Davis and Simmt discuss in their article,”Understanding Learning Systems: Mathematics Education and Complexity Science”, the learning process and how individuals and groups learn as a complex system which is adaptive and self-organizing (137-138). Complexity science, the authors state, includes both the “co-implicated processes of individual sense-making” and “collective knowledge-generation” (142). Cultural influence as well as social learning are key aspects to the latter (143). Creating social and collective learning can “increase the likelihood of complex transcendent possibilities” (145), and Brent and Davis demonstrate this through a case study of a Mathematics classroom (145-147). They expand on the idea of internal diversity and the importance of diversity within a group of learners, yet there is also importance in redundancy or similarities between individuals because compensation for each others’ failings is also important (148-150). Decentralized control also results in successful learning environments, but this is not to be interpreted as ‘who is in charge’ but rather who is the focus; “the locus of learning is the individual” (152). The authors continue their discussion by focusing in on “organized randomness” (154-155), “neighbor interactions” (156-157) and how these relate to how a teacher should organize an actual mathematics classroom (157-163). Most importantly, the main point is to view the classroom as a complex and systematic community which is adaptive and self-organizing (164).
My first reaction to this article relates to the idea of regarding one thing as complex and something else as not as complex, or as “complicated.” I feel as though there are complexities in everything and that it is somewhat ignorant to rank these complexities just because the human mind understands what it deems a satisfactory amount of knowledge about a certain thing. If you think something is not complex, you are not looking deeply enough for the complexities, in my opinion. But perhaps this is too philosophical.
So that moves me to my second point: The article discusses the benefits behind incorporating community and communication into the Mathematics classroom. I feel as though it is very significant that the authors focus in on Mathematics here. In an humanities or social science class, this sort of collaborative learning discourse and community naturally occurs, generally speaking. Mathematics is traditionally a more individual subject, but I wonder, what is the problem with that? When I was a kid in Math classes, I enjoyed the time to myself and to think through problems on my own and work at my own pace. It was a sort of meditative thing for me. I consider myself a very social individual though, so I’m quite sure these awesome feelings of approaching Math “alone” were even stronger in some of my peers.
All kids learn differently, and I think that for those students who do not care to work in groups or to chat about their thought processes, Math is a sort of release. This doesn’t mean that this place to be alone cannot be switched to another subject at times, and Math can be a social place at times as well, but the key is balance, in my opinion. But I think when kids say that they “like Math” they mean that they like solving problems and thinking through things, alone. It would be difficult to change this societal relationship with Math, and I don’t really know why there is such a strong desire to. I think balance is the key in any subject, actually, and for the sake of the shy, quiet, or perhaps ESL student, individual-based assignments need to maintain their position in the classroom.
So how do we accommodate the shy, quiet, or perhaps ESL student in the classroom, if the main goal is to create social and constructive learning environments?