Abstract: The primary goal of the study presented in this dissertation is to describe 11th-graders' understandings, through different representations, of: (1) the definition of function, (2) the production of a function, and (3) the interpretation of a function. In addition, this dissertation seeks to describe the relationship between 11th-graders' scores on written assessments given at various ti... read moremes during the school year and their understandings of the concept of function. This will be achieved through a case study analysis of eight 11th-grade students in a traditional Algebra 2 Honors class. The eight participants were recruited from the same high school in Boston, Massachusetts, which serves a diverse racial, ethnic, and cultural community. The participants were interviewed individually about questions pertaining to the definition, production, and interpretation of functions. The participants were also given a written assessment at the beginning, middle, and end of the school year, which was based on the content of their Algebra 2 curriculum. The detailed analysis of the interview responses by each participant (within-case analusis) revealed that the students had some understanding of the concept of function and led to several themes that were used in the analyses of the whole group's performance (cross-case analyses). The cross-case analyses revealed that the 11th-grade students lack an understanding of the definition of function, but are able to produce various functions that may or may not meet a given constraint and are able to interpret the given properties of a function. In addition, in spite of not understanding the definition of a function, these students exhibit a flexible understanding of the concept of function; that is, they are able to translate a function from one representation to others and/or use different approaches towards producing and interpreting functions.
Thesis (Ph.D.)--Tufts University, 2012.
Submitted to the Dept. of Education.
Advisor: Barbara Brizuela.
Committee: Analucia Schliemann, Judah Schwartz, Marjorie Hahn, and David Carraher.