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.