How Do Teachers Expect Students to Represent Mathematical Work?A Study of Teachers' Recognition of Routine Ways that Proofs are Presented and Checked in High School Geometry.

geometry;proof;mathematical communication;norms;Education;Social Sciences;Educational Studies

Dimmel, Justin K.Chazan, Daniel I. ;

University of Michigan

关键词: geometry;    proof;    mathematical communication;    norms;    Education;    Social Sciences;    Educational Studies;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/111382/jkdimmel_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This dissertation investigates how teachers expect students to represent mathematical work. The goal of the study is to identify routine ways that students communicate in mathematics classrooms and to determine whether mathematics teachers recognize these routines. The instructional setting of the study is US high school geometry. The study looks specifically at how students are expected to communicate when doing proofs. The study consists of two parts. The first part of the study examined video episodes of geometry classrooms to identify how students use different modes of communication when presenting and checking proofs in geometry classrooms. From the analysis of video episodes, I ground hypotheses of routine ways in which students use communication modalities; I call them semiotic norms. The second part of the study is an experiment that uses representations of geometry instruction to investigate the extent to which secondary teachers recognize specific semiotic norms that I call details and sequence. The details norm describes what students are expected to include in the written statements of a proof. The sequence norm describes the expected order of events contributing to the writing and reading of proofs that students present proofs to the class. The second part of the study used storyboards that represent episodes of geometry classrooms as probes for a multimedia questionnaire. Participants in the experiment viewed storyboards that represented teachers breaching or complying with the hypothesized norms. Seventy-three high school mathematics teachers from schools within a 60 mile radius of Midwestern University completed the questionnaires. The results of the experiment indicate that secondary mathematics teachers recognize that the details and sequence norms describe routine communication practices of the activity of doing proofs in geometry. The work reported here identifies communication practices that students use in geometry classrooms when doing proofs. By describing these practices, the research reported in this dissertation contributes subject-specific knowledge of what routinely happens in mathematics classrooms. Knowledge of the routine ways that students communicate is valuable because it provides a foundation for developing discipline-specific communication skills in mathematics classrooms. In turn these inform our understanding of literacy practices in the mathematics classroom.