Phenomena that occur in microdroplets are described to the undergraduate chemistry community. Droplets having a diameter in the micrometer range can have unique and interesting properties, which arise because of their small size and, especially, their high surface area-to-volume ratio. Students are generally unfamiliar with the characteristics of…

We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given tau greater than 0, the free plate eigenvalues omega and eigenfunctions upsilon are determined by the equation Delta Delta upsilon - tau Delta upsilon = omega upsilon together with…

A shape grammar is a formalism that has been widely applied, in many different fields, to analyzing designs. Computer implementation of a shape grammar interpreter is vital to both research and application. However, implementing a shape grammar interpreter is hard, especially for parametric shapes defined by open terms. This dissertation…

Mass-volume relationships are a useful tool emphasized for problem solving in many geo-science and engineering applications. These relationships also have useful applications in soil science. Developing soils students' ability to utilize mass-volume relationships through schematic diagrams of soil phases (i.e., air, water, and solid) can help to…

It has been suggested that young children can only reorient, locating a target object, when the geometry of an enclosed space provides distinctive shape information [e.g., Hermer, L., & Spelke, E. (1994). A geometric process for spatial reorientation in young children. "Nature," 370, 57-59]. Recently, however, young children were shown to specify…

This study is a literature review to investigate the effects of implementing technology into a high school mathematics classroom. Mathematics has a hierarchical structure in learning and it is essential that students get a firm understanding of mathematics early in education. Some students that miss beginning concepts may continue to struggle with…

The study examined the effects of two modes of computer-assisted instructional package on solid geometry achievement amongst senior secondary school students in Minna, Niger State, Nigeria. Also, the influence of gender on the performance of students exposed to CAI(AT) and CAI(AN) packages were examined. This study adopted a pretest-posttest…

Diagram describing texts are integral part of science and engineering subjects including geometry, physics, engineering drawing, etc. In order to understand such text, one, at first, tries to draw or perceive the underlying diagram. For perception of the blind students such diagrams need to be drawn in some non-visual accessible form like tactile…

The purpose of this study was to determine how to integrate technology into mathematics classes using clickers in the high school setting. The ability to integrate technology into instruction is a current requirement for mathematics teachers in the United States; however, students have been traditionally taught to solve equations using pencils and…

In my personal interactions with elementary preservice teachers (EPSTs) at a large Midwestern university in United States, many EPSTs held negative beliefs and attitudes about geometry learning. Although finding ways to help EPSTs change their negative beliefs and attitudes is an important issue, it can be best addressed by first investigating how…

This study attempted to explore a possible relationship between diagrammatic reasoning and geometric knowledge of pre-service mathematics teachers. Diagrammatic reasoning skills, as a sequence of steps from visualization, to interpretation, to formalisms, are at the core of teachers' content knowledge for teaching. However, there is no course…

Considerable literature has documented both the pros and cons of students' use of empirical evidence during proving activities. This article presents an analysis of a classroom episode involving in-service middle school, high school, and college teachers that demonstrates that learners need not be steered away from empirical investigations during…

The integration of digital technology confronts teachers, educators and researchers with many questions. What is the potential of ICT for learning and teaching, and which factors are decisive in making it work in the mathematics classroom? To investigate these questions, six cases from leading studies in the field are described, and decisive…

This dissertation reports the results of a qualitative research project on area measurement. The study utilized structured, task-based interviews with students to (a) investigate the ways students enumerate and structure two-dimensional space with a variety of area units; (b) identify conceptual, procedural, and intuitive aspects of area…

Feedback is an important component of interactive learning software. A conclusion from cognitive learning theory is that good software must give the learner more information about what he did. Following the ideas of constructivist learning theory the user should be in control of both the time and the level of feedback he receives. At the same time…