Complexity of affective disposition and reflective transphenomenality: An exploratory study of middle school mathematics teacher and student self-positioning and positioning-by-others toward mathematics, mathematics teaching, and learning.

摘要

The purpose of the mixed methods study was to examine the phenomenon of transphenomenal simultaneity between teacher and student disposition that contributed to the phenomenological conflict of teacher self-positioning and positioning-by-others toward mathematics, mathematics teaching and learning. The intent was to provide a view of self-reported and observed middle school teacher and student experiences in mathematics, based on the analysis of affective dispositional characteristics within the context of its complexity.;There is evidence that documents a relationship between teacher and student disposition, but to what extent and encompassing what characteristics and factors has not been sufficiently substantiated. Beyers (2011) identified two key impacts of disposition on learning: (1) "...teachers play an essential role in shaping students dispositions with respect to mathematics", and (2) "students dispositions with respect to mathematics affect student learning by means of opportunities to learn" (p. 70). The study investigated and delineated the nature of positioning, as evidence of transphenomenality in self-positioning and positioning-by-others, addressing a gap in the research. The research questions were 1) Within the complexity framework, what are teacher and student affective disposition characteristics which contribute to a phenomenological conflict between teacher self- positioning and positioning-by-others?; 2) How, and to what extent, is transphenomenal simultaneity in teacher positioning reflected by student positioning?; and 3) What evidence is present in support of or in contradiction to shifting and closing the gap of stereotypical gender disparity in disposition toward mathematics? .;Utilizing survey/case study research in multiple stages, the findings suggest middle school mathematics teachers' self-positioning was challenged by positioning-by-others (students) revealing simultaneous transphenomenality as a manifestation of complexity of the main construct of the study---teacher affective disposition. Simultaneity of transphenomenality that reflected "events or phenomena that exist or operate at the same time" (Davis, 2005, p.14) was recognizable in the dynamic and multifaceted nature of disposition which contributed to emergent and shifting mathematical disposition. Fluidity in teacher positioning, measured by multiple instruments, was representative of metamorphoses between teacher-as-engineer and teacher-as-technician positioning (Tchoshanov, 2011) and resultant student disposition. Additionally, analysis of the question "Would you consider yourself a mathematician?" showed no statistically significant relationship between gender and consideration of oneself as a mathematician among participating students existed.;The importance of this study is three-fold: 1) an overall neutral with a slight positively inclined affective disposition and self-positioning for middle school teachers and students existed. This finding challenged existing claims of prevalent negative dispositions toward mathematics; 2) no statistically significant gender difference among middle school students in considering oneself a mathematician was observed. This finding indicates a shift in affective disposition toward mathematics from prior studies in stereotype; and 3) self-positioning and positioning-by-others demonstrated simultaneity of transphenomenal affective characteristics of disposition toward mathematics, mathematics teaching and learning.