This article discusses two mechanisms through which understanding static mathematical concepts (basic and more advanced mathematical concepts) in terms of fictive motions or motion events enhance our understanding of these concepts. It is suggested that at least two mechanisms are involved in this enhancing process. The first mechanism enables us…

Reasoning is handled as a basic process skill in mathematics teaching. When the literature was examined, it was seen that many types of reasoning related to mathematics education were mentioned. In the present study, it was focused on visual reasoning, which is one of the types of reasoning and also used in different research areas. The purpose of…

Inclusion and differentiation--hallmarks of the current educational system--require a paradigm shift in the way that educators run their classrooms. This article enumerates the need for techno-kinesthetic, visually based activities and offers an example of a calculator-based programming activity that addresses that need. After discussing the use…

Data from a cough challenge study are displayed with dot charts to demonstrate the importance of graphs in understanding data, principles of graph construction and visual perception. The data are available for use in the classroom.

Art uses mathematics in many ways. The author's teaching and involvement with mathematics and art in the Bridges Conference connecting the two have convinced him more and more that concepts for understanding mathematics can be achieved by the use of art. The author states that one reason he believes in teaching mathematics through art is that it…

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.)

In the summer of 2009, a professional development partnership was established between the Peoria Public School District (PPSD), a local education agency (LEA), and Illinois State University (ISU) to improve geometric and trigonometric knowledge and skill for high school mathematics teachers as part of the Illinois Mathematics and Science…

This paper presents an assessment tool which can be used during the first weeks of calculus to measure students' visual thinking skills. We have developed and applied this instrument in classes for the last three years, tabulating results and interviewing students on a regular basis. We discuss our findings and provide hints to using the…

Shows that graphs can reveal much about feedback systems that formula conceal, especially as microcomputers can provide complex graphs presented as animations and allow students to interact easily with them. Describes feedback systems, evolution of the system, and phase diagram. (YP)