This paper presents a theoretical model we draw on when designing and developing ICT-based systems for mathematics teaching and learning which falls within the cultural-historical framework inspired by the work of Vygotsky. The main objective of this work is to demonstrate that technological tools can assume a crucial role in supporting teaching and learning processes if they allow teachers to reconfigure mathematical objects with the aim to create activity settings where students can interact with mathematical knowledge integrating a perceptive-motor approach to mathematical knowledge with a symbolic-reconstructive one. Re-configuring a mathematical object, which is abstract and formal, means transforming it in order to make it more concrete with the aim of using it in the student's Zone of Proximal Development, where learning can occur and teaching can be defined. In the paper two examples of application of the model will be furnished, making reference to the work of design and implementation we are developing within a European project called aITALES.
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