Abstract
The concept of equivalence class plays a significant role in the structure of Rational Numbers. Piaget taught that in order to help elementary school children develop mathematical concepts, concrete objects and concrete reflection-enhancing-activities are needed. The “Shemesh” software was specially designed for learning equivalence-classes of fractions. The software offers concrete representations of such classes, as well as activities which cannot be constructed without a computer. In a discrete Cartesian system students construct points on the grid and learn to identify each such point as a fraction-numeral (a denominator-numerator pair). The children then learn to construct sets of such points, all of which are located on a line through the origin point. They learn to identify the line with the set of its constituent equivalent fractions. Subsequently, they investigate other phenomena and constructions in such systems, developing these constructions into additional fraction concepts. These concrete constructions can be used in solving traditional fraction problems as well as in broadening the scope of fraction meaning. Fifth-graders who used “Shemesh” in their learning activities were clinically interviewed several months after the learning sessions ended. These interviews revealed evidence indicating initial actual development of the desired mathematical concepts.
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Arnon, I., Nesher, P. & Nirenburg, R. Where do Fractions Encounter their Equivalents? – Can this Encounter Take Place in Elementary-School?. International Journal of Computers for Mathematical Learning 6, 167–214 (2001). https://doi.org/10.1023/A:1017998922475
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DOI: https://doi.org/10.1023/A:1017998922475