A Graph-Theoretic Approach to Improved Curriculum Structure and Assessment Placement

Abstract

INTRODUCTION Assurance of student learning is now required by many accrediting bodies as a key component of initial and reaccreditation requests (AACSB, 2010; SACS, 2010; MSC, 2009; HLC, 2009, Jones, 2007). The United States government has also embraced the practice as evidenced by the final version of the Spellings Report (Spellings, 2006). This report was commissioned by the U.S. Department of Education as a roadmap for the future of higher education in the United States. In this report, the Commission recommended the following: To meet the challenges of the 21st century, higher education must change from a system primarily based on reputation to one based on performance. We urge the creation of a robust culture of accountability and transparency throughout higher education (Spellings 2006, p. 21). This aspiration is shared by state governments and school districts across the nation (No Child Left Behind, 2009; Jones, 2007). Clearly, the mood of the tax-paying population and the representatives they elect is one of educational accountability and outcome-based results. In an attempt to comply with this mandate, colleges and universities are rushing to incorporate direct program assessment processes into their curricula. For some institutions this is a fairly minor task because outcome-based performance measures and assessment were already a part of the academic culture. For others, the required inclusion of assessment is a massive undertaking of program redesign, process creation, data collection, and corrective analysis. In both cases, decisions must be made involving curriculum redesign and assessment structure. For example, institutions must decide what goals and objectives are appropriate for programs, what topics should be covered to achieve objectives, where the topics should be taught, where objective assessment should be performed, what is the threshold of a successful assessment, etc. These questions must be answered and the solutions implemented quickly if the institution is to gain or maintain its accreditation. Unfortunately, program redesign and haste are incompatible concepts even under ideal conditions. Given the current state-of-the-art of program redesign and the paucity of research applicable to assessment inclusion, conditions are far from ideal for most institutions. The purpose of this research is to address this problem by answering some of the key questions involved in incorporating formal assessment into an existing curriculum. Specifically, this paper will deal with the following questions. * Where in the curriculum should introductory topic coverage be placed? * Where should reinforcement of assessment topics take place? * Where should primary and secondary objective assessment be located? * Where should changes identified by assessment feedback be implemented? These are fundamental structural questions that must be answered by the faculty and administrators tasked with assessment inclusion. Currently, there are no generally agreed upon methods to deal with these structural concerns. Without a systematic, repeatable methodology to deal with these issues, the resulting assessment scheme can be arbitrary, inconsistent, and ineffective. Given the public interest in educational accountability and outcome-based learning, this is not good enough. The approach developed and described by this paper will use graph-theoretic metrics and visualization to analyze an existing curriculum structure. The graph visualizations will show the courses, pre-requisite chains, program memberships, and course types of the curriculum. From these networks, basic graph theory metrics will be calculated and used to indicate the appropriate location for assessment components and modifications within the curriculum. While the locations determined are not proven to be optimal within the curriculum, they are based on a theoretical background that is systematic, defensible, and repeatable. …