Download PDF by Heinz Steinbring: The Construction of New Mathematical Knowledge in Classroom

By Heinz Steinbring

The development of latest Mathematical wisdom in school room Interaction bargains with the very particular features of mathematical conversation within the school room. the overall examine query of this publication is: How can daily arithmetic educating be defined, understood and built as a educating and studying surroundings during which the scholars achieve mathematical insights and extending mathematical competence via the teacher’s tasks, deals and demanding situations? How can the ‘quality’ of arithmetic educating be learned and safely defined? And the subsequent extra particular examine query is investigated: How is new mathematical wisdom interactively developed in a regular tutorial conversation between scholars including the trainer? that allows you to resolution this query, an test is made to go into as in-depth as attainable lower than the outside of the seen phenomena of the observable daily instructing occasions. which will achieve this, theoretical perspectives approximately mathematical wisdom and verbal exchange are elaborated.

The cautious qualitative analyses of a number of episodes of arithmetic educating in basic university is predicated on an epistemologically orientated analysis Steinbring has built over the past years and utilized to arithmetic educating of alternative grades. The ebook bargains a coherent presentation and a meticulous software of this primary study technique in arithmetic schooling that establishes a reciprocal courting among daily lecture room communication and epistemological conditions of mathematical wisdom developed in interaction.

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When performing a mathematical activity, the learners have to be aware of the epistemological particularity of the mathematical knowledge in their process of interpreting and understanding and, in this way, they themselves have to construct the new mathematical relations. A central criterion of theoretical mathematical knowledge - also observable in the course of its historical development - lies in the transition from pure object, or substance thinking, to relation or fUnction thinking. Every one knows that there are things, and relations between things.

Lakoff and R. Nuiiez develop a foundation of mathematics in which mathematical concepts and mathematical knowledge are traced back to human everyday experiences and actions, with the help of the so-called Mathematical Idea Analysis. We have found that mathematical ideas are grounded in bodily-based mechanisms and everyday experience. Many mathematical ideas are ways of mathematicizing ordinary ideas, as when the idea of subtraction mathematizes the ordinary idea of distance, or as when the idea of a derivative mathematicizes the ordinary idea of instantaneous change (Nuflez, 2000, p.

Thus, given the circumstances, neither reference contexts nor signs / symbols are external nor fixed, but are mental ideas which embody structures. Furthermore, it is important to be aware that the reference contexts (objects) do not simply precede the mathematical signs, neither temporally nor logically. On the contrary, the sign-systems can, by means of their internal structure in the (historical) development, increasingly gain independence and autonomy toward the reference contexts and thus act upon the reference contexts and project a structural interpretation, on them.

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