gender gaps in mathematics achievement and attitude as measured by the U.S. National Assessment of Educational Progress (NAEP) from 1990 to 2003. Analyzing relationships among achievement and mathematical content, student proficiency and percentile levels, race, and socioeconomic status (SES), we found that gender gaps…

This article describes the activities that fifth-grade students experienced when learning about the moon, its phases, and eclipses. It illustrates how mathematics and science can be integrated to enhance the learning of both. (Contains 3 figures.)

Accumulating evidence, particularly from research using the disorientation technique, demonstrates early sensitivity to geometric properties of space. However, it is not known whether children can use geometric cues to interpret a map. The current study examined how 3- to 6-year-olds use geometric features of layouts in solving mapping tasks.…