Download Networking of Theories as a Research Practice in Mathematics by Angelika Bikner-Ahsbahs, Susanne Prediger PDF

By Angelika Bikner-Ahsbahs, Susanne Prediger

How do we care for the variety of theories in arithmetic schooling? This was once the most query that led the authors of this ebook to discovered the Networking Theories team. ranging from the shared assumption that the lifestyles of alternative theories is a source for arithmetic schooling learn, the authors have explored the probabilities of interactions among theories, similar to contrasting, coordinating, and in the neighborhood integrating them.

The ebook explains and illustrates what it capacity to community theories; it provides networking as a difficult yet fruitful examine perform and exhibits how the crowd handled this problem contemplating 5 theoretical techniques, specifically the technique of motion, creation, and communique (APC), the speculation of Didactical events (TDS), the Anthropological conception of the Didactic (ATD), the strategy of Abstraction in Context (AiC), and the speculation of Interest-Dense events (IDS).

A man made presentation of every concept and their connections exhibits how the job of networking generates questions on the theoretical, methodological and functional degrees and the way the paintings on those questions results in either theoretical and functional development. The middle of the e-book contains 4 new networking case stories which illustrate what precisely may be received by way of this procedure and what sort of problems may perhaps arise.

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In fact our model aims at better giving account of learning processes as dynamic phenomena, so overcoming the limits pointed out by Freudenthal, when he wrote: Indeed, didactics itself is concerned with processes. Most educational research, however, and almost all of it that is based on or related to empirical evidence, focuses on states (or time sequences of states when education is to be viewed as development). States are products of previous processes. As a matter of fact, products of learning are more easily accessible to observation and analysis than are learning processes which, on the one hand, explains why researchers prefer to deal with states (or sequences of states), and on the other hand why much of this educational research is didactically pointless.

2 and in particular in the teacher’s answers to question 17, about 1 month previously the students had been introduced to continuous linear model and linear discrete dynamic systems, and to discrete exponential models. Carlo investigates the case with base 1, that is, y = 1x, to check whether the function becomes a line. Then they explore the function for negative abscissas, saying that it goes towards 0, and check the value for 0 (that is, y0 = 1) (lines 19–56). 20 C. Sabena While activating the Trace function in the DGS, they observe what happens on the screen.

With respect to mathematical competences, I hope that students read the text of the posed problems very carefully and that they begin to do some explorations, either mental explorations or with the help of technological tools. These explorations have the aim to create context, to create meaning, to provide experience of problem situations; they encourage the production of conjectures and should motivate students to validate their produced conjectures. I hope that students often ask themselves why they observed some patterns, some regularities.

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