Growing and growing: promoting functional thinking with geometric growing patterns Public Deposited

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Last Modified
  • March 20, 2019
Creator
  • Markworth, Kimberly A.
    • Affiliation: School of Education
Abstract
  • Design research methodology is used in this study to develop an empirically-substantiated instruction theory about students' development of functional thinking in the context of geometric growing patterns. The two research questions are: 1. How does students' functional thinking develop in the context of geometric growing patterns? 2. What are effective means of support to facilitate functional thinking? A conjectured local instruction theory about students' development of functional thinking in the context of geometric growing patterns was identified. Based on a review of the literature, figural reasoning, i.e., attention to the physical structure of the geometric growing pattern in reasoning about the functional relationship, was found to be important to students' development of functional thinking. The theoretical framework identified a possible learning progression for the development of students' functional thinking in the context of geometric growing patterns and potential means of support. A hypothetical learning trajectory was developed, including a sequence of geometric growing pattern tasks designed to support students' development of functional thinking through pattern exploration. This instructional sequence was implemented in two classroom-based teaching experiments in the first macrocycle of the design research, and a revised instructional sequence was implemented in two classroom-based teaching experiments in the second macrocycle. The data analysis identifies ways in which students' functional thinking progressed through the sequence of geometric growing pattern tasks, effective means of support for students' learning, and challenges to students' development of functional thinking and the design of the instructional sequence. Findings indicate that the figural reasoning approach utilized in this study supports students' development of functional thinking in the context of geometric growing patterns. Potential means of support identified in the conjectured local instruction theory are found to be effective in supporting students' development of functional thinking, but to varying degrees. A revised local instruction theory is presented as a result of this study's findings, including a revised learning progression and a revised instructional sequence. The design research process is found to be an effective methodology for constructing and refining a local instruction theory about the development of students' functional thinking in the context of geometric growing patterns.
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  • In Copyright
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  • "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the School of Education."
Advisor
  • Friel, Susan N.
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Place of publication
  • Chapel Hill, NC
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  • Open access
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