This article shows how concrete materials can be used in the context of partitions of integers to develop recursive definitions of concepts amenable to spreadsheet modeling. It demonstrates how numerical evidence made possible by the representational power of a spreadsheet when combined with other computational tools such as Maple allows for the conjecturing of rather sophisticated relationships among different types of integer partitions. A spreadsheet is then used to confirm these relations in special cases yet at a higher cognitive level than at the beginning of partitioning experiments. Finally, concrete materials are used again to demonstrate the correctness of computations. It is argued that whereas a spreadsheet is powerful enough to be used as a single computational tool in various mathematical contexts, its joint use with other tools, both digital and physical, is worth exploring in education.
Partitions of integers, Ferrers-Young diagrams, and representational efficacy of spreadsheet modeling,
Spreadsheets in Education (eJSiE):
2, Article 1.
Available at: http://epublications.bond.edu.au/ejsie/vol5/iss2/1