Shape Transforms through Dissection-Motion-Operations (DMO) in 2D & 3D Euclidean Spaces: Hands-on Activities & Computer Animation
Dr Medhat Rahim, Dave Cristopher Bopp, Jennifer Anne Bopp.
A sequence of hands-on activities will be presented through shape-dissection and shape-composing operations. The audience will be operatively participants rather than merely listeners.
The shape-dissection operation is based on the Theory of Dissection described in Eves’ text: A Survey of Geometry (1972). The shape-composition is based on the basic transformations (motions): translation or slide, rotation or turn, reflection or flip, or any combination of them. These motions are described in many recent texts such as Knill et al. text: Mathpower 9 (1994, pp. 533-563).
The purpose of these hands-on activities is to implement the National Council of Teachers of Mathematics Standards (NCTM, 1989 & 2000) position focusing on the spatial sense and the formation of mathematical conjectures about geometric relationships. The Standards (1989) state that when children investigate the result of combining two shapes to form a new one, draw a shape after it has been rotated a half turn, or explore what happens when the dimensions of a shape are changed, they acquire deeper understanding of shapes and their properties (NCTM, 1989, p. 49). The Standards (2000) further indicate that whenever possible, students should develop formulas and procedures meaningfully through exploration and investigation mathematical models rather than memorization (NCTM, 2000, p. 244).
Some particularly accessible and rich tasks for such investigation are the areas of a right, acute, or obtuse triangle and the possible resulting simple shapes after dissecting the triangle into two or three pieces and moving the pieces (Rahim, 1986, 1999, 2003).
Dr Medhat Rahim (Canada)
Professor of Mathematics
Faculty of Education
I am a full professor of mathematics & mathematics education. Earned a B. Sc. Mathematics & M. Phil in pure mathematics (probability measure), and a Ph. D. in Mathematics Education. Published and presented more than one hundred (100) refereed articles. My main interest id in modelling mathematical concepts, concrete manipulative, and computer animation/simulation.
Dave Cristopher Bopp (Canada)
Korah Collegiate & Vocational School
Jennifer Anne Bopp (Canada)
Algoma District School Board
(60 min. Workshop, English)