PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Multiplication by sunlight: How can a geometric definition be realized in a physical tool?
Page: 1193
McLoughlin and Droujkova (2013) developed a diagrammatic definition of multiplication that uses parallel lines to continuously scale the length of one segment by the length of a different segment. This contemporary treatment of the constructability of products (and quotients) is potentially significant for the undergraduate mathematical preparation of pre-service elementary teachers, who tend to conceptualize multiplication in terms of repeated addition. We take up here the design challenge of constructing a physical tool that models multiplication as a continuous scaling operation as opposed to a repeated grouping operation. We ask: How can the parallel shadows interpretation of real-number multiplication be used to design a physical tool?