Access to quality mathematics content and instruction has been equated as a civil
right (Moses & Cobb, 2001), as it is a gatekeeper to higher education and lucrative
careers. Unfortunately, access to empowering mathematics is not a reality for many
urban youth. Data show an achievement gap between Black, Hispanic and American
Indian students and their peers which, in turn, result in unequal access to education and
economic opportunities (NAEP, 2007; U.S. Department of Education, 1997).
This evaluative case study focused on eight racially diverse high school students
from an urban charter school who were studying Algebra 1 in classroom contexts that
were student-centered and discourse-based. The study took place after a sequence of six
lessons that introduced representations of linear functions through geometric patterns.
Pairs of students participated in a series of interview tasks, largely modeled from
problems in their curriculum Algebra Connections (Dietiker, Kysh, Sallee, Hoey, 2005),
that focused on their understanding of representations of functions (tables, graphs,
equations and context), the embodiment of rate of change in the representations and
translating among the representations.
The study sought to understand the nature of the students’ initial understandings
of representations and translations including their natural language when describing
observations, the perspectives from which they approached the tasks (explicit or
recursive) and how their thinking compares to literature in the field. The students were
able to translate linear functions directly between any two representations and many were
able to extend their thinking to novel problems involving non-linear functions.
University of Minnesota Ph.D. dissertation. February 2010. Major: Education, Curriculum and Instruction. Advisors: Dr. Kathleen A. Cramer and Dr. Terry Wyberg. 1 computer file (PDF); x, 281 pages, appendices A-F.
Whitney, Stephanie Rae.
Multiple representations and rate of change: the nature of diverse Students' Initial Understanding..
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