Date of Award


Document Type


Degree Name

Master of Science (MS)


College of Science and Mathematics



Thesis Sponsor/Dissertation Chair/Project Chair

Ashuwin Vaidya

Committee Member

Eileen Fernandez

Committee Member

Mika Munakata


The core goal of this thesis project is to formalize the complex system that exists naturally in a formal classroom environment. The three factors that are considered in this study are the roles of the student, the roles of the teacher, and the respective environments from which these members arise and how these act as determinants of curriculum development and design. At the curricular scale, educational practices should be treated as a complex system composed of various inherently connected concepts and exchanges of ideas and ways of knowing. This synthesis of previous work and ongoing research efforts employs a network theory mediated analysis to investigate the affordances of curriculum and, in particular, its alignment with student learning processes.

Via the utilization of various lenses of network theory, connected curriculum design, and modern learning curve theory, this body of research generates the postulate that education is inherently a complex system at various scales and stages of the learning process. Therefore, the task of a proper educator lies in elucidating these connections and helping students make their own connections. A network theoretic perspective of the precalculus curriculum proves to be helpful in identifying and motivating key features of the subject as they appear in course texts. Of these, hubs and time-series developments of relevant computed metrics have been particularly useful in mapping the alignment between the preset goals of the precalculus course, as identified in previous literature and execution of taxonomic principles.

At the same time, this analysis has also been valuable in identifying the trajectory of the textbook curricula to adequately prepare precalculus students for success in calculus and beyond. Highly successful texts retain inherent commonalities, including the display of a power law with respect to frequency distribution of connected topics (􁷍 = 0.05). The most well-connected topics (hubs) are regarded as necessary markers of classroom discourse, and the extent to which they are considered in taxonomical goals is measured with respect to the empirical distributions of both the intended curriculum and enacted curriculum.

Moreover, the implications of this work seek to assist in the optimization of the complex system synthesizing various feedback-based designs within educator roles, student response, and the interactions between the two as they pertain to various stages of the curriculum development process. This allows both students and educators alike to personalize learning through standardized exhaustive procedure and provide an equity-based environment conducive towards ‘meaning making’ or assigning new meaning from the foundation of old ideas. The results of this study aim to not only provide a deeper understanding of how intended and enacted curriculums interact with each other, but also considers to what extent the components of an andragogical system can be refined via the magnitude of their presence in both course materials and feedback provided directly by active participants in the learning environment.

File Format


Included in

Mathematics Commons