Classroom explorations of mathematical writing with nine- and ten-year-olds

Phillips, Marilyn Eileen (2002). Classroom explorations of mathematical writing with nine- and ten-year-olds. PhD thesis The Open University.



In this dissertation, writing as a teacher-researcher, I present my longitudinal explorations (1992-2002) of the area of mathematical and paramathematical writing with grade four pupils (nine- and ten-year-olds) who have been members of my classroom (a public elementary school in Vancouver, British Columbia, Canada). Five main writing sites were used: mathematical journal writing, computer research journal writing, pen-pal letter writing (in conjunction with university pre-service students), different forms of in-class extended writing including reports of mathematical investigations undertaken by the pupils and (most significantly in terms of this dissertation) pupil textbook writing. The pupil writing from the last two sites came from one year, 1997-1998.

The 'writing debate' in English language concerning issues of teaching writing through 'creative process' or through explicitly teaching specific 'genre features' has a particular connection with this work, although my study is not formulated precisely within those terms. Certainly, during 1997-1998, my pupils were exposed to a variety of mathematical writing genres which contributed to their ability to produce the sophisticated textbook writing they did (even if it took me considerable time and effort in order to appreciate its nature).

My analysis of their writing focuses on aspects of five key and interrelated features of writing: audience, purpose, form (genre), content and voice. Within these (increasingly overlapping and blurring) categories, I use certain tools of discourse analysis (in particular, attention to pronouns and general verb tense and mood) to identify and discuss specific features of their writing. In addition, l employ Eco's notion of model reader and Bakhtin's concept of addressivity in order to examine larger-scale features of my pupils' writing. These connect to conventional textbook forms and work reported in the research and professional literature, under the heading 'writing to learn mathematics'.

I coin the term paramathematical writing, in order to discuss writing that supports mathematics even though it is not directly mathematical by itself. I identify two forms of paramathematical writing: explicit personal text alongside more overtly mathematical writing and certain syntactic choices (allied to 'voice') when writing text with the explicit intent of helping another pupil learn some mathematics. Finally, at a meta-level, throughout this dissertation, genuineness, caring and trust are themes that arise and interleave themselves through the discussion. Teacher research is examined as a generative process that produces, along with its particular products, seeds for on-going research.

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