Developing and Managing Knowledge through the Eyes of the Young Learner: ‘Alive’ Manipulatives before Abstract Notions

The current study has been influenced by that aspect of the philosophy of Realistic Mathematics Education which holds that mathematics should be learned as an activity of progressive mathematization. In this study I have used the Geometer’s Sketchpad to design tasks for young learners, anticipating their reactions. My aim is to propose and introduce types of tasks /problems designed for primary-level learners, concentrating on two aspects: (a) using play-based “alive” tasks to demonstrate mathematical concepts (b) linking the sequential visual representations with instrumentally decoded math notions, thus making the whole figural diagram “alive”, while giving the students the potential to focus their attention on simultaneous modifications (and transformations) of objects on the screen. In the current study, I paraphrase Pestalozzi’s words "things before words, concrete before abstract” as “active or alive manipulatives before words, ‘dynamic’ concrete before abstract".