Inquiry-Based Instruction in a Secondary Mathematics Methods Course: A Catalyst for Faculty and Course Development

• In Event: Scholars of Studying Teaching Collaborative: A Cross-Disciplinary Initiative to Improve Our Practice as University Instructors

Abstract

Objectives
In 2000, the National Council of Teachers of Mathematics (NCTM) published its Principles and Standards for School Mathematics and, in it, supported inquiry-based instruction. In order to realize the vision outlined by the NCTM, instructors must find ways to design instruction in mathematics methods courses that support teachers as they plan and implement inquiry-based instruction. In so doing, it would seem that these courses should also be taught using inquiry-based instruction. However, few materials are available to guide methods instructors who would like to teach in these ways, particularly at the secondary level. As a result, the author conducted a self-study to investigate the challenges and successes associated with an attempt to use inquiry-based instruction in secondary mathematics methods courses.

Theoretical Framework
Operating from a constructivist approach (Piaget, 1977) an underlying assumption of this study is that individuals learn by building upon prior knowledge through exploration. Inquiry-based instruction provides opportunities to engage in meaningful explorations, discover new ideas, and communicate their findings (NCTM, 2000; Marshall, Smart, & Horton, 2009; Towers, 2010). Though inquiry-based instruction is usually associated with learning mathematics content, this study investigates the feasibility of its use in instruction addressing mathematics teaching and learning.

Methods
The methodology for self-study is one offered by Samaras (2011). After having identified an initial research question, the author created a group of “critical friends” and corresponded with those individuals throughout the researching process. The author also wrote journals both before each class session and after each class session. Each class session was videotaped. This corpus of data was analyzed to determine both the successes and the challenges the author faced in implementing inquiry-based instruction in a secondary mathematics methods course.

Results
Analysis of the data is ongoing. Preliminary analyses, however, point to the challenges and successes the author faced in using inquiry-based instruction as the dominant form of instruction in a secondary mathematics methods course. Challenges included: (1) difficulty constructing explorations that would develop prospective teachers’ thinking about inquiry-based learning, (2) time required to complete meaningful explorations, (3) struggles the prospective teachers faced in thinking about inquiry-based learning without having had teaching experience, and (4) difficulty developing authentic explorations that do not involve real secondary students. Successes were found with particular problems that effectively elicited meaningful exploration of issues related to the teaching and learning of mathematics. Based on these findings, the author has spent time restructuring the course. These changes will be investigated in a future study.

Significance
As one of a few studies of the role of faculty in designing inquiry-based secondary mathematics methods course, this study provides considerations for others who might design such as course. The study also points to the need for more clearly defined learning goals for methods courses so that explorations can be designed to promote prospective teacher learning so that they are prepared to design and implement instruction aligned with NCTM’s vision for mathematics teaching and learning.

Author

• Toni M. Smith, American Institutes for Research