Date of Award
Spring 6-13-2025
Document Type
Dissertation
Degree Name
Ph.D. in Quantitative Research Methods
Organizational Unit
Morgridge College of Education, Research Methods and Information Science, Research Methods and Statistics
First Advisor
P. Bruce Uhrmacher
Second Advisor
Duan Zhang
Third Advisor
Brette Garner
Fourth Advisor
Bin Ramke
Copyright Statement / License for Reuse
All Rights Reserved.
Keywords
Collaborative learning, Community building, Mathematical discourse, Mathematical thinking, Metacognitive reflection, Small learning community, Auto-criticism
Abstract
The rise of artificial intelligence and the decline in students’ mathematical proficiency signals the need for innovative pedagogical strategies in mathematics education. The search has intensified for instructional strategies focusing on creating a learning environment promoting deep engagement in mathematical thinking and reasoning. Emphasizing personalized learning, such as small learning community settings, promises to address the challenges mathematics education is facing by focusing on mathematical practices that promote visible engagement and mathematical thinking. This study aimed to explore the nature of small learning community in mathematical teaching practices, fostering high school students’ deep engagement in mathematical thinking. A qualitative method of auto-criticism was employed using metacognitive reflection practices of past and present lesson planning processes and teaching practices of a high school mathematics teacher. Data analysis was conducted using annotation, comparative analysis, and critical reflection. The findings revealed that in a small learning community, the teacher provides the conditions for students to immerse in genuine mathematical discourse and deep engagement in mathematical thinking by promoting an environment of collaboration and transforming the teacher's role into a facilitator of learning.
Copyright Date
6-2025
Publication Statement
Copyright is held by the author. User is responsible for all copyright compliance.
Rights Holder
Analyn A. Alquitran
Provenance
Received from ProQuest
File Format
application/pdf
Language
English (eng)
Extent
133 pgs
File Size
1.1 MB
Recommended Citation
Alquitran, Analyn A., "An Auto-Criticism of Mathematics Beyond the Equations" (2025). Electronic Theses and Dissertations. 2546.
https://digitalcommons.du.edu/etd/2546
Included in
Curriculum and Instruction Commons, Educational Assessment, Evaluation, and Research Commons, Educational Methods Commons, Science and Mathematics Education Commons