Reflections on teaching a mathematics education course.

摘要

Teaching and learning involve reflexive actions and should be chosen thoughtfully and deliberately, not because someone has decided "what works." In this study, I examine how complex conversations might offer pedagogical and theoretical (re)considerations in a teacher education course on mathematics. The term "math methods" is a doubly weighted phrase, for both mathematics and methods connote particular ideologies prevalent in current educational rhetoric. In order to unpack the impact of these words, I engage in research based on inquiry, historical analysis, and personal reflections, all of which I use in an eclectic, thoughtful, and explorative manner.; The two main research questions I will explore in this dissertation involve effort by "teacher" and "student" in which both are learners, knowers and participants. The first question is how can complex conversations---those involving multiple perspectives---aid pre-service teachers in becoming reflective practitioners, effective professionals, and inquiring pedagogues? Specifically, teaching mathematics as a relational activity---in which a hermeneutical perspective is crucial---brings forth epistemological questions and issues. The historical situatedness of teacher education and mathematics education become relevant with respect to current epistemological perspectives of teachers and researchers, and these influences are examined in the context of pre-service teachers' positionalities. The second question involves an examination of how I am transformed as I experience and reflect on participation in these complex conversations. While engaged as an instructor, I am simultaneously influenced by research in complexity theory, curriculum theory, and teacher education.; In complex conversations, we can find possibilities for teaching and learning, even potential ways of being that we do not yet know. Complex conversations encourage a different form of interaction, a different way of imagining the world---different from a Ramist method of hierarchies, different from a patriarchal positioning of supervisors over teachers and teachers over students, and different from mathematics as what is. In (re)imagining what mathematics can be, it is important to recognize how mathematics is currently construed. May mathematics education be(come) a field of study that allows for differences, multiple perspectives, and authentic questions, where ideas do not converge or diverge but co-emerge.