Mathematical Problems and Mathematical Questions: Academic Tasks for Students as a Window Into the Institutional Obligations of Teaching

• In Event: The Role of the Professional Obligations for Mathematics Teaching in Mathematics Teacher Education

Abstract

Purpose. Chazan, Herbst, and Clark (2016) describes four obligations on those who take on the role of teacher in instruction and suggest that those obligations frame the nature of justifications teachers provide for instructional decisions (Herbst & Chazan, 2012). The aim of the study is to explore how these obligations on the role of the teacher, particularly what they call institutional obligations, are influenced by the institutional contexts of mathematics instruction.

Academic tasks (Doyle, 1983) structure “the work students do … by setting specifications for products and explaining the processes that can be used to accomplish work” (p.169). This study uses academic tasks posed to students as a window into the institutional contexts of teaching and learning and instructors’ reasoning about the nature of posed tasks to surface ways in which institutional obligations on the role of teacher differ by institutional contexts.

Methods, Data Sources, Data Analysis. The teacher/researcher in this study uses their own practice as a site for studying teaching (Ball, 2000). The study makes use of naturally occurring variation as a single teacher teaches the same exploratory mathematical material on continued fractions across different course contexts to undergraduate students and doctoral candidates in mathematics education. In all of the course contexts, the teacher considers how to produce tasks that will support exploration of student mathematical questions. In mathematics classrooms, academic tasks are often described as problems or exercises (Love & Pimm 1996) and can be exploratory or novel (Herbst, 2003). The teacher in this study also considers ways to have exploring mathematical questions as an academic task. The study proceeds through analysis of instructional artifacts that present the shifting nature of the academic tasks used in the courses and diary entries and correspondence in which considerations about academic tasks for the courses are described.

Findings and Significance. Initial findings suggest that mathematical questions and mathematics problems are integrally connected, with novel mathematics problems often having an implicit mathematical question in mind. In this sense, novel mathematics problems can be thought of as a structure to collect data relevant to this implicit mathematics question. Considerations related to the nature of academic tasks in different courses are closely connected to matters of grading and expectations about the nature of students’ expectations given the institutional context of a course.

Author

• Daniel I. Chazan, University of Maryland