Friday

4:05 – 4:35 pm

Session 17– Contributed Reports

Marquis A

On the use of dynamic animations to support students in reasoning quantitatively

Grant Sander

This study addresses the well-documented issue that students struggle to write meaningful expressions and formulas to represent and relate the values of quantities in applied problem contexts. In developing an online intervention, we drew from research that revealed the importance of and processes involved in conceptualizing quantitative relationships to support students in conceptualizing and representing quantitative relationships in applied problem contexts. The results suggest that the use of dynamic animations with prompts that focus studentsÕ attention on conceptualizing and relating quantities can be effective in supporting students in constructing meaningful expressions to represent the value of one quantity in terms of another, and formulas to define how two co-varying quantities change together.

Paper

12

Marquis B

Inquiry-oriented instruction: A conceptualization of the instructional the components and practices

George Kuster and Estrella Johnson

In this paper we provide a characterization of inquiry-oriented instruction. We begin with a description of the roles of the tasks, the students, and the teacher in advancing the mathematical agenda. We then shift our focus to four main instructional components that are central to carrying out these roles: Generating student ways of reasoning, Building on student contributions, Developing a shared understanding, and Connecting to standard mathematical language and notation. Each of these four components is further delineated into a total of eight practices. These practices are defined and exemplified by drawing on the K-16 research literature. As a result, this conceptualization of inquiry-oriented instruction makes connections across research communities and provides a characterization that is not limited to undergraduate, secondary, or elementary mathematics education. The ultimate goal for this work is to serve as a theoretical foundation for a measure of inquiry-oriented instruction.

Paper

45

Marquis C

Design research on inquiry-based multivariable calculus: Focusing on studentsÕ argumentation and instructional design

Oh Nam Kwon, Younggon Bae and Kuk Hwan Oh

In this study, researchers design and implement an inquiry-based multivariable calculus course to enhance studentsÕ argumentation in mathematical discussions. This research aims to understand the studentsÕ argumentation in proof constructions activities, and to derive the characteristics of three sites of intervention: instructional design, classroom interaction, and the instructorÕs role. Over the course of 14 weeks, 18 freshmen mathematics education majors participated in this study. Multiple sources of data were collected, studentsÕ reasoning in the classroom discussions were analyzed within the ToulminÕs argumentation structure, and the instructional interventions were gradually revised according to the iterative cyclic process of the design research. The studentsÕ argumentation structures presented in the classroom gradually developed into more complicated forms as the study progressed, and the researchers conclude that the interventions were effective at improving studentsÕ arguments.

Paper

67