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A Correlational Study of Active Learning,Academic Proficiency and Completion Rates of African American Students
Enrolled in Developmental Mathematics Courses
A dissertation submitted
byHope E. Essien
toBenedictine University
in partial fulfillmentof the requirements for the degree of
Doctor of Educationin
Higher Education and Organizational Change
This dissertation has been accepted for the facultyof Benedictine University
M.Vali Siadat Ph.D., D.A. ________________________ __________Dissertation Committee Director Date
Sunil Chand, Ph.D. _________ _________________________ __________Dissertation Committee Chair Date
JoHyun Kim, Ph.D.__________ _________________________ __________Dissertation Committee Reader Date
____________________________ Sunil Chand, Ph.D. _________ __________Program Director, Faculty Date
____________________________ Eileen Kolich, Ph.D. _________ __________ Faculty Date
____________________________ Ethel Ragland, Ed.D., M.N.,R.N. __________ Dean, College of Education and Health Services Date
Copyright© by Hope E. Essien, 2015All rights reserved.
I dedicate this dissertation to my wife, Antoinette Ford Essien. Her contributions
and advice continue to transform my life. Without the assistance, affection, and support
of my friends and family, it would not have been possible to complete my dissertation.
Additionally, to my parents, Norah and Edem Essien Ekanem, for instilling the
importance of education in my life – thank you. I dedicate my dissertation also to those
who hoped to see this day come true; however, they have transitioned from this life to the
next. I especially dedicate this research and work to you, “Joyce father” – I love you. In
the words of nineteenth century Quaker missionary Etienne de Grellet, “I shall pass this
way but once; any good that I can do or any kindness I can show to any human being; let
me do it now; let me not defer nor neglect it, for I shall not pass this way again.”
Finally, and in the words of Paul Tillich, “The courage to be is rooted in the God
who appears when God has disappeared in the anxiety of doubt” (The Courage To Be,
1952). Lastly, this dissertation is dedicated to my sisters, Joyce and Gloria, and to my
brother, Felix. To be sure, “I can do all things through Christ who strengthens me”
(Philippians 4:13, New King James Version).
ACKNOWLEDGMENTS
In writing these acknowledgments, I am constantly reminded of several occasions marked
by wondering whether this day would ever come to pass. For this reason, I am eternally grateful
to those who made this dissertation possible. I wish to acknowledge several people who
contributed positively to my career and academic achievements. Without their support, this dream
would not have materialized. In completing this dissertation process, I have been rewarded
through the edification of my personal, professional, and educational growth. I also would like to
thank the Creator for making all things possible through Him.
To my committee members, I extend my sincere gratitude. Thank you to Dr. Sunil Chand,
my dissertation Chair, and Dr. Vali Siadat, my dissertation Director, for braving one of Chicago’s
coldest winters (January 2013) to meet with me. Thank you both, also, for reviewing multiple
drafts and for presenting suggestions, questions, and recommendations in the development of the
various arguments presented in my dissertation. I additionally extend my gratitude to Dr. JoHyun
Kim who served as my dissertation reader. Dr. Kim’s dedication, encouragement, and support
helped make this dream a reality. To all who are aforementioned, you are and have been my role
models.
I would like to thank Dr. Anthony Munroe, Dr. Antonio Gutierrez, Dr. Christopher
Robinson-Easley, Dr. Lynette Stokes, Byron Javier, Byron Bell, Gené Stephens and Kimberly
Hollingsworth for their assistance and support during my dissertation preparation and writing.
Finally, to my Cohort at Benedictine University, Hope Community College and the Oko-
Ita community, thank you for your words of wisdom. I wish you all the best.
iv
ABSTRACT
Nationally, according to Bahr (2010), one in four students (22%) were enrolled in
developmental mathematics, whereas 46% of African American students were enrolled in
developmental mathematics and earned credit in these courses. Only 54% of students
enrolled in Fundamentals of Arithmetic and Intermediate Algebra at HCC (Hope
Community College, a pseudonym) were successful in completing these developmental
mathematics courses with a grade of “C” or better. To address these issues and explain
alternative methods to help African American students become more successful at HCC
and proficient in developmental mathematics, this research measures the effectiveness of
active learning on the academic proficiency and completion rates of African American
students enrolled in developmental mathematics at a two-year college.
Active learning is a method of teaching that promotes student-centered learning,
which intends to raise the student’s motivational level and encourage thinking beyond the
information and details provided during instruction (Brody, 2009; Boylan & Bonham,
2012; Bailey, Jeong, & Cho, 2010). Active learning also correlates with academic
proficiency, success rate, persistence, and completion (Nash, 2005). However, the need to
find alternate methods is supported by the fact that only 43% of freshmen at two-year
colleges are ready to succeed in college-level mathematics courses (Li et al., 2013).
A quantitative method (Creswell, 2011) will be utilized to gather, investigate, and
analyze data for this study.
v
TABLE OF CONTENTS
ACKNOWLEDGMENTS..................................................................................................ivABSTRACT....................................................................................................................v
CHAPTER 1: INTRODUCTION........................................................................................1Issue Statement................................................................................................................1Theoretical Framework....................................................................................................6Research Environment.....................................................................................................8Research Questions........................................................................................................10
Major Research Questions.................................................................................................10Hypotheses.....................................................................................................................11Significance of the Study...............................................................................................12Definition of Terms........................................................................................................13Study Assumptions, Limitations, and Delimitations.....................................................15
Study Assumptions............................................................................................................15Study Limitations.......................................................................................................15
Delimitation.......................................................................................................................16Chapter One: Summary.................................................................................................16
CHAPTER 2: REVIEW OF LITERATURE.....................................................................17Developmental Mathematics.............................................................................................17Why Developmental Mathematics Courses at Community Colleges................................19Distinctiveness of Developmental Mathematics Students.................................................20Learning Theories..............................................................................................................22Constructivist Learning Theory.........................................................................................22Experiential Learning Theory............................................................................................24Active Learning in Classroom...........................................................................................26Benefits of Active Learning to Students............................................................................27Correlation of Active Learning and Performance in Mathematics....................................30
Chapter Two: Summary.................................................................................................32CHAPTER 3: METHOD AND DESIGN..........................................................................33Population and sample of the study...................................................................................33Course and student distribution.........................................................................................34Data Collection Procedures...............................................................................................35Data Analysis and Research Approach..............................................................................36
Privacy and Confidentiality...........................................................................................39
vi
Additional Required Information..................................................................................40Declaration of Conflicting Interest....................................................................................40Benefit of the Project.........................................................................................................40NIH/CITI...........................................................................................................................41
Chapter Three: Summary...............................................................................................41Research Questions............................................................................................................41CHAPTER 4: ANALYSIS OF DATA AND RESULTS....................................................43
Demographic Background.............................................................................................43Research Question One......................................................................................................47Research Question Two.....................................................................................................56
Chapter Four: Summary................................................................................................58CHAPTER 5: DISCUSSION............................................................................................60
Summary of Study.........................................................................................................60Discussion of Research Question One...............................................................................62Discussion of Research Question Two..............................................................................64
Future Research and Recommendations........................................................................68REFERENCES..................................................................................................................71
Appendix A: Syllabus for Developmental Mathematics Course.................................144Appendix B: Active Learning Project..........................................................................154
vii
CHAPTER 1: INTRODUCTION
Chapter one of this investigation presents the following: (1) issue statement; (2)
purpose of the study; (3) research environment to be studied; (4) research questions; and
(5) explanation of the overarching significance of this research to the developmental
learning of African Americans.
Issue Statement
A panel of experts assembled by the United States Department of Education
(2008) determined that students have difficulties with fractions, simple interest, and
calculations needed for everyday living. Similarly, Brown and Quinn (2007) have in their
research examined the relationship between fraction proficiency and success in algebra,
including developmental mathematics. The United States Department of Education’s
(2008) statistics additionally revealed that 78% of students were not able to calculate the
interest paid on a loan; 71% were not able compute gas mileage of a car per distance
travelled on a trip; and 58% were incapable of calculating a 10% gratuity on a lunch bill.
About 75% of students enrolled at two-year colleges are mandated to take at least one or
more developmental mathematics courses (Boylan & Bonham, 2012). Furthermore,
student inadequacy in developmental mathematics courses stems from elementary
education and continues through high school before participants are even enrolled in
community colleges (Venezia & Perry, 2007; Sierpinska, Bobos, & Knipping, 2008).
1
In a report presented to the Department of Education, Noel-Levitz (2006) mentioned that
developmental mathematics is a difficult course to pass. According to Spradlin (2009),
students’ failure or success in mathematics courses may determine whether they complete
their education or gain meaningful careers.
Research conducted by the National Center for Postsecondary Research (NCPR,
2010) indicates that traditional teaching approaches have not demonstrated proficiency in
developmental mathematics. Consequently, mathematics instructors are supplementing
traditional approaches with teaching techniques that emphasize active learning, concepts
and real life application (Spradlin, 2009). As part of President Barack Obama’s challenge
to the American Association of Community Colleges (AACC) to educate five million
students by 2020, AACC (2013) supports the emergence of active learning, which
includes discovery and experiential exploration to enhance student engagement in
problem solving and learning (Rosenshine, 2012).
Although constructivists grapple with the challenges of implementing and
connecting this theory of instruction to teaching and learning practices, the
constructivists’ theory has the ability to create an educational experience that requires
students to be active participants in learning process (Gordon, 2009). Despite difficulties
confronting the constructivists’ approach incorporating a balance of active learning and
experiential instructional method, developmental mathematics instructors should
advocate a change in how students learn, embrace active learning, and work with their
students toward building, interpreting, and discovering their own knowledge (Hoang &
Caverly, 2013).
2
Since active learning or student-centered instruction entails knowledge discovery,
mathematics students should take ownership and responsibility for their edification by
coming to class prepared and ready to be engaged in group projects (Fister and
McCarthy, 2008). To facilitate the process of active learning, Hoang and Caverly (2013)
suggest that developmental mathematics instructors can assign instructional activities in
developmental mathematics via DropBox, Google Drive, and YouTube. Similarly, Khan
Academy utilizes interactive DVD exercises that give students active learning or practical
experiences that simplify complex developmental mathematics problems to real life
applications, thereby making mathematics come alive. (Lambert, 2012; Johnson, Flagg,
& Dremsa, 2010).
In the study conducted by Daniel Jacoby (2006), the author argued that active
learning may not be properly implemented in community colleges due to the profound
dependence by community colleges on adjunct faculty. Jacoby (2006) further argued that
adjunct faculty members employed in community colleges adversely affect students’
educational proficiency since they lack the needed equipment and materials necessary to
support active learning approaches. Additionally, Jacoby (2006) contended that over-
reliance on adjunct faculty may challenge successful student integration. To paraphrase
the author, the graduation rate of a two-year college is inversely proportional to the
number of adjunct faculty employed (Jacoby, 2006).
Jacoby’s research also determined that part-time faculty members are “relatively
unavailable” and “use less challenging instructional methods” (Jacoby, 2006, p. 1083). In
essence, adjunct faculty pedagogical perceptions could adversely impact active learning
implementation (Michael, 2007). Finally, Jacoby maintained that adjunct faculty
3
members use active pedagogical techniques less frequently, place less emphasis on
educating a well-rounded scholar, include diversity in classroom instruction less
frequently, and spend inadequate time preparing for class (Jacoby, 2006). Additionally,
professional development activity would be effective in improving instructional skills,
knowledge and teaching practice, thereby promoting communication among instructors
(Garet et al., 2001).
To meet the challenges of developing successful student outcomes in
developmental mathematics, educational researchers have determined that active learning
methods of teaching are efficient and can improve the educational performance of
students more than the traditional, instructor-centered style of teaching (Starke, 2012;
Barkley, Cross, & Major, 2005). Rabin & Nutter-Upham (2010) additionally contended
that implementation of active learning in and out of the classroom with student-centered
learning competencies improves student learning and can assist students in developing
problem-solving skills (Freeman et al., 2007; Visher, Butcher, & Cerna, 2010). Further,
research indicated that the use of instructor-centered lectures does not permit students to
be enthusiastically engaged in the teaching and learning process (Killian & Dye, 2009;
Sternberg, 2003).
Instructor-centered learning—or the “chalk and talk”—places students in a
passive role that restricts the participants’ classroom activities to information
memorization (Loch et al., 2011; Dembele & Miaro II, 2003). Kamii, Rummelsberg and
Kari (2005) observed that by implementing active learning in the classroom, students’
thinking abilities are enhanced, thereby improving high school and elementary students’
scores in mathematics. Research advocated by Shirvani (2006) promotes educational
4
standards such as students’ engagement in classroom, problem solving initiation, and
encouragement of communication in the classroom, as well as moving toward
mathematical understanding instead of memorization of materials covered in class.
Research conducted by Rumberger (2004) and Gates Foundation (2006) explained that
inadequate student engagement is a predictive factor of student persistence and lack of
completion rate. Research also revealed that engaged students gain and retain more
knowledge and benefit more from active learning than do students who are not engaged
(Freeman et al., 2007; Voke, 2002; Hancock & Betts, 2002).
Despite research indicating the ways in which active learning can have a
constructive effect on student learning, there was little evidence in the literature for the
inclusion of active learning in a curriculum for African American students enrolled in
developmental mathematics courses at the community college level. The paucity of
research on the use of active learning approach and its effectiveness is a profound gap in
efforts to support and encourage students’ active learning method (Waltz, Jenkins & Han,
2014).
Consequently, the purpose of this study was to investigate whether there is any
correlation between active learning methods of instruction and the academic proficiency
and completion rates of African American students in developmental mathematics
courses in post-secondary institutions and, specifically, in a community college setting.
5
Theoretical Framework
Today’s students are learning in a more technologically advanced environment
(Hsu, 2008). Since students live in a fast-paced, ever-changing environment, traditional
methods of instruction are inadequate to serve their educational needs (Shults, 2008;
Loch et al., 2011). The traditional teaching method of past generations required
participants to be non-engaged receivers of instruction. The traditional teaching approach
has produced a high student attrition rate in the classroom and low passing rate (Spradlin,
2009). Actively generating information is a vital element for improving student learning
objectives (Giers & Kreiner, 2009). The finding by Giers and Kreiner (2009) indicated
that students demonstrated higher academic performance and better retention of
information presented in the classroom when active learning was incorporated into
student learning approaches. The traditional delivery approach known as the passive
learning method is often referred to as “chalk and talk,” i.e., as the instructor talks, the
student listens and writes (Friesen, 2011). In the “chalk and talk” instructional delivery,
the instructor is seen as the only source of authority of information (Ali, 2011). On the
other hand, Trinter, Moon, and Brighton (2014) contend that when instructors teach with
active learning methods, the result is that students constantly participate in class; and that
these techniques contribute to mathematical student successes (Trinter, Moon, &
Brighton, 2014).
In traditional methods of teaching, the instructor displays more procedural
approaches that are stressed through a kind of “sage on stage” method (White-Clark et al,
2008). This direct instructional method is also characterized as teacher-centered
6
instruction. Teacher-centered instruction requires the instructor to present the materials
and guide the practice while the student accepts the materials and instructional correction
modeled by the teacher (Killian & Dye, 2009; Kinney & Robertson, 2003). Furthermore,
in the traditional approach, teacher-centered methods of instruction, decisions in the
classroom are made by the teacher who determines the content and context of materials
covered (Gningue et al., 2013). In the teacher-centered method, the content of materials
to be presented is directly transmitted from the instructor to students (White-Clark,
DiCarlo, and Gilchriest, 2008). Gningue et al. (2013) also claim that knowledge is
passively transmitted when students receive information from an omniscient expert or
instructor. Additionally, Brown (2003) contended that it is the responsibility of the
instructor to do all the thinking, while the students rehearse and regurgitate covered
materials.
In contrast to the traditional lecture style of teaching, active learning is team-
based and problem-based, containing simulated and cooperative learning methodologies.
In an active learning model, the instructor is viewed as a facilitator of knowledge rather
than the originator and keeper of knowledge (Orey, 2010). In active learning or students-
centered learning, emphasis is placed on students’ ability to discover and learn
information. The instructors are viewed as a “guide on the side” that facilitates students’
understanding of content and construction of meanings (White-Clark et al., 2008).
A benefit of active learning is that “students actually learn math by doing math
rather than spending time listening to someone talk about doing math” (Boylan et al.,
2012, p. 16). It is also suggested that active learning improves student learning
7
engagement and performance in examinations (Yoder and Hochevar, 2005). Active
learning is also advantageous for the following reasons:
(1) students are not passive listeners;
(2) students are engaged in reading, writing, problem solving, and discussions;
(3) student motivation is increased;
(4) students receive instant feedback; and
(5) students are engaged in critical thinking, analysis, evaluation, and synthesis.
(Michel, Cater, & Varela, 2009)
In this study active learning is the independent variable, and the academic
proficiency and completion rate of African American students enrolled in a
developmental mathematics course are dependent variables. Within the framework of this
study, students are deemed proficient in the developmental mathematics course when
they attain at least a letter grade of ‘C’ or better using quantitative assessment tasks
stipulated on the course syllabus.
Research Environment
The site for this study was an urban two-year college located in a large municipal
area of the Midwest of the United States. The college is made up of a diverse student
population. The ethnic breakdown of the students is 70% African American, plus a
variety of other ethnic groups. Many students who arrive at a two-year community
college are unprepared to complete successfully a degree or certificate program of study
in the time frame prescribed by Title IV permission (Bailey, 2008). In addition, many
students come from lower socioeconomic backgrounds and have limited exposure to
8
postsecondary educational experiences (White House, 2014). National Center for
Education Statistics (NCES, 2003) indicates that 50% of students enrolled in community
colleges depart at the end of the first two semesters. From Fall 2009 to Fall 2010, 20% of
all students enrolled at Hope Community College (HCC) were proficient in intermediate
algebra. HCC registered over 5500 students and 500 of those students were registered in
intermediate algebra. From HCC internal assessment documents, data indicated a high
population percentage of African American students in intermediate algebra. HCC
college administration made an effort to improve students’ success by proposing an
initiative to implement three intervention (active learning) classes and three control group
(non-active learning) classes of intermediate algebra from Fall 2010 to Fall 2013 to
investigate the effect of active learning. In Fall 2010, the implementation of active
learning in a developmental mathematics course, intermediate algebra, was designed to
provide students with additional support to be proficient in completing intermediate
algebra.
The implementation of active learning in an intermediate algebra course may also
assist intermediate algebra students through collaboration with fellow students and may
provide the motivation for students to persist in their educational endeavours. It is
anticipated that using an active learning approach is an effective method of teaching that
will improve students’ understanding of mathematical concepts (Van De Walle, 2004).
Research showed that active learning improves elementary, middle school and high
school achievements (Fuchs & Fuchs, 2001). Active learning may also improve two-year
college proficiency, particularly at HCC.
9
Understanding the issues confronting two-year colleges, community colleges are
compelled to use nontraditional methods of teaching that can prepare students for the
workforce in a rapidly changing economy (Shults, 2008).
The National Collaborative for the Study of University Engagement (NCSUE)
contended that colleges and universities have worked to realign their educational
curriculum with high schools and other academic institutions (Bueschel & Venezia, 2006;
NCSUE, 2010). More specifically, most community college students arrive with a basic
educational level of eight years elementary education and four years secondary education,
with little extracurricular knowledge. These students who complete high school are
eligible to later enroll in postsecondary institutions such as community colleges, four-
year universities, and technical schools (Bush & Bush, 2004). However, upon reaching
postsecondary institutions, over 60% of students (particularly those enrolled in two-year
colleges) are found to be deficient in mathematics and require additional training in
developmental mathematics to help them effectively complete their personal learning and
professional objectives (Stigler, Givvin, & Thompson, 2011). Thus, developmental
mathematics courses are offered to prepare students for a college-level mathematics
curriculum (Bragg, 2011).
Research Questions
Major Research Questions
The following research questions were used to direct this investigation:
1. Is there any relationship between active learning and the academic proficiency
of African American students who participate in active learning intervention
10
and the academic proficiency of African American students who receive
traditional instruction?
2. Is there any relationship between active learning and the completion rate of
African American students who participate in active learning intervention and
the completion rate of African American students who receive traditional
instruction?
Hypotheses
The investigation tested the following hypotheses:
For research question one.
Null Hypotheses (Ho): There is no relationship between active learning and the
academic proficiency of African American students who participate in active learning
intervention and the academic proficiency of African American students who receive
traditional instruction.
Alternative Hypotheses (Ha): There is a relationship between active learning and
the academic proficiency of African American students who participate in active
learning intervention and the academic proficiency of African American students who
receive traditional instruction.
For research question two.
Null Hypotheses (Ho): There is no relationship between active learning and the
completion rate of African American students who participate in active learning
intervention and the completion rate of African American students who receive
traditional instruction.
11
Alternative Hypotheses (Ha): There is a relationship between active learning and
the completion rate of African American students who participate in active learning
intervention and the completion rate of African American students who receive
traditional instruction.
.Significance of the Study
Tien (2009) clearly articulated the essence of critical thinking and students’
inabilities to solve mathematical problems, by addressing the fundamental needs and
students’ deficiencies in mastering basic mathematical skills. Mathematics instructors are
confronted with a growing demand for integrating active learning into their instruction
(CDE, 2010). The reluctance of community college instructors to adopt active learning
methods in the classroom is associated with the inadequate professional development of
instructors (Pundak, Herscovitz, Schacham, & Wiser-Biton, 2009). Some instructors are
embracing active learning as an ideal method of instructional presentation, while other
instructors continue to cling to traditional methods of teaching (Shore & Shore, 2003).
Gningue, Peach and Schroder (2013) argued that for learners to be prepared for
challenges of the 21st century, an active learning approach is appropriate. The
Mathematical Association of America (MAA, 2008) proposed that an increase in active
learning instruction will result in increased student engagement and student achievement,
which will decrease teacher-centered andragogy.
This study is significant because through it the investigator seeks to demonstrate,
through statistical and student data, the effect of the active learning model on academic
proficiency and completion rates of African American students in a developmental
mathematics course at the community college level.
12
Measuring and examining the effectiveness of active learning through study and
analysis of the academic proficiency of African American students registered in
developmental mathematics serves to enhance the body of knowledge in the field of
mathematics education. In addition, the results of this investigation could be used to
strengthen the implementation of active learning and academic proficiency in
developmental mathematics (Ashby, Sadera, & McNary, 2011). The results obtained in
this study may also be crucial in creating future recommendations for developing
students’ college level mathematical skills, instructional training, and educational
policies.
This correlational study analyzes the impact of active learning experienced by
students who are taught developmental mathematics using the active learning approach.
The utilization of active learning pedagogy may or may not encourage administrative
support of this instructional method; however, the study promises to foster healthy
discussions about the need for, and use of, nontraditional instructional approaches.
Finally, the study could be used to further reinforce important theories concerning active
learning and could create a path for further study in this area.
Definition of Terms
Academic Proficiency. Within the framework of this study, students were
considered proficient in the developmental mathematics course when they attained at
least a letter grade of “C” or better.
Active learning. A learning environment in which students learn a subject in the
classroom and are engaged in “doing” rather than sitting at their decks reading, filling out
worksheets, or listening to a teacher. Active learning is self-guided and involves problem
13
solving rather than learning through passive, “tutorial-like, prompted interaction”
(Leaper, 2011, p. 27). Jones explained that active learning is contingent on the idea that,
if participants are not active, they are neither fully engaged nor learning as much as they
could (Jones, 2009).
African American. For the purpose of this study, African Americans were
students identified in the data provided by Hope Community College (HCC).
Completion rate. The rate calculated as the total number of completers within
150% of normal time divided by the revised adjusted cohort. (IPEDS, 2014).
Community College. A two-year institution of higher learning offering
postsecondary education ranging from specialized certificates to Associate level degrees.
Developmental mathematics. College mathematics courses offered to students
who are inadequately prepared for college-level mathematics (Fike and Fike, 2012).
Developmental mathematics student. Any student who has tested into a
developmental mathematics class through COMPASS-college placement examination-or
consent of the mathematics department chairperson (Frame, 2012).
Intermediate Algebra. A developmental mathematics course offered by two-
year colleges or universities that covers topics such as systems of linear equations,
polynomials, rational and radical expressions, Quadratic equations, functions, exponents,
and geometry.
Traditional or direct instruction. Face-to-face education conveyed by an
instructor who utilizes lectures with some group discussion and group work. Typically,
the traditional instructional model is one in which the instructor is the conveyor of
information and knowledge (White-Clark, DiCarlo & Gilchriest, 2008).
14
Under-prepared students. The population of students enrolled in a community
college or a university that lacks the skills necessary for success in a college level course.
Such students need some form of remediation.
Study Assumptions, Limitations, and Delimitations
Study Assumptions
The data analyzed were accurately recorded and free from human error and bias.
The students in this study were enrolled in a developmental mathematics course
because of their scores on their academic placement test.
Hope Community College is similar to other urban community colleges.
The findings of this investigation can be generalized to other community colleges.
Other students also enroll in this developmental mathematics course after
successfully obtaining a grade of “C” or better in Elementary Algebra with
Geometry
Study Limitations
Several factors may have affected the validity of this study. These factors are
generally referred to as internal validity threats. It has been suggested that internal
validity threats are “experimental approaches, treatment, or experiences of the
participants that threaten the researcher’s ability to draw correct inferences from the data
about the population in an experiment.” (Vogt, 2007, p. 122). There are several possible
threats to any study; however, this study could be affected by the following threats:
1. This research was restricted to one community college and limited to the
population enrolled in this developmental mathematics course.
15
2. This investigation was limited to student records obtained from Hope
Community College.
3. Part of the limitation of this investigation to warrant a reasonable comparison is
the difficulty of comparing two groups of instructors with different teaching
styles, experiences, number of students and teaching methods. Clearly, these
issues introduce independent variables that this study did not address. However,
all instructors were full-time, with at least ten years of experience, and all used
rubrics provided by Hope Community College. In addition, the study included
data from six years and the population was neither randomized nor convenient.
Delimitation
One delimitation of this investigation is that students registered for this research
are from an intermediate algebra course at HCC. Another delimitation is that this
investigation was conducted using an intermediate algebra course in a community college
instead of a university.
Chapter One: Summary
To advance their education and further their career paths, it is necessary for our
students to learn basic mathematical skills. Such skills will allow our students to
successfully function in a fast changing and scientifically advanced world, particularly at
the two-year college level. Chapter two discusses the literature review of this
investigation.
16
CHAPTER 2: REVIEW OF LITERATURE
Chapter two addresses the literature concerning this study and outlines , in detail:
(1) definition of developmental mathematics; (2) why the need for developmental
mathematics course at community college; (3) distinctiveness of developmental
mathematics students; (4) learning theory (5) active learning in classroom, and (6)
benefit of active learning to students.
Chapter two also summarizes the current position of active learning usage in
developmental mathematics courses. There is a vast literature, but the majority of these
studies are qualitative, descriptive, and mixed method. However, quantitative studies of
the relationship between academic proficiency, completion rate and the new learning
pedagogy (active learning) are just developing. Overall, quantitative studies measuring
the effect of active learning are few.
Developmental Mathematics
Developmental mathematics courses are those designed to enable students
achieve desired mathematical competency of enrolling as college freshmen (Harwell,
Medhanie, Dupuis, Post, & LeBeau, 2014); 11.6% of students completed a minimum of
one developmental mathematics course (Harwell et al., 2014). An intermediate algebra
course is established by colleges to prepare learners for further course work that uses
mathematical concepts and processes (Bettinger & Long, 2009). Nationally, there is
concern about the mathematical literacy of United States’ citizens and the extent to which
17
students are prepared by elementary, high school, and community colleges for careers
(Nomi & Allensworth, 2013). Students who test below the cut off scores are placed into a
developmental mathematics course (Harwell et al., 2014). Developmental mathematics
courses are generally viewed as “gatekeeper courses” in which students have to be
proficient before they can advance to take college level mathematics courses (Paul,
2005). Recent research suggests a different paradigm with respect to developmental
mathematics to re-conceptualize it from gatekeeper courses to gateway courses (Bryk &
Triesman, 2010). Nonetheless, when referring to developmental mathematics, some
authors utilize the term “remedial mathematics” (Perrin & Charron, 2006).
Developmental mathematics, according to Boylan (2002, p. 3), “enables under-
prepared students to advance, and advanced students then begin to excel.” The term
“developmental” also incorporates a holistic method that focuses on the academic, social,
and emotional growth of the learners. The central objective of a developmental
mathematics course is remediation of students’ academic deficiencies or mathematical
skills so that they are better prepared for college-level mathematics courses, such as
calculus, statistics, college algebra, and differential equations (Armington, 2003;
Attewell, Lavin, Domina, & Levey, 2006). Developmental mathematics were presented
using two approaches: Traditional (instructor-centered) and Active learning (students-
centered). The traditional or lecture approach involves mathematical coverage and
encourages lecture memorization as part of teaching strategies (Khalid & Azeem, 2012).
The traditional approach, as some researchers argue, emphasizes traditional activities;
instruction in the traditional approach is unilateral and orthodox in nature (Khalid &
18
Azeem, 2012). In this research, active learning which is students-centered engages the
learner in the learning process.
Why Developmental Mathematics Courses at Community Colleges
The history of developmental mathematics spans more than two centuries, when
institutions of higher education admitted students deficient academically in order to
provide educational opportunities to those who were underprepared (Merisotis & Phipps,
2000). Every year, there is an increasing number of freshmen students, from 60% to 75%,
enrolled at two year colleges who need a developmental mathematics course (Howard &
Whitaker, 2011). Many colleges require that students enrolled in developmental
mathematics successfully complete the required developmental mathematics course
before they are permitted to enroll in college level courses (Howard et al., 2011).
According to Cafarella (2013), the number of students placing into developmental
mathematics courses and the degree of underprepared developmental mathematics
students has amplified. Recent research suggests that 82% of students who registered for
developmental mathematics courses never completed an associate degree or certificate or
transferred to another university (Bahr, 2008). Fifty-seven percent to sixty-one percent of
community colleges or universities use placement tests as an indicator to identify students
who need developmental mathematics (Harwell et al., 2014). Low high school Grade
Point Average (GPA) and ACT/SAT are indicators of placement into developmental
mathematics (Cafarella, 2014; Harwell et al., 2014). Harwell et al. (2014) affirmed that
high school mathematics curricula completed by students play a vital role in student
readiness for college level mathematics. Redden (2010) affirmed that students placed into
developmental mathematics courses could not retain the course content in high school.
19
Stigler, Givven and Thompson (2010) contend that developmental mathematics
students do not invest adequate time to effectively study or learn to master the content of
developmental mathematics. Nonetheless, research on the success rate of developmental
mathematics is limited (Esch, 2009; Ashby, Sadera & McNary, 2011).
Hofmann and Hunter (2003) ascertain that teaching methodologies and strategies
to redesign mathematics courses make developmental mathematics meaningful, and they
increase the student learning and success rates of the course.
In 2004, research studies conducted by the National Center for Developmental
Education indicated that more attention is being placed on two-year colleges (Gerlaugh,
Thompson, Boylan, & Davis, 2007). According to Clutts (2010), a survey of 3,230
colleges and universities indicated that 99% of community colleges teach one or more
remedial courses. Community college students placed into developmental mathematics
courses are required to take about 10 hours of mathematics courses before given the
opportunity to be enrolled in a college-level mathematics course (Bonham & Boylan,
2012). Research indicates that the success rate in developmental mathematics is low due
to the open door policy; 79% of participants are registered in a two-year college
developmental mathematics course (Esch, 2009). Community college students lack the
basic mathematics skills taught to them in both elementary and high school (Stigler,
Givvin & Thompson, 2009).
Distinctiveness of Developmental Mathematics Students
Students enrolled in community colleges or universities are deficient in
mathematics for various reasons. First, developmental mathematics students in high
school did not take relevant mathematics courses. Secondly, students registered for
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developmental mathematics, while enrolled in the relevant courses, did not, however,
master the content and context of the materials covered. Finally, students enrolled in
developmental mathematics courses may not remember much of the materials previously
mastered (Fike & Fike, 2012).
Furthermore, the composition of the developmental student population consists of
traditional (18-25 years) and non-traditional (over 25 years) students; students in the over
25 years group have a lower level of algebra skills, have not taken a mathematics course
for a while, and have completed fewer developmental mathematics courses. These
students need refresher courses in developmental mathematics to be proficient in the
mathematics course of their career choice (Howard & Whitaker, 2011).
Although literature review is mixed on the report concerning students’ completion
of a minimum of one developmental mathematics course, researchers contend that
student enrollment in developmental mathematics reduces the probability of students’
completion (Martorell & McFarlin, 2010). Bettinger and Long (2009) argue the opposite.
Regularly, mathematics is taught by instructors who do not fully understand nor have
mastered the subject materials themselves (Hammerman & Goldberg, 2003; Hill, Rowan,
& Ball, 2005).
Additionally, students enrolled in developmental mathematics have deficiencies in
organizational and study skills, which are vital tools in the achievement of higher
education (Armington, 2003; Calcagno, Crosta, Bailey, & Jenkins, 2007).
Unfortunately, evidence reveals that while community college instructors are
more knowledgeable about mathematics than are their elementary or high school
colleagues (Lutzer et al., 2007), there are few differences in the instructional methods
21
utilized for developmental mathematics in colleges and elementary or high schools
(Grubb, 2010). "Drill-and-skill" continues to dominate developmental mathematics
instructional delivery (Goldrick-Rab, 2007).
Learning Theories
In this section of the study, the investigator reviews the teaching and learning
theories and methods that influence the active learning pedagogy and andragogy in
developmental mathematics. Specifically, the goal of this section is to present a
framework of how students learn.
Constructivist Learning Theory
Constructivist learning theory holds the view that individuals construct
knowledge via experience. Constructivism argues that learning is a social collaborative
activity in which human beings create meaning as a result of their interactions with one
another (Schreiber & Valle, 2013). Constructivist teaching and learning in the classroom
requires a shift in teaching from a traditional instruction relationship to an interactive
students-centered relationship (Schreiber et al., 2013).
For instructors to design effective and efficient teaching methods, it is vital for
them to understand the theory of teaching and learning. According to Schunk (2000), it is
impossible to use a learning theory to explain every style of learning or the difficulties
pertaining to learning. Learning theory, particularly constructivist, affirms that students
should be “active” or engaged to accomplish effective learning. Given their vital role,
constructivist learning theories show how students are steered toward learning through
experiences (Prince & Felder, 2007).
22
Schreiber and Valle (2013) posits that in a constructivist classroom, the instructor
encourages students to learn material presented by asking leading questions, promoting
knowledge discovery, guiding and supporting students until they are able to
autonomously complete the assigned task (Schreiber & Valle, 2013). Chance (2005)
suggested that an active learning method would help students synthesize their application
of knowledge.
Recently, there has been a change in paradigm from scripted learning and
teaching to critical thinking in the understanding of mathematics (Woodard, 2004; Cavas,
2010). The constructivist learning theory studies how students learn and the way students
develop or construct the meaning of learning by themselves. The theory explains how the
nature of acquiring knowledge affects students’ learning. The theory additionally
demonstrates the ways student knowledge is acquired through engagement and
involvement in tasks rather than reproduction or replication. Essentially, the
constructivist learning theory promotes individual generation and assembly of thoughts
and comprehension of lessons through communication and processes based on what
students think and know from their daily activities (Boudourides, 2003).
Constructivist theories provide instructors with a framework for instructing
mathematics that fosters problem solving, critical thinking, and communication (Brewer
& Daane, 2002). The constructivist learning theory allows instructors to view, reassess,
and change student teaching and learning by focusing on processes and by documenting
student transformation. Research indicates that constructivist classroom students have
better understanding and are more successful in mathematics courses than their
counterpart in traditional classrooms (Brewer et al., 2003). Constructivist learning is an
23
active process. Based on this understanding of learning, the instructor will be able to
realign curriculum, restructure developmental mathematics courses with better andragogy
or pedagogy, and use concept mapping that will encourage learning that is meaningful
and applicable to real life experiences (Christensen, 2003). Constructivism posits that
best learning occurs when students utilize peer interactions, past experiences, and their
individualized constructs in order to develop their knowledge (Wright, 2008). For the
constructivist, the process of learning and teaching is not merely the transmission of
knowledge to the student; instead it assists the learner in constructing knowledge by
tasking students to be engaged and develop the process of problem solving.
Constructivists also advocate for alternative methods of engagement relative to learning
by developing a robust and communicative environment (Pineda-Baez et al., 2014).
Finally, constructivists affirm that social interactions are important to student growth
(Prince & Felder, 2006). Scholars have in fact proposed that a “hybrid” or “balanced”
method that combines the best of constructivist and behaviorist approaches may yield the
best results in learning (Grubb et.al, 2011).
Experiential Learning Theory
Learning theorists such as Kolb and Boyatzis (2001), as well as Light, Cox, and
Calkins (2009, p. 55), define experiential learning as “the process in which knowledge is
created through the transformation of our experiences.” Experiential learning was
originally introduced in the 1970s by David Kolb. This form of learning contains four
dimensions, which include “concrete experience, reflective observation, abstract
conceptualization, and active experiment” (Kolb, 1984). The theory also stresses the vital
function active learning plays in the education process. Light, Cox, and Calkins (2009)
24
explained that experiential learning follows a “cycle of learning” from formation and
implementation to reflection that repeats. Furthermore, Suraweera (2002) concurred with
Kolb’s experiential model by explaining that an effective instructor should guide students
from abstract concepts to generalization by helping them to reflect on their own
experiences.
There are four major learning stages in experiential learning. In the first stage,
students feel and observe the world around them in a concrete experience dimension and
contemplate on the problem presented to them in the classroom. The second stage of the
process, reflection, is one in which students consider their experiences on a personal level
through listening, active attention, and review and adjustment of their ideas and goals. In
the third stage, known as abstract conceptualization, students generate new concepts, gain
additional knowledge, and develop strategies and conclusions from which their
experiences are drawn. The final stage encompasses active experimentation and learning
where students model and test their new knowledge in different settings (Lisko & O’Dell,
2010).
According to Beard and Wilson (2006), students learn through their sensations
and experiences, or through contextual situations. Others, however, learn through
perception, abstract conceptualization, or symbolic representation. In addition, Kolb and
Boyatzis (2001, p. 245) explained that “learning has an active form-experimenting
influence or change.”
Experiential learning confirms the importance of active learning, which can
influence or change a situation (Kolb and Boyatzis, 2001). Furthermore, students learn
with different styles, which can be a basis for effective teaching and learning in
25
developmental mathematics. The experiential theory elucidates how a course, such as
developmental mathematics, can be taught in non-traditional ways so as to accomplish
more successful teaching and learning outcomes for students. The experiential learning
theory also promotes student engagement in collaborative, interdisciplinary, discovery of
learning (Knisley, 2002).
Active Learning in Classroom
The notion of active learning was first presented by Brazilian educator Pablo
Friere (Boylan, 2002). In active learning, students are not permitted to sit through
lectures; they are required to discover knowledge for themselves (Boylan, 2002, p.101).
Research indicates that students learn well when they are actively engaged in the course
material (Fiume, 2005; Dennick, 2012; Pineda-Baez et al., 2014). Students who are active
learners retain materials covered in class longer than those who are non-active learners
(Lujan & DiCarlo, 2006). The use of active learning materials is connected to increased
confidence with materials presented in classroom (Cherney, 2008). The use of active
learning in the classroom led to higher critical thinking skills (Smith, Sheppard, Johnson,
& Johnson, 2005). Active learning strategies used in the classroom includes cooperative
or team-based learning (Michael, 2006; DeBourgh, 2008). Inquiry based learning, which
is a form of active learning, provides students the chance to be critical thinkers, reflective
thinkers which in turn fosters students to be self-directed learners (Justice, Rice, Warry,
Inglis, Miller, & Sammon, 2007). Traditional classrooms where students face the
instructor are not ideal for peer collaboration (Milne, 2006). For active learning to take
place, classrooms that include moveable chairs, laptop connection for shared network,
large overhead projectors and circular layout are designed to encourage active learning
26
and collaborative student learning (Dori, 2007). Techniques that entail collaborative
learning, group problem solving, think pair and share, simulation, problem based
learning, planning, and developing a solution promote students to take responsibility for
their learning (Cavanagh, 2011). Additionally, delivery methods such as podcasting are
also used to engage students during active learning (McGarr, 2009). The role of instructor
shifts to learning coach or facilitator while students have a positive attitude in the
classroom and are able to collaborate with their classmates (Cotner, Loper, Walker, &
Brooks, 2013). Student in active learning classrooms have a higher success rate (Cotner
et al., 2013). Our version of active learning does not supplant instruction. In fact good
teaching can inspire the students, motivating them to better engage in the learning
process. This is especially true in a remedial classroom where students are often
unmotivated and lack the necessary self-esteem. In our intervention classes, well-planned
and well-thought out instruction and guidance were provided to all students. This was
supported by cooperative team work and group discussion which contributed to deep
learning of the material.
Benefits of Active Learning to Students
Silberman, Silberman, and Auerbach (2006) stated that learning, and active
learning, takes place in the following form:
What a student hears, a student forgets.
What a student hears and sees, a student remembers a little.
What a student hears, sees, discusses, and does, a student understands.
What a student teaches to another student, the student masters.
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Silberman et al. (2006), in their study, found active learning to be predicated on
performing an action. The action involves performing an activity that could be physical
or mental, but is one that is distinct from the traditional teaching pedagogy. The use of
active learning allows for and requires students’ active participation in developmental
mathematics activities as facilitated by the instructor. Additional research indicates that
active involvement of participants, both in and out of the classroom, fosters the students’
ability to think in a critical manner (Meyer, 2009).
When one thinks of active learning, students are engaged intellectually; therefore,
students are not expected to memorize and regurgitate material covered during the
presentation (Donovan & Loch, 2013; Abrahams & Singh, 2010). The instructor
anticipates that students will utilize critical thinking, problem solving, and analysis of the
presented information, because the information enables students to exercise freedom and
control over the organization of the activity covered (Dolder, Olin & Alston, 2012).
In addition, the process of active learning occurs when students are provided with
an engaging, interactive association with developmental mathematics. The process of
active learning enables students to generate knowledge instead of receiving knowledge.
When active learning is practiced, the function of the instructor is to facilitate the
presentation of the material in a way that will engage students in the process, enabling
them to obtain and understand the lesson and materials through interaction with their
colleagues.
Active learning pedagogy or andragogy also entails activity-based learning, which
could be classified as a conversation with self or conversation with others (Fink, 2003). A
“conversation with self” occurs when a student thinks reflectively about the material
28
covered in class. Conversely, a “conversation with others” occurs when an instructor
forms a group activity. Loch, Galligan, Hobohm, and McDonald (2011) explained that
active learning occurs when a student actually does an activity (Daley, 2003). Some
mathematics instructors at community colleges have integrated several strategies to
engage students in their classrooms, including the use of active learning strategies, rather
than utilize passivity in developmental mathematics courses (Cavanagh, 2011).
For example, one model, the Keystone method, incorporates the dynamic
assessment of student learning and cooperative group work with computer technology to
improve student outcomes in developmental mathematics (Siadat et al., 2012). In another
model, instructors limit classroom presentations to a maximum of 15 minutes per class
session to provide additional classroom instruction accompanied by active individual or
group projects (Jackson & Wilson, 2012).
Analyzed in a different way, active learning engages the students to: (1) be critical
thinkers and active listeners (Garrett, Sadker, & Sadker, 2010); (2) solve problems; and
(3) take ownership of their education and build a supportive educational community
(Bonham & Boylan, 2012; Armington, 2003). Additionally, active learning strategy
encourages students to be self-assured, which also decreases their anxiety about learning
and grasping mathematical concepts (Loch et al., 2011). Similarly, the utilization of
supplemental developmental mathematics instruction, which is a form of active learning,
is vital to the overall academic proficiency of students (Gerlaugh, Thompson, Boylan, &
Davis, 2007). Employing an active learning strategy at the community college level could
result in a higher mathematics proficiency rate (Cole & Wasburn-Moses, 2010; Hall &
Ponton, 2005).
29
Research conducted by Vi-Nhuan, Lockwood, Stecher, Hamilton, and Martinez
(2009) illustrates that active learning engages students in the efficient and effective
learning of mathematics. Active learning permits participants to explore ideas and to
experiment and develop concepts (Cherney, 2008). This method of learning can be
particularly helpful in developmental mathematics.
Researchers contend that active learning assists students in developing social and
learning experiences between students and teachers, as well as among student peer
groups both within and outside of the classroom (Shen et al., 2007). Additionally, Yoder
and Hochevar (2005) explained that active learning is acclaimed to be beneficial for
learning in higher education. Furthermore, researcher Cherney (2008) reasoned that
active learning enables students to reflect on the covered materials in a way that is
meaningful, which improves students’ learning outcomes. Through his research, Cherney
demonstrated that students remember active learning materials.
Correlation of Active Learning and Performance in Mathematics
Recent mathematical research has endorsed active learning approaches rooted in
constructivist pedagogy or andragogy (Gibson & Van Strat, 2001). As a result of active
learning, the instructor facilitates the student’s construction of knowledge, thereby
developing the participant’s eagerness to learn mathematical concepts that meet
curriculum standards, and thereby improve the student’s academic performance in
mathematics (Peak, 2010). In essence, active learning entails collaboration, discussion,
and critical thinking, and it encourages students to ask the right questions needed to solve
mathematical problems (Cotner et al., 2013; Michael, 2006). Furthermore, supporters of
active learning argue that, when students work together, they are provided the opportunity
30
to learn from one another to share responsibility and leadership skills (Peak, 2010).
According to Watt, Huerta, and Lozano (2007), much research regarding active learning
shows an affirmative outcome on the student’s accomplishment and readiness to enroll in
college level mathematics courses. Moreover, active learning approaches support college
readiness and completion rate (Watt et al., 2006). As Muis (2004, p. 342) puts it, the
utilization of active learning is significantly associated with fundamental “motivation,
self-efficacy and self-regulation as well as course grades.” Dudley (2011), investigated
the significance relationship between a computer-based individualized mathematics
tutorial program, IPASS and grade school students’ performance in mathematics.
There is a high correlation between active learning and the role of improved
retention of knowledge, student thinking, and student problem solving abilities (Donovan
& Loch, 2013; Abrahams & Singh, 2010). As Desimore, Garet, Birman, Porter, and Suk
Yoon (2003) argued, the utilization of active learning opportunities by mathematics
instructors promotes classroom assessments in post-secondary education. In research
conducted to investigate the impact of virtual learning environment on final grades and
student learning, Mogus, Djurdjevic, and Suvak (2012) demonstrated that a positive
relationship exists when students are actively engaged or participate in a learning
environment. Similarly, Alemu (2010) conducted research and found a progressive
connection concerning the relationship between the active learning method and students’
academic proficiency at a university in Ethiopia. In a separate study, Arslan (2012) also
discovered an association between active learning and academic proficiency. Although
these studies investigated the connection between active learning and mathematics,
31
neither Alemu (2010) nor Arslan (2012) focused on African American students enrolled
in developmental mathematics at the community college level.
Chapter Two: Summary
Generally, students learn best by doing (Moye et al., 2014). Much work has been
done on active learning and constructivist learning approaches; however, active learning,
which is a student-centered approach, is more effective than the instructor-centered or
traditional teaching approach for achieving successful student learning outcomes
(Timmermans & Van Lieshout, 2003). Furthermore, conceptual knowledge of learned
mathematical concepts occurs when students are given a chance to cognitively connect
between mathematical concepts (Setati & Adler, 2000). The use of active learning is vital
in information processing, skills development, and maintenance of students’ attitudes.
Students exposed to active learning take ownership of learning.
Chapter three discusses the method and design of this investigation.
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CHAPTER 3: METHOD AND DESIGN
Chapter three discusses the design and quantitative data collection procedures of
the study. This chapter additionally measures how the data were collected to ensure
research integrity.
Population and sample of the study
The study populations were African American students at a two-year community
college, in an urban setting, registered in a developmental mathematics course (i.e.,
Intermediate Algebra with Geometry). The population of this study was placed into these
courses because of their academic performance on a computer adaptive test (COMPASS)
that placed them in appropriate classes based on their examination scores. COMPASS is
an online placement test developed by ACT (ACT, 2014). Other students also enroll in
this developmental mathematics course after successfully obtaining a grade of “C” or
better in Elementary Algebra with Geometry.
African American students enrolled in this investigation were freshman and
sophomore students who took their developmental mathematics course from the Fall
2010 to the Fall 2013 semesters. The students ranged in ages from 18 to 71 years. As part
of the study, HCC granted the investigator permission to access and utilize students’
academic records; IRB approval was also obtained by the researcher from HCC. The
total population of students enrolled from Fall 2010 to Fall 2013 was 3572 students,
33
while the sample population investigated was 2190 students who were enrolled in
developmental mathematics. Because 479 students had an incomplete grade and were
excluded from the data, the sample population for this investigation was reduced to 1711
African American students enrolled into an intermediate algebra course.
Course and student distribution
The investigator conducted the study in a public two-year college in an urban area
of the Midwest. Developmental mathematics courses at a two-year community college
typically refer to courses designed and offered as below college level. These
developmental mathematics courses or foundational studies included Pre-Algebra (3
credits), Elementary Algebra with Geometry-Mathematics (4 credits), and Intermediate
Algebra with Geometry-Mathematics (5 credits). The Intermediate Algebra with
Geometry, which was the subject of this investigation, included a review of elementary
Algebra with Geometry and its application, which is further outlined in more detail in the
course syllabus (see Appendix A). Intermediate Algebra with Geometry usually covers
topics such as absolute values, factorization, rational expressions, systems of equations,
and applications. Additionally, radical equations also are covered in an Intermediate
Algebra with Geometry course.
Three full-time instructors in this study from the Fall 2010 to the Fall 2013
semesters consistently used an active learning based curriculum with the following
assigned text book: Introductory and Intermediate Algebra, 4th edition (Bittinger &
Beecher, 2011). The control group was instructed by three full-time faculty members
who also used the same text. However, these instructors did not employ active learning
34
techniques. All sections met for 16 weeks during the semester, including the Fall 2013
semester; each section enrolled 35 students.
Sections that incorporated active learning throughout the developmental
mathematics course were designated as the intervention group, while sections that did not
incorporate active learning and instead used traditional teaching were designated as the
control group.
The active learning instruction focused on students interacting with the content of
developmental mathematics by participating actively in generating ideas instead of
receiving knowledge. This active learning process was designed through reading
developmental mathematics materials, writing, discussing, simulating, and solving
contextual problems (Efstathiou & Bailey, 2012; Clark, Nguyen, Bray & Levine, 2008;
Beers, 2005). The interactive project designed for this course included group projects,
students collaborating in pairs, and solving real life developmental mathematics
problems. The active learning project permitted students enrolled in the developmental
mathematics course to use active learning approaches to formulate questions, brainstorm
on the proposed developmental mathematics problem, think on the mathematics problem,
and explain and discuss the problems by actively engaging in the resolution of the given
problem (Salman, 2009). One of the activities for this course is enclosed in Appendix B.
Data Collection Procedures
In this study, the investigator utilized data on students from the Fall 2010 to the
Fall 2013 semesters as indicated in Table 1. The investigator’s measure of the impact of
active learning was based on two dependent variables: their academic proficiency and
completion rate. The completion rate for the purpose of this investigation is computed on
35
the students who completed the developmental mathematics course and graduated at the
host community college. The academic proficiency of students who completed the course
with a grade of C or better was then measured. Lastly, disaggregated data were obtained
and mined from HCC’s institutional research office that included student demographics.
The investigator collected and analyzed data for this investigation from the Fall 2010 to
the Fall 2013 semesters through HCC’s institutional research office. The disaggregated
demographics data entails age, ethnicity, gender, race, socioeconomic background, and
students’ proposed area of study. The investigator self-funded the investigation.
Table 1
Population Numbers for the Study
Number of Students Years Intervention /Control
Group 1 831 Fall 2010 – Fall 2013 Intervention
Group 2 880 Fall 2010 – Fall 2013 Control
Total 1711
Data Analysis and Research Approach
The investigator utilized a non-experimental design to investigate the relationship
between active learning methodologies and the academic proficiency and completion rate
of African American students enrolled in developmental mathematics classes. Following
36
the initial work on the state of HCC in developmental mathematics, specifically
intermediate algebra, the college worked with the faculty members of the mathematics
department to design and implement active learning approaches that impact student
learning outcomes. Six instructors volunteered to teach the intermediate algebra course,
but in two different classrooms. One classroom was designed for active learning while
the second classroom was designed for traditional lectures. Both active and traditional
classroom sections were taught two times per week and the class met for 16 weeks.
Course materials, homework assignments, and examinations were the same. It is
important to mention here that students who participated in this investigation were
enrolled voluntarily to the active learning classroom, while other students registered
voluntarily for the traditional lecture classroom. Furthermore, homework assignments,
quizzes, and examinations were identical. To control for instructor, attempts were made to
ensure that all instructors teaching with active learning kept the same course materials
and administered the designed activities while the traditional classroom for intermediate
algebra used lectures (Cotner et al., 2013).
In Fall 2010, HCC gathered several data, and the college then implemented an
initiative called “active learning approach.” First, the investigator obtained student
records from the HCC institutional research office. Second, the researcher obtained
sample assessments tools from the chairperson at HCC showing mathematical knowledge
on a cross section of intermediate algebra topics. HCC also approved an IRB request
which permitted the researcher to conduct this investigation. Data analysis was conducted
using SPSS (SPSS version 22, Statistical Package for Social Science) to analyze the data.
37
The analysis was set at 0.05 confidence level. A cross tabulation, Chi square and
Cramer’s V value were calculated.
A Chi-square test was used to measure the correlation presented in the research
questions. Chi-square, according to McMillan (2008), can determine “questions of
relationships between two independent variables that report frequencies of responses or
cases” (p. 265). According to Nardi (2006), Chi-square measures independence of two
variables and also inquires whether what the investigator observed is significantly
different from what the investigator would have expected to get by chance alone. Chi
square test is a statistical tool to investigate differences between categorical or nominal
variables (Wu et al., 2012). Chi square is commonly used to measure the association of
variables. Chi-square analyses were used to check the significance when the researcher
noticed that active learning (the independent variable) had an impact on academic
proficiency and/or completion rate (dependent variables).
Cramer’s V, on the other hand, is the most widely nominal association used to
measure the strength of relationship regardless of the data set sample size. Cramer’s V is
used to measure effect size. Named after Swedish statistician Harald Cramer, Cramer’s V
is the most widely used Chi-square based measure of dependency between categorical or
nominal variables. Cramer’s V measures the strength of relationship for any size of
contingency table, and it offers good norming values from 0 (zero) to 1 (one) for relative
comparison of the strength of correlation regardless of the table size. For 2X2, Cramer’s
V is the same as Phi-value. It is worth mentioning here that Cramer’s V is an index of the
strength of association only. Additionally, the limitation of Cramer’s V is that it cannot be
utilized to compare the strength of one relationship to another correlation. For Cramer’s
38
V, 0.0 to 0.30, the strength is considered no relationship to weak; for Cramer’s V, 0.31 to
0.70, the strength is considered moderate relationship; while for Cramer’s V from 0.71 to
1.0, the strength of the relationship is considered strong.
Additionally, this study utilized a paired samples t-test to compare two means of
the results of pre- and post-tests administered from Fall 2010 through Fall 2013 at the
beginning of each semester before class started and then at the end of the semester to
measure any significant gain reflected on college preparation for underprepared students.
Specifically, HCC only provided disaggregated data for pre-test and post-test from Fall
2010 to Fall 2013 school years. A pre-test administered on the first day of class in Fall
2010 to Fall 2013 and a post-test administered at the end of the semester of Fall 2010,
Fall 2011, Fall 2012 and Fall 2013 measured any impact of active learning on the
intervention group.
Privacy and Confidentiality
The disaggregated data for this investigation already existed with the college of
study (HCC). Students’ names and personal information were not released to the
investigator. The faculty teaching the intervention group and the control group were
coded in the HCC data base and kept confidential for this study. Additionally, the identity
of the host community college was kept confidential for this study (referred to as Hope
Community College-HCC). Number identifiers were used so that the researcher collected
data anonymously. Data specifically used for this research have been kept in a locked
box, secured for a minimum of seven years, and will be obliterated upon completion by
the investigator once the initial purpose of the research has ceased.
39
Additional Required Information
Declaration of Conflicting Interest
Although the researcher teaches utilizing an active learning teaching
methodology, this research was totally quantitative, objective and confidential.
Benefit of the Project
I believe this study can be significant and beneficial to HCC in particular, and to
community colleges in general, because it seeks to demonstrate, through statistical and
student data, that learning methodologies based on active participation have a positive
impact on student learning objectives in a developmental mathematics course.
Furthermore, according to Salman (2009), active learning instructors benefit from this
approach by enhancing their teaching skills; the active learning approach also frees
instructors from the teacher-centered approach of teaching developmental mathematics to
students. In addition, the findings of this study may improve teaching delivery of
developmental mathematics to students entering post-secondary institutions, and they
may enhance student learning outcomes in the field of mathematics education. The results
will be shared with the administration. Said data will be used to continue the
conversation within the initiative to increase students’ academic proficiency and/or
increase the success rates of African American students, and to reach the completion
goals set by the college chancellor and administrators when active learning techniques are
utilized.
40
NIH/CITI
NIH and CITI certificates were completed to enable the researcher to conduct this
investigation.
Chapter Three: Summary
Chapter three addressed the method and design utilized to gather data from HCC
and how these data were uploaded as an Excel spreadsheet into the SPSS version 22
(Statistical Package for Social Science). Both the independent (active learning) and the
dependent (academic proficiency and completion rate) variables were identified
accordingly to calculate the investigation descriptive statistics. This quantitative
investigation utilized descriptive statistics to address research questions to investigate the
connection between active learning and the academic proficiency and completion rate of
African American students enrolled in developmental mathematics. A cross tabulation
was generated to interpret the data received from the host community college. The
investigator used Chi-square tests to analyze data obtained from HCC office of
institutional research, and Cramer’s V was used to provide answers to two research
questions. To analyze gathered data, frequencies of occurrence of every group were
calculated. Using the data for this quantitative investigation, the investigator attempted to
provide answers to the following research questions.
Research Questions
The following research questions directed this investigation:
41
Is there any relationship between active learning and the academic proficiency
of African American students who participate in active learning intervention
and the academic proficiency of African American students who receive
traditional instruction?
Is there any relationship between active learning and the completion rate of
African American students who participate in active learning intervention and
the completion rate of African American students who receive traditional
instruction?
In this chapter, the design of this investigation was described, and the activities and
methods used for data collection were elucidated. In chapter four, the researcher presents
the result of the quantitative data using statistical analysis, tables, and graphs or figures.
42
CHAPTER 4: ANALYSIS OF DATA AND RESULTS
Chapter four of this investigative study presents: (1) deliberations on findings of
data obtained from this investigation, and (2) an explanation of the analysis of data
obtained from this research concerning African American students enrolled in a
developmental mathematics course.
Demographic Background
The aim of this quantitative study is to investigate the effectiveness of active
learning on the academic proficiency and completion rates of African American students
enrolled in an intermediate algebra course. Data received from HCC indicated that 7,972
students enrolled in developmental mathematics courses (Intermediate Algebra with
Geometry) from Fall 2007 through Fall 2013. As this study is concerned with African
American students, the investigator excluded non-African American students from 7,972
students registered in the Intermediate Algebra with Geometry course. Additionally, the
investigator excluded students enrolled in mini sections of the course as it could not be
determined whether they were enrolled in an active learning intervention approach
program after it had been established in Fall 2010.
This left a population of 1711 African American students who participated in the
target course from Fall 2010 through Fall 2013. The data further demonstrate that from
Fall 2010 to Fall 2013, 831 African American students were enrolled in the intervention
course (48.6%), while 880 students were African Americans enrolled in the control
43
course (51.4%); see Table 1. The African American students assessed ranged in age from
18 to 71 years with an average age of 25.5 years (SD = 8.84); see Table 2. Eighty percent
were female, 19.9% were male; see Table 3.
Table 2
Descriptive Statistics of Ages
N Minimum Maximum Mean Std.Deviation
Age 1711 18 71 25.53 8.84
Table 3
Gender of African American Students include the control and intervention groups
Gender Number Percentage Control Intervention
Female 1370 80.1 705 665Males 341 19.9 175 166
Total 1711 100 880 831
The investigator imported archived data into statistical analysis software,
SPSS version 22 (2014), and coded the data for analysis. The results of these analyses are
segmented into the following research questions that directed this study:
Is there any relationship between active learning and the academic proficiency
of African American students who participate in active learning intervention
and the academic proficiency of African American students who receive
traditional instruction?
44
Is there any relationship between active learning and the completion rate of
African American students who participate in active learning intervention and
the completion rate of African American students who receive traditional
instruction?
Chi-square testing measured the relationship of two categorical variables to
answer research question one, which looked for any relationship between active learning
and the academic proficiency of African American students who participated in the
intervention and the proficiency of African American students in the control group.
Active learning and academic proficiency of African American students were the
variables investigated. The investigator obtained data from the HCC office of institutional
research and coded grades as 1 for F, 2 for D, 3 for C, 4 for B and 5 for A, and then
recorded these data as 1 through 2 as “0,” and 3 through 5 as “1.” Similarly, zero was
again re-coded as lacking academic proficiency and one was re-coded as academically
proficient. Therefore, the investigator deemed African American students enrolled in the
target course who made grades D and F as not academically proficient, and African
American students who made A, B, and C grades as academically proficient.
Similarly, for the second research question concerning completion rate, using data
obtained from the office of HCC institutional research, for students who received a
certificate, associate degree or both from Fall 2010 to Fall 2013, the investigator coded
students who received associate degree or diploma as “1” and those who did not receive
associate degree or certificate as “0” (zero). This Excel file was then uploaded into SPSS
(version 22).
45
Research Question One
Is there any relationship between active learning and the academic proficiency
of African American students who participate in active learning intervention
and the academic proficiency of African American students who receive
traditional instruction?
To investigate research question one, the investigator analyzed the gathered data
using Chi-square test. Academic proficiency of African American (AA) was measured
using grades, and the information was coded accordingly. The result showed that after
implementing the intervention, 72.2% of African Americans with active learning were
proficient, while 54.7% of African Americans who did not participate in active learning
were proficient in developmental mathematics courses.
Tables 4 and 5 present frequency tables for academic proficiency of the
intervention and the control groups. African American students in the intervention groups
were more proficient.
46
Table 4
Academic Proficiency: Control and Intervention Groups
Variable(Grade)
Control Intervention TOTAL
Academic proficiency (A)Count 104 122 226
Academic proficiency (B)Count 161 233 394
Academic proficiency (C) Count 216 245 461
Non-proficiency (D) Count 102 88 190
Non-proficiency (F) Count 297 143 440
Total Count 880 831 1711
Percent of Total 51.4% 48.6% 100%
47
Table 5
Cross-Tabulation of Academic Proficiency for Control and Intervention Groups
Variable Control Intervention TOTAL
Non-academic proficiency Count
399 231 630
Percentage (45.3) (27.8) (36.8)
Academic proficiency
Count 481 600 1081
Percentage (54.7) (72.2) (63.2)
Total Count 880 831 1711
Percent of Total 51.4% 48.6% 100%
48
Table 6
Chi-Square Test Results
A Chi-square test, as shown in Table 6, indicated significant association between
intervention and academic proficiency, χ2 (1, n = 1711) = 56.54, p < .001, Cramer’s V
= .182.
Based on the results, the investigator rejects the null hypothesis and concludes
there is a relationship between active learning and the academic proficiency of students
of African American students who participate in the active learning intervention and the
academic proficiency of African American students who received traditional instruction.
Figures 1 and 2 represent in bar chart format the content of Tables 4 and 5.
49
Value Df Asymp. Sig.
(2-sided)
Pearson Chi Square 56.543 1 .000
Likelihood Ratio 57.070 1 .000
Linear-by-Linear
Association56.510 1 .000
Total 1711
Figure 1
Bar Graph showing Academic Proficiency of Control and Intervention Groups
1=F 2=D 3=C 4=B 5=A0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
Academic Proficiency for Control and Intervention Groups of African American Students
0=Control Group
1=Intervention Group
Perc
ent
Control group = Blue Bar; Intervention group = Red Bar
50
Figure 2
Bar Graph showing Academic Proficiency of Control and Intervention Groups
0
10
20
30
40
50
60
70
80
Academic Proficency Rate Control and Intervention Groups
No Academic Proficency Yes Academic Proficency
Control group = Blue Bar; Intervention group = Red Bar
Academic Proficiency Measured by Pre-and Post-Test Results
Several tests were conducted to compare the pre-test and the post-test results of
intervention and the control groups earning grades A, B and C (academically proficient).
Grades D and F (not academically proficient) were excluded from these data.
The pre-test results of mean and standard deviation of the intervention and control
groups are shown in Tables 7.
51
Table 7
Means of Pre-Tests for Students Earning A, B, or C (Academic Proficient) for
Intervention and Control groups
N Mean Std.Deviation
Intervention 600 2.848 .7232
Control 481 2.843 .7878
The descriptive statistics in Table 7 show that the mean of the pre-test scores for
both intervention and the control groups are equivalent.
A mean difference was conducted to evaluate whether Intervention group pre-test
and post-test were statistically different in mean. (See Table 8)
Table 8
Mean of Pre-Test and Post-Test scores for Intervention groups
Mean N Std. DeviationPair 1 Intervention Pre-Test 2.843 600 .7232
Intervention Post-Test 3.338 600 .7777
The researcher conducted a mean difference to determine if there was any
significant difference between the pre-test mean and the post-test mean of the
intervention groups. The finding in Table 9 indicates that the mean for pre-test (M=
2.843, SD = .7232) was significantly less than the mean of the intervention post-test
groups (M = 3.338, SD = .7777), t (599) = -11.248, p < .01. The results demonstrate that
52
the gains from pre-test to post-test were highly significant. The 95% confidence interval
for the difference in means was -.5814 to -.4086. The mean difference of -.4950 falls
firmly within the confidence interval.
Table 9
A Paired sample t-test of Means of Pre-Tests and Post-Test for Intervention Group
t df Sig.
(2-tailed) Mean Difference
95% Confidence Interval of theDifferenceLower Upper
Intervention -11.24 599Pre-Test andPost-Test(A,B,C)
.000 -.4950 -.5814 -.4086
Similarly, a mean difference was conducted to evaluate whether control group
pre-test and post-test scores were statistically different in mean. (Table 10).
Table 10
Mean of Pre-Test and Post-Test Scores for Control Group
Mean N Std. DeviationPair 1 Control Pre-Test 2.848 481 .7878
Control Post-Test 2.786 481 .8126
The researcher conducted a paired sample t-test to determine if there was any sig-
nificant difference between the pre-test mean and the post-test mean of the control
53
groups. The finding in Table 10 indicates that the mean for pre-test (M= 2.848, SD
= .7878) was higher than the mean of the control post-test groups (M = 2.786, SD
= .8126), t (480) = 1.83, p = .068. The results demonstrate that the control group lost pro-
ficiency even though the loss was not statistically significant. The 95% confidence inter-
val for the difference in means was -.005 to .1293. (Table 11) The mean difference
of .0624 falls firmly within the confidence interval.
Table 11
A Paired sample t-test of Means for Pre-Tests and Post-Test for Control Group
t df Sig.
(2-tailed) Mean Difference
95% Confidence Interval of theDifferenceLower Upper
Control 1.830 480Pre-Testand Post-Test
(A,B,C)
.000 .0624 -.005 .1293
With reference to the findings and discussions of Tables 8 to 11, it is clear that the
intervention group gained academic proficiency at a highly significant statistical level
whereas the control group proficiency actually declined. Therefore null hypothesis 1 is
rejected. An active learning approach is more effective for African American students
than traditional instruction.
54
Research Question Two
Is there any relationship between active learning and the completion rate of
African American students who participate in active learning intervention and the
completion rate of African American students who receive traditional instruction?
In order to determine completion, the 150% of normal time to graduation
calculation is applied. This measure is normally applied to first-time, full-time, degree-
seeking students. While the population for this study consisted of part-time and full time
students, the 150% measure is used in order to provide a uniform and consistent unit.
Contingency tables of cross tabulation revealed that the intervention group had about
8.2% completion rate and the control group had about a 7.8% completion rate (see Table
12).
55
Table 12
Cross-Tabulation Completion Rates for Control and Intervention
Variable Control Intervention TOTAL
Non-CompletionCount 811 763 1574
Percentage 92.2 91.8 92.0
CompletionCount 69 68 137
Percentage 7.8 8.2 8.0
TotalCount
880 831 1711
To test the relationship between active learning and the completion rates of the
intervention and control groups, the researcher conducted Chi-square tests. The
association between the intervention group and completion rates was not statistically
significant, χ2 (1, n = 1711) = .068, p < .001. ( In a separate calculation, Cramer’s V
= .006). The result of the Chi-Square in Table 13 indicates that African American students
who participated in the intervention group and completed an Associate degree, certificate
or both from Fall 2010 through Fall 2013 had a higher completion rate than the control
group even though the result was not statistically significant.
56
Table 13
Results of Chi-Square Tests Completion Rates for Intervention and Control
Value df Asymp. Sig.
(2-sided)
Pearson Chi Square .068 1
Likelihood Ratio .068 1
Linear-by-Linear
Association.068 1 .859
Total 1711
The findings from the cross tabulation table showing that students in the control group
who received a degree, certificate or both had a completion rate of 7.8 %, while those in
the intervention group who received an Associate degree, certificate or both, had a 8.2%
completion rate. However, these findings were not statistically significant. Therefore the
researcher does not reject the null hypothesis.
Chapter Four: Summary
The investigator collected data from HCC, coded, recoded and then uploaded the
data into SPSS, version 22 (the Statistical Package for the Social Sciences). Through
quantitative investigation, the researcher examined the effectiveness of active learning on
the academic proficiency of African American students enrolled in developmental
mathematics at a two-year college, and identified independent and dependent variables.
This study utilized descriptive statistics to determine findings for two research
questions. The researcher isolated and analyzed a data subset consisting of African
57
American students enrolled in developmental mathematics (intermediate algebra) using
four 2X2 Chi-square tests and a t-test. The researcher affirmed a correlation between the
academic proficiency of African American students who participate in active learning
intervention and the proficiency of African American students who receive traditional
instruction. These data supported the first hypothesis. Secondly, the researcher
investigated the existence of any statistically significant relationship between active
learning and the academic proficiency of African American students enrolled in
developmental mathematics, and supports the alternative hypothesis. For the second
research question, the investigator affirmed that there is no statistically significant
relationship between the intervention and control groups and the completion rate of
African American students enrolled in the target course. It is necessary to mention here
that the investigator did not account for students who completed intermediate algebra but
transferred to other community colleges or universities, or enrolled in developmental
mathematics courses for professional or personal edification.
In summary, chapter four addressed the research problem, the purpose of this
investigation, research questions and findings. This section also described data
interpretations. Discussion, summary, conclusion and recommendations are indicated in
chapter five.
58
CHAPTER 5: DISCUSSION
Chapter five of this investigation summarizes, discusses and concludes the
findings outlined in chapter four. It presents recommendations for further study related to
the effect of active learning on the academic proficiency and completion rates of African
American students enrolled in an intermediate algebra course.
Quantitative data were collected for this investigation. The research supports the
premise that active learning is effectively associated with better academic proficiency.
However, the findings of this investigation indicate no statistically significant relationship
between active learning and the completion rate of African American students.
This investigation aimed to answer two research questions:
Is there any relationship between active learning and the academic proficiency
of African American students who participate in active learning intervention
and the academic proficiency of African American students who receive
traditional instruction?
Is there any relationship between active learning and the completion rate of
African American students who participate in active learning intervention and
the completion rate of African American students who receive traditional
instruction?
Summary of Study
Data were obtained from HCC from Fall 2010 to Fall 2013. The intervention
group received instructions via an active learning approach, while the control group
received instruction using the traditional lecture approach. Three instructors taught in the
intervention groups, while three instructors taught in the control groups. Student
59
demographic data were collected and coded according to ethnicity, gender, grade level
(freshman or sophomore), and letter grades for academic proficiency (A, B, C, D or F).
Additionally, completion rates data were obtained from the office of institutional research
of HCC from Fall 2010 to Fall 2013. Students in the intervention group who received an
associate degree, certificate or both from Fall 2010 to Fall 2013 were coded as “1” by the
investigator and those in the control group were coded as “0”. A pre-test measuring
students’ mathematical proficiency at the beginning of the course was administered, and a
post-test at the end of the course was administered.
The quantitative information was coded and uploaded from Excel into SPSS
software. A Chi-square, and a paired samples t-test were conducted to investigate the
correlation between active learning and academic proficiency and active learning and
completion rates of African American students enrolled in an intermediate algebra course.
Research Question One
Is there any relationship between active learning and the academic proficiency of African
American students who participate in active learning intervention and the academic
proficiency of African American students who receive traditional instruction?
The results of data analysis indicate the existence of a relationship between the
teaching method used for the intervention and control groups and their academic
proficiency. The findings indicate that after implementing the intervention, 72.2% of
students in the intervention group were proficient, while 54.7 % of students in the control
group demonstrated proficiency. A particularly salient finding demonstrated that students
60
in the intervention group achieved mathematics proficiency at a higher level, i.e., they
earned more grades of A and B than those in the control group.
Discussion of Research Question One
The use of active learning fosters collaborative learning that encourages students
to perform academic assignments in groups in and out of the college environment. These
interactions improve communication and peer to peer learning leading to the
improvement of students’ problem solving and quantitative reasoning skills.
Consequently, utilization of active learning enables students to develop social networks
that form academic community that facilitates the attainment of higher order learning.
When active learning is applied, it promotes student engagement resulting in
transformative change.
Students who learn actively often recollect learning experience far into the future,
as opposed to those learning from memorization. Developmental mathematics instructors
may benefit from identifying with this concept. Efforts to integrate active learning
principles into developmental mathematics may lead to new curriculum development that
requires faculty and staff collaboration and problem solving, resulting in transformative
change to curriculum as well. Gaining knowledge then becomes a lifelong and never-
ending experience for both students and teachers.
The utilization of active learning provides community college instructors with an
alternative to the traditional method of teaching developmental mathematics courses. Our
research findings offer an argument for developmental mathematics departments to
integrate this teaching methodology as part of their andragogy. As this investigation
affirms, students are more engaged with active learning and active learning approaches
61
maybe useful for closing the achievement gap between African American and non-
African American students.
This investigation shows that the incorporation of active learning may offer a
solution to persistent challenges facing many African American students enrolled in
intermediate algebra courses. With active learning, students learn by engaging in group
activities, increase classroom participation and resolve problems through peer
collaboration. Students are encouraged to develop academic independence, enhance
creativity, increase critical thinking, and reflect increasingly upon materials discussed,
while integrating learning into their cultural and life experiences. Academic
administrators, instructors, family and academic advisors who traditionally view African
American students as unmotivated to engage in mathematics are encouraged to adopt and
promote active learning teaching methods.
At HCC, administration, faculty and staff are cognizant that effective
transformation is internal. The use of active learning is designed as a part of that
transformation. This study affirms that the intervention at HCC does succeed in
promoting the achievement of academic proficiency in African American students. To
ensure long-term student success, the college must strive to sustain active learning
initiatives that are effective. HCC plans to support continuous improvements with
administration and members of faculty and staff to develop performance objectives,
rubrics, and methods of assessment by proposing and developing collaborative courses
and programs. By utilizing the active learning framework, HCC expects to create a
collaborative, non-static, cultural environment by fostering effective partnership among
HCC programs, departments and staff to positively affect the academic proficiency,
62
retention and completion rates of its students.
Research Question Two
Is there any relationship between active learning and the completion rates of African
American students who participate in active learning intervention and the completion
rates of African American students who receive traditional instruction?
For research question two, to determine completion rates, the 150% of normal
graduation calculation was applied. The independent variable was active learning and the
dependent variable was completion rates. Alpha was set at 0.05 level of significance. The
finding indicates that after implementing the intervention, the intervention completion
rate percentage was 8.2, while the completion rate percentage of the control groups was
7.8. The result obtained in this investigation supports, even if only by a marginal factor,
the researcher’s expectation. However, it needs to be clear that the correlation between
the completion rates of the intervention and control groups was not statistically
significant, χ2 (1, n = 1711) = .068, p < .001, Cramer’s V = .006.
Discussion of Research Question Two
Unlike the very significant differences in the academic proficiency achieved by
the intervention and control groups, Research Question 1, this study found very little
difference in the completion rates of students in the two groups.
Given the finding in Research Question 1 that students in the intervention group
achieved greater academic proficiency and achieved it at higher levels (grades of A and
B) the finding for Research Question 2, positive but statistically not significant, was
counterintuitive and disappointing. Nothing in the data permits the researcher to
speculate about why results are as they are. It is clear to the researcher that this particular
63
phenomenon needs further study. Quantitative analysis of performance in subsequent
courses and of retention and persistence trends might offer some insight. A qualitative
approach would probably offer more useful information about student behavior.
Of course, the underlying problem is the poor completion rates of community
college students in general. Factors influencing those low rates would obviously have
influenced both groups in this study. At HCC, two factors are known to operate. Students
entering HCC are often unprepared for the rigors of college academic life and are prone
to dropping out after their first semester when met with academic challenges. Secondly
many students entering HCC are first generation college students whose parents or
relatives never experienced college life and as a result could not provide them with
mentoring and guidance as to how to succeed in college and meet its multitude of
challenges.
HCC has developed, maintained, and is implementing an early alert referral
system in which instructors refer students to an advisement and academic support center
to assist them in their academic endeavors. The college is also creating a program on
college success coursework for freshmen to teach them the necessary study skills to
maintain good grades. Lastly, students are encouraged and required to maintain a
continuous relationship with their assigned educational advisor to ascertain that they are
provided the service and support needed for college completion. When the above
initiatives are implemented, HCC may experience a rise in graduation rates.
It is imperative that community colleges account for the academic and socio-
economic challenges facing their students, especially African American students, and
devise systems and programs to reverse the low completion trends and increase retention
64
and success rates. To improve the success and completion rates of African American
students in community college courses, especially in developmental mathematics such as
intermediate algebra, two-year colleges should develop efficient assessment tools to
identify specific weaknesses of these students requiring customized support and
mentoring programs that will address the students’ specific needs, removing all obstacles
towards their success. In order to better prepare the incoming college students for the
academic rigor of the college and improve their success and completion, it is prudent that
the colleges collaborate with high schools to better align their curriculum and improve
pedagogy. It is therefore, recommended that HCC collaborate with neighboring feeder
schools to develop bridge programs to assist African American students become college-
ready and proficient in developmental mathematics. Moreover, lack of career
opportunities and educational resources may be another factor that contributes to the low
completion rates of African American students in community colleges. To address this
issue, community college leaders should collaborate with local business leaders to
provide funding for the programs and to host career opportunities to assist the smooth
transition of African American students from graduation to employment.
Finally, there is the question of the unit used to measure completion rates. For the
study, the 150% of time to degree was used as a practical and uniform measure. The
researcher is fully aware that this measure is appropriately used for first-time, full-time
degree seeking students at a community college. However a practical unit was necessary
in order to provide a uniform measure for the two groups in the study, and 150% of time
was selected. Applying it to both groups provided uniformity. There is no claim that the
65
figures resulting are correct in any absolute sense. They are only used for the correlation.
The figures should in no way be used to suggest the performance of HCC.
In addition to the issues raised by the 150% of time measure, this investigator
recognized but chose not to include the variable of students who attend HCC and transfer
before completing degrees. HCC struggles to account for African American students who
completed developmental mathematics courses but did not graduate and instead
transferred to another community college or four-year university and graduated. The
investigator speculates that when the definition of completion rates includes transfer
students or students who attended a mathematics developmental course for professional
development, or when the graduation is defined at 300%, community colleges should
experience improved graduation rates.
In contrast to Pfaff and Weinberg (2009), who found that active learning had no
effect on nor was any impediment to students’ academic performance, Alemu (2010),
Arslan (2012) and Dudley (2011) found a positive correlation with active learning. The
implementation of active learning in this investigation has proven to have a positive
impact on the academic proficiency of African American students enrolled in a
developmental mathematics courses; the findings regarding the impact of active learning
on the completion rates was very small and not significant. While developmental
mathematics courses often use outdated pedagogy and andragogy that do not effectively
prepare African American students, active learning methodologies can serve to correct the
disparities and improve student proficiency in intermediate algebra courses, particularly
for minority students. The success of African American students in developmental
mathematics is a vehicle for their success in college-level mathematics courses. Success
66
in college mathematics prepares students for careers which require the knowledge of
mathematics and its applications. Considering the severe underrepresentation of
minorities, particularly African Americans, in Science, Technology, Engineering,
Mathematics (STEM) disciplines, active learning approaches may well improve the
academic proficiency of African American students and help to address this national
need.
Future Research and Recommendations
Clearly this investigation has demonstrated that the use of active learning
approaches is effective for raising academic proficiency in intermediate algebra courses;
the results for completion rates are positive but statistically inconclusive. This study has
also shown that developmental mathematics, in particular, and community colleges, in
general, could benefit immensely from the utilization of active learning approaches to
influence positively the academic proficiency of African American students in
developmental mathematics courses. A longitudinal study is recommended to expand the
study on the impact of active learning on the academic proficiency and completion rates
of African American students enrolled in intermediate algebra courses. Based upon the
findings from this investigation, my recommendation is to increase advocacy for active
learning methods in order to develop a fresh curriculum in developmental mathematics
courses.
This investigation is based solely on quantitative data; its findings and
implications are derived from quantitative research. The investigator intends to conduct
further studies replicating this investigation using qualitative, and mixed-method
approaches.
67
With reference to completion rates, a larger sample size investigation should be
conducted to better assess developmental mathematics students’ learning profiles. This
investigation should include qualitative and mixed-methods to solicit and effectively
assess students’ experiences and feedback on the effectiveness of active learning. Lastly,
HCC should employ strategic planning and quality initiatives to ensure the sustainability
and scalability of proposed solutions and to evaluate regularly their effectiveness.
As mention earlier, the results of this study did not consider African American
students enrolled in intermediate algebra courses who transferred to another two-year
college or a four-year university or did not obtain a basic certificate or an Associate
degree from the host two-year college (HCC). The investigation on the correlation of
active learning and completion rates of African American students enrolled in
developmental mathematics courses should be expanded to encompass those students.
Additional research is needed to check and validate the findings of this investigation.
Building strong research that encourages the utilization of effective methods of teaching
and learning is a vital work that requires institutional and individual efforts. More
investigations are required to build a body of evidence concerning the implementation of
active learning approaches. Modified versions of this investigation that would study
differential changes between African American genders, age groups, and other ethnic
populations are recommended. Since the sample size of African American male students
was small (341 students), it would be valuable to replicate the above investigation with a
focus on African American male students enrolled in developmental mathematics courses
to study how active learning impacts male students’ proficiency and completion rates.
68
Additional research is needed to determine advantages of active learning methodologies
on the performance of African American students in other courses.
The use of active learning approaches and their potential to engage students is
optimized when developmental mathematics faculty members embrace emerging
technologies, tools, and a holistic learning environment. This approach will only
materialize when developmental mathematics instructors assess what students learn, how
students learn, where students learn, and when student learning takes place (Farrell,
2014).
The results from this investigation add to the body of knowledge that the
utilization of active learning promotes the success of African American students enrolled
in intermediate algebra courses. It may encourage developmental mathematics instructors
to apply this method of teaching and also guide future investigations in conducting
longitudinal studies to track students’ performance over a longer period of time.
Finally, the investigator believes it is vital for educators to be cognizant that
without students, there is no classroom. It is the investigator’s hope that this investigation
will serve as a catalyst for scholars and other educators to utilize active learning as an
alternative andragogy or pedagogy, to help students succeed at college.
69
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Appendix A: Syllabus for Developmental Mathematics Course
(Intermediate Algebra with Geometry)
HOPE COMMUNITY COLLEGE
Fall 2013
COURSE SYLLABUS Mathematics ***
(This course syllabus will be uploaded to Blackboard “Syllabus” tab)
Course Title and Section (Intermediate Algebra with Geometry, IAI Code: None & ***):
Length of Course: 16 Weeks
Credit Hours: 5 Credit Hours Contact Hours: 5 Contact Hours
Class Meeting Times: 8:30:00 AM ‒10:40 AM Building / Room: 3***
INSTRUCTOR: Prof Intermediate Algebra
E-MAIL: [email protected] PHONE: (773)000-0000
OFFICE: ROOM 3**8
OFFICE HOURS: (8:00AM-8:55AM Tuesday &Thursday)(1:15PM-2:00PM Tuesday &Thursday)(7:30AM-8:25AM Monday &Wednesday)(12:45PM-1:45PM Monday &Wednesday)
COURSE WEBSITE: (Blackboard: ***.blackboard.com & coursecompass.com-
MyMathLab)
Course Description
Algebraic operations involving rational exponents, including scientific notation
(also calculator version). Algebraic expressions, including radical and rational
expressions. Solutions of quadratic, quadratic in form, rational, radical, and absolute
value equations. Solutions of compound linear inequalities. Solutions and manipulations
of literal equations. Graphical and algebraic solutions of systems of linear equations in
two and three variables; graphical solutions to systems of linear inequalities. Graphs of
linear and quadratic equations. Geometry: perimeter, area of geometric figures, triangles,
rectangles, and circles; volume of sphere, cylinder, and pyramid. Pythagorean Theorem
and distance formula, Similarity and Proportions.
Applications of problem-solving skills are emphasized throughout the course.
Students should be exposed to graphing calculator technology and/or computer
Algebra systems. Writing assignments, as appropriate to the discipline, are part
of the course.
Prerequisites
Prerequisite: MATH 098 with a minimum grade of ‘C’ OR Placement Test OR Consent of
Chair
(This is the description found in the “Course Description” section of the current catalog).
Required Texts and Materials
Text. Introductory and Intermediate Algebra 4/e by Marvin Bittinger and Judith
Beecher (2011), Published by Pearson
Materials. Texas Instruments TI-83/84 Plus Graphing Calculator 10-Digit LCD or
better and access to a computer.
Students Course is expected to serve
This course is intended for students who are both liberal arts majors and STEM
majors that require other mathematics course for their undergraduate degree.
Course Objectives
This course is designed with learning activities, special assignments, group
projects, case studies, and activity-based learning in a contextualized learning
environment. Student will be able to relate the materials covered to real life situations.
The learning environment will be both in and out of class.
1. Interpret and draw inferences from mathematical models such as formulas,
graphs, tables, and schematics.
2. Represent mathematical information symbolically, visually, numerically, and
verbally.
3. Use arithmetic, algebraic, geometric, and/or statistical methods to solve
problems.
Measurable Student Learning Outcomes
Upon satisfactory/ Successful completion of the course, students will be able to:
1. Simplify expressions containing rational exponents.
2. Perform operations on and simplify radicals.
3. Perform operations on and simplify rational expressions.
4. Solve quadratic equations with real solutions, including the use of the
quadratic formula.
5. Solve rational equations.
6. Solve absolute value equations of the form .
7. Solve radical equations of the form: .
8. Solve compound linear inequalities.
9. Solve systems of linear inequalities in two variables.
10. Solve systems of linear equations in two and three variables.
11. Formulate and apply an equation, inequality or system of linear equations to
a contextual (real-world) situation.
12. Solve and evaluate literal equations, including nonlinear equations.
13. Formulate and apply nonlinear literal equations to a contextual (real-world)
situation.
14. Graph linear and quadratic equations.
15. Determine equations of lines, including parallel and perpendicular lines.
16. Determine whether given relationships represented in multiple forms are
functions.
17. Determine domain and range from the graph of a function.
18. Formulate and apply the concept of a function to a contextual (real-world)
situation.
19. Interpret slope in a linear model as a rate of change.
20. Apply formulas of perimeter, area, and volume to basic 2- and 3-
dimensional figures in a contextual (real-world) situation.
21. Apply the Pythagorean Theorem to various contextual (real-world)
situations.
22. Apply the concepts of similarity and congruency of triangles to a contextual
(real-world) situation.
Student will also be able to select and apply appropriate models for solving real-world
problems.
Topical Outline
In meeting the above objectives, we will cover the following topics:
Week Topic
01-02 Algebraic Expressions
03-05 Linear Equations & Inequalities-graphs of linear equations-compound linear inequalities-systems of linear equations-graphs of systems of linear inequalities-literal equations, area and volume-applications
06 Review
07 Exam I
08 Exponents & Scientific Notations
09 Quadratic Equations-graphs of quadratic equations-factoring-radical expressions-radical and quadratic equations-quadratic formula-applications, Pythagorean Theorem
10 Review Exam II
11 Rational and Absolute Value Equations
Exam III
12 Geometry
13-14 Functions
15 Review/ Final
16 Final Exams
Method of Instruction
1. Problem-based activities, collaborative-learning techniques, case studies and
lecture will be used as appropriate.
2. Discussion/Facilitation
3. Small group work/Activity Based Learning
4. Calculator and computer applications
Definition / Statement of Active Pursuit of the Course
District and College attendance policies are listed in the college catalog and the
Student Policy Manual: http://HCC/Student/files/Student_Policy_Manual_8.25.09.pdf
Attendance
It is mandatory. Students are expected to inform the instructor about his/her
absence(s) due to extenuating circumstances and to obtain any handouts given. Be sure
to come to class on time and regularly. Poor attendance usually yields poor exam scores,
which can lower a student’s GPA. It is the student’s responsibility to drop a class (with a
‘W’) before the drop date or reinstate accordingly. **Please, It is NOT advisable to use
cell phone in class. Thank you.**
Test
Tests will be announced by instructor, usually one week in advance after the
coverage of each chapter and quizzes are assigned every Wednesday. There will be “no”
makeup for quizzes. Makeup tests are not advised. Students have the responsibility, upon
failing an examination, to obtain tutorial assistance necessary to pass the upcoming
examination. It is students’ responsibility to initiate withdrawals- deadline 11/23/2013.
All assigned work should be completed on or before the beginning of the next session.
All work submitted late will be penalized by 20% of the project .Check the hours posted
in the Lab for tutorials. Final Exam will be comprehensive and 1 hour 40 minutes in
length. Also, students are not allowed to bring their children to classroom. Let us have
some fun!
“No Show” Policy
If a student registered for the course before the start time of the first class period,
but (a) did not attend the first 2 classes, or (b) attended only 1 of the first 3 classes and
failed to notify the instructor of his or her intentions to continue the class, the Registrar’s
Office will remove the student from the course.
Academic Integrity
The HCC students are committed to the ideals of truth and honesty. In view of
this, students are expected to adhere to high standards of honesty in their academic
endeavor. Plagiarism and cheating of any kind are serious violations of these standards
and will result, minimally, in the grade of “F’ by the instructor.
Student Conduct
HCC students are expected to conduct themselves in a manner which is
considerate of the rights of others and which will not impair the mission of the College.
Misconduct for which students are subject to College Discipline (e.g,. educational
expulsion) may include the following: (a) all forms of dishonesty such as stealing,
forgery, (b) obstruction or disruption of teaching, research, administration, disciplinary
proceeding, (c) physical or verbal abuse, threats, intimidation, harassment, and/or other
conduct that threatens or endangers the health or safety of any person, and (d) carrying or
possession of weapons, ammunition or other explosives.
Disability Access Center
Any student with a disability, including a temporary disability, who is eligible for
reasonable accommodations, should contact the Disability Access Center as soon as
possible: (773) 000-0000. The DAC is located in room A, and is open Monday – Friday
from 9AM to 6PM.
Classroom Etiquette
Cell phones, PDAs, food/drinks, talking, leaving the classroom are not permitted.
Grading
These are clearly explained in the grading system as it applies to your
assignments points, percentages, etc.
Methods of Evaluation
Final Test…………………………...20%
Exams………………………………20%
Home Work/MyMathLab…………..20%
Quizzes……………………………..15%
Projects……………………………..15%
Classroom Participation…...……….10%
Total Percentage…………….. 100%
The weight given to exams, quizzes, and other instruments used for evaluation will be
determined by the instructor.
Methods of Assessment:
Exams, quizzes, homework, in-class activities and other assessments will be used
as appropriate to measure student learning.
Assignments:
Class Participation:
Quizzes:
Homework
Exams
Projects/Research Papers
Final Exam
Grade Distribution
90% to 100% = A
80% to 89% = B
70% to 79% = C
60% to 69% = D
Below 60% = F
What the Grades Mean (Use specific evaluative language to explain each grade.)
A ‒ Student learning objective/ arguments are well constructed and developed; mastery
reflects the standards of student learning objective.
B ‒ Mostly well-constructed arguments/mathematical skills and meaning; mathematics
shows evidence of mastery
C ‒ Evidence of occasional argument and transparent meaning of the subject matter
covered; errors in mathematical computation or expressions.
D ‒ Many lapses in mathematical argumentation and careless use of numbers/language
F ‒ No evidence of mathematical argument or deliberately constructed on the subject.
Exit Essay None required
Late Work and Make-up Assignments
Late assignment will be penalized by 20% and will not be accepted after one
week.
Topical Outline / Course Calendar:
Calendar: (Will cover topics and or chapters)
As indicated on the topical outline
(The above is a week-by-week schedule that clearly indicates what topics and
assignments will be covered on specific weeks.)
Your Course ID:******7
All cellular telephones and electronic devices that are not directly related to instruction must be
turned off upon entering the classroom. Let us have some fun!
Adapted on 12/22/2011 from:
Office of the ********, Arts & Sciences
Fall 2011
Appendix B: Active Learning Project
HOPE COMMUNITY COLLEGE PROJECT ACTIVE LEARNING LESSON PLANNING TEMPLATE MODELING PARABOLIC EQUATION FOR
REAL LIFE - MATH 099
SLO What SLO(s) will be addressed in
the lesson?
Formulate and apply a nonlinear equation to a contextual (real world) situation
Additional Skills What additional skills (mathemati-
cal or nonmathematical) will be ad-dressed in the lesson?
Knowledge of quadratic formula Ability to evaluate a linear and non-
linear equation. Know how to tabulate data Know how to use a calculator
(computer)Activity
What problem will be used to en-courage students in their own learn-ing? How will it be inquiry-base?
This activity may be completed in group.A student at Hope Community College is practicing for a Mathematics Department presentation. So, the student wants to model the physical situation for the para-bolic equation of water from a drinking fountain.This parabolic path can be modeled with quadratic equation.Let point A with coordinate (0, 0) be the point where water is shooting out of the water fountain and point B is where the wa-ter lands. If we use a ruler to measure the length from point A to that of B denoted as
( ,0) .If we find the x coordinate of
the mid-point of A to B to be .Suppose we measure the height of the water from
the mid-point to a point C to be .Then
the coordinate of point C will be ( , ). Collect data for the vertex C of the para-bolic path and tabulate your data as shown on the data sheet.Plot the point on a rectangular coordinate system. Sketch the curve through point A, B and C.Identify the coordinates of points A, B and
C.Write the equation or model in terms of
and explain your reason.Enter your data into a graphical calculator how does your model compare?
Data Table X YPoint A 0 0Point BPoint C
Formative Assessment What will be used to gauge student
understanding?
Ask students: What does the initial velocity
mean? What does the initial height mean? What is the maximum height at-
tained by the water? At what time does the water return
to the level of the mouth of the per-son drinking it?
What is the water’s velocity just be-fore it hits the second point?
What is the height of the water?Peer Interaction
What cooperative learning strate-gies are utilized in the lesson?
Student should work in a group of three.
Summative Assessment What summative assessment will be
used to gauge student understand-ing of the overall SLO?
Student will be assessed with using multi-ple questions including:
Problem assessing factoring Problem assessing the use of qua-
dratic formula. Problems will assess the use of par-
abolic model which includes vertex, line of symmetry, initial and final velocity.
Student will be required to include the use of Pythagorean Theorem in this project.
Student Activity 6
Parabolic Equation For Real Life
This activity may be completed in groups:
A student at Hope Community College is practicing for a Physics Department presenta-tion. The student will model the physical situation for the parabolic equation of water from a drinking fountain. This action is similar to work that was done in the Middle Ages, when Galileo Galilee found that the path of a projectile is parabolic in nature. This parabolic path can be modeled with quadratic equation.
Let point A with coordinate (0, 0) be the point where water is shooting out of the water fountain and point B is where the water lands. If we use a ruler to measure the length
from point A to that of point B and the measurement equal with coordinate ( ,0). If
we find the x coordinate of the mid -point of A to B as ( , ). Suppose we measure the
height of the water from the mid-point to a point C to be .Then the coordinate of point
C will be ( , ).Collecting data for the vertex C of the parabolic path and tabulate your data as shown on the data sheet.
o Plot the point on a rectangular coordinate system.o Sketch the curve through point A, B and C.o Identify the coordinates of points A, B and C.
o Write the equation or model in terms of and explain your rea-son.
o Enter your data into a graphical calculator. How does your model compare?
Data Table:
X YPoint A 0 0Point BPoint C
Appendix A: SOLUTION TO PARABOLIC EQUATION FROM GROUP A:
