Accuracy Indices for Measuring the Alignment of Student Metacognition in Undergraduate Mathematics Education
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| Title: | Accuracy Indices for Measuring the Alignment of Student Metacognition in Undergraduate Mathematics Education |
|---|---|
| Language: | English |
| Authors: | Preheim, Michael |
| Source: | ProQuest LLC. 2023Ph.D. Dissertation, North Dakota State University. |
| Availability: | ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site: http://www.proquest.com/en-US/products/dissertations/individuals.shtml |
| Peer Reviewed: | N |
| Page Count: | 124 |
| Publication Date: | 2023 |
| Intended Audience: | Teachers; Researchers |
| Document Type: | Dissertations/Theses - Doctoral Dissertations |
| Education Level: | Higher Education Postsecondary Education |
| Descriptors: | Undergraduate Students, Mathematics Education, College Mathematics, Metacognition, Evaluation Methods, Mathematical Logic, Validity, Algebra, Confidence Testing, Student Behavior, College Students |
| ISBN: | 979-83-7961-874-2 |
| Abstract: | Knowledge assessments in undergraduate mathematics education commonly evaluate response correctness to determine learner proficiency. However, simultaneous evaluation of learner metacognition more accurately assesses the multiple dimensions of knowledge and has been shown to increase assessment validity and reliability. Research into multidimensional methods has primarily evaluated the alignment of correctness with learner's certainty that their provided response is correct. Learner confidence before assessment, however, has not been thoroughly investigated alone or in conjunction with certainty for use in performance evaluation, especially at the undergraduate level. Student confidence provides new and valuable information to education researchers, educators, and students. Effective proof comprehension and proof-writing are necessary for student success in undergraduate mathematics. Determining the validity of deductive arguments is particularly critical for proof-writing. Research suggests student difficulty with this task is related to proficiency in proof comprehension and that training in specific metacognitive skills can improve students' proof comprehension abilities. The objective of this project is to present and investigate the efficacy of an assessment method which simultaneously assesses pre-assessment confidence and post-response certainty alongside response correctness in undergraduate mathematics (hereinafter referred to as the 3C method). These three factors were assessed via routine examinations in an undergraduate linear algebra course. Accuracy indices were developed to measure the alignment of confidence and certainty with respect to correctness. Analyses of the 3C method and these accuracy indices presents insights that may inform teaching methods, improve examination items and structure, and identify concerning student behaviors early for corrective intervention. The presented methods can be implemented into routine course design by researchers and educators to collect confidence and certainty alongside correctness. Proof comprehension assessments adapted to utilize this 3C method were administered to students at the beginning and end of a transition-to-proof course. The accuracy indices were used to investigate student metacognitive behaviors at local and holistic aspects of a proof by induction. Among items addressing holistic aspects of proof comprehension, students in the lower performance quartile of their class exhibited decreasing accuracy of confidence and certainty over time and outlying metacognitive behaviors illuminated additional considerations for application of metacognition in proof comprehension research. [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.] |
| Abstractor: | As Provided |
| Entry Date: | 2023 |
| Access URL: | https://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:30419072 |
| Accession Number: | ED635373 |
| Database: | ERIC |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: eric DbLabel: ERIC An: ED635373 AccessLevel: 3 PubType: Dissertation/ Thesis PubTypeId: dissertation PreciseRelevancyScore: 0 |
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However, simultaneous evaluation of learner metacognition more accurately assesses the multiple dimensions of knowledge and has been shown to increase assessment validity and reliability. Research into multidimensional methods has primarily evaluated the alignment of correctness with learner's certainty that their provided response is correct. Learner confidence before assessment, however, has not been thoroughly investigated alone or in conjunction with certainty for use in performance evaluation, especially at the undergraduate level. Student confidence provides new and valuable information to education researchers, educators, and students. Effective proof comprehension and proof-writing are necessary for student success in undergraduate mathematics. Determining the validity of deductive arguments is particularly critical for proof-writing. Research suggests student difficulty with this task is related to proficiency in proof comprehension and that training in specific metacognitive skills can improve students' proof comprehension abilities. The objective of this project is to present and investigate the efficacy of an assessment method which simultaneously assesses pre-assessment confidence and post-response certainty alongside response correctness in undergraduate mathematics (hereinafter referred to as the 3C method). These three factors were assessed via routine examinations in an undergraduate linear algebra course. Accuracy indices were developed to measure the alignment of confidence and certainty with respect to correctness. Analyses of the 3C method and these accuracy indices presents insights that may inform teaching methods, improve examination items and structure, and identify concerning student behaviors early for corrective intervention. The presented methods can be implemented into routine course design by researchers and educators to collect confidence and certainty alongside correctness. Proof comprehension assessments adapted to utilize this 3C method were administered to students at the beginning and end of a transition-to-proof course. The accuracy indices were used to investigate student metacognitive behaviors at local and holistic aspects of a proof by induction. Among items addressing holistic aspects of proof comprehension, students in the lower performance quartile of their class exhibited decreasing accuracy of confidence and certainty over time and outlying metacognitive behaviors illuminated additional considerations for application of metacognition in proof comprehension research. [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.] – Name: AbstractInfo Label: Abstractor Group: Ab Data: As Provided – Name: DateEntry Label: Entry Date Group: Date Data: 2023 – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="https://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:30419072" linkWindow="_blank">http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:30419072</link> – Name: AN Label: Accession Number Group: ID Data: ED635373 |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=ED635373 |
| RecordInfo | BibRecord: BibEntity: Languages: – Text: English PhysicalDescription: Pagination: PageCount: 124 Subjects: – SubjectFull: Undergraduate Students Type: general – SubjectFull: Mathematics Education Type: general – SubjectFull: College Mathematics Type: general – SubjectFull: Metacognition Type: general – SubjectFull: Evaluation Methods Type: general – SubjectFull: Mathematical Logic Type: general – SubjectFull: Validity Type: general – SubjectFull: Algebra Type: general – SubjectFull: Confidence Testing Type: general – SubjectFull: Student Behavior Type: general – SubjectFull: College Students Type: general Titles: – TitleFull: Accuracy Indices for Measuring the Alignment of Student Metacognition in Undergraduate Mathematics Education Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Preheim, Michael IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2023 Identifiers: – Type: isbn-print Value: 979-83-7961-874-2 Titles: – TitleFull: ProQuest LLC Type: main |
| ResultId | 1 |
