The Construction of New Mathematical Knowledge in Classroom Interaction

Mathematics is generally considered as the only science where knowledge is uni­ form, universal, and free from contradictions. „Mathematics is a social product - a 'net of norms', as Wittgenstein writes. In contrast to other institutions - traffic rules, legal systems or table manners -, which are often internally contradictory and are hardly ever unrestrictedly accepted, mathematics is distinguished by coherence and consensus. Although mathematics is presumably the discipline, which is the most differentiated internally, the corpus of mathematical knowledge constitutes a coher­ ent whole. The consistency of mathematics cannot be proved, yet, so far, no contra­ dictions were found that would question the uniformity of mathematics" (Heintz, 2000, p. 11). The coherence of mathematical knowledge is closely related to the kind of pro­ fessional communication that research mathematicians hold about mathematical knowledge. In an extensive study, Bettina Heintz (Heintz 2000) proposed that the historical development of formal mathematical proof was, in fact, a means of estab­ lishing a communicable „code of conduct" which helped mathematicians make themselves understood in relation to the truth of mathematical statements in a co­ ordinated and unequivocal way.

The Construction of New Mathematical Knowledge in Classroom Interaction deals with the very specific characteristics of mathematical communication in the classroom. The general research question of this book is: How can everyday mathematics teaching be described, understood and developed as a teaching and learning environment in which the students gain mathematical insights and increasing mathematical competence by means of the teacher’s initiatives, offers and challenges? How can the ‘quality’ of mathematics teaching be realized and appropriately described? And the following more specific research question is investigated: How is new mathematical knowledge interactively constructed in a typical instructional communication among students together with the teacher? In order to answer this question, an attempt is made to enter as in-depth as possible under the surface of the visible phenomena of the observable everyday teaching events. In order to do so, theoretical views about mathematical knowledge and communication are elaborated.

The careful qualitative analyses of several episodes of mathematics teaching in primary school is based on an epistemologically oriented analysis Steinbring has developed over the last years and applied to mathematics teaching of different grades. The book offers a coherent presentation and a meticulous application of this fundamental research method in mathematics education that establishes a reciprocal relationship between everyday classroom communication and epistemological conditions of mathematical knowledge constructed in interaction.