Date of Graduation

12-2011

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Curriculum and Instruction (PhD)

Degree Level

Graduate

Department

Curriculum and Instruction

Advisor/Mentor

Kent, Laura B.

Committee Member

Collins, Kathleen M. T.

Second Committee Member

Dingman, Shannon W.

Third Committee Member

Imbeau, Marcia B.

Keywords

Education; CGI; Cognitively guided instruction; Elementary mathematics education; Gifted; Mathematically gifted; Mathematics education

Abstract

This study examined to what extent and in what ways mathematically gifted students were challenged in two elementary classrooms taught by exemplary teachers using the principles of Cognitively Guided Instruction (CGI). The two case studies included a third grade class and a fourth/fifth split grade class, with five mathematically advanced participants from each grade. A top tier and a second tier of mathematically advanced students were identified, with the top tier of five students identified as mathematically gifted. Classroom observations of CGI math lessons, interviews with students and teachers, and analysis of students' problem-solving strategies were conducted over a five week period. A synthesis of literature from mathematics education and gifted education was used to craft an operational definition of what it means for a mathematically gifted student to be challenged, focusing on exploration of mathematical relationships, exposure to new mathematical ideas, and experience of Ascending Intellectual Demand on a continuum toward expertise. An alignment of CGI problem-solving strategy levels with levels of Ascending Intellectual Demand served as a conceptual framework for locating and describing the level of challenge experienced in their classrooms. This framework also was used to identify which elements were lacking and suggest what could provide further challenge. The findings revealed a classroom environment that was supportive of mathematical challenge with a variety of ways for extending students' thinking. However, although the students reported high levels of enjoying the lessons and worked with advanced topics, they reported low to mediocre levels of challenge, with the top tier group reporting less challenge than the second tier group. The self-reported challenge levels decreased as the students' grade level increased, with the fifth grade top tier student indicating the least perceived challenge. Analysis of the mixed results suggests that the challenge level of the assigned mathematical task should be elevated.

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