Geometry and Topology Commons^™

Mathematical Knowledge For Teaching And Visualizing Differential Geometry, Nathan Pinsky

HMC Senior Theses

In recent decades, education researchers have recognized the need for teachers to have a nuanced content knowledge in addition to pedagogical knowledge, but very little research was conducted into what this knowledge would entail. Beginning in 2008, math education researchers began to develop a theoretical framework for the mathematical knowledge needed for teaching, but their work focused primarily on elementary schools. I will present an analysis of the mathematical knowledge needed for teaching about the regular curves and surfaces, two important concepts in differential geometry which generalize to the advanced notion of a manifold, both in a college classroom and …

Measuring A Circle: A Math Lesson For Grades 5-10, Robert C. Moore

Faculty Publications

This article is designed to promote teaching methods that engage students in active learning and result in deep conceptual understanding by offering a sample lesson to help students (grades 5-10, ages 10-15) answer questions about and gain a deeper understanding of how to measure the circumference and area of a circle.

Session D-3: Discrete Mathematics: A Great Curriculum Connector, Donald Porzio

Professional Learning Day

Many topics that fall under the umbrella of Discrete Mathematics cut across the traditional high school curriculum areas of algebra, geometry, and pre-calculus. Come try some classroom-ready hands-on Discrete Mathematics activities that illustrate the true interconnectedness of mathematics.

Symmetry From Nature To The Classroom, Rochelle Lueders

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Fan Cohomology And Its Application To Equivariant K-Theory Of Toric Varieties, Suanne Au

Department of Mathematics: Dissertations, Theses, and Student Research

Mu-Wan Huang, Mark Walker and I established an explicit formula for the equivariant K-groups of affine toric varieties. We also recovered a result due to Vezzosi and Vistoli, which expresses the equivariant K-groups of a smooth toric variety in terms of the K-groups of its maximal open affine toric subvarieties. This dissertation investigates the situation when the toric variety X is neither affine nor smooth. In many cases, we compute the Čech cohomology groups of the presheaf K_q^T on X endowed with a topology. Using these calculations and Walker's Localization Theorem for equivariant K-theory, we give explicit formulas …

Empirical Development Of An Instructional Product And Its Impact On Mastery Of Geometry Concepts, Donaldson Williams

Dissertations

Problem

Relatively poor levels of mathematical thinking among American school children have been identified as a major issue over the past half century. Many efforts have been made to increase the mathematics performance of children in schools. Additionally, out-of-school-time programs have attempted to address this issue as well. Holistic development is one of the distinguishing features of Seventh-day Adventist instructional programs. Yet, as of 2007, the Pathfinder program, an informal educational program operated by the world-wide Seventh-day Adventist church, had no instructional product designed to foster participants’ cognitive development in mathematics. This study focused on the empirical development of an …

Wallpaper Groups, Cassondra Fett

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

The Effects Of The Use Of Dynamic Geometry Software On Student Achievement And Interest, Heidi B. Hansen

Mathematics Graduate Theses

This study examines the current research that exists on the effects that the use of dynamic geometry software has on student achievement and interest level in mathematics. Additional questions examined are whether using dynamic geometry software has a greater impact on high or low achievers, and what current methods of implementation are suggested by the research. A review of the relevant literature indicates that the use of dynamic geometry software does have a positive effect on student achievement, particularly achievement in areas of high-level thinking. Insufficient research has been done on the effect that the use of dynamic geometry software …

The Use Of Realistic Imagery To Represent The Relationships In A Four-Dimensional Coordinate System, Randal J. Bishop

Humanistic Mathematics Network Journal

No abstract provided.

Transformational Geometry Unit, Elizabeth Ann O'Neill

All Graduate Projects

The study included the development and writing of a unit on transformational geometry which involved a holistic approach including the cognitive, psychomotor, and affective domains. This unit was taught to the eighth grade class in the Oakville School District in Oakville, Washington. The results showed support that the teaching of this unit was effective.

The Spieker Circle And Certain Related Configurations, Berthola Elmo Lumzy

Electronic Theses and Dissertations

This thesis, presented to the Department of Mathematics at Xavier University in partial fulfillment of requirements for the degree of Master of Arts in 1952, examines the Spieker circle, a circle inscribed in the median triangle of a given triangle, and extends its defining properties to related geometric configurations. Lumzy first establishes a series of analogies between the Spieker circle and the nine-point circle, demonstrating parallel relationships involving radius, center, harmonic conjugates, and homothetic centers relative to the incenter, median point, and Nagel point of a triangle.

The thesis then proves that the Spieker circle is inscribed in two congruent …

Experimental And Observational Geometry, Albert D. Field

University of the Pacific Theses and Dissertations

Geometry has the distinction of being one of the oldest subjects given in the high-school.

Its subject-matter was formulated and organized by the Greeks into a fine system of thought before the time of Christ. Since leaving the hands of the Greeks, geometry has received only a few minor changes, and these largely in recent years.

Heretofore, the study of geometry has been made almost entirely dependent upon memory and reasoning. Geometricians have been slow in adopting the laboratory and observational methods.

This thesis has been written to encourage the student in his work of observing geometrical forms, and in …