Networking of Theories as a Research Practice in Mathematics Education by Angelika Bikner-Ahsbahs & Susanne Prediger

Author:Angelika Bikner-Ahsbahs & Susanne Prediger
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The teacher’s expectation of the use of semiotic games is directed towards a future opportunity for the students to better understand the formal view: When I tell about the formal aspects of the derivative I often make some reference to these experiences and activities. It seems to me that also a lot of students are able to make these connections to give meaning to formal aspects. (Answer to question 13, Sect. 2.​2.​2)

The previous local view observed in lines 287–289 (“the geometric representation of the derivative as a tangent”) corresponds to what the teacher calls LOCAL – a little segment that approximates the function locally.

Let us consider the GLOBAL view which is expressed in C* – a transition from a local view to a global view: the exponential function can be approximated by many small lines which have an increasing slope. This view as expressed in the RBC analysis is different from the teacher’s view. For AiC, GLOBAL was the global approach to the exponential function – the envelope – but for the teacher LOCAL–GLOBAL is the transition from the local to the global aspects of the derivative. More precisely, for the teacher, the global is the function derivative compared with the derivative at a point as a local approximation. The transition from the local to the global aspects of the derivative will be reached by recognizing the characteristics of the derivative function (itself an exponential). The teacher expressed his aim: …to pay attention to the slope of the little segments, because their slope gives information on the growth of the function. (Answer to question 5, Sect. 2.​2.​2)

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