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ERIC Number: ED552805
Record Type: Non-Journal
Publication Date: 2013
Pages: 122
Abstractor: As Provided
Reference Count: N/A
ISBN: 978-1-2679-9846-0
Cognitive Hierarchies of Mathematics Learning: An Analysis of the ST Math Curriculum
Kibrick, Melissa Courtney
ProQuest LLC, Ph.D. Dissertation, University of California, Irvine
This dissertation tests a dynamic assessment-based cognitive hierarchy model and attempts to identify mathematical concepts that predict student learning potential on more advanced mathematical concepts using the units from ST Math, a self-paced curriculum, for third, fourth, and fifth grade students. The quantitative analyses compared a traditional model for predicting student performance with the dynamic assessment model, explored how learning ability in previous modules predicts learning potential in a target module, and examined the how the predictive patterns of students varied based on proficiency in English and Mathematics. The qualitative analysis created visualizations of the predictive models and described the pedagogy and content of modules identifying possible explanations for the predictive patterns. A traditional measure of achievement, the previous year's CST Math, did not add meaningful explanation of the variance beyond the dynamic measure of achievement, measures of student learning ability on previous ST Math modules. These traditional assessments measure student's knowledge gained from previous mathematics courses. This disadvantages students who have the ability to learn but come from impoverished learning environments. This dynamic measure and the comparison of learning across modules allows for more finely tuned predictions of student learning potential. Robust predictive relationships appeared between concepts that repeated every year with similar pedagogical content and similar mathematical concepts. A visualization of these robust relationships showed a cognitive hierarchy of mathematical concepts for student's ability to learn. Additionally, this analysis revealed inverse relationships where struggling on a given mathematics concept led to quicker learning of a future mathematics concept. This could be an instance of desirable difficulty, where students who struggle through the material develop a more advanced mastery of the material than students who easily solve the earlier levels. The interaction models showed some modules where English Learners and students Below Proficient in Mathematics outperformed their proficient counterparts. Either the ST Math curriculum taps into different abilities than the CST Math and language placement, or traditional measurement fails to accurately measure the potential of students to learn. Additionally, the below proficient students had fewer robust connections making it difficult to predict their potential to learn future mathematical concepts. [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: Elementary Education; Grade 3; Primary Education; Early Childhood Education; Grade 4; Intermediate Grades; Grade 5; Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A