A Network Theory Approach to Curriculum Design

Abstract

In this paper we hypothesize that education, especially at the scale of curriculum, should be treated as a complex system composed of different ideas and concepts which are inherently connected. Therefore, the task of a good teacher lies in elucidating these connections and helping students make their own connections. Such a pedagogy allows students to personalize learning and strive to be ‘creative’ and make meaning out of old ideas. The novel contribution of this work lies in the mathematical approach we undertake to verify our hypothesis. We take the example of a precalculus course curriculum to make our case. We treat textbooks as exemplars of a specific pedagogy and map several texts into networks of isolated (nodes) and interconnected concepts (edges) thereby permitting computations of metrics which have much relevance to the education theorists, teachers and all others involved in the field of education. We contend that network metrics such as average path length, clustering coefficient and degree distribution provide valuable insights to teachers and students about the kind of pedagogy which encourages good teaching and learning.

Investigating Pedagogies in Undergraduate Precalculus and their Relationships to Students’ Attitudes Towards Mathematics and Perseverance in Problem-Solving

“…The Precalculus: Pathways to Calculus curriculum (Carlson et al, 2021) was developed and refined based on research on the understandings and reasoning abilities students need to succeed in calculus (Carlson et al, 2002;Carlson et al, 2010). Studies have shown that Pathways can support students in making connections between precalculus concepts (O'Meara & Vaidya, 2021) and have linked the Pathways curriculum to students' improved covariational reasoning, conceptual learning of precalculus concepts, and subsequent success in calculus (Carlson et al, 2003;McNicholl et al, 2021;Moore & Carlson, 2012). Pathways was designed to assist precalculus instructors in surfacing and advancing student thinking through rich problem-solving experiences that help students to make mathematical connections across concepts, functional representations, and to real-world contexts (Carlson et al, 2021).…”