M. Jayne Fleener and Stacy Reeder
What should we teach? This question permeates all of education. We will address it by pursuing Ludwig Wittgenstein’s advice that teaching should be guided by “teaching etcetera” (Genova, 1995), by teaching “that which ‘points beyond’” (Wittgenstein, 1953, p. 208). Implicated by and inherent in Alfred North Whitehead’s process philosophy (1929b) and rhythms of education (1929a), John Dewey’s logic as inquiry (1938) and philosophy of experience (1925), and Wittgenstein’s philosophy of meaning (1953) and culture (1980), this paper will explore a way of envisioning teaching and experiencing learning from the perspective of “teaching etcetera.”
We who have survived the education system have experienced teaching etcetera in one form or another. When we go beyond that which is “given” in class, using ideas, techniques, or knowledge outside of school or in different contexts, we have experienced teaching etcetera. For many of us who teach mathematics, we know the experience. We feel the joy of a new problem challenging us to rethink our mathematics, apply our techniques, and invent new approaches from those we have practiced in mathematics classes. We also know the frustration with students who have not gone beyond the specific exercises assigned as homework, who cannot apply their knowledge to different contexts, or who do not experience the joy of problem-solving challenges as we have experienced them. How do we provide classroom experiences that encourage students to “go beyond,” to experience mathematics as a way of meaningfully approaching their world and not as the drudgery of homework problems hastily done to avoid a zero on their grade?
To offer a context for an emergent curriculum that follows the ebbs and flows of classroom discourse, providing opportunities for the teacher and the students to experience mathematics as a way of life and a system of meaning, we will explore how one middle school teacher teaches etcetera by considering the dynamics of his curriculum (Fleener, 2002) and the language games of his classroom. How he engages his students in and develops strategies for teaching etcetera will be explored. Teaching etcetera in this classroom, as considered through an examination of the language games of the class, will reveal a relational approach to mathematics teaching and learning, an inherent rhythm, as the beating of a heart, central to an emergent curriculum and on-going learning.