Addressing Misconceptions in Geometry through Written Error Analyses

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Autor/in	Kembitzky, Kimberle A.
Titel	Addressing Misconceptions in Geometry through Written Error Analyses
Quelle	(2009), (330 Seiten) PDF als Volltext Verfügbarkeit Ph.D. Dissertation, The Ohio State University
Sprache	englisch
Dokumenttyp	gedruckt; online; Monographie
ISBN	978-1-1096-0332-3
Schlagwörter	Hochschulschrift; Dissertation; Mathematics Achievement; Geometric Concepts; Geometry; Misconceptions; Teaching Methods; Mathematics Instruction; Writing (Composition); Reflection; Error Correction; High School Students; Secondary School Mathematics; Comparative Analysis; Statistical Analysis; Qualitative Research; Evaluation Methods; Student Evaluation; Spatial Ability; Comprehension; Metacognition; Cognitive Style + Suchen Sie Ihr Suchwort? Thesis; Dissertations; Academic thesis; Mathmatics sikills; Mathmatics achievement; Mathematical ability; Mathematische Kompetenz; Elementare Geometrie; Geometrie; Missverständnis; Teaching method; Lehrmethode; Unterrichtsmethode; Mathematics lessons; Mathematikunterricht; Schreibübung; Korrektur; High school; High schools; Student; Students; Oberschule; Schüler; Schülerin; Studentin; Statistische Analyse; Qualitative Forschung; Schulnote; Studentische Bewertung; Räumliches Vorstellungsvermögen; Verstehen; Verständnis; Meta cognitive ability; Meta-cognition; Metakognitive Fähigkeit; Metakognition; Cognitive styles; Kognitiver Stil
Abstract	This study examined the improvement of students' comprehension of geometric concepts through analytical writing about their own misconceptions using a reflective tool called an ERNIe (acronym for ERror aNalyIsis). The purpose of this study was to determine whether the ERNIe process could be used to correct geometric misconceptions, as well as how the accuracy at which the students were able to analyze their misconceptions related to their ability to correct their misconceptions over the course of an entire academic year. Other relationships studied were the influence that student levels of mathematical achievement and spatial ability had on the type of misconception, the accuracy at which the misconceptions were analyzed, and whether the misconceptions were repeated on subsequent assessments. The participants in this study were geometry students from a large suburban high school. The treatment group consisted of three sections of geometry classes (n = 61) taught by the researcher and the comparison group consisted of eight sections of geometry classes (n=214) taught by five geometry teachers. The treatment group used the ERNIe process on every quiz, while the students in the comparison group used the ERNIe process on unit tests only or the occasional quiz. Both qualitative and quantitative methodologies were used in this study. The misconceptions of those participants in the treatment group were identified as they occurred on an initial assessment and were traced until the second semester exam, to determine if they were repeated. The treatment of the ERNIe process was implemented on each quiz for each student in the treatment group. They were analyzed and coded for accuracy of analysis, as well as correctness of their resubmitted solutions. The purpose of this coding process was to identify which students accurately analyzed their misconceptions and if they were able to correct those misconceptions over the rest of the academic year. Also, student beliefs and attitudes regarding the process of analyzing their own errors through writing were qualitatively analyzed and themes were identified. The results of this study were that students who accurately analyzed their own misconceptions through writing were significantly less likely to repeat them. The factor that most strongly influenced the level of accuracy at which a student was able to analyze a misconception was prior and present mathematical achievement. However, mathematics achievement level alone did not ensure that the misconception was corrected. Spatial ability level alone did not influence the accuracy at which the error was analyzed. However, the higher the spatial ability level the less likely the misconception would be repeated. Other findings indicate that the use of the ERNIe process on a regular basis was more effective than using it on unit tests or randomly on quizzes throughout the year. Participants indicated that using ERNIeS (1) improved their comprehension of the concept; (2) enhanced their metacognitive abilities concerning their errors; (3) were complementary to different learning styles; (4) prevented the repetition of the misconception; and (5) were an excellent study tool. [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: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.] (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10