Browsing by Subject "Algebra"
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Item Multiple representations and rate of change: the nature of diverse Students' Initial Understanding.(2010-02) Whitney, Stephanie RaeAccess 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.Item A Proposed Algebra Problem-Analysis Model(2015-08) Walick, ChristopherThe National Mathematics Advisory Panel (2008) states that algebra is a gateway to high school graduation and college success. While existing research emphasizes the importance of quality algebra instruction, the current body of research on algebra problem-analysis for struggling secondary students is small. This paper proposes a problem-solving model to help support those students struggling with algebra. The model integrates the recommendations from math policy boards and research. It is composed of five core sections, each section focusing on a specific critical component of school algebra. The study examines the relationship between the five skills within the model to an established measure of algebra, as well as the validity of the measures being used to assess the different skill areas The results indicate that there is a significant relationship between the five sections of the model and algebra proficiency, and that the model is able to identify non-proficiency students with a high degree of accuracy.