Running head: MATH LEVELS OF ECONOMICS STUDENTS. Math Levels of Economics Students

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1 Running head: MATH LEVELS OF ECONOMICS STUDENTS Math Levels of Economics Students Rick Fillman Institutional Research Analyst Planning and Research Office December 2010

2 Page 2 of 6 Introduction Many four-year universities now require completion of Intermediate Algebra as a prerequisite for lower-division Economics courses in order for the course to fulfill the requirements for lower-division major preparation. At present the recommended preparation for both Economics 1A and Economics 1B at Cabrillo College is Eligibility for ENGL 100, READ 100 and MATH (Elementary Algebra). In other words, neither Elementary Algebra (MATH-154) nor Intermediate Algebra (MATH- 152) need be completed prior to taking Economics. The lack of an Intermediate Algebra requirement for Cabrillo s Economics course may jeopardize the potential of this transferable course to fulfill a transfer student s lower division major preparation requirements. If Cabrillo s Economics course were not accepted for major preparation purposes, students would need to repeat the course at the four year institution, resulting in a time and cost penalty to the student. Note that a prerequisite of MATH-152 would require that students complete, or demonstrate mastery of, both Elementary and Intermediate Algebra prior to enrolling in Economics. If such a prerequisite were instituted locally, at Cabrillo College, how many students might be impacted? Methodology Student records for ten years of enrollments in Economics courses were gathered, with the aim of determining a student s math achievement level at the time of the student s first enrollment 2 in either Introduction to Macroeconomics (ECON-1A) or Introduction to Microeconomics (ECON-1B). There are three ways to meet a prerequisite: assessment/placement, satisfactory completion of an equivalent course elsewhere, or completion of the prerequisite course at Cabrillo. Data from assessment/placement scores and equivalencies from other institutions is gathered from the Datatel student information system. Enrollment data for Cabrillo Math enrollments where the student completed the Math course with a satisfactory grade are assembled from the Cabrillo 1 Cabrillo College Catalog 2 Repeat enrollments in ECON courses are excluded from the analysis. The repeat rate is about 9.9% for ECON -1A, and about 8.7% for ECON-1B, using 10 years of enrollment data. Page 2

3 Page 3 of 6 research data warehouse. These data are chronologically aligned with the Economics course enrollments, and the Math level at the time of the enrollment is determined by the most recently completed Math course prior to the term of the Economics enrollment. In cases where there is no satisfactory Math completion record (the student didn t take Math at Cabrillo, or did and received a grade of D, F, or W), then the students assessment/placement and/or equivalency level, if available, is used to determine the Math level. The Math level of some students cannot be determined. If the student never attempts to enroll in a Math course at the college, they may not have been required to undergo assessment/placement in Math. Further, the Economics prerequisite (eligibility for MATH-154) is not electronically enforced via the student enrollment system, but is evaluated by the instructor. Records of instructor evaluation of prerequisites are not entered into the Datatel student information system. How many students would be impacted? If a Intermediate Algebra was established as a prerequisite for economics courses, this would preclude or delay enrollment for at least one in four students in ECON-1A sections, and one in three students in ECON-1B sections. An additional number of students from the unknown Math level group would likely be impacted as well. About 46% of first-time enrollees in ECON-1A and about 56% of enrollees in ECON-1B would have clearly met the hypothetical prerequisite by the time of their enrollment in Economics. The chart below shows the number of students who would have met or not met this hypothetical prerequisite at the time of their first enrollment in ECON-1A or 1B, respectively. These data are compiled from ten years of enrollment records from academic years through Historical percentage of students meeting or not meeting a hypothetical Intermediate Algebra prerequisite for Economics ECON-1A Headcount Percent Prereq. met % Prereq. not met % Prereq. status unknown % Page 3

4 Page 4 of 6 ECON-1B Headcount Percent Prereq. met % Prereq. not met % Prereq. status unknown % An examination of the data for trends over time showed that the percentage of students meeting the prerequisite varies little from year to year. How would enrollment in Economics courses be affected? Introduction of such a prerequisite would likely result an reduction of in the number students who enroll in Economics classes. Those without the hypothetical prerequisite will abstain from or delay their enrollment until after completing the Math prerequisite. Under-represented students 3 are less likely to be in the group having met the hypothetical prerequisite. The chart below illustrates this phenomenon, by listing the proportion of underrepresented students who meet or do not meet the hypothetical prerequisite as contrasted with the proportion of Whites and Asians. Students meeting the hypothetical Intermediate Algebra prerequisite ECON1A Underrepresented Whites & Asians Prereq. met 41% 49% Prereq. not met 46% 35% Prereq. status unknown 13% 16% ECON1B Underrepresented Whites & Asians Prereq. met 51% 58% Prereq. not met 36% 28% Prereq. status unknown 13% 13% 3 Underrepresented includes Native Americans, African Americans, Filipinos, Hispanic/Latino and Pacific Islanders, with Latino by far the most numerous of the under represented groups. Page 4

5 Page 5 of 6 Does Math level affect success in Economics? If students were required to complete Intermediate Algebra before enrolling in Economics, would students be better prepared? Overall, the success rate 4 for students in Macroeconomics (ECON-1A) courses is 68.7%. The rate for Microeconomics (ECON-1B) students is 69.8%. There is some minor variance from term to term. When calculated separately for the group that met the hypothetical prerequisite, as opposed to those who did not, students who have completed Intermediate Algebra (or the equivalent) have a markedly higher rate of success in Economics courses. The chart below illustrates success rates for the three groups. Course success rate by Intermediate Algebra completion Hypothetical Algebra prerequisite met? ECON-1A ECON-1B Prereq. met 78.5% 79.1% Prereq. not met 58.2% 79.1% Prereq. status unknown 65.4% 60.0% Higher success rates are observed for those students who have completed the Algebra sequence in advance of their enrollment in Economics. But, is the association between completion of Intermediate Algebra with success in Economics classes due to students completing the Algebra sequence, or is it possible that other factors, such as pre-existing differences between Algebra sequence completers and Algebra sequence non-completers, are responsible for differences in average success rates in Economics courses? Other factors which influence success in Economics Statistical analysis suggests that level of Math preparation alone explains only about 5% of the variance in success between the group who met the hypothetical prerequisite as compared with those who did not. It would appear that success in an Economics course can be attributed to a mix of factors. When attempting to account for success in Economics courses, there are likely other variables with equal or greater explanatory power. 4 Ratio of students receiving a grade of A, B, C, or Pass to the number enrolled on the census roster. Data are from academic years through Page 5

6 Page 6 of 6 Two additional student variables were added to the statistical model. Ethnicity, in the form of underrepresented or not, and students cumulative Cabrillo grade point average (GPA) were included. Each of these proved to be statistically significant in relation to success in economics courses. Together, the three variables account for about one-third of the variance in student success in Economics. The strongest association is with students prior cumulative GPA. Algebra completion comes second, with about half the explanatory power as compared with GPA. Underrepresented status has a negative influence on course success in economics, but the influence is weaker than Algebra completion. It appears that overall academic readiness (based on prior academic success) has more to do with success in an Economics course than does the level of Math achievement. 5 Summary Instituting a prerequisite of completion of Intermediate Algebra for Economics courses would substantially reduce enrollment. It would potentially affect up to half of the students who are taking Economics today. It would likely have a disproportionate impact on underrepresented students. Even though Intermediate Algebra completion is correlated with success in Economics courses, multivariate statistical analysis reveals that Algebra completion has a relatively small predictive value, and that general academic preparedness is a stronger predictor of success. 5 For Econ1A, the beta values for the predictors are: GPA=.490, completed Intermediate Algebra=.225 and underrepresented status=-.162 with R square=.256. For Econ1B, the beta values for the predictors are: GPA=.469, completed Intermediate Algebra=.232 and underrepresented status=-.120 with R square=.238. Page 6

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