INTRODUCING ALGEBRA THROUGH THE GRAPHICAL REPRESENTATION OF FUNCTIONS: A STUDY AMONG LD STUDENTS.
Abstract: 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 interpreta... read moretion 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.
Thesis (Ph.D.)--Tufts University, 2013.
Submitted to the Dept. of Education.
Advisor: Analúcia Schliemann.
Committee: Judah Schwartz, Montserrat Teixidor i Bigas, and David Carraher.
Keyword: Mathematics education.read less