Improving student knowledge about fraction magnitude: an initial study with students in Early Elementary Education
Keywords:
Early Elementary Education, Non-Symbolic and Symbolic Fractions, Measurement, 4A- Instructional ModelAbstract
The idea of magnitude is central to understanding fractional numbers. To investigate this relationship, we implemented a design research project in a school in the USA, to examine the potential of a measuring perspective and the mathematical notion of fraction-of-quantity to enhance second-grade students’ conceptual understanding of fraction magnitude. We used ideas from the history of mathematics and mathematics education within a cultural-historical framework to define what fractions are and to construct tasks. The research team consisted of a university professor, two doctoral students, one of whom was an administrator of the municipal board of education, eight elementary school teachers, and a mother. The research sessions involved 35 students, divided into two classes, meeting one hour per session, twice a week, for a total of 12 weeks. The students used Cuisenaire rods to develop the idea that a fraction is a multiplicative comparison between two measurable quantities. The results that we present indicate that the students appropriated the idea of the magnitude of fractions-of-quantity and that, based on mentally evoked images of the rods, were able to construct expressions involving fractional comparisons.
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