Collaborative mathematics learning in online environments. (English)

Martinovic, Dragana (ed.) et al., Visual mathematics and cyberlearning. Dordrecht: Springer (ISBN 978-94-007-2320-7/hbk; 978-94-007-2321-4/ebook). Mathematics Education in the Digital Era 1, 23-48 (2013).

Summary: In formal education, learning mathematics is typically done by receiving direct instruction within the confines of a classroom. From first grade through graduate school, students are expected to learn mathematics primarily by being taught by instructors with previous knowledge of the subject. Research mathematicians, on the other hand, must rely on other methods; the mathematics they are trying to understand may not, as yet, be known to anyone else. Hence, they learn primarily through experimentation, self-directed study, and collaboration with peers. In recent years, these methods have been expanded to use modern tools and ideas. Research mathematicians initiated several successful large-scale online collaboration projects, such as the Polymath project and the MathOverflow website. In this chapter, we discuss these two projects, along with various other examples of online collaborative learning of mathematics. Our primary motivation is captured in the following question: why aren’t we all learning math this way? While a complete answer is beyond the scope of this work, we hope to at least stimulate a debate among a wide audience. The major part of our discussion is thus informal; we defer the contextualization of these examples within modern education research until the end of the chapter.