This longitudinal study evaluates the impact of a new Algebra 1 course at a High School for language-based learning-disabled (LD) students. The new course prioritized the teaching of relationship graphs and functions as an introduction to algebra. Across three studies, the dissertation documents and evaluates the progress made by LD high school students in Algebra 1 on the interpretation and production of relationship graphs. The first two studies examine intervention and control students' answers to a written assessment on time-distance graphs, immediately after and two years after the intervention. The third study, examines other intervention and control students' written assessment answers on graphs relating variables other than time and distance, two years after the Algebra 1 course. Data from the first study show significantly better results for the intervention group in the post-assessment results and significantly better results for the intervention group's post-assessment results in comparison to the control group. Results for the control students taking Algebra 2 were similar to those of the intervention group's pre-assessment results. The second study, again, shows significantly better results for the intervention group two years later. In the third study, even though the intervention group performed slightly better than the control group, the difference between groups was not significant, with both groups showing high levels of performance. Because discussions in the entire department aimed at including a multi-representational view of algebra at all levels, this may have led to changes among the Algebra 2 teachers' views and ways of teaching algebra. This set of results supports the view that beginning Algebra 1 with instruction on the graphical representation of functions, instead of focusing on the alpha-numeric representation of algebra, allows for learning among LD students that remains over the years. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]