Supporting Students to Develop Mathematical Explanation: Studying the Work of Teaching.

The Work of Teaching;Decomposition;Mathematical Explanation;Education;Social Sciences;Educational Studies

Kwon, MinsungBall, Deborah Loewenberg ;

University of Michigan

关键词: The Work of Teaching;    Decomposition;    Mathematical Explanation;    Education;    Social Sciences;    Educational Studies;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/116645/mskwon_1.pdf?sequence=1&isAllowed=y

瑞士|英语

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

【 摘 要 】

The practice of explanation is widely seen as key to developing students’ ability to understand mathematics, but it has not been well cultivated in mathematics classrooms.Efforts have been made to increase students’ discursive activities but these have largely overlooked the specific ways of constructing knowledge in the discipline.Approaching the practice of explanation on disciplinary grounds, this dissertation conceptualizes the work of teaching entailed in supporting students to develop mathematical explanation by decomposing the work into its constituent components.To provide an empirical basis for such a conceptualization, I analyzed instructional interactions managed by one teacher, teaching the same mathematical tasks to five different cohorts of students sampled from the same school district.Designing the study to hold other variables of instruction (teacher and content) relatively constant while only varying the class composition of students, this study leverages a core predicament of teaching—its dependence on students—to explore how instructional interactions unfold with different groups of students and how instruction might be adjusted to meet different students’ needs.By further performing this analysis with multiple mathematical tasks, this dissertation identifies ;;mathematical-task generality” and ;;mathematical-task specificity” in constructing mathematical explanations and elucidates how mathematical tasks shape the level of mathematical supports and the role of instructional resources.This dissertation decomposes the work of teaching entailed in supporting students to develop mathematical explanation into four core tasks of teaching and two instructional resources, while articulating a structure and rationale for such a decomposition.Beyond the benefits of specifying this important aspect of teaching, this study serves to address one targeted problem of teaching—the uncertainties and unexpectedness arising with students—by gradually increasing the demands of unpacking students’ ideas and the complexities of managing multiple interactions among students so that teaching is rendered more understandable, doable, and learnable by teachers.This dissertation advances a study design that addresses the problem of how the particularities of students matter for teaching, contributes to establishing a grammar of decomposition by specifying the decomposition’s underlying rationale, and provides conceptual tools that can be used to develop effective teacher education.