In my last RYSK post, I joined some other math teachers in discussing Richard Skemp's Relational Understanding and Instrumental Understanding (1976). Skemp's is a classic article that wrestles with a duality; in Skemp's case, the distinction between math for procedural skill versus a deeper mathematical understanding. For this meeting we turned the clock back further to Dewey's The Child and the Curriculum (1902), another classic article struggling with a duality in learning.
As D. C. Phillips (1998) noted in his review of The Child and the Curriculum, Dewey had a particular passion for dualisms, addressing more than three dozen of them in Democracy and Education (1916) alone. As Skemp and many others have shown, dualisms can be a starting point towards building a more nuanced understanding, as "neither is the world divided into a series of polar opposites, nor is it one" (Phillips, 1998, p. 404). Somewhere in between the opposites and the same lies the understanding many of us seek.
The Child and the Curriculum presents a particular dualism that very much persists to this day: should education be rooted in content, or in the needs and wants of the child? In Dewey's time, the push for a content focus was seen in the report by The Committee of Ten, not totally unlike how we currently push for content with documents like the Common Core State Standards. Dewey, like Skemp, also uses the metaphor of the map, using it to describe the logical versus psychological ordering of subject matter. Again, we still struggle with this duality today; last November Jere Confrey remarked at a conference, "There are some parts of the common core standards that I would express as mathematicians’ thought experiments," meaning we often guess how mathematical understanding is developed based on the structure of the mathematics instead of research on how children actually learn. These, of course, are not opposites, but they aren't the same, either.
Most of our discussion used Dewey as a prompt for thinking how Dewey's words more than a century ago frame modern challenges in education. (Reading Dewey seems particularly good for this kind of activity.) I was joined by +Nik Doran, +Bryan Meyer, +Nat Banting, and +Chris Robinson was feeding us ideas in the chat as we went along.
I plan to have more of these discussions, and hope we can get into some literature that really addresses research in math education versus some of these more theoretical or philosophical pieces. If you have suggestions for articles to read, please add them and vote them up or down in Google Moderator!
References
Phillips, D. C. (1998). John Dewey’s The Child and the Curriculum: A century later. The Elementary School Journal, 98(5), 403–414.