Date on Master's Thesis/Doctoral Dissertation

12-2011

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Psychological and Brain Sciences

Committee Chair

Pani, John Robert

Author's Keywords

Algebra; Education; Mathematics; Algebraic thinking; Elementary; Learning

Subject

Algebra--Study and teaching (Elementary); Mathematical ability; Learning, Psychology of

Abstract

The current study explored the impact that algebra knowledge in 1st and 2nd grade can have in growth and achievement in mathematics through 5th grade. Previous studies have shown the positive impact of teaching algebra in middle school (e.g. Smith, 1996). Other studies have shown that students can learn and apply fundamental algebra concepts even earlier, including early elementary grades (e.g. Schifter et al., 2008; Brizuela and Earnest, 2008). The current study aimed to expand upon this research by showing students' knowledge of early algebra concepts can predict positive longitudinal outcomes. This would support cognitive and education theories that students can use algebraic concepts to structure their overall mathematics knowledge. The current study utilized an archival dataset with five years of student data from one district. District assessments measured student knowledge of algebra in 1st and 2nd grade. Students' standardized mathematics test scores and district assessments for mathematics were collected for 3rd, 4th, and 5th grade. Algebra knowledge in 1st and 2nd grade predicted students' mathematics ability on the state standardized assessment in 5th grade. It also predicted growth in scores from 3rd through 5th grade. Algebra was a significant predictor in a model that included students' abilities in other areas of mathematics, reading ability, and race. The model also included school level socioeconomic data. Parallel models were done using the district assessments in 3rd through 5th grade as the outcome measure. Algebra knowledge in 1st and 2nd grade was a significant predictor of 5th grade mathematics knowledge on these assessments. Algebra knowledge did not predict growth from 3rd through 5th grade. Overall, this study underlines the importance of including algebra in early elementary teaching, standards, and assessment. Early algebra may help students structure their mathematics knowledge from the beginning of their education. This can lead to improved longitudinal mathematics knowledge and performance.

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