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theses

The majority of American college students pursue a degree outside one of the STEM fields (US News & World Report, 2015), yet these same students must still complete a minimum level of coursework in mathematics for graduation. The intent of liberal arts math courses is to help students who are majoring in one of the liberal arts successfully meet these mathematics proficiency requirements. Colleges offer liberal arts math courses to students who are unlikely to need specialized math skills, instead aiming to improve functional mathematical literacy, provide a sample of practical applications and problem-solving techniques, and to develop an overall appreciation of mathematics. Liberal arts mathematics, and the subset of quantitative literacy courses, are presently characterized by a diversity of curricular offerings with an absence of consistently defined core concepts (Dingman & Madison, 2010). Furthermore, many of these programs fail to support the overarching mission of a liberal arts education – to literally liberate the mind and prepare individuals for fully-informed and active citizenship, across multiple disciplines (King, Brown, Lindsay, & VanHecke, 2007; Stanton, 1987). The first part of this study explores three prototypical textbooks for liberal arts mathematics. The textbooks are examined for their commonalities, strengths and weaknesses, and the extent to which they facilitate the objectives of a liberal arts education. The second part of this study summarizes a progressive new curriculum for liberal arts mathematics, founded upon the notion of threshold concepts (Meyer & Land, 2003), and developed in the context of social justice. The practice of deductive reasoning, while attending to matters of probability and personal preference, collectively outline a new theory of subjective rationalism in this paper. The third part of this study presents a retrospective analysis on the creation and evolution of the new curriculum. This research explored the idea that the optimal set of math skills is neither computational nor algorithmic, rather, it lies within the realm of mathematical reasoning – the essence of which is founded upon key principles in logic and probability. The identification and cultivation of threshold concepts in mathematical reasoning offers to bring clarity and consistency into the field of liberal arts mathematics. This research is significant because a liberal arts math program may be a student’s only postsecondary math course and the last opportunity to develop a useful set of math tools. Research data in this retrospective analysis spans five years across secondary and postsecondary implementations of the evolving curriculum; data include multiple iterations of the curriculum and the research practitioner’s field notes reflecting on instructional interventions and classroom discourse, as well as reflections on students’ performances with written assessments.

ETD_9627

Ph.D.

Includes bibliographical references

doi:10.7282/t3-43qy-wj13

ETD doctoral

The author owns the copyright to this work.