Alpert dissertation 2013

FACTORS SUPPORTING COLLEGE MATHEMATICS SUCCESS: ORIENTATION, VOICE, AND TECHNOLOGICAL PEDAGOGICAL CONTENT KNOWLEDGE A Dissertation by ANNA PAT LUCAS ALPERT Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Chair of Committee, Mary M. Capraro Committee Members, Robert M. Gonzalez y Gonzalez Head of Department, Yeping Li August 2013 Major Subject: Curriculum and Instruction Copyright 2013 Anna Pat Lucas Alpert ABSTRACT The purpose of this study was to examine factors supporting college mathematics success. First, effect of a brief high school orientation to mathematical technologies used for college placement testing was examined.

Secondly, the voice of participants in this orientation was heard. Finally, bootstrapped orientation data were presented to teachers and instructors of introductory statistics courses as a scaffold to their technological pedagogical content knowledge (TPCK) as these teachers and instructors strive to actively engage students to achieve college mathematics success. Many entering college students are placed into developmental mathematics classes based on scores from college placement assessments that allow extremely limited use of calculating technology and have various time constraints. Students in a rural central Texas 3A high school that were enrolled in Algebra II course were given pre- and post- tests in Arithmetic and Algebra.

Each 20-minute test contained 15 mathematical content questions and one qualitative question. The post-test was given approximately a week after the pre- test. During the week, students were provided time to explore review material using only pencil and paper for the arithmetic review, and a four-function calculator on the algebra review questions. Effects of the orientation were analyzed using mean scores, confidence intervals, effect size, and GLM for whole-group and sub-groups.

A paired samples t-test was calculated. These effects were discussed. A case study involving participants of the orientation was conducted. Twelve participants were interviewed after each had entered college.

Five themes emerged from these interviews: (1) Knowledge of College Mathematics, (2) Technology and Mathematics, ii (3) Mathematics Tests/Assessments, (4) Teaching and Learning Mathematics, and (5) Mathematical Experiences, Hopes and Dreams. Each theme is discussed. Using Microsoft Excel, bootstrapping is presented to instructors of first year introductory statistics courses in support of student success as instructors’ technological pedagogical content knowledge is developed. A course project demonstrating and developing application of computational technology by bootstrapping confidence intervals at the 95 % level using Microsoft Excel is presented.

Data from the orientation were further analyzed in the bootstrapping project. Confidence intervals were empirically calculated from bootstrapped resamples of the mean. The number of resamples used was 250 at each of three levels: Over-sampling, at-sampling, and under-sampling. Graphs of bootstrapped confidence intervals, using the Rule of Eye 4, showed statistically significant differences between pre-test and post-test scores for all pairs of data sets.

iii DEDICATIONS ~~~~~~~ To my Lord and Saviour, Jesus Christ. Who gives me all good things and the strength to have met requirements for this degree. To my loving husband, Ken. Whose love, encouragement, support, and late-night driving made this journey a success.

To my beloved children, David, Benjie, Seth, Samantha, and Hannah. Who encouraged me to become an Aggie “Dr. To my dear grandchildren, Trevor, Emily, Cason, Olivia, Abigail, Breck, and Sarah. Who provided incentive to enjoy my life while pursuing this degree and battling BC.

To my strong parents, Benny & Nell Lucas. Whose examples of educational service have inspired me to also serve educationally. To my encouraging Delta Kappa Gamma International Sorority sisters. Whose scholarship dollars, love and encouragement helped this dream to become reality.

To my dear friend and colleague, Dr. Who encouraged and inspired me with words and food. iv ACKNOWLEDGEMENTS A plethora of praise and thanks goes to my awesome committee, who guided my research and writing, each making unique contributions to my mathematical and research education. Thank you Dr.

Mary Margaret Capraro for encouraging me to keep moving in a forward direction, even if only a bit at a time, providing me with benchmark deadlines and proofreading my writing for content integrity and APA compliance. My special appreciation extends to Dr. Capraro for never accepting any excuse whatsoever, always holding me to the highest standard of excellence, and providing my husband words of perseverance and encouragement. Davis, thank you for your illumination of a world of new and wonderful educational technologies along with the concept of TPCK.

For illustrating qualitative research to be real and about real people, thank you Dr. Heartfelt appreciation goes to Dr. Richard Sanchez and the board of trustees of Navarro College for their belief in, and support of, NC faculty. Appreciation and gratitude to Natasha Brown for the encouragement and support you have kindly given during this past very difficult year.

Last, but not least, thank you, Dr. Gerren, for paving the way, and Chris Murphy for driving that pavement during all sorts of weather to get me to class on time! v TABLE OF CONTENTS Page ABSTRACT ……………………………………………………………. ii ii DEDICATIONS……………………………………………………. v TABLE OF CONTENTS ………………………………………………….

vi LIST OF TABLES ………………………………………………………. viii LIST OF FIGURES ……………………………………………………………….…… ix CHAPTER I INTRODUCTION ……………………………………………. 1 Student Success Quest …………………………………………………….…… 10 CHAPTER II SUPPORTING COLLEGE MATHEMATICS SUCCESS: HIGH SCHOOL ORIENTATION TO COLLEGE PLACEMENT ASSESSMENT ……………………………. 29 Conclusions ……………………………………………………………………… 31 CHAPTER III SUCCESS IN COLLEGE MATHEAMTICS?! STUDENT VOICE IDENTIFIES SUPPORTING FACTORS …………………………….

59 Discussion and Recommendations ……………………………………………. 63 vi Page CHAPTER IV TPCK FOR STATISTICS: SUPPORTING STUDENT SUCCESS THROUGH MICROSOFT EXCEL BOOTSTRAPPING ………………….……… 86 … Recommendations for Future Research in Statistics TPCK …………….……… 86 CHAPTER V SUMMARY AND DISCUSSION ………………………………. 87 Orientation to Mathematics Placement Assessments …………………………… 87 Factors Supporting College Mathematics Success ……………………. 109 vii LIST OF TABLES TABLE Page 1 Demographics of Participants ………………….

17 2 Results of Paired Samples t-test ………………. 24 3 Results of Arithmetic Assessments: Difference of Post-test and Pre-test ………………………………….…………… 25 4 Results of Arithmetic Self-Confidence: Difference of Post-test & Pre-test ……………………….…… 26 5 Results of Algebra Assessments: Difference of Post-test and Pre-test ………………………………………….… 27 6 Results of Algebra Self-Confidence: Difference of Post-test and Pre-test ……………………………….………………28 7 Results of GLM Analysis: Difference of Post-test and Pre-test…………………………………………….… 29 8 Demographics of Participants .……………………………………………… 38 9 Description of Eight Data Sets………………. 79 viii LIST OF FIGURES FIGURE Page 1 Race/ethnicity of participants……………………………………………………. 18 2 Race/ethnicity partitioned by academic level ……………………………….

19 3 Academic level partitioned by race/ethnicity……………………………. 19 4 Microsoft Excel syntax for producing an element in a bootstrap re-sample ……………………….…… 81 5 Microsoft Excel syntax for computing the mean of the 250 means of the bootstrap re-samples ………. 81 6 Microsoft Excel syntax for computing 2.5 percentile value of the 250 means ……………………….… 82 7 Microsoft Excel syntax for computing the 97.5 percentile value of the 250 means ………………….… 82 8 Bootstrapped 95 % CIs of Pre/Post Arithmetic Test by Re-Sample Factor ……………….… 83 9 Bootstrapped 95 % CIs of Pre/Post Arithmetic Question by Re-Sample Factor…………………. 84 10 Bootstrapped 95 % CIs of Pre/Post Algebra Test by Re-Sample Factor………………………….

84 11 Bootstrapped 95 % CIs of Pre/Post Algebra Question by Re-Sample Factor…………………………….… 85 ix INTRODUCTION Student Success Quest President Obama (2009) issued a challenge for the United States to regain the lead in having the highest proportion of college graduates in the world by the 2020. Organizations offering their support for similar goals include The Bill and Melinda Gates Foundation, pledging millions of dollars to support doubling the number of low-income students earning degrees by 2025 and Lumina Foundation for Education, aiming to increase the percentage of people with high-quality degrees by the time frame of 2025 (Parker, Bustillos, & Behringer, 2010). America, needing to develop the necessary workforce of the 21st century in order to hold on to its global prominence, is looking to harness the strengths of its citizenry (Parker et al. The President has urged every American to enroll in at least one year of postsecondary education in order to help increase America’s global competitiveness (Obama, 2009).

State policy makers have been similarly urged to support workforce development by empowering and embracing universities and community colleges to develop mechanisms to support postsecondary mathematics success: Mathematics is THE bridge to high paying jobs in STEM (Science, Technology, Engineering and Mathematics) fields (Capraro, 2011). This national focus on college completion has shifted the debate concerning remedial or developmental education from the philosophical view of access vs. excellence to a more evidence-based view of benefits vs. cost (Parker et al.

History of Developmental Education Academically underprepared students have been of concern to American higher education since the 1630s when Harvard College provided Latin tutors for incoming students (Breneman & Haarlow, 1998). The first remedial education program that included courses in 1 reading, writing, and arithmetic was offered at the University of Wisconsin in 1849 (Breneman & Haarlow, 1998). In the twentieth century, junior colleges and community colleges began to assume the front role in remedial education (Breneman & Haarlow, 1998). The Serviceman’s Readjustment Act or G.

Bill of 1944 provided financial aid for education to veterans returning from World War II, thus providing community colleges a financially prepared population of academically underprepared students (Mellow, 2000). Financial aid provided by The Higher Education Act of 1965 removed the cost barrier for all students, thus opening the doors to higher education, effectively making community colleges the Ellis Island of American Higher Education (Breneman & Haarlow, 1998; Mellow, 2000). This influx of students, most of whom were underprepared for higher education experiences, led to the need for assessment testing in the areas of mathematics, reading and writing as a way for proper placement at an appropriate academic level. By the mid 1970s, institutions of higher education such as Navarro Community College of Corsicana, Texas were voluntarily using assessment testing, sometimes with volatile results (T.

Stringer, personal communication, May 4, 2012). Assessment testing was federally mandated in the 1980s (Breneman & Haarlow, 1998). Placement Assessment The Texas Academic Skills Program (TASP), established in 1987, served as a diagnostic tool and placement device in the areas of mathematics, reading and writing (Breneman & Haarlow, 1998). More recently, the College Board’s ACCUPLACER test battery was employed for placement and diagnosis (Mattern & Packman, 2009).

However, many students take placement tests without realizing their purpose or the high-stakes nature 2 of the assessment such as placement into developmental studies increasing the cost and time for degree completion (Bailey, 2009; Bailey, Jeong, & Cho, 2010; Safron & Visher, 2010). Placement assessment testing is poorly understood by high school students, and not well aligned with entry-level courses, only assessing one dimension of college readiness – basic content knowledge (Conley, 2007). As Conley (2010) so aptly states in his address to the National Center for Postsecondary Research (NCPR) Developmental Education Conference, in which he gave comparisons of several college readiness assessment tests including the Computer-Adaptive Placement Assessment and Support System (COMPASS) developed by the American College Test (ACT), ACT, Assessment of Skills for Successful Entry and Transfer (ASSET), ACCUPLACER which was developed by the College Board, and the Scholastic Aptitude Test (SAT): The exam score is not designed to provide insight into the specific nature of and reason for any deficiency. It is not clear if the student simply has forgotten material learned previously and needs only to refresh his or her memory, or if he or she has never been exposed to the material in the first place.

The test cannot determine if a student needs a small amount of focused review or re-teaching of the material from scratch. It may not be clear if the problem is lack of content knowledge or lack of study skills. In short, while tests may identify deficiencies, they are not particularly useful in helping to identify how to remedy any particular deficiency. 6) The assessment-placement policy of states can result in developmental education placement when supports and enrollment in college-level classes would better serve some students (Collins, 2009).