Western Kentucky University TopSCHOLAR® Dissertations Graduate School Fall 2017 The Evolution of College Algebra: Competencies and Themes of a Quantitative Reasoning Course at the University Of Kentucky Scott Taylor Western Kentucky University, scott.edu Follow this and additional works at: https://digitalcommons.edu/diss Part of the Higher Education Commons, History of Science, Technology, and Medicine Commons, Other History Commons, and the Science and Mathematics Education Commons Recommended Citation Taylor, Scott, "The Evolution of College Algebra: Competencies and Themes of a Quantitative Reasoning Course at the University Of Kentucky" (2017).edu/diss/139 This Dissertation is brought to you for free and open access by TopSCHOLAR®. It has been accepted for inclusion in Dissertations by an authorized administrator of TopSCHOLAR®. For more information, please contact topscholar@wku. THE EVOLUTION OF COLLEGE ALGEBRA: COMPETENCIES AND THEMES OF A QUANTITATIVE REASONING COURSE AT THE UNIVERSITY OF KENTUCKY A Dissertation Presented to The Faculty of the Educational Leadership Doctoral Program Western Kentucky University Bowling Green, Kentucky In Partial Fulfillment Of the Requirements for the Degree Doctor of Education By Scott Taylor December 2017 1 CONTENTS LIST OF FIGURES.
vi LIST OF TABLES. vii CHAPTER I: STATEMENT OF THE PROBLEM .5 College Algebra as a Quantitative Reasoning Course .10 UK and KCTCS. 13 Purpose and Central Research Questions .14 Empirical Research Questions. 16 CHAPTER II: REVIEW OF LITERATURE .19 College Algebra in Kentucky.
23 Instrument variation and the myth of college readiness. 24 History of Educational Reform .31 Mathematics and Early American Colleges .31 The Mathematical Association of America (MAA) .33 MAA and QR. 42 iii Quantitative Reasoning Requirement .44 Current administrative policies. 44 Institutional missions & philosophies of QR.
46 Government, Politics, and War .49 WWII/GI Bill.49 The Space Race—an essential STEM race.50 National education reform.52 Effects of Economics and Funding.53 Chapter II summary. 55 CHAPTER III: METHODOLOGY .57 Role of the Researcher. 59 Denial of the one-to-one function. 60 Rejecting CA as the default QR.
62 Sources of Data. 69 iv Overview of Instrumentation .69 Procedures/Data Collection .70 Delimitations and Limitations of this Study .72 Chapter III summary. 74 CHAPTER IV: FINDINGS .76 Common Topics—Textbooks Once Used in CA .77 Common topics—functions. 77 Common topics—polynomial functions.
87 Common topics—rational functions. 94 Common topics—exponential functions. 98 Common topics—logarithmic functions. 104 Common Topics—Relating RQ1 with Textbooks.111 Common Topics—Course Descriptions from Catalogs .112 Common topics—Relating RQ1 with Course Descriptions .121 Summary of RQ1—transition to RQ2.
123 Internal Forces—Documents from the UK Archives and the Math Website .123 Internal forces—examinations. 127 Internal forces—syllabi. 128 Internal Forces—Relating RQ2 with archival and website documents .131 Summary of RQ2—transition to RQ3. 131 QR Evolution—Documents from the Self-Study .132 v QR Evolution—Relating RQ3 with Self-Study Documents.136 Chapter IV summary.137 Summaries on RQ1 .137 Summaries on RQ2 .141 Summaries on RQ3 .143 Significance to Educational Leadership .145 Performance-based funding.
145 Pathways and meta-majors. 146 Liberal arts philosophy and academic integrity. 147 Suggestions for Further Research .151 APPENDIX A: Data References .181 APPENDIX C: Catalog Notes .200 APPENDIX D: First-Round Coding on Textbooks.227 APPENDIX F: Sample HCC Syllabus .229 vi LIST OF FIGURES Figure 1. Excerpt from Maura Corley’s CA fall syllabus.
Definition of a function from ABN. Evaluating functions as Example 1 from ABN. Revised definition of a function from ABN. Bold bullets were added in the third edition of ABN in Example 1.
Flow of material from definitions to Example 1 to Example 2. Example 1, part a, from the first edition of the MLS text. Definition of a polynomial function from MLS. Definition of a rational function from the ABN textbook.
Definition of a rational function from MLS. Definition of an exponential function from ABN. The graph of the same exponential function with different domains. A four-part theorem regarding properties of exponential expressions.
The MLS definition of an exponential function. Definition of a logarithm from the first edition of the ABN text. Properties of logarithms from the first edition of the ABN text. The definition of a logarithm from the first edition of the MLS text.
The definition of a logarithm from the third edition of the MLS text. The definition of a logarithm from the fourth edition of the MLS text. Five properties of logarithms as given in the first edition of ABN. Screenshot of the UK catalog from 1865.
Screenshot of the UK catalog from 1892. The first mention of college algebra in the 1908-1909 catalog. The return of specific topics in CA from the 1913-1914 catalog. The removal of functions in the 1918-1919 catalog.
The 1921-1922 catalog returned to a limited information format. The 1931-1932 catalog returned to a limited information format. The 1940-1941 catalog included specific topics. The 1950-1951 catalog excluded specific topics.
The wording from the 1976-1977 catalog was mostly unchanged. Another professor White in the 1908 edition of The Kentuckian. The 1909 edition of The Kentuckian described J. The 1910 The Kentuckian described CA.
125 viii LIST OF TABLES Table 1. Topics covered in CA identified by era and starting year ……………122 ix THE EVOLUTION OF COLLEGE ALGEBRA: COMPETENCIES AND THEMES OF A QUANTITATIVE REASONING COURSE AT THE UNIVERSITY OF KENTUCKY Scott Taylor December 2017 233 Pages Directed by: Janet Tassell, Kristin Wilson, and Kimberlee Everson Educational Administration, Research, and Leadership Western Kentucky University For many institutions, especially community colleges, college algebra has been the default mathematics or quantitative reasoning requirement. However, the topics that have been taught in college algebra, teaching methods, and the goals of a quantitative reasoning requirement have changed and vary over time and among different institutions. Because of history, policy, and political influences, this study sought to explore commonalities and disparities of college algebra as it has evolved through the University of Kentucky.
The three central research questions were What have been the common topics or themes of the competencies and topics covered in CA over the years at UK? (RQ1), What internal forces have led to topic coverage or attribute changes in CA? (RQ2), and How has QR evolved at UK? (RQ3). Through a review of literature, common topics were discovered among Kentucky college algebra course descriptions. These commonalities were used as a foundation by which, through the qualitative lens of historical methods, the history of college algebra was measured and studied. The origins and motivations for these changes were explored using multiple sources of data.
x CHAPTER I: STATEMENT OF THE PROBLEM Introduction Within a general education curriculum, most institutions require a mathematics or statistics course for the purpose of meeting a quantitative reasoning (QR) requirement. The purpose of a general education curriculum in Kentucky has traditionally grown from a liberal arts education philosophy that insisted all students have a broad, common knowledge base in order to graduate not only with intense knowledge of their major discipline, but also with breadth of knowledge from many areas (Eastern Kentucky University, n.; Kentucky State University, 2014a; Northern Kentucky University, n.a; Southern Association of Colleges and Schools [SACSCOC], 2012; University of Kentucky, 2016a). QR has historically been one of those areas. Any approved QR course, therefore, could serve myriad degree programs unless a particular major prescribes specific QR or mathematics coursework (Latzer, 2004).
For example, a degree program in chemistry may mandate two semesters of calculus, for which College Algebra (CA) would typically be the prerequisite. If all three courses in that sequence met institutional QR requirements, no chemistry major had to worry about failing to meet the general education requirement of QR. However, history majors may not have an explicit QR course outlined in their program. Therefore, in order to meet the QR requirement of the core curriculum, they may have chosen a course they wanted in order to meet this requirement, assuming the institution offered a variety that satisfied the QR requirement.
In many instances, the QR course of choice appears to have been, by default, a mathematics or statistics course, especially at community colleges. Despite the range of potential courses—mathematics 1 or non-mathematics—that could satisfy QR requirements, CA has been the default mathematics requirement in the thinking of many institutional policy makers (Vandal, 2015). This study investigates the content that has been covered in CA at the University of Kentucky (UK) as the course has evolved over the years, examining reasons for content change. This qualitative research focuses on historical events at the university, state, and the national levels that have played a role in the evolution of mathematics curriculum at UK.
By using historical methods (document analysis), changes to the course competencies and course description are highlighted for the purposes of determining the reason the current incarnation of CA covers specific topics while excluding others. The discernments gleaned from this project will be useful in establishing (a) what CA is, (b) why it contains the specific material taught, and (c) historical context that will challenge why CA seems to be the default quantitative reasoning class of choice for many institutions, especially community colleges. College Algebra Every year over a million college students enroll in CA, a proverbial cash cow of the department and institution, yet close to half fail the course (Gordon, 2008). Further, as with most college classes, material covered in CA varies from institution to institution.
While some topics may be common to many colleges, there are invariably differences in content and focus, as no national consensus or uniformity of curriculum exists among colleges and universities for any general education curriculum; in fact, the SACSCOC allows for variation (SACSCOC, 2012; Toombs, Amey, & Chen, 1991). While this in itself may not necessarily constitute a problem, any expectations of consistency would be 2 an issue. As CA typically serves as a prerequisite for other mathematics coursework such as calculus (Vandal, 2015), taking CA at one institution while taking calculus at another may represent a conundrum under the fallacy of consistency. This research reveals the deficit of uniformity in definition as to that which has constituted college-level algebra.
In addition, within any individual institution, there will be a course description outlining the topics that an aforementioned institutional class covers, although depth of topic emphasis is at the discretion of the instructor. Many times instructors pick their books, so different sections of the same course may manifest themselves in radically different fashions. One instructor may mention a particular topic in passing, while another spends several weeks working with it. As such, there has been no consensus as to what CA should entail across the nation or even within a single college.
CA textbooks may also play a role in the selection of topic coverage. Instructors, especially adjuncts, whose numbers are starting to increase with the reduction of full-time college instructors (Jolley, Cross, & Bryant, 2014), may follow a textbook’s organizational structure more so than their own particular thoughts (or that of the institution) about what should be emphasized. Within any given institution, common competencies or course descriptions would allow for continuity among different sections and instructors. Western Kentucky University (WKU) has regularly offered trigonometry; in fact, students could choose from 13 sections taught by eight different instructors in the fall 2016 semester, all of which shared the similar course description asserting the course would include “unit circle, trigonometric functions and graphs, trigonometric identities and equations, right triangle trigonometry, laws of sines and cosines, DeMoivre’s Theorem, vectors and applications of trigonometry” (WKU, 2016, p.
While the course description 3 outlined specific topics to be covered, the length of time each instructor spent on each topic may depend upon instructor discretion. The books used by individual section also varied by instructor—per WKU’s online bookstore, different sections of the same course required different textbooks (WKU Store, 2017). Additionally, course descriptions have never precluded topics; they have simply stated what will allegedly assuredly be covered. Professors have enjoyed the academic freedom of electing the material they wish to supplement to their courses as it benefits their field (Post, 2008; Stone, 2006).