Writing for an Audience in a Mathematics Methods Course
Flores, Alfinio, Cwikla, Julie, Brittain, Carmina M., Martinez-Cruz, Armando, Teaching Children Mathematics
During their first mathematics methods course, many prospective elementary teachers confront their previous conceptions about mathematics and its teaching for the first time. This juncture makes the course important in their evolution as teachers of mathematics. Prospective teachers in a mathematics methods course must develop the ability to reflect on their actions, beliefs, knowledge, and attitudes. Writing in a mathematics methods course fosters reflection in a natural way; it serves as a tool for documentation, analysis, and discussion to help prospective teachers internalize what they learn and reach new levels of comprehension. At the same time, what teachers in training write gives teacher educators a window into their reflection and growth process.
In the October 2003 article published in this department, we described the benefits of writing in mathematics for students, as well as the benefits of writing in a mathematics methods course for prospective elementary teachers (Flores and Brittain 2003). We also described some of the writing tasks used with prospective teachers (see table 1). This article focuses on the writing process and the importance of writing for an audience in an elementary mathematics methods course. The writing examples presented here were collected in several one-semester courses taught by the first author. The second author participated as a student in one of the courses.
The Process of Writing
Britton and his colleagues categorize mature writing according to function (Britton et al. 1975). The categories are transactional, expressive, and poetic. Writing completed in the mathematics methods course falls into the expressive and transactional categories. Britton et al. describe transactional writing as--
language to get things done: to inform people (telling them what they need or want to know or what we think they ought to know), to advise or persuade or instruct people. Thus the transactional is used for example to record facts, exchange opinions, explain and explore ideas, construct theories; to transact business, conduct campaigns, change public opinion. (Britton et al. 1975, p. 88)
Within the informative function of transactional writing are recording and reporting, as well as writing with increasing levels of generalization.
Expressive writing includes the kind of writing that might be called "thinking aloud on paper," which is intended for the writer's own use; for example, a diary entry that attempts to record and explore the writer's feelings, moods, opinions, and perceptions of the moment (Britton et al. 1975). Writing addressed to a limited audience that shares much of the writer's context and many of his or her values, opinions, and interests also has an expressive function. Britton et al. make three generalizations about the expressive function:
Firstly, expressive language is language close to the self. It has the functions of revealing the speaker, verbalizing his consciousness, and displaying his close relation with a listener or reader. Secondly, much expressive language is not made explicit, because the speaker/writer relies upon his listener/reader to interpret what is said in the light of a common understanding (that is, a shared general context of the past), and to interpret their immediate situation (what is happening around them) in a way similar to his own. Thirdly, since expressive language submits itself to the free flow of ideas and feelings, it is relatively unstructured. (Britton et al. 1975, p. 90)
The expressive function plays an essential developmental role, according to Britton et al. From expressive writing, students develop more differentiated forms of mature writing as they grow. For mature writers, the first draft of a transactional writing often is essentially expressive.
The Process of Writing to Learn in Mathematics
Because writing is a tool to learn, asking whether using writing will improve students' learning of mathematics is more important than asking whether writing in a mathematics class will improve students' writing abilities (Connolly and Vilardi 1989). …