1.2. Effects on Mathematical Conceptualisation The educational context described above may cause undesirable effects on mathematical conceptualisation. As Goldenberg (1987) has already pointed out: “students often misinterpreted what they saw in graphic representations of functions. Left alone to experiment, they could induce rules that were wrong ... How do misconceptions distort the information that students glean from the graph?”. We will present examples of student behaviour when faced with screen representations provided by graphic calculators. These examples demonstrate the insight of Goldenbery’s comments. Figure 2. A representation of én x +10 sinx on a TI-82 screen. Figure 3. From an artifact to an instrument, the instrumental genesis. Figure 4. No recognition of the exact value of cos /16 by the TI-92 CAS. software). These constraints shape its potential in terms of types of actions and their management. They are specific to TI-92 but, with some modifications, they could be adapted to any calculator of the same type. Figure 5. A diagram showing the consequence of a discrete trace: an unusual period for the sine function. (2) the constraints linked to the discrete traces on a screen composed of a finite number of pixels. This discretization phenomenon (the same for graphic and symbolic calculators) may lead to inconsistent graphic representations depending on the chosen window. For instance, if the displayed function is periodic and if the distance between two calculated points on the x-axis is almost equal to the period (so that the calculated images are near), the graphic calculator joins the successive calculated points, and in this way masks the oscillations between them. Above (see Figure 5) is a diagram illustrating this process. It will be shown in Section A that, in spite of the presence of DERIVE, the misleading effects such images may encourage do not immediately disappear when the TI-92 takes the place of the graphic calculator. Figure 6. No recognition of the roots. Figure 7. The resolution of e* = x°? calculating mode. on several intervals, in exact, then in approximate Figure 8. Organisation of a lesson in a calculator environment. Figure 9. Practical sessions in a calculator environment. Figure 10. Calculation in a calculator environment. Figure 11. Typology of the different types of student behaviour.
