Running head: 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

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.

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 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 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 should not be interpreted with the same rigidity as α is often chosen in statistical 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.

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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 ................
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