This study investigated the effects of students' constructions of geometrical concepts related to the circle on their construction and validation of proofs. The participants were 110 high school students. A questionnaire was administered; both qualitative and quantitative methods were used to analyze the results. Afterwards, in-depth interviews…

This study presents a characterization of prospective early childhood teachers' (ECEPTs) and prospective elementary school mathematics teachers' (EMEPTs) concept images and concept definitions of triangles through a defining task and an example generation task. Data consisted of 62 EMEPTs' and 72 ECEPTs' written statements for the definition of a…

Developing design concepts is crucial in architectural engineering education, yet helping students to develop these concepts is a challenging task. Despite previous research exploring design concepts, statistical analysis is scarce to evaluate their effectiveness. This study used the body movement methods from existing literature, combined with…

This research describes technical drawing techniques applied in a project involving digitizing of existing hard copy subsurface mapping for the preparation of three dimensional graphic and mathematical models. The intent of this research was to identify work flows that would support the project, ensure the accuracy of the digital data obtained,…

The objective of this paper is to present applications of solid modeling aimed at modeling of complex geometries such as splines and blended surfaces in advanced CAD courses. These projects, in CAD-based Mechanical Engineering courses, are focused on the use of the CAD system to solve design problems for applications in machine design, namely the…

The paper presents a unique approach in associating perspective projection with the image beheld by the eye and demonstrates that all graphical and photographic perspective projections must contain distortion when compared to the image beheld by the eye. (Contains 8 figures.)

Geometric modeling provides graphic representations of real or abstract objects. Realistic representation requires three dimensional (3D) attributes since natural objects have three principal dimensions. CAD software gives the user the ability to construct realistic 3D models of objects, but often prints of these models must be generated on two…

A group of high school students created a drawing of a circle using a device called the Drawing Machine. To describe their experiences, we propose an alternative to the idea that to master a tool one must create a mental version of the tool. We suggest, instead, that as students change their relationships to a tool over time, their lived-in spaces…