Re-mythologizing mathematics through attention to classroom positioning

Abstract

With our conceptualization of Harré and van positioning theory, we draw attention to immanent experience and read transcendent discursive practices through the moment of interaction. We use a series of spatial images as metaphors to analyze the way positioning is conceptualized in current mathematics education literature and the way it may be alternatively conceptualized. This leads us to claim that changing the way mathematics is talked about and changing the stories (or myths) told about mathematics is necessary for efforts to change the way mathematics is done and the way it is taught.With growing awareness of the significance of social interaction in the development of mathematical understanding, researchers in mathematics education are attending increasingly to the nature of interpersonal positioning within classroom relationships. In addition to explicit attention to positioning, the word 'position' sneaks into conversations about dispositions, impositions, juxtapositions, oppositions, propositions, and transpositions.These position words are similar to each other because they are all nouns, but dispositions seem more stable than propositions, juxtapositions, transpositions, and oppositions because people talk about having dispositions. By contrast, an imposition, proposition, juxtaposition, or opposition is made-made in relation to other people or to other people's arguments. This difference raises questions for us about how these words Educ Stud Math (2009) 72:1-15

Common Sense and Necessity in (Ethno)Mathematics

“…We suggest that this kind of reciprocity of relationships between cultures is related to the reciprocity amongst individuals in interpersonal positioning. This reciprocity is described by van Langenhove and Harré (1999) and taken up by Wagner and Herbel-Eisenmann (2009) in the mathematics education context. In any interaction, when one person positions the other people in certain ways, they comply or resist this positioning, and thus take up their responsibility for the positioning in the interaction.…”

Remythologizing Mystery in Mathematics: Teaching for Open Landscapes versus Concealment

“…We are most interested in the way the mystery myth in mathematics positions students. It is important for us to clarify that we are not using the term "remythologization" in the same sense that one of us (Dave) used it previously-where remythologization meant the generation of new stories within mathematics to change its face for students [7]. Perhaps a better word for this earlier use would have been "neomythologization," because it asked for new stories.…”

“…First, positioning theory focuses on the immanent: language is taken only as a concrete occasion of language in use [8]. This focus on immanence has been problematized in the mathematics education context by Wagner and Herbel-Eisenmann [7], because some scholars have described positioning of students and/or teachers in relation to mathematics, which is transcendent, not immanent. However, our remythologist interests highlight the power of focusing on immanence, because we seek to identify the rights and duties of people when the texts we analyze gloss over those rights and duties in deference to some truth outside of the people doing mathematics.…”

Appraising lexical bundles in mathematics classroom discourse: obligation and choice

“…Furthermore, Moschkovich (2007) argued that, if students see themselves relating to the discipline, this sense of the discipline can be imagined in many different ways. We have elaborated further on the implications of positioning theory in Wagner and Herbel-Eisenmann (2009).…”

“…Whether this attribution referred to the authors or to the textbook personified does not matter; they can be taken as representing the discipline of mathematics. (For detailed analysis of the use of "they" in relationship to mathematics textbooks, teachers and students, see HerbelEisenmann (2009), and for theorization of how people are positioned as mediums of the discipline of mathematics, see Wagner and Herbel-Eisenmann (2009). ) Tr: They want you to give them a problem in which the answer is in between a certain number that they give.…”