Developing Meaning for Algebraic Procedures: An Exploration of the Connections Undergraduate Students Make Between Algebraic Rational Expressions and Basic Number Properties

dc.contributor.advisor Barlow, Angela en_US Yantz, Jennifer Lynne en_US
dc.contributor.committeemember Holmes Rowell, Ginger en_US
dc.contributor.committeemember Stephens, Chris en_US
dc.contributor.committeemember Strayer, Jeremy en_US
dc.contributor.committeemember Vanosdall, Rick en_US
dc.contributor.department Basic & Applied Sciences en_US 2014-06-02T19:07:52Z 2014-06-02T19:07:52Z 2013-07-16 en_US
dc.description.abstract The attainment and retention of later algebra skills in high school has been identified as a factor significantly impacting the postsecondary success of students majoring in STEM fields. Researchers maintain that learners develop meaning for algebraic procedures by forming connections to the basic number system properties. The present study investigated the connections participants formed between algebraic procedures and basic number properties in the context of rational expressions. en_US
dc.description.abstract An assessment, given to 107 undergraduate students in precalculus, contained three pairs of closely matched algebraic and numeric rational expressions with the operations of addition, subtraction, and division. The researcher quantitatively analyzed the distribution of scores in the numeric and algebraic context. Qualitative methods were used to analyze the strategies and errors that occurred in the participants' written work. Finally, task-based interviews were conducted with eight participants to reveal their mathematical thinking related to numeric and algebraic rational expressions. en_US
dc.description.abstract Statistical analysis using McNemar's test indicated that the undergraduate participants' abilities related to algebraic rational expressions and rational numbers were significantly different, although serious deficiencies were noted in both cases. A small intercorrelation was found in only one of the three pairs of problems, suggesting that the participants had not formed connections between algebraic procedures and basic number properties. The analysis of the participants' written work revealed that the percent of participants who consistently applied the same procedure in the numeric and algebraic items of Problem Sets A, B, and C were 56%, 47%, and 37%, respectively. Correct strategies led to fewer correct solutions in the algebraic context because of a diverse collection of errors. These errors exposed a lack of understanding for the distributive and multiplicative identity properties, as well as the mathematical ideas of equivalence and combining monomials. These fundamental mathematical ideas need to be better developed in primary and secondary education. At the post-secondary level, these ideas should serve as the foundation for interventions that are designed to support underprepared students. The results of the interviews were consistent with the quantitative analyses and the qualitative examination of the strategies used by the participants. The findings in all three areas of the study point to a disconnect between numeric and algebraic contexts in the participants' thinking. en_US Ph.D. en_US
dc.publisher Middle Tennessee State University en_US
dc.subject Connected Representations en_US
dc.subject Precalculus en_US
dc.subject Rational Expression en_US
dc.subject Rational Number en_US
dc.subject STEM Education en_US
dc.subject Undergraduate Education en_US
dc.subject.umi Mathematics education en_US
dc.subject.umi Higher education en_US
dc.subject.umi Mathematics en_US
dc.thesis.degreegrantor Middle Tennessee State University en_US
dc.thesis.degreelevel Doctoral en_US
dc.title Developing Meaning for Algebraic Procedures: An Exploration of the Connections Undergraduate Students Make Between Algebraic Rational Expressions and Basic Number Properties en_US
dc.type Dissertation en_US
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