Thinking aloud together: A teacher's semiotic mediationof a whole-class conversation about percents

摘要

How does classroom interaction support students' apprenticeship into the waysof speaking, writing, and diagramming that constitute the practice of mathematics? Weaddress this problem through an interpretative analysis of a whole-group conversation aboutalternative ways of solving a problem involving percent discounts that occurred in a sixthgrade classroom. This research study draws upon Dewey's theory of inquiry, Vygotsky'scultural–historical psychology, Freudenthal's realistic mathematics education, and Halli-day's systemic functional linguistics (SFL). From Freudenthal, we borrow the notions ofmathematizing and guided reinventionthe former notion offers a view of mathematics asan activity of structuring subject matter and the latter one provides insights into theprocesses whereby mathematizing is learned and taught in the classroom. We glean fromDewey his view of reflective thinking as inquiry and the role that conversations may servetherein. We rely upon Vygotsky's notions of a verbal thinking plane and a social phase oflearning in order to reconsider the function of whole-class interaction in apprenticingstudents into mathematizing. Finally, SFL provides us with tools for explaining the choicesof grammar and vocabulary students and teachers make as they realize meanings in whole-group conversations. Treating the selected whole-class conversation as a text, we focus ouranalysis on how this text came to mean what it did. Our central questions are as follows:What meanings were realized in the whole-class conversation by teacher and students andhow were these meanings realized? How did the teacher's lexico-grammatical choices guide the students' choices? In addressing these questions, we advance an interpretation ofthe conversation as paradigmatic of students and teacher thinking aloud together aboutpercents.