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.…

This article describes lessons that link mathematics topics with literature, the NCTM's Navigations series, and art projects. Each lesson is designed around a theme and is laced throughout with fantasy. (Contains 13 figures.)

Students get a fun challenge from puzzling over an old, seemingly magical distance measurement technique. (Contains 5 figures.)

Some "drag-to-fit" solutions given by student teachers to three geometric construction problems in a dynamic geometry environment (DGE) are analysed. The responses of a group of experienced mathematics teachers to the question whether or not such solutions can be considered "legitimate" are then discussed. This raises fundamental questions…

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…

This resource book for geometry contains games, tricks, and quick activities for the classroom. Categories of activities include picky puzzlers, plane figures, constructions, vectors, and measurement. Included are eight picky puzzler problems, 19 activities with plane figures, and 25 geometric construction activities. Three vector activities and…

Function Probe is a multi-representational software for Apple Macintosh computers. It was designed to allow students to approach problems in different ways and/or use different representations. This case study describes a 16-year-old student as he creates a path among a variety of representations of transformations of functions while using the…

This guidebook is designed to assist teachers and other local school district personnel in the planning and the teaching of the high school geometry course, with essential elements as mandated by the Texas State Board of Education in 1989. Research on student learning in geometry provides the logical rationale for the instructional sequencing and…