Appelbaum, Peter. (2008). Children’s Books for Grown-Up Teachers: Reading and Writing Curriculum Theory. New York, NY: Routledge.
8. Dark Matter and All that Jazz (part 1)
Dark matter as a metaphor offers an interesting way to examine the educational experiences of disenfranchised groups within society, both in terms of the role in educational policy of researchers who may identify as members of a disempowered social group, and in terms of the secret treasure that is promised by the invisibility of disenfranchised experiences of schooling in mainstream curriculum studies. (p. 143)
Using Chris Raschka’s Charlie Parker Played Be-Bop (1992) and Mysterious Thelonius (1997) as foundations for the discussion of finding the hidden light in the dark matter of children’s books about jazz musicians, Appelbaum questions the presumed authority of the classroom teacher. In deciding whether Raschka “got it right” in one or both of these books, a classroom teacher in the Platonic tradition of being the knower and presenting knowledge for children to accept without question, Appelbaum suggests that the elements of surprise and humor are missing. If we (teachers) are reading children’s literature in order to more clearly understand our role as curriculum theorizers, then we need to approach our work as if we are learning alongside our students. The process of learning alongside and with our students brings a spark to the classroom, a light that may be missing if we operate as the sage on the stage.
Applying rhythm, surprise and humor to mathematics education, Appelbaum describes a basic rhythm of mathematics originated by Georg Polya.
First, one works to understand the problem; second, one devises a plan for working on the problem; third, one carries out the plan; finally, one looks back over what has happened in order to identify a new problem and start the process all over again. (p. 149)
As the student utilizes Polya’s rhythm, patterns begin to emerge from the phases of mathematical work, “melodic and harmonic progressions of Polya’s questions” (p. 149). New questions arise.
Does my answer make sense? What is the meaning of my answer? Now that I am at this point in my work, can I see another way of working that may have been simpler, more interesting, or otherwise better in some sense? And then, What new questions do I have at this point, prompted by my work? (p. 149)
There are other rhythms of working in mathematics that complement Polya’s phases. John Mason et al. (1982) developed a system of looking at special cases depending upon the problem presented. From the results of trying special cases within a specific mathematical question, then generalizing for categories or patterns, leads to the goal of inferring or deducing a general statement (p. 151). As anyone who has ever searched for a mathematical pattern knows, once one solution is found, many more problems or mysteries present themselves.
Authority and knowledge
Using Polya and Mason et al. as models is attractive from a Deweyan point of view. However, “this is a radical notion of education since it undermines a Platonic sense of knowledge as truth, and apparently shifts authority from the teacher who knows this truth to the student who composes her own version of truths” (p. 151). However, Appelbaum reinforces that teachers cannot start with the assumption that students can direct their own learning. Another critical question arises.
What, then, is the relationship between the institutional authority of the teacher and the emergent authenticity of the student?
There is an improvisational process to utilizing the authority of teacher to empower students. It is a process fraught with starts and stops; attempts to regain control; moments when students shine strongly; and moments when the teacher must step into the middle and meddle.
All a teacher can do is make informed conjectures, only to be surprised by the incompatibility of these conjectures with the latter, jointly constructed meaning. This, to me, is the parallel jazz of curriculum that accompanies the jazz of learning. (p. 153)
Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. New York: Addison-Wesley.
Polya, G. (2004). How to solve it. Princeton, NJ: Princeton University Press.
Raschka, C. (1992). Charlie Parker played Be-Bop. New York: Scholastic Books.
Raschka, C. (1997). Mysterious Thelonius. New York: Scholastic Books.