Students' conceptions of trigonometric functions and positioning practices during pair work with Etoys

Mathematics Education;Collaboration;Technology;Learning;Computer Programming;Algebra

DeJarnette, Anna

关键词: Mathematics Education;    Collaboration;    Technology;    Learning;    Computer Programming;    Algebra;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/49404/Anna_DeJarnette.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This dissertation is an examination of how students learn mathematics when interacting with peers and using a computer-programming environment.Students’ use of technology tools in mathematics classrooms raises important questions of how students’ mathematical thinking and learning is shaped by those tools.At the same time, students’ learning is shaped by how they interact with peers and make sense of mathematics together.To answer questions about the intersection of students’ work with peers and use of technology tools, I conducted a study of several pairs of students working with a programming environment called Etoys on a problem about sine and cosine functions.The dissertation is situated around three interrelated strands of work.First, I use the cK¢ model of conceptions to examine students’ learning about sine and cosine functions.By combining the conceptions framework with the theory of instrumented activity, I consider specifically how students integrated the tools of Etoys into their mathematical thinking.In the second strand, I combine the conceptions analysis with quantitative measures of student learning gained through pre- and post-tests, illustrating how standard measures of learning can be complemented and informed through an analysis of cases.Finally, I use Systemic Functional Linguistics to extend Hiebert and Grouws’s construct of productive struggle, to consider students’ collaborative efforts towards solving a problem.Methodologically, I illustrate how the cK¢ framework and resources from Systemic Functional Linguistics can operationalize the constructs of students’ conceptions and, respectively, collaboration.These strands of work offer views of students’ learning through the lenses of their thinking about a specific concept as well as their participation in collaborative problem solving.My findings include a description of conceptions of sine and cosine functions that students invoked through their work.More importantly, I have identified ways in which students’ use of the tools in Etoys supported them to develop increasingly sophisticated conceptions.Students appropriated the tools of Etoys in different ways, and some students were able to transfer their use of Etoys to their work on a new problem.Regarding students’ positioning practices, I found that when students challenged one another, they created opportunities for collaborative productive struggle, an activity of collaboration among students leading to positive problem solving outcomes.These findings constitute a step towards understanding when and how students can challenge one another in ways that support productive collaboration.My findings indicate that students appropriate technology tools in different ways, suggesting that tasks with technology should be designed specifically to provoke students to move beyond overly simplistic conceptions in mathematics.Implementing norms for group and pair work, especially for how students can ask questions and challenge their peers, can promote collaborative settings where students learn mathematics through collaboration around the computer.