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|Title: ||Analyzing Students' Mathematical Thinking in Technology-supported Environments|
|Authors: ||Karadag, Zekeriya|
|Advisor: ||McDougall, Douglas Emerson|
|Department: ||Curriculum, Teaching and Learning|
|Keywords: ||Mathematical thinking|
technology in mathematics education
frame analysis method
|Issue Date: ||24-Feb-2010|
|Abstract: ||This study investigates how five secondary students think mathematically and process information in a technology-supported environment while solving mathematics problems. In the study, students were given open-ended problems to explore in an online dynamic learning environment and to solve the problems in computer environments. Given that all the work was done in the computer environments, both online and offline, students’ work was recorded by using screen capturing software. A new method, the frame analysis method, was used to describe and analyze students’ thinking processes while they were interacting with mathematical objects in the dynamic learning environment and solving mathematics problems. The frame analysis method is a microgenetic method based on information processing theory and is developed to analyze students’ work done in computer environments. Two reasons make the analysis method used in this study unique: (a) collecting data with minimized disturbance of the students and (b) analyzing students’ artefacts through researcher’s (teacher) perspective, meaning that integrates teachers within the analysis process.
The frame analysis method consists of multiple steps to observe, describe, interpret, and analyze students’ mathematical thinking processes when they are solving mathematics problems. I described each step in detail to explain how the frame analysis method was used to monitor students’ mathematical thinking and to track their use of technology while solving problems.
The data emerged from this study illustrates the importance of using dynamic learning environments in mathematics and the potential for transformation of mathematical representational systems from symbolic to visual. Moreover, data suggest that visual representation systems and linked multi-representational systems encourage students to interact with mathematical concepts and advance their mathematical understanding. Rather than dealing with the grammar of algebra only, students may benefit from direct interaction with the visually represented mathematical concepts.
It appears that recording students’ problem-solving processes may engage teachers and mathematics educators to seek opportunities for implementing process-oriented assessment into their curriculum activities. Furthermore, students may benefit from sharing their work through peer collaboration, either online or offline, and metacognition and self-assessment. Suggestions for further studies include using audio and video recording in the frame analysis method.|
|Appears in Collections:||Doctoral|
Department of Curriculum, Teaching and Learning - Doctoral theses
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