This study examined understanding of linear functions held by students with visual impairments. The purpose of this study was to determine students‘ level of knowledge and type of understanding of linear function and to describe students‘ abilities in using the four main representational forms of a function: (a) description, equations, tables, and graphs. Other aspects studied were students‘ preferred representation of function and students‘ perceived influences in his or her mathematics education. Participants in this study included four high school and four college students who were receiving educational services for a visual impairment and who had completed at least one course in algebra.

Data collection and analysis followed a qualitative research design. Three instruments were used for data collection, (a) the Mathematics Education Experiences and Visual Abilities (MEEVA) Interview, (b) the Function Knowledge Assessment (FKA), and (c) the Function Competencies Assessment (FCA). The MEEVA provided demographic information and responses provided information on students‘ previous educational experiences in mathematics. The FKA and the FCA were mathematics assessments that consisted of problems related to linear functions and their applications. Student responses from the FKA and the FCA provided information on student knowledge of linear functions and student abilities when solving word problems involving linear functions. Instruments were given orally and responses were audio recorded. Each participant met with the researcher one-on-one on two different occasions to complete the three data collection instruments.

Data analysis followed the tenets of the Constant Comparative Method (Glaser & Strauss, 1967). Student responses to the MEEVA, FKA, and FCA were transcribed and coded for student understanding in the four function competencies, (a) modeling, (b) interpreting, (c) transcribing, and (d) reifying as described by O‘Callaghan (1998). Students‘ level of knowledge of linear function was further described by students‘ ability to comprehend and apply knowledge when solving word problems, as described by Wilson (1971).

Results indicate that the understanding of modeling and interpreting problems involving linear functions of high school and college students with visual impairments was stronger than that of either translating between representational forms of a function or the ability to reify the function concept. A positive relationship was observed between students‘ graphing abilities and his or her overall understanding of function. Results also show that students were most comfortable with gaining information on functions through tables and were least comfortable gaining information through graphs. The perceived influences on students‘ mathematics education were that of individualized education and the use of appropriate materials that allowed for independent access to the curriculum.