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ERIC Number: ED518732
Record Type: Non-Journal
Publication Date: 2010
Pages: 201
Abstractor: As Provided
Reference Count: 0
ISBN: ISBN-978-1-1242-4806-6
A Cognitive Analysis of Developmental Mathematics Students' Errors and Misconceptions in Real Number Computations and Evaluating Algebraic Expressions
Titus, Freddie
ProQuest LLC, Ed.D. Dissertation, University of Houston
Fifty percent of college-bound students graduate from high school underprepared for mathematics at the post-secondary level. As a result, thirty-five percent of college students take developmental mathematics courses. What is even more shocking is the high failure rate (ranging from 35 to 42 percent) of students enrolled in developmental mathematics courses. Many studies in the literature have addressed this high failure rate from the prospective of environmental challenges, but very few explored the root of students' mathematical errors. This study sought to determine the error patterns of developmental mathematics students in real number computations. And, in addition, this study explores students' use the order of operations in simplifying arithmetic expressions and evaluating algebraic expressions. Lastly, this study explored the misconceptions that undergirded those errors and gave some possible reasons for those misconceptions. The study encompassed a mixed method design--both quantitative (item analysis) and qualitative (interview)--in order to answer the research questions. The results of the item analysis were used to determine which problems were missed due to procedural errors or misconceptions. The qualitative analysis included the examination of the students' paper and pencil tests and video interviews. The researcher (a) examined the solution to each test item on the students' tests, (b) discerned steps believed the students took to arrive at the solutions, and (c) coded the steps. A convenience sample of students enrolled in ten sections of Developmental Mathematics 0371 (DMTH 0371) taught by eight instructors during the spring semester of 2010 were used in this study. Data collection included: (a) students' test results, work, and scratch paper on the DMTH 0371 test; (b) video-taped interviews; (c) demographic information; and (d) the placement test and results used to place students in DMTH 0371, which were gathered from the Student Information System (SIS) and Banner. Two forms of the assessment instruments were used in this study: a selected-response (multiple-choice item format) test and constructed-response (open-ended response format) test. The results of this study identified four types of error patterns made by developmental mathematic students. Most of the students demonstrated a fragmented understanding of signed-number arithmetic (negative numbers), sign errors, fractions, distributive property (parentheses), and exponential errors in simplifying both arithmetic and algebraic expressions. The students also misinterpreted operations and executed buggy algorithms both arithmetically and algebraically. Thus, across all of the students' errors made in different problems, a weak understanding of negative numbers seems to be the fundamental sources of their different errors. These students simply ignored the presence of the "negative sign" in order to get an answer (i.e., these students try to "repair" a new situation). These findings typically suggest that any remediation program should go beyond students' procedural errors to the aspect of "conceptions." The information provided by this study could be of value to the instructional practices community colleges and universities developmental mathematics programs. However, this study should be replicated and extended to include a larger population to determine if the errors and misconceptions can be generalized to all developmental mathematics students with similar characteristics. Similar studies should be conducted to either validate or argue the results obtained in this study. Research should be done to determine appropriate remediation instructional strategies for the errors presented in this study. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page:]
ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site:
Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A