College Algebra
Running head: COLLEGE ALGEBRA
College Algebra as a Transition Course: What Teachers and Students Should Know?
Linda Reichwein Zientek
Department of Mathematics
Blinn College
G. Donald Allen
Department of Mathematics
Texas A&M University
College Station, TX 77843
Mel Griffin
Department of Mathematics
Texas A&M University
College Station, TX 77843
Gloria White
Charles A. Dana Center for
Mathematics and Science Education
Paula Wilhite
Department of Mathematics
Northeast Texas Community College
Inquiries concerning this paper can be addressed to Linda Zientek, Blinn College, 902
College Avenue, Brenham, Texas 77833, lzientek@blinn.edu, 979-830-4437
College Algebra 1
Abstract
The success of our nation depends on the academic excellence of our students.
With the increase in enrollment in dual-credit and developmental mathematics courses,
the line between collegiate and secondary education is less apparent, and the two can no
longer operate as separate entities. For the sake of the next generation, we must begin to
understand disconnects and help provide a smoother transition for our students. Results
from the present study suggest that (1) community college and university mathematics
departments parallel each other on instructional modality, use of technology, and
assessment methods with slight variations between institutions; (2) neither community
colleges nor universities have moved far from the traditional classroom; and (3) the
transition from community college to university is rather seamless in regards to teaching
environment, but high school students emerging from non-traditional classrooms are
faced with adjusting to the traditional class settings in higher education.
Submitted for publication.
College Algebra 2
The success of our nation depends on the academic excellence of our students.
With a national push to Close the Education Gaps between socio-economic groups, the
reality that a large percentage of students are not academically ready to enter college
mathematics classes has been brought to the forefront. On average, approximately 42% or
more of community college students are initially enrolling in developmental mathematics
courses (National Center for Educational Statistics, 2000). In Texas, where the present
study was situated, 51% of community college students and 28% of university students
entered developmental mathematics courses with some institutional rates as high as 80%
(Texas Higher Education Coordinating Board, 1999a).
Curriculum Movements
The past decade has been replete with reform movements to improve teaching and
learning in mathematics. In 1997, the Texas Higher Education Coordinating Board
(THECB) adopted the exemplary objectives for the required core curriculum hours in
mathematics. Written as a mandate to Texas institutions of higher education, the
mathematics objective of the core curriculum was to create a quantitative literate graduate
(THECB, 1999b). In 2000, the National Council of Teachers of Mathematics (NCTM)
unveiled the Principles and Standards - an extension of NCTM’s original Standards that helped bring about colossal changes in the classroom. These standards, accompanied
with the advances and affordability of technology, aided in changing the delivery of
instruction and methods of learning.
The Committee on the Undergraduate Program in Mathematics (CUPM) of the
Mathematics Association of America (MAA) sought to reconsider a mathematics
curriculum developed in the 1950s that contained traditional topics and methodology of
mathematics focusing on preparing students to enroll in calculus. The CUPM’s goal was
to develop a curriculum encompassing relevant real-world applications that would build
quantitative literacy and enhance the use of technology such as graphing calculators,
spreadsheets, and computer algebra systems.
The student population of the 50s differed markedly in background, maturity, and
outlook from today’s student population. Therefore, the curriculum of the 50s was
insufficient to help students of the 21st century reach their goals. In the 50s, only a mere
12% of students attempted college and most students attended as full-time students.
Today, more than 66% of high school completers are attending college and many of these
students attend as part-time students (United States Census Bureau, 2006). In addition,
students are bringing with them a diverse array of mathematical abilities ranging from
having mastered only basic mathematical skills to completing Advanced Placement
mathematics courses (Mathematical Association of America’s Committee on
Undergraduate Programs, 2004).
College Ready
Despite the efforts to improve mathematics teaching and learning, a large
percentage of students are not college ready. In a report by Hart and Associates (2005),
college mathematics instructors estimated that approximately half of their students were
not ready for college-level work, and only 28% of college instructors believed that public
high schools adequately prepared graduates to meet college expectations. Students
participating in the Hart and Associates survey indicated had they known what they know
now, they would have applied themselves more in high school (65% and 77%; college
and workforce students, respectively). Hart and Associates found that students who had
College Algebra 3
been challenged and who had faced high expectations were more likely to feel prepared
in college.
In order for high school graduates to be college ready, effective communication
between students, parents, and higher education needs to begin before students enter high
school and continue throughout the high school years. According to a report by the
American Diploma Project (ADP; 2004), the majority of 8th graders (90%) and their
parents (67%) considered college a necessity. Yet, academic inconsistencies within our
system – among high schools, colleges, and universities - make college readiness difficult
to determine and hinders our students’ ability to attain college readiness.
Mathematics standards set by states rarely reflect real-world demands and
standardized exams often reflect 8th and 9th grade skills rather than skills needed at the
time students graduate (ADP, 2004; Callan, Finney, Kirst, Usdan & Venezia, 2006). In
addition, very few states specify the particular mathematics courses students need to
complete nor do they have “effective mechanisms for ensuring that the course content
reflects the knowledge and skills required for success in college and work” (ADP, p. 7).
Determining college readiness by transcript review is difficult because inequities exist
between high schools. A grade in a course or a high school diploma does not establish
college readiness. The ADP report states that “high school students earn grades that
cannot be compared from school to school and often are based as much on effort as on
the actual mastery of academic content” (p. 2). The ADP report concluded that
No state can now claim that every student who earns a high school
diploma is academically prepared for postsecondary education and work.
The policy tools necessary to change this do in fact exist — but they are
not being used effectively (p. 7).
For this reason, colleges typically do not rely solely on transcript review to
determine course placement and often rely on placement examinations. The ADP
concluded that the array of placement exams that varied between college campuses and
sometimes within a single college system becomes even more confusing for students and
educators.
Beginning in fall 2008, Texas will require a fourth year of mathematics for all
students pursuing the recommended or distinguished graduation plan. Mechanisms
established to increase the number of required mathematics courses is a positive move
towards improving student success and college readiness (Neely, 2006). However, a
fourth year of mathematics will not guarantee college readiness unless both the
coursework and instruction are considered high quality. Both the quality of courses and
teachers play key roles in student preparedness. According to a report by Callan et al.
(2006), ”The quality and level of the coursework and instruction, and their level of
alignment with postsecondary expectations, are the key elements of reform” (p. 7). In an
Illinois statewide study, researchers found that both the quality of the course and the
teacher were essential for college readiness with a possible exponential relationship
existing between teacher quality indices and college readiness of students who completed
trigonometry or other advanced mathematics courses. In the Illinois study, 52% of
students who completed Calculus from a low quality teacher were classified as not
college ready or the least ready compared to 6% of students who completed calculus from
a high quality teacher (Presley & Gong, 2005). In addition to quality coursework and
College Algebra 4
instruction, Callan et al. recommended that states provide financial incentives to support
K-12 and post-secondary collaborations on improving college readiness.
Purpose
While Texas has a common course numbering system that eases the
transfer of credits between institutions, the transition from secondary to higher
education has not been as seamless. The purpose of this survey is (a) to
investigate in detail the current status of College Algebra (Math 1314), (b) to
determine what colleges expect from students, (c) to determine what students can
expect when they enroll in College Algebra, and (d) to discover possible
disconnects between high schools, community colleges, and universities.
Method
Participants
The population consisted of about 145 mathematics department chairs from
community colleges and universities in Texas that offered College Algebra. Forty-six
departmental chairs or designees completed the survey. Thirty-three were community
colleges (72%) and 13 were universities (28%).
College Algebra
College algebra was selected for the following reasons:
1. College Algebra has retained the status of having the highest
enrollment of any credit-bearing course over the past 30
years – 173,000 nationally in 2000 (Lutzer et al., 2002);
2. Although not guaranteed, success in subsequent courses is
inherently related to success in College Algebra;
3. Algebra at all levels has been identified as the gatekeeper
to higher education (Moses, 2001); and
4. College Algebra is a core requirement and a prerequisite
mathematics course for advanced mathematics required of most
liberal arts and science, technology, engineering, and
mathematics (STEM) majors.
Instrumentation
In an attempt to determine consistencies between institutions of higher education,
the survey was developed by five educators who have K-20 experience. The survey was
distributed at a statewide departmental meeting and also by email through statewide
mathematics organizations. The survey requested information on students’ future
mathematical intentions, departmental grade distributions, mathematics topics,
instructional modality, prerequisite scores, technology, assessments, and liaisons. The
present study depended on the departmental chair or designee’s ability to read their
department’s teaching style. Topics considered important for students to understand were
rated on a 3-point scale: (a) most important, (b) somewhat important, or (c) marginal or
no importance. Instructional delivery and teaching methods were dummy coded as “1” =
“method was used” and “0” = “method was not used”.
Data Analysis
Reporting recommendations of the APA Task Force on Statistical Inference were
followed. P-values, descriptive statistics, and effect sizes were reported (Wilkinson &
APA TFSI, 1999). Effect sizes aid in meta-analyses and in interpreting results
(Thompson, 2000; 2006). While Cohen arbitrarily assigned effect size benchmarks, they
College Algebra 5
significance testing (Thompson, 2001). For the present study, effect sizes greater than .05
were considered noteworthy.
Analyses
Comparing higher education with K-12 research will help in identifying possible
inconsistencies between high school, community colleges, and universities. Research on
teaching and learning at the collegiate level has been relatively sparse. By investigating
College Algebra, the present study sought to identify possible disconnects and similarities
between community colleges, universities, and K-12 education by answering the
following questions:
1. What are the future mathematical intentions of College Algebra students?
2. What are the departmental grade distributions of College Algebra?
3. What topics and prerequisites do mathematics departments believe are
important for incoming College Algebra students?
4. What should College Algebra students expect in the classroom (i.e.,
instructional modality, technology, and assessment)?
5. Are liaisons being formed between K-12 and higher education?
1. Future Mathematical Intentions
Departmental chairs identified the percent of students who were enrolling in
College Algebra (a) as a terminal course, (b) as a prerequisite for other mathematics
courses, (c) with plans to enroll in a calculus course, and (d) with plans to enroll in a
statistics course. Figure 1 illustrates future mathematical intentions of College Algebra
students. Analysis of variance (ANOVA) results indicated noteworthy differences
between community college students and university students in enrollment in College
Algebra as a terminal course (F(1, 38) = 4.49, p = .04, η2 = .11; M = 65.76, SD = 24.71;
M = 46.25, SD = 29.33; community colleges and universities, respectively) and in
enrollment in a subsequent statistics course (Welch-statistic(1, 11.70) = 3.94, p = .07, η2
= .18; M = 6.51, SD = 15.69; M = 22.95, SD = 24.44; community colleges and
universities, respectively). The Welch statistic was provided because the homogeneity of
variance assumption was not met. Community college students were more likely than
university students to take College Algebra as a terminal course and less likely to enroll
in statistics, at least at the community college institution.
College Algebra 6
INSERT FIGURE 1 ABOUT
HERE
ANOVA results, with effect sizes close to zero, did not indicate noteworthy
differences between community college and university on their students’ enrollment in
College Algebra as a prerequisite for higher level mathematics courses (F(1, 39) = .591, p
= .48, η2 = .02; M = 31.94, SD = 24.76; M = 38.75, SD = 28.35; community colleges and
universities, respectively, η2 = .02) or on the percent of College Algebra students that
later enrolled in calculus (F(1, 38) = 1.23, p = .27, η2 = .03; M = 9.31, SD = 7.60; M =
12.88, SD = 12.56; community colleges and universities, respectively, η2 = .03). These
results indicated only a small percentage of College Algebra students intended to enter
STEM fields.
2. Grade Distributions
Student retention rates were defined as the percent of students who did not
withdraw from the course. Completer success rates were defined as the percent of
students, excluding withdrawals, who received a passing grade (i.e., A, B, or C). In the
present sample, student retention rates were 72% with a 70% completer success rate. The
homogeneity of variance assumption was met and effect sizes from analysis of variance
(ANOVA) results indicated noteworthy differences between community colleges and
universities on the distribution of C’s (F(1, 34) = 3.44, p = .07, η2 = .09; M = 27.88, SD =
7.48; M = 23.53, SD = 2.89; community colleges and universities, respectively),
somewhat noteworthy differences on the distribution of A’s (η2 = .05), and no
noteworthy differences on the distribution of B’s (η2 =.03), D’s (η2 <.01) or F’s (η2 <.01).
Standard deviations suggested that universities were more dispersed on the percentage of
students earning A’s (SD = .11) and community colleges were more dispersed on the
percentage of students earning F’s (SD = .12).
The dispersion of A’s at universities ranged from 8% to 40% and the dispersion of
F’s at community colleges ranged from 6% to 53%. Variations in grade distributions
illustrated in Figure 2 shows that universities were more disperse than community
colleges on the percent distribution of A’s. While the dispersion of F’s for community
colleges was sizeable, the range and standard deviations appeared to be influenced by
outliers. As illustrated in Figure 2, removing the outliers gives a more accurate depiction
of community college F rates and suggests rates comparable to universities.
INSERT FIGURE 2 ABOUT
HERE
Despite the existence of outliers in community college grades, no outliers existed
when computing pass or failure (i.e., D’s or F’s) rates and no statistically significant
differences existed between passing rates of universities (M = .68, SD = .13; Range =
53% to 88%) and community colleges (M = .70, SD = .12; Range = 44% to 85%). The
one outlier community college that had 53% of their College Algebra students fail had
College Algebra 7
only 2% of their students obtaining a D. Therefore, the percentage of students
collectively not passing did not constitute a far reaching percent from the remaining
community colleges in the present sample.
3. Succeeding in College Algebra
Important Topics. Departmental chairs rated eight mathematics topics on their
importance for incoming College Algebra students to know in order to be successful in
College Algebra. Topics were rated on a three-point scale: (1) most important, (2)
somewhat important, or (3) marginal or no importance. Cross-tab results indicated no
statistically significant differences between universities and community colleges on what
topics were deemed important. As presented in Table 1, 100% of mathematics
departmental chairs identified algebraic manipulation as being most important. Fractions
were considered the second most vital topic for students to know with just over 80%
believing this was most important and the remaining indicating fractions were at least
somewhat important.
Identified as the least important topics for incoming students were (a) regression
modeling, (b) trigonometry, and (c) group work. Cross-tab results indicated no
statistically significant differences by topics considered important and the percentage of
students who passed/failed, withdrew, or obtained an A, B, C, D, or F.
INSERT TABLE 1 ABOUT
HERE
Prerequisites. Departments reported prerequisite scores on five examinations: (a)
ACCUPLACER, (b) ACT, (c) COMPASS, (d) SAT, and (e) the Texas Higher Education
Assessment (THEA). Only eight schools reported prerequisite scores on all five
placement examinations. As presented in Table 2, bivariate correlations indicated that
prerequisite scores on THEA were related to prerequisite scores on ACT, COMPASS,
and ACCUPLACER but not SAT. Effect sizes from ANOVA results indicated possibly
noteworthy differences between community colleges and universities on ACT (F(1, 23) =
2.25, p = .147, η2 = .09) and SAT scores(F(1, 24) = 10.27, p = .004, η2 = .30) with
squared effect sizes on the remaining exams less than .02. The predominant prerequisite
score for THEA was 270 (M = 258.64, 17.63; M = 264.29, SD = 14.12; community
colleges and universities, respectively), SAT was 500 (M = 514.00, 21.22; M = 476.25,
SD = 39.26; community colleges and universities, respectively), and ACT was 19 to 21
(M = 20.75, 1.98; M = 19.67, SD = 1.11; community colleges and universities,
respectively). Prerequisite scores on COMPASS ranged from 39 to 70 (M = 57.18, 14.50;
M = 56.25, SD = 11.84; community colleges and universities, respectively) and
prerequisite scores on ACCUPLACER ranging from 39 to 109 (M = 69.08, 16.58; M =
67.00, SD = 19.86; community colleges and universities, respectively) with a cluster of
scores around 63 and 64.
INSERT TABLE 2 ABOUT
HERE
College Algebra 8
4. Experiences in the Classroom
Instructional Modality. Department chairs identified the traditional lecture
method as the predominant instructional modality for College Algebra professors. On
average, community college professors lectured approximately 91% of instruction time
and university professors lectured approximately 94% of instruction time. The occasional
institution served as an outlier institution where lecturing occurred only about 70% of
class time. Twenty percent of community college departments lectured around 80% of
the time. Eight percent of university departments and 3% of community college
departments integrated group work into the course with another 12% of community
college departments integrating online components into their teaching.
Technology. Our study focused on teaching with technology. Figure 3 illustrates
instructional delivery methods by institutions in our study. For providing instruction,
these institutions most often used overhead and calculator projectors. Community
colleges (82%) were slightly more likely to have used overhead projectors in their
classrooms than universities (58%). Only 38% of community colleges and 25% of
university mathematics departments utilized computer labs for College Algebra courses.
The use of calculator projectors indicated that mathematics professors were incorporating
technology in their teaching (76% of community colleges and 58% of universities).
Multiple regressions indicated that the percentage of passing grades did not depend on
whether or not departments used calculator projectors or computer labs (F (2, 33) = .45, p
= .642, R2 =.03).
INSERT FIGURE 3 ABOUT
HERE
Assessment Methods. The NCTM Principles (2000) emphasized the need for
various forms of assessments. In the present study, departmental chairs were asked about
a full gamut of assessment methods, which were dummy coded as “1” = “Used” and “0”
= “Not Used”. As illustrated in Figure 4, traditional exams were the predominant
assessment method (100% of universities and 97% of community colleges) with 60%
using multiple-choice answers on at least one examination and/or quiz. The one
community college that did not choose traditional tests marked that their exams were
multiple-choice. Community colleges (52%) were more likely than universities (29%) to
assess students with technology and collaborative group work. Approximately 39% of
community colleges and about 1% of universities administered projects as a part of their
assessment measures. A small percent used other assignments typically in the form of
homework (12% and 17%; community colleges and universities, respectively) and direct
observations and/or essays (3% and 8%; community colleges and universities,
respectively).
INSERT FIGURE 4 ABOUT
HERE
College Algebra 9
Sixteen percent of the mathematics departments had common exams and 56% had
common finals. Community colleges (61%) were slightly more likely to administer
common finals than universities (42%). ANOVA results indicated no statistically
significant differences in grade distributions between schools that did or did not
administer common exams or finals with effect sizes close to zero.
6. Liaisons
Forty-three percent of higher education institutions in the present sample
identified liaisons between their institution and area high schools. The extent of
involvement varied. Some mathematics departments indicated they met once a year or
they met to discuss dual-credit enrollment. Only a few mathematics departments met to
discuss curriculum items. Two mathematics departments indicated substantial interaction.
One university indicated they were working on a city-wide initiative to address high
school and College Algebra curriculum, and one community college visited with high
school counselors and teachers, distributed brochures, and arranged on-campus activities
for high school students.
Discussion
The future of our society depends upon the academic success of our students. In
essence, we begin preparing students for college the minute they walk into our schools;
yet, many high school graduates are unprepared to embark on the journey into higher
education. Educators must begin to investigate why the journey has been so difficult and
how best to prepare students to proceed. Without sacrificing academic rigor, barriers
should be removed that preclude students from excelling, and students should be
equipped with the skills necessary to achieve their goals. The present study sought to
provide information about the aspirations and goals of College Algebra students,
plausible disconnects between high school and higher education, and a glimpse of what
was occurring in College Algebra classrooms.
College Algebra Students
The typical College Algebra student did not enter STEM-based fields nor did they
subsequently enroll in statistics or calculus. Figure 1 illustrates the future mathematical
intentions of College Algebra students. In the present study, College Algebra was the
terminal course for the majority of community college students and for a high percentage
of university students. Community college results would naturally be influenced (1) by
transfer students who enrolled in mathematics courses at the university and (2) by
students who completed technical or vocational degrees. Therefore, in isolation, the
community college results may not be an accurate depiction of students’ final
mathematical intentions. However, these results coupled with the university results
indicated that College Algebra was a terminating course for many students.
The College Algebra curriculum was traditionally designed to prepare students
enrolling in Calculus. Results from the present study, which were supported by findings
from the CBMS study, suggested that College Algebra’s primary purpose has changed
and that only a small percentage of College Algebra students are subsequently enrolling
in Calculus (Lutzer et al., 2002).
Important Topics
University and community colleges were consistent in their beliefs about what
topics were considered important for incoming College Algebra students to know, but
these topics were more aligned with the traditional curriculum than the NCTM standards-
College Algebra 10
based curriculum. These results identified a possible disconnect between the curriculum
of secondary and higher education. As presented in Table 1, mathematics departments
believed students who entered College Algebra should be proficient with algebraic
manipulation, fractions, and problem solving. Knowledge of trigonometric functions,
regression for modeling, group work, and graphing calculators were considered the least
important skills for incoming students. These results suggest that the NCTM
constructivist curriculums’ primary focus on problem solving with a de-emphasis on
algebraic manipulation may be leaving the very children they hope to help without the
skills they need to succeed. Arranging problems where solutions require both problem
solving skills and algebraic manipulation in balance may well serve students better when
then enter the collegiate environment and may help promote future success.
What Students Should Expect
The incoming College Algebra student should expect to spend the majority of
class time in a traditional lecture taking notes from an overhead project or laptop
computer. They should also expect that assessments will be traditional examinations and
quizzes that are contingent on algebraic manipulation and problem solving. However,
professors will often use graphing calculators to help teach concepts. A very small
percentage of students will be afforded time to work in groups, on projects, or in
computer labs. Compared to university students, community college students will be
more likely to be assessed on projects – some of which contain technology and
collaborative efforts.
Grade Distributions. With the exception of a few outliers, grade distributions of
community colleges were fairly consistent. Universities varied on the percent of A’s
earned by students in College Algebra. The distribution of A’s at community colleges
ranged from 7% to 25% compared to 6% to 40% at universities. Community colleges and
universities were aligned on pass rates with the trade-off being an increased distribution
of C’s at the community colleges. The higher distribution of A’s at some universities may
be related to stringent admission requirements that created a classroom whose students
were more homogenous with regard to academic backgrounds than community colleges
or universities with open door policies and more diverse levels of learners.
Instructional Modality and Delivery Methods. University and community college
teachers were consistent in their delivery of instruction. These results, which were
gathered six years after the 2000 CBMS survey, corroborated earlier findings by CBMS
that the “predominant instructional modality continued to be the standard lecture method”
(Lutzer et al., 2002, p. 126). All university departments indicated their professors lectured
over 90% of the time and at least 50% or more lectured 100% of the time. While
community college professors lectured slightly less on average (91% of the time) than
university professors (94% of the time), lecturing was still the predominant teaching
modality.
In the present sample, there was the occasional community college mathematics
department who spent 20% to 30% of class time not lecturing, but these were the
exception and not the norm. A small percentage of university (8%) and community
college (3%) departments integrated group work into their teaching, and a small percent
(12%) of community college mathematics departments also taught College Algebra
online. While some of these were hybrid with the traditional courses, the percent of
online courses was slightly higher than the 2000 CBMS results of 7% (Lutzer et al.).
College Algebra 11
Technology in Teaching
The large percent of professors teaching by means of overhead projectors and
laptops supported the traditional classroom lecture. However, as illustrated in Figure 3,
the use of calculator projectors indicated graphing calculators were being utilized in
classroom teaching. In the present sample, 58% of university departments and 76% of
community college departments taught with a calculator projector, which was
comparable to the 2000 CBMS national sample of CC teachers (74%) (Lutzer et al.,
2002). These results indicated that the majority of students, particularly in the community
college setting, received part of their learning employing multiple representations by
learning concepts graphically, numerically, verbally, and symbolically.
Assessments
Major Exams and Quizzes. In the present sample, the majority of teachers in
higher education assessed their students in the traditional method of major exams and
quizzes. As illustrated in Figure 4, approximately half of the departments also used
multiple-choice responses on at least one exam. Approximately 8% of university
mathematics departments identified that direct observations were used to assess students.
The one community college not identifying with traditional exams and quizzes indicated
their exams were multiple-choice.
Slightly more community colleges administered common finals than universities,
but the majority of institutions did not administer common exams. These results
suggested that professors in higher education have some autonomy and control over their
classrooms. Research has identified that high school mathematics and science teachers
who left teaching were often dissatisfied with the lack of autonomy and control they
experienced in their classroom (National Science Board, 2006). These results then imply
that retention of mathematics and science professors in higher education may be higher
than teachers in secondary schools. The use of common finals by approximately half of
the institutions suggested institutions had some form of curriculum accountability.
Projects and Collaborative Work. The modest effort by professors to assess with
group work (25% and 52%; universities and community colleges, respectively) along
with community college instructors assessments with technology & collaborative projects
(39%) suggested that instructors in higher education were aligned with secondary
educators and the recommendations by the American Mathematical Association of TwoYear Colleges (AMATYC) Crossroads in Mathematics (2006). While these numbers
indicated a modest attempt by some universities to move beyond traditional methods,
they also indicated that the majority of universities are continuing to rely primarily on
traditional assessments.
The AMATYC Crossroads in Mathematics recommends that mathematics faculty
“provide learning activities, including projects and apprenticeships that promote
independent thinking” (p. 4). The use of (1) technology and collaborative group work and
(2) projects for assessing students suggested instructors, especially community college
instructors, were moving beyond the limitation of traditional exams and understanding
the benefits of collaborative reasoning to solve a problem. Working in groups has been
advocated by MAA as a method (1) to improve problem solving skills beyond skill
acquisition, (2) a way to build classroom camaraderie, and (3) a method to introduce
multiple problem solving methods (Kasube & McCallum, 2005).
The lack of extensive use of group work and projects by university departments
College Algebra 12
may possibly be a reflection of the structure of higher education rather than differences in
philosophy. University professors often have classrooms in excess of a 100 students
compared to community college classrooms of less than 30 (Lutzer et al., 2002). Even
two large university classes would exceed the number of students taught in five
community college classes. Large class sizes accompanied with obligations to research
and publish limits the time university professors can devote to preparing and grading
student projects. Grading over a hundred projects per class would entail unfeasible time
constraints. This thought is reflected by the strikingly small percent of university
departments that indicated students were assessed with (a) projects (1%) and (b)
technology and collaborative work group-projects (25%) compared to community college
professors (39% and 52%; projects and technology and collaborative group-projects,
respectively). Despite these differences, the small percent of university professors
utilizing group work in their teaching suggested that some university faculty
acknowledged the value added when students discuss and solve problems collaboratively.
Prerequisites
Community colleges and universities were using placement examinations.
Therefore, students entering College Algebra should expect some form of placement
criteria beyond high school grades or terminal high school mathematics course. The use
of some form of placement exams by all institutions in the present study suggested that
departments did not believe high school courses or grades were sufficient indicators of
college readiness. Our results were consistent with the 2000 CMBS study, which found
that “Virtually all two-year colleges with mathematics programs had diagnostic or
placement testing” (Lutzer et al., 2002, p. 126).
Placement criteria such as the Texas’ 10% rule along with standardized exams
completed while in high school further complicates accurate placement of students in
mathematics courses. The top 10 percent rule guarantees that Texas students who are in
the top 10 percent of their class have automatic admission to any public Texas university
(THECB, 2006a). Neither standardized exams nor the 10 percent rule encourages student
enrollment in advanced mathematics courses.
In Texas, educators are emphasizing to students and parents the need for more
advanced mathematics for college-bound students. In Texas, House Bill 1 “requires four
years of mathematics and science in the recommended and distinguished high school
programs, beginning with students entering Grade 9 in school year 2007-2008” (Neeley,
2006, p. 1). The importance of completing a mathematics course their senior year is not a
new concept. According to Bidwell and Clason (1970/2002), the 1899 Report of
Committee on College-Entrance Requirements stated
When a student who is preparing for college does not intend to offer
advanced algebra, he should defer some or all of the mathematics at the
eleventh grade until the last year of his school course, or be given
opportunity for mathematical reviews in that year. (p. 194)
Requiring four-years of mathematics is a move forward in preparing students to
be college ready. Unfortunately, guaranteeing a fourth course does not guarantee college
readiness. The quality of the course and teacher play an essential role in student
preparedness (Presley & Gong, 2005). First generation college students – who often enter
community colleges - rely upon the advice of counselors to determine what courses best
College Algebra 13
prepare them for college. Requiring more mathematics reinforces the message that more
rigorous mathematics correlates with college readiness.
Because of inconsistencies among courses, prerequisite requirements consisting
of placement examinations will probably continue to prevail in higher education.
Community colleges and universities were consistent on their prerequisite placement
examination scores on three of the five reported exams. Community colleges tended to
set more stringent requirements on SAT scores. While a cluster of institutions set College
Algebra SAT prerequisite scores at 500, one university set the score as low as 400 and 3
of the 18 community colleges using SAT scores set them as high as 550. In the present
sample, 44% of community colleges set SAT prerequisite scores higher than 500
compared to 0% of universities.
Universities tended to set more stringent THEA scores but a smaller percent
tended to use them as a prerequisite requirement. The minimum passing score of 230 was
set by the THECB (2006b) with a recommended score of 270 for College Algebra. In the
present study, THEA scores ranged from 230 to 270 with the majority of schools (72%)
setting 270 as their College Algebra benchmark and 6% setting their benchmark at 250.
Only one university set the THEA score below 270 compared to 39% of community
colleges with 32% (n = 9) of these schools setting the score as low as 230. The one
university who set the THEA score at 230 was the same university who set the SAT score
at 400. Table 2 shows the relationship between departmental benchmark scores.
According to the standards established by ACT, Inc. (2006), some universities
who set College Algebra prerequisite scores below 19 and the majority of community
colleges who set ACT scores at 19 were setting benchmarks for students to enter with
minimal proficiency in solving equations, graphing, and number concepts. ACT scores
ranging from 20 – 23 appear to correspond better with the topics identified as important
by the present sample by departmental chairs than the common value of 19 often used by
institutions as an indicator for skills sufficient for College Algebra.
Liaisons
The fact that approximately half of schools in higher education had liaisons with
local high schools suggests that institutions in higher education are realizing the value
added of increased communication, but the degree of this involvement varied. Some
school liaisons were limited to administrators, whereas others involved dual-credit
courses. One university indicated a city-wide committee had been established to discuss
curricula items, and one community college indicated they had formulated on-campus
activities for high school students. The latter two examples seemed to be the exception.
While communication between secondary and higher education appeared to exist, the
present results indicated communication appeared to be inconsequential on areas of
curriculum and relating more to dual credit or administrative concerns outside of the
department.
Conclusion
In order to smooth the transition into the collegiate environment, we must begin to
compare teaching modality and curriculum among institutions of higher education. While
the present study was limited to community colleges and universities and was dependent
upon departmental chairs understanding of their professors, these results gave us a
glimpse into what was transpiring in College Algebra classrooms. Results from the
present study suggested that (1) community college and university mathematics
College Algebra 14
departments paralleled each other on instructional modality, use of technology, and
assessment methods with slight variations between institutions, and that (2) neither
community colleges nor universities have moved far from the traditional classroom.
These results indicated that instructional modality was remarkably similar across
institutions of higher education with the traditional methods prevailing. Unfortunately,
the students who struggle in mathematics will probably be the students who will have
more difficulty transitioning from a constructivist curriculum to the traditional classroom
settings in the collegiate environment.
The present study found the following consistencies:
1. College Algebra students were typically not entering STEM
fields;
2. University and community colleges were consistent in their
beliefs about what topics students should know with algebraic
manipulation and fractions topping their list;
3. University and community college teachers predominant
instructional method was traditional lecture, but graphing
calculators were incorporated in teaching in learning with
variations between institutions;
4. Professors in higher education typically assessed students in
traditional methods of exams and quizzes; and
5. High school courses and grades were not enough to predict
students’ college readiness.
The consistency of traditional lectures across institutions suggests that underlying
factors besides teaching modality impact student performance in College Algebra. Future
studies should investigate direct linkages between teacher grade distributions and teacher
attitudes in the collegiate environment. Despite the limitations of studying across
departments, the results of the present study gave us an insight into what was occurring in
the College Algebra classroom and showed consistencies and inconsistencies across
institutions of higher education.
While conceptually based state assessments and accountability measures helped
facilitate reformations in K-12 classrooms, the transition away from traditional methods
has been much slower in higher education. While some will contend that K-12 educators
moved too quickly and maybe went too far in the reform movement, others will contend
students’ failures are due to disconnects between K-12 and higher education in teaching
methods, assessments, and expectations.
We must continue to empirically investigate what is occurring in college
classrooms and the expectations of higher education. With the increase in enrollment in
dual-credit and developmental mathematics courses, the line between collegiate and
secondary education is less apparent, and the two can no longer operate as separate
entities. For the sake of the next generation and in an effort to fulfill the vision set forth
by NCTM, AMATYC, and MAA where all students excel to their highest potential, we
must improve communication between institutions and obtain a better sense of
disconnects occurring across the P-16 spectrum.
College Algebra 15
References
ACT, Inc. (2006). College readiness standards. Retrieved October 24, 2006 from
http://www.act.org/standard/planact/math/index.html
American Diploma Project [ADP]. (2004). Ready or not: Creating a high school diploma
that counts. Washington, DC: Achieve, Inc. Retrieved November 11, 2006, from
www.achieve.org/files/ADPreport_7.pdf
American Mathematical Association of Two-Year Colleges (AMATYC). 2006.
Crossroads in Mathematics Executive Summary. Author. Retrieved October 12,
2006 from http://www.amatyc.org/Old/Crossroads/CrsrdsXS.pdf
Bidwell, J. K., & Clason, R. G. (Eds.). (1970/2002). Readings in the history of
mathematics education. Reston, VA: National Council of Teachers of
Mathematics.
Callan, P., Finney, J., Kirst, M., Usdan, M., & Venezia, A. (2006). Claiming common
ground: State policymaking for improving college readiness and success.
Washington, DC: National Center for Public Policy and Higher Education.
Retrieved November 11, 2006, from
http://www.highereducation.org/reports/common_ground/index.shtml
Frick, R. W. (1996). The appropriate use of null hypothesis testing. Psychological
Methods, 1, p. 379-390.
Hart Research Associates / Public Opinion Strategies. (2005, February). Rising to the
challenge: Are high school graduates prepared for college and work? A study of
recent high school graduates, college instructors, and employers (Conducted for
Achieve, Inc.). Washington, DC: Author. Retrieved November 11, 2006 from
www.achieve.org/files/pollreport.pdf
Kasube, H., & McCallum, W. (2005). Mathematics: Crafty curriculum mathematics project.
In Curriculum foundations project: Voices of the partner disciplines (pp. 109-113).
Retrieved December 2, 2006 from http://www.maa.org/cupm/crafty/Chapt12.pdf
Lutzer, D. J., Maxwell, J. W., & Rodi, S. B. (2002). Statistical abstract of undergraduate
programs in the mathematical sciences in the United States. Providence, RI:
American Mathematical Society. Retrieved October 13, 2006 from
http://www.ams.org/ams/copyright.html
Mathematical Association of America’s Committee on Undergraduate Programs
(CUPM). (2004). Undergraduate programs and courses in the mathematical
sciences: CUPM curriculum guide 2004. Retrieved December 2, 2006 from
http://www.maa.org/cupm/curr_guide.html
Moses, R. P. (2001). Algebra and activism: Removing the shackles of low expectations –
A conversation with Robert P. Moses. Educational Leadership, 59(2), 6-11.
National Center for Education Statistics. (2000). Remedial education at degree-granting
postsecondary institutions in fall 2000. Retrieved June 15, 2006 from
http://nces.ed.gov/pubs2004/2004010.pdf
National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and
evaluation standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards
for school mathematics. Reston, VA: Author.
National Science Board. (2006). Science and engineering indicators 2006. Retrieved
May 16, 2006 from http://www.nsf.gov/statistics/seind06/ca/cas3.htm
College Algebra 16
Neely, S. J. (2006, September). Proposed Amendments to 19 TAC Chapter 74,
Curriculum Requirements, Subchapter A, Required Curriculum, and Subchapter
F, Graduation Requirements, Beginning with School Year 2007-2008 (First
Reading and Filing Authorization). Retrieved October 23, 2006 from
http://www.tea.state.tx.us/sboe/schedule/0906/whole/item/7_rule_ch74_ltrprop_i.
html
Presley, J.B., & Gong, Y. (2005). The demographics and academics of college readiness
in Illinois. (IERC 2005-3). Edwardsville, IL: Illinois Education Research Council.
Retrieved October 14, 2006 from
http://ierc.siue.edu/documents/College%20Readiness%20-%202005-3.pdf
Texas Higher Education Coordinating Board [THECB] (1999a). The effectiveness of
developmental education at Texas public higher education institutions. Retrieved
June 15, 2006, from http://www.thecb.state.tx.us/reports/pdf/0177.pdf
Texas Higher Education Coordinating Board [THECB] (1999b). Core curriculum:
Assumptions and defining characteristics (Rev. 1999). Retrieved December 3,
2006, from
http://www.thecb.state.tx.us/AAR/UndergraduateEd/fos_assumpdef.cfm
Texas Higher Education Coordinating Board [THECB] (2006a). CollegeForTexas.Com:
Top 10 percent rule for admissions. Retrieved November 28, 2006, from
http://www.collegefortexans.com/additional/top10rule.cfm
Texas Higher Education Coordinating Board [THECB] (2006b). Developmental education
– Frequently asked questions. Retrieved June 15, 2006, from
http://www.thecb.state.tx.us/OS/SuccessInitiatives/DevEd/faq.cfm#Q17
Thompson, B. (2000). A suggested revision to the forthcoming 5th edition of the APA
Publication Manual. Retrieved June 25, 2005 from
http://www.coe.tamu.edu/~bthompson/apaeffec.htm
Thompson, B. (2001). Significance, effect sizes, stepwise methods, and other issues:
Strong arguments move the field. The Journal of Experimental Education, 70(1),
80-93.
Thompson, B. (2006). Foundations of behavioral statistics: An insight-based approach.
New York: Guilford.
United States Census Bureau. (2006). The 2007 statistical abstract: The national data
book. Retrieved December 22, 2006 from
http://www.census.gov/compendia/statab/
Wilkinson, L., & APA Task Force on Statistical Inference. (1999). Statistical methods in
psychology journals: Guidelines and explanations. American Psychologist, 54,
594-604.
College Algebra 17
Figure 1. Variations in Mathematical Intentions of College Algebra Students.
Note. Stars and circles represent outliers. Boxed numbers are the number of institutions
responding.
College Algebra 18
Figure 2. Grade Distributions for College Algebra by School.
Note. Stars and circles represent outliers. Boxed numbers are the number of institutions
responding.
College Algebra 19
Figure 3. Technology Used in College Algebra Classrooms.
Note. Boxed numbers are the number of institutions responding.
College Algebra 20
Figure 4. Assessment Methods of College Algebra University and Community College
Professors.
College Algebra 21
Table 1
Topics Indicated by Departmental Chairs as Important for Incoming College Algebra Students
________________________________________________________________________________________
Percent by University
Percent by Community College
_________________________________ _________________________________
Most Somewhat Marginal or Most Somewhat Marginal or
Topics
Important Important No Importance Important Important No Importance
________________________________________________________________________________________
Algebraic
Manipulation
100
0
0
100
0
0
Problem
Solving
67
25
8
84
16
0
Fractions
83
17
0
84
16
0
Logarithmic/
Exponential
18
55
27
16
68
16
Trigonometry
0
36
64
3
13
84
Regression
Modeling
9
9
82
3
20
77
Graphing
Calculator
18
55
27
6
47
47
Group Work
9
27
64
0
48
52
________________________________________________________________________________________
College Algebra 22
Table 2
Correlations Between Prerequisite Scores and Departmental Grade Distributions
________________________________________
Placement
Exams SAT THEA COMPASS ACCUPLACER
________________________________________
ACT
.373 .506*
.459 .821**
SAT
THEA
.470*
.680** .206
.846** .520*
COMPASS
.453
________________________________________
Note. * indicates statistically significant at the .05 level. Effect sizes greater than .4 are
italicized and considered noteworthy.