Mathematical Investigations: A Primary Teacher Educator's Narrative Journey of Professional Awareness
Bailey, J. (2004). Mathematical Investigations: A Primary Teacher Educator’s Narrative Journey of Professional Awareness (Thesis, Master of Education (MEd)). The University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/2472
Permanent Research Commons link: https://hdl.handle.net/10289/2472
Over a period of twenty months a mathematics teacher educator uses narrative inquiry, a form of story-telling, to investigate her professional practice in working alongside pre-service primary teachers. Two main themes emerge in this research. The first of these centres around the use of mathematical investigations as a vehicle for supporting pre-service primary teachers to consider what the learning and teaching of mathematics may entail. As part of this process the author personally undertook several mathematical investigations. This resulted in significant learning about previously unrecognised personal beliefs about the nature and learning of mathematics. These beliefs were discovered to include ideas that 'real' mathematicians solve problems quickly, do so on their own and do not get stuck. Surprisingly, all of these subconscious assumptions were contrary to what the author espoused in the classroom. A consequence of this learning included some changed beliefs and teaching practices. One such change has been moving from a conception of mathematics as a separate body of 'correct' mathematical ideas, and where the emphasis when doing mathematics was on attaining the correct answer, to now viewing mathematics as a sense-making activity involving discovering, doing and communicating in situations involving numbers, patterns, shape and space. Thus, mathematics is now perceived to primarily be found in the 'doing' rather than existing as a predetermined body of knowledge. As such one's interpretations of a mathematical problem are important to consider. Changes in teaching include using mathematical investigations as a teaching approach with the belief that students can effectively learn mathematical ideas using this approach; an acceptance that this may involve periods of being 'stuck' and that this does not mean that the teacher needs to immediately support the students in becoming 'unstuck'; more in-depth interactions, including questioning, to support this mathematical learning; and an acceptance that mathematics can be learned by people working in a collaborative manner. The second theme encountered in this narrative inquiry involves the exploration of narrative as a powerful means with which to pursue professional development. Narrative inquiry, including a mention of differing forms of narrative writing, is described. Issues also considered include the place of reflection in narrative; the notion of multiple perspectives that are encountered in qualitative research such as this; issues of validity and authenticity; a consideration of what the products of narrative research might be and who may benefit from such research; a brief mention of collaboration; and the place of emotion in qualitative research. The concept of change occurring within a narrative inquiry is not seen to imply an initial deficit position. Rather the research process is regarded as the building of a narrative layer that supports and grows alongside the writer's life as it occurs (Brown Jones, 2001). Thus there is not a seeking of perfection or an ideal, but a greater awareness of one's professional practice. The results of narrative research therefore, are not definitive statements or generalisations about an aspect of that which is being researched (e.g., Winkler, 2003). As such, a definitive statement about how to be a teacher of pre-service students learning mathematics is not offered. Rather, a story is shared that may connect with the stories of the reader.
The University of Waikato
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