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Pedagogical Possibilities for ICT

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Visual cognition and creative thinking

Visualization of inner mental imagery and the outer graphic presentation of reality in pictures, drawings, diagrams, lists, and charts is a fundamental part of creativity, discovery, invention, and problem solving. The vital importance of visualization is affirmed by the fact that a surprisingly large proportion of the human cortex is devoted to vision and visual analysis, and that the bandwidth of the visual channel is greater than that of any other sense. In many instances, the eye, and those parts of the brain that process visual information, lay the foundation for enhancing conscious thinking, which in turn, grows from our preconscious mental activity.

To take full advantage of the capabilities of the eye, the goal of visualization should be objectification. This means that a phenomenon, inherently visual or not, should be represented as having form, colour, texture, motion and other qualities of objects.

Inductive thinking relies to a great extent upon the human ability to visualize on this preconscious level. Major portions of the visual system including the retina, the structures ascending to the visual cortex, and parts of the visual cortex itself fall into the preconscious category. More powerful than a supercomputer, these functional entities relentlessly perform information-processing miracles, creating a three-dimensional, coloured visual environment that our conscious self exploits in a logical way to serve definite practical purposes. Our conceptual images are constantly being analyzed at a preconscious level, and produce useful data for establishing spatial relations, making conscious representations and building plans. In other words, the outcomes of these subliminal mental activities become the elements, tools, and procedures of rational thinking.

This is where computers make an enormous difference. When we visualize with the help of computers, video camcorders, and big-screen high-resolution projection, we restructure a problem situation so that more of it can be processed by the preconscious part of our brain – the visual system that is our silent partner. In this way, consciousness can be devoted to higher levels of critical analysis and synthesis. Especially interesting, are virtual worlds that model nothing but themselves, as do many games, chess among them. Nevertheless, by representing spatially the system of abstract relations between chessmen on a chessboard, a professional chess player can think in images. Similarly, it is also possible to visualize on a computer screen the spatial interrelations of elementary predicates and, consequently, to represent complex formulas of predicate logic (Bederson and Shneiderman 2003; Card, MacKinlay, and Shneiderman 1990; Friedhoff and Benzon 1989; Rieber 1995).

As a kind of modeling, visualization has many aspects. One is aestheticemotional. For example, nobody will deny that visualized mathematical objects and functions can be aesthetically beautiful. Fractal animated cartoons, captivatingly spectacular and shown on TV all over the world, have already inspired works of fine art (even if not eternal masterpieces). Beyond any doubt, it is precisely because of their aesthetic components that such themes as chaos, fractals, and the like, have become so popular in academic mathematical courses.

Another aspect of 'visualization as modeling' is, as in the classical art of painting, selecting and making visible essential traits of the object or phenomenon depicted. By forcing us to pay attention only to what can be seen and perceived by the eye, visualizing helps to impart a meaning to a problem and makes it easier to find its solution. In the simplest case of a virtual constructor used to build interactive models of physical phenomena, we may get a picture of an ideal experiment, which is mathematically correct within a set degree of accuracy.

Using a similar learning environment under a teacher’s guidance, the student can trace all levels of abstractions in modeling. For instance, there could be genuine physical objects and processes (say, a carousel on which children have a ride), material (LEGO-like) models, videotapes, computer simulations (virtual realities), graphical representations of processes’ characteristics by co-ordinates and velocities within a set referential system, and symbolic modeling by algebraic and differential equations.

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