In this article, the author describes how a curricular unit that provided opportunities for active engagement and participation was used to support the geometric reasoning of sixth grade African American (AA) male students. The curricular unit was designed to support students' understanding of quadrilaterals. Data sources (pre- and post-tests,…

How can illustrations motivate learners in multimedia learning? Which features make illustrations interesting? Beside the theoretical relevance of addressing these questions, these issues are practically relevant when instructional designers are to decide which features of illustrations can trigger situational interest irrespective of individual…

Dynamic geometry environments (DGEs) provide computer-based environments to construct and manipulate geometric figures with great ease. Research has shown that DGEs has positive impact on student motivation, engagement, and achievement in mathematics learning. However, the adoption of DGEs by mathematics teachers varies substantially worldwide.…

This compendium organizes information on the math and science projects sponsored by NCER and NCSER into two main sections: Mathematics and Science. Within each section, projects are sorted into chapters based on content area, grade level, and intended outcome. In determining the chapters, we considered the emerging college- and career-readiness…

The catenary is usually introduced as the shape assumed by a hanging flexible cable. This is a "physical" description of a catenary. In this article we give a "geometrical" description of a catenary. Specifically we show that the catenary is the locus of the focus of a certain parabola as it rolls on the x-axis.

In this article we study a specific lattice classification of converse quadrilaterals, based on the relations between diagonals. This lattice contains 16 = 2[superscript 4] elements, which form a hypercube, and therefore it is a Boolean lattice. "Complementary" species of quadrilaterals thus appear and may be related in the lattice diagram. We…

Although ITSs are supposed to adapt to differences among learners, so far, little attention has been paid to how they might adapt to differences in how students learn from help. When students study with an Intelligent Tutoring System, they may receive multiple types of help, but may not comprehend and make use of this help in the same way. To…

This study examines the impact of successive versus non-successive scheduling of mathematics courses on the achievement of ninth-grade students in a suburban Oregon high school. The Oregon Assessment of Knowledge and Skills and student performance on the geometry course final exam were employed to compare the achievement of intact groups of…

What types of mathematical justifications do pre-service elementary teachers find convincing? To investigate this question, a task-based interview which was designed to elicit arguments of what students find convincing was administered to two female students who were enrolled in a geometry course at a large Midwestern university. These arguments…

Research on naive physics and naive optics have shown that people hold surprising beliefs about everyday phenomena that are in contrast with what they see. In this article, we investigated what adults expect to be the field of view of a mirror from various viewpoints. The studies presented here confirm that humans have difficulty dealing with the…

This article aims to present the changes in student selection and placement examinations in secondary education by focusing on the geometry content during the postreform period. The methodology, also used by Petway (2000), includes three steps toward the aim of examining the following: technical aspects, content coverage, and examination results.…

The article demonstrates that multiple solution tasks (MSTs) in the context of geometry can serve as a research instrument for evaluating geometry knowledge and creativity. Geometry knowledge is evaluated based on the correctness and connectedness of solutions, whereas creativity is evaluated based on a combination of fluency, flexibility, and…

Getting students to think about the relationships between area and perimeter beyond the formulas for these measurements is never easy. An interesting, nonroutine, and accessible problem that will stimulate such thoughts is the Lattice Octagon problem. A "lattice polygon" is a polygon whose vertices are points of a regularly spaced array.…

The process of developing definitions is underemphasized in most mathematics instruction. Investing time in constructing meaning is well worth the return in terms of the knowledge it imparts. In this article, the authors present a third approach to "defining," called "constructive." It involves modifying students' previous understanding of a term…

We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…