Mathematics Education

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Materials authored by Dr. Eva Knoll pertaining to Mathematics Education.

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Polyhedra, Learning by Building: Design and Use of a Math-Ed. Tool.
(Bridges: Mathematical Connections in Art, Music, and Science, 2000) Knoll, Eva
This is a preliminary report on design features of large, light-weight, modular equilateral triangles and classroom activities developed for using them. They facilitate the fast teaching of three dimensional geometry together with basic math skills, and create a lasting motivational impact on low achievers and their subsequent performance in math and science. In directed discovery activities, lasting from 20 to 90 minutes, large models of basic polyhedra are made, enabling their properties to be explored. Faces, edges and vertices can all be counted and tabulated, providing opportunities to see number patterns and inter-relationships, to plot graphs, to extract algebraic relationships and to look for proofs of those relationships. These building activities can be kept central, under the teacher’s control for large classes with limited time, or building can be split out into groups of children where co-operative problem solving skills are also developed. In interviews, children have stressed the effectiveness of learning by building the shapes themselves. In classroom activities, it is clear to see that these triangles make children excited. Learning by building gives a concrete, active, authentic and personal experience of mathematics to children and teachers enabling them to feel the full excitement of the subject.