Common errors encountered by freshman students in college algebra: an analysis

Date of Publication


Document Type

Master's Thesis

Degree Name

Master of Science in Teaching Major in Mathematics

Subject Categories

Algebra | Analysis | Number Theory


Br. Andrew Gonzalez FSC College of Education


Science Education

Thesis Adviser

Dr. Maxima J. Acelajado

Defense Panel Chair

Dr. Auxencia A. Limjap

Defense Panel Member

Dr. Bee Ching Ong
Dr. Fe G. De La Rosa


This study identifies the errors committed by freshman students in College Algebra, determine their possible causes, classify the errors and propose corrective measures. The analysis centered on the top three common errors encountered by students in special products, factoring algebraic expressions and algebraic fractions. Further, the classroom instruction used was anchored on three learning theories, namely, the Meaning Theory, Associationism and the Information-Processing. The three stages under which the study was undertaken were the identification stage, the collection stage and the analysis stage. In the identification stage, the students' academic background in high school, mental aptitude, perceptions towards Mathematics were gathered to determine the entry characteristics. In addition, some algebraic errors reflected in the diagnostic tests were also identified during the course of learning the topics covered by the study. In collecting errors, the students were given a series of activities and long quizzes. The results of the tests with respect to the same topic were compared and the specific error types along with the probable sources were descriptively investigated. Thirty-eight common errors and seventeen potential sources were discovered.

Findings reveal that some of the common errors were seen to be persistent and the sources from which they were derived were not consistent. Thus, the students' errors occurred in varied ways in problem-solving situations. In the final analysis, five major classifications were formulated under which the common errors encountered by students occurred. These were errors due to deficiency in conceptual knowledge, procedural knowledge, problem-structure recognition, a priori conception of facts and rules, and non-structured errors. Using Two-factor ANOVA, the number of errors encountered by students only differed significantly in the activities but not in the quizzes with respect to the topics covered. However, the observed number of errors did not differ significantly in both activities and quizzes considering the type of high school they graduated from and their interaction effects. Using Chi-square goodness-to-fit test, the quantitative data gathered also showed a significant difference in the number of errors committed between students from exclusive and non-exclusive schools. The errors that differed significantly between the two groups were failure to square the numerical and/or literal coefficient (activities) and failure to factor completely (activities and quizzes).Lastly, the study proposed student consultation for remedial sessions, giving extra assignments/seat works and group discussion as measures to remediate the errors but the effects of which on the students' achievement were not investigated.

Abstract Format






Accession Number


Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

320 leaves


Error analysis (Mathematics); Mathematical ability -- Testing; Algebra; Mathematical analysis; College freshmen

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