Relationships with tools, the media and, the way we communicate and interact with the world, are changing at a pace that is almost unreachable. The same is happening with the plethora of “intellectual technologies”(Bell, 1974) available to create a variety of artefacts weather to learn, to teach or maybe just to express ourselves. According to Carr (2010) “it is our intellectual technologies that have the greatest and most lasting power over what and how we think. They are our most intimate tools, the ones we use for self-expression, for shaping personal and public identity, and for cultivating relations with others. (p.45)”
Although these technologies are part of young peoples’ daily lives it is not the case that they are an integral part of education (Peer 21). There are not embedded in the teachers’ daily strategies, as is the case of the blackboard or smart-boards, notebook, textbooks and lectures among others. There has always been an important gap between what the technological world has to offer in connections with new ways of processing information and transforming it in knowledge and what schools and teachers decide to use and integrate into their strategies. The affordances technological tools offer to education. Bureaucracy consumes much of their time!
It is indeed difficult to keep up with technology innovations and their affordances. Not only a new scale is introduced, as McLuhan said, but also a new approach to express us. Multimodality is a new construct introduced by Jewit (2008). It refers to communication using more than one mode (image, action, sound, writing, music and a bricolage  of all). Consequently, new forms to relate with knowledge come to the fore and with it, new forms of learning and teaching. Jewit (Op cit.) argues that the way knowledge is represented is a crucial aspect of knowledge construction, making the form of representation integral to meaning.
Adding to the latter, Carr (2010) made a noteworthy comment in his book: “At fist I’d figure that the problem was a symptom of middle-age mind rod. But my brain, I realized, wasn’t just drifting. It was hungry. It was demanding to be fed the way the Net fed it –and the more it was fed, the hungrier it became […] I wanted to be connected” (p.16)
[Here an interesting article related to this idea]This personal feeling expressed by the author is supported with empirical data from neuroscience throughout the book, making it clear, that indeed our way of thinking and feeding our mind has had change with the ubiquity of ICT –‘Intellectual tools’ in our lives. Much more is the case for the digital natives (Prensky, 2011) or also called millenials (Oblinger, 2003) that where born under this new way of perceiving the world.
How knowledge is understood, defined, conceived, produced and, shared has changed throughout time. Moreover, knowledge is shaped by the agents of its time; i.e. “The technology of the map advanced the evolution of abstract thinking throughout society. […] It gave to man a new and more comprehending mind, better able to understand the unseen forces that shape his surroundings and his existence” (Carr, 2010. p. 41).
The invention of writing is another example; it had important effects on mental processes, being Plato’s philosophically analytical thought a materialization of one of those new mental processes (Ong, cited by Carr, 2010).
Knowledge has and is always evolving. Understanding it in a particular realm of time is critical to align our spaces and structures with the nature of it. Space, in a broader sense, is a social production (Lefebvre, 1991). From natural spaces, considered as absolute to more complex spaces whose significance is socially produced. Lefebvre argues that the production of space throughout time is a three-part dialectic between everyday life and perception (and that is shaped by actual social values), the representation or theory of space, and the spatial imaginary of the time. Therefore I advocate for a creative imaginary that belongs to an open and networked society.
It is in this endeavour of creative imaginary and the search of new utopias for education where I want to explore and research. This idea of complex spaces socially produced, where teaching and learning can take place in an innovative way is fascinating. I see a powerful means for the teaching and learning in general and for the learning of mathematics in particular, for young generation of students that feel disengaged and disaffected with their education process.
There are several questions that I ask to myself: How to construct this space? Who will: the teacher, the students, or both? Is it open, free, interoperable? Will it need guidance and scaffolding, and if, who’s guidance? What would be the role of the student in the process of designing this learning space; designers of such a learning space? Will students guide the teacher in the process of building the space? Or maybe there can be pre-constructed scaffolding used by every one? How is teaching and learning taking place in such a space?
My particular vision of this space responds to the conception of education as complex phenomena; a complex system. Complex systems are based on nonlinear relationships and are self-organised. Where emergence and self organisation are fundamental properties to look at, how and what emerges from the space, how they can self-organise? It is a network where components are interconnected and it is in constant evolution.
French term meaning the construction or creation of a work from a diverse range of things that happen to be available, or a work created by such a process.