Thinking As Communicating Book Review

“Thinking as Communicating” is an outline of the commognitive perspective of research in mathematics. Sfard separates the book into two sections, the first is an analysis of the theoretical significance behind the thesis while the second part, which focuses specifically on mathematics as a discourse, details how the commognitive paradigm explains mathematical activity, thinking and learning. Sfard discusses her thesis that mathematics is a form of communication and presents numerous examples from the historical development of mathematical objects to authenticate the argument that discursive objects are a expected outcome of mathematical communication. Sfard begins the book with the introduction of five persisting and vexing quandaries to

By realising that research is a form of communication, Sfard (2008, 35) describes research as a “particular, well-defined kind of discourse producing cogent narratives with which other human practices can be mediated, modified, and gradually improved in their effectiveness and productivity”. Objectification is introduced when speculating on how to find answers to the quandaries as well as to answer many questions about thinking that have remained unanswered. Sfard (2008, 52) finds that there are two types of communicational gains produced by objectification which increase the effectiveness of communication and often establishes the resulting discourse as a much more helpful tool in understanding our experience and organising the consequential practical actions. The two claims Sfard (2008, 52) makes are that reification increases the communicative effectiveness of discourse and objectification increases the practical effectiveness of

Mathematics, as discussed by Sfard (2008, 129), begins where the tangible, real-life objects end and where reflection on discourse about these objects begins and Sfard (2008, 161) describes mathematics as a multi-layered, recursive structure of discourse about discourse and therefore its objects are discursive constructs. According to Sfard (2008, 161) the autopoietic feature is a challenge to both mathematists (Sfard’s description of participants in mathematical discourse) and outside observers of mathematical discourse as there seems to be a precondition for participation with the familiarity with the objects of the discourse while participation in the discourse is a precondition for gaining this familiarity. Sfard is very clear the mathematics is a discourse and this is very different from mathematics is a language. Sfard (2008, xviii) utilises the notion that mathematics is an autopoietic system by identifying mechanisms that underlie the historical development of mathematics research and show how commognition becomes central to how thinking and learning progress within communities of