Dissertation
Student logical implications and connections between symbolic representations of a linear system within the context of an introductory linear algebra course employing inquiry-oriented teaching and traditional lecture
Doctor of Philosophy (PhD), Washington State University
01/2017
Handle:
https://hdl.handle.net/2376/12928
Abstract
This study aimed to explore how inquiry-oriented teaching could be implemented in an introductory linear algebra course that, due to various constraints, may not lend itself to inquiry-oriented teaching. In particular, the course in question has a traditionally large class size, limited amount of class time, and is often coordinated with other sections of the same course. Additionally, I aimed to explore student understanding of mathematical connections within this classroom context. I considered two types of mathematical connections that are often emphasized within introductory linear algebra: connections between symbolic representations of a linear system and logical implication connections. Thus, this study was conducted with the goal of answering the following research questions:
• What does it look like when a teacher attempts to incorporate inquiry-oriented teaching in an undergraduate introductory linear algebra class?
• What mathematical connections do students appear to evoke within the context of an introductory linear algebra course that employs inquiry-oriented teaching?
To answer these questions, I conducted an action research study in three consecutive introductory linear algebra courses that I taught. Throughout the study, my inquiry-oriented teaching evolved and took form in response to my teaching goals of helping students develop mathematical connections and in response to the constraints that I faced in teaching this particular course. Inquiry-oriented teaching was largely reserved for the teaching of mathematical connections; in an attempt to create more time for inquiry-oriented teaching of mathematical connections, lecture was utilized for the teaching of other concepts. I have defined the resulting implementation as a hybrid approach to inquiry-oriented teaching. The hybrid approach shows great potential as a tool for helping instructors transition to inquiry-oriented teaching; in particular, the hybrid approach is useful for accomplishing a specific set of teaching goals, for example, the teaching of mathematical connections. The mathematical connections that students evoked throughout this study appear to have formed, at least in part, as a result of the opportunities that students had to engage in mathematical inquiry throughout the course.
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Details
- Title
- Student logical implications and connections between symbolic representations of a linear system within the context of an introductory linear algebra course employing inquiry-oriented teaching and traditional lecture
- Creators
- Spencer Payton
- Contributors
- Libby Knott (Advisor)Kimberly Vincent (Advisor)Shiv Karunakaran (Committee Member)Judi McDonald (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Teaching and Learning
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 280
- Identifiers
- 99900581631101842
- Language
- English
- Resource Type
- Dissertation