Social constructivism is having a powerful effect on the "aims, content, teaching approaches, implicit values, and assessment of the mathematics curriculum, and above all else, the beliefs and practices of the mathematics teacher" (Ernest, 1992). It also facilitates the sharing of ideas among students as they work in collaboration. This aspect is discussed in detail in the ‘ Mathematics Matters’ report published by the National Centre for Excellence in the Teaching of Mathematics after consulting over 150 Maths teachers from all over the UK (NCETM, 2008). For real learning to take place, ultimately it is essential that the student constructs his or her own framework for understanding and applying Mathematics.
Nothing is more pleasurable for a teacher of Mathematics than when seeing their students truly fascinated by the subject; when they grasp concepts and solve problems for the first time when they discover more elegant solutions by themselves, notice underlying connections and relationships, and so on. Some of these points are also mentioned under the ‘ Importance of Mathematics at key stage 4’ (QCDA, 2010b). Considering the scope for using ICT in the teaching of Mathematics, we shall focus exclusively on computers.
These are especially useful in two areas: (1) in performing tedious and complex calculations, and (2) in generating and visualizing complex models. They are also useful as tools for teaching Mathematics in interactive and stimulating ways. When computers are heavily involved in the instruction process, it is known as Computer Assisted Instruction (CAI) or Computer Assisted Learning (CAL). From the social constructivist perspective, computers alter the way we do mathematics (Smith, 1998). As regards generating graphics and models, computers have been used as an aid to teaching Mathematics since the beginning when computer technology had graphical capabilities.
However, their use has increased as the technology has improved over time with respect to speed and graphical processing power. Computers have a distinct advantage in this case over manual drawings (as long as they are used appropriately). For example, ICT tools can generate graphics and graphical models much more quickly and accurately. They can also be manipulated in ways that are not easy to do by hand without redrawing. This is useful, for example in seeing the effects of changing some parameter values on a graph.
The time savings can also allow teachers to concentrate on other aspects of the Mathematics curriculum.
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