Inquiring and learning with DGS Cui-Rods: a proposal for managing the complexity of how primary-school pupils’ mathematically structure odd even numbers

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Inquiry approaches using coloured manipulatives are a fruitful field for the investigation of mathematical concepts, embedded in a re-conceptualized, research-based curriculum. Manipulatives are designed to mediate between a particular mathematical concept and the way pupils learn that concept. Many researchers highlight the advantages of computer manipulatives including DGS manipulatives for teaching and learning. Moreover, the effectiveness of the Cuisenaire–Gattegno approach in the teaching and learning of mathematics in primary schools has been the subject of many math-investigations, supporting positive outcomes. In terms of the present study, it is interesting to mention the introduction of DGS Cui-Rods that I created in the Geometer’s Sketchpad dynamic geometry environment. The main focus of the current study is a fundamental pattern structure of our number system: odd and even numbers. The study will propose a multiple representation approach to aid pupils understanding odd and even numbers. The proposed DGS material can be displayed, inquired and managed through properly set-up tasks, using linking representations. Finally, it is important to continue teaching concepts through activities, tasks and problems that involve children in the inquiring and learning process; it is the best route for them to how to develop, interpret, and make sense of mathematical concepts.