Factors influencing student performance in the introductory management science course.
There is a growing concern about the poor performance of undergraduate students in the introductory management science course, which is a core requirement in most business degree programs and a prerequisite for advanced courses. At Hampton University, business students are required to earn a C grade or higher in this course (Quantitative Methods) to fulfill graduation requirements. The number of students not meeting this requirement in their first attempt is high, with approximately one-third of the students earning less than a C grade, thus having to repeat the course. This exerts a financial strain on the students, lowers overall GPA, delays graduation, and causes overcrowding of management science classes.
The main motivation behind this study is to establish the underlying causes of higher failure rate in this course. The literature review shows that statistical techniques are extensively applied to model student academic performance in several courses. A number of researchers used statistical models to study factors influencing performance in accounting, economics, and finance courses. However, there is a lack of application of similar statistical techniques to analyze performance in management science courses. A small number of recent studies have been reported which analyze students' performance in such courses. Furthermore, these studies do not necessarily agree on the reasons for poor performance. Grossman (2001) provided several reasons for poor performance ranging from student lack of preparation to ineffective course design. Brookshire and Palocsay (2005); Peters et. al. (2002); and Mukherjee (2000) have studied management science courses and arrived at somewhat different causes of poor performance. This indicates that further investigation may be necessary to understand the root causes of poor performance and recommend corrective measure to improve students' performance in the management science course.
This paper attempts to highlight a wide range of significant factors which could be responsible for the poor performance in the management science course (Quantitative Methods) offered by the Department of Management at Hampton University. The study was conducted over two academic years covering around 300 students in 10 sections taught by a single instructor using a standardized course syllabus and grading criteria. In order to protect the confidentiality of student, personal identities were not disclosed and the study was approved by the University's Institutional Review Board (IRB).
The study initially considered a wide range of independent variables that could possibly influence the performance. Preliminary statistical tests resulted in elimination of the non-significant variables. A multiple regression model was developed relating nine independent variables to student performance measured by the simple average of tests and final examination scores. A final multiple regression model was created using stepwise method resulting in four independent variables as a predictor for student performance. These four variables were current class grade point average, average homework score, course utilization ratio (ratio of total hours earned by total hours attempted), and completion of precalculus prerequisite.
A number of studies have been conducted worldwide to assess the students' performance in various introductory undergraduate courses. The literature does not agree on a set of factors which influences the performance of the students in introductory college level courses. Certain factors are found to influence the performance at some institutions while not at others. A review of the literature highlighting the numerous factors that could possibly influence performance follows.
Student Demographics (major, age, gender, and race)
Most business majors are required to complete the introductory management science course. Students registered in a major that includes the introductory course are expected to perform better than students from other majors. Brookshire and Palocsay (2005) found significant difference in mean quality points for the management science course among students from different majors, although no conclusion was drawn for any particular major.
It is commonly believed that older students have a higher performance due to increased level of maturity and responsibility. Eikner and Montondon (2001) found that older nontraditional students had a higher success rate in an Intermediate Accounting I course. A highly significant positive relationship existed between age and grade in a financial accounting course (Munro, 2001). Age did not impact the performance in an introductory management accounting course (Monem, 2007) and among accounting graduating students (Al-Rashed, 2001). A study on mostly traditional students ages 19 to 23 taking an introductory management science course found no significant difference in performance (Brookshire and Palocsay, 2005).
An increase in percentage of female student attending universities has drawn the interest of researchers studying the relationship of gender on performance. The performance of males was higher in an introductory information systems course (Kruck and Lending, 2003). Monem (2007) found males marginally outperform females in an introductory management accounting course. The female students in an introductory accounting course studied by Sugahara and Boland (2006) performed significantly better than males. Gracia and Jenkins (2003) and Tho (1994) found females outperform males in accounting and finance courses. A similar study found females outperformed males in first year accounting and auditing courses, while no gender difference was found in the final year courses (Gammie et.al. 2003). Graduating female students performed better than male students in the accounting and business programs (Alfan and Othman, 2005). Other researchers have found no significant difference in the performance of male and female students (Brookshire and Palocsay, 2005; Eikner and Montondon, 2001; Al-Rashed, 2001).
The study of influence of race on performance has produced inconclusive results. Eikner and Montondon (2001) included the race variable (minority, non-minority) in their final regression model, but found it was not significant at conventional levels. While, Alfan and Othman (2005) found student's performance in accounting and business programs is dependent on their race.
Course Structure (class size, duration, timing, and length)
The introductory undergraduate courses are generally taught in large lecture classes, at different day times, and varying class duration and semester length. The effect of class size on performance has long been a topic of debate in the school systems with no conclusive results (Salvin, 1989). At the college level, introductory accounting courses taught in large lecture sections had no significant impact on performance (Eskew and Faley, 1988). The performance of students in an introductory finance course was not affected by class size, duration of 75 or 150 minutes, and time of the day time class meetings, but students in evening classes performed lower than their day time counterparts (Wilson, 2002). According to Devadoss and Foltz (1996), students preferred 50 minute classes held on Monday, Wednesday, and Friday. In a larger study covering a wide subject area, Gibbs et. al., (1996) confirmed the hypothesis that students would perform less well in larger classes. Ewer et. al., (2002) found that students perform equally well in a four week and 16 week semester length.
Instructional Methods (instructor status and presentation style)
The course instructor plays a major role in student learning. College level teaching is a skill acquired through education and years of experience. Many introductory level courses are taught by adjunct or part-time faculty. Contrary to the general belief that courses taught by full-time tenured faculty would result in a higher performance, Wilson (2002) found that student taught by lecturers had a higher performance than those taught by tenured and tenure track faculty. Reporting on the performance in the introductory management science course, Brookshire and Palocsay (2005) found a significant difference in the performance of students taught by five different instructors, but further information of instructor status was not available. The use of audiovisual aids is helpful especially in large lecture classes. Powerpoint is a common aid used by many instructors from various fields of study, and is used extensively by conference participants. Its real effectiveness in improving performance is debatable. Most students say it helps in following the lecture while keeping the instructor focused on the topic. A study by Sugahara and Boland (2006) showed that student who prefer Powerpoint lectures scored lower on the final examination as compared to students who prefer the traditional whiteboard presentation.
Student Motivation and Effort (attendance, homework, and quizzes)
A motivated student will attend class regularly and participate in the assignments. By simply recording attendance, Shimoff and Catania (2001) found an increase in class participation and corresponding increase in overall academic performance. A study conducted by Devadoss and Foltz (1996) provides strong empirical evidence of the positive impact of class attendance on performance. Marburger (2001) has reported that performance in the Principles of Microeconomics examination was significantly affected due to absenteeism.
The role of homework on the performance of school grades has been studied extensively (Trautwein and Koller, 2003). At the college level, researchers have supported the usefulness of homework as a supplement to classroom learning and in improving performance especially in introductory courses. Sasser (1981) found the performance of college students in a freshman algebra course receiving homework was significantly greater than those not receiving homework. Kruck and Lending (2003) found effort/motivation, measured by homework scores was significantly related to performance. According to Neilson (2003), the effectiveness of homework is related to time constraint. When there is no time constraint, it can be beneficial but its effectiveness lessens under time constraints especially experienced by working students. In an introductory operations management course, Peters et. al., (2002) found grading homework did not affect examination performance on quantitative questions but contributed significantly to performance on non-quantitative questions. The graded homework returned to students and once again reviewed before a test has shown to improve performance (Mukerjee, 2000).
The number of quizzes taken was significantly related to examination performance (Eskew and Faley, 1988). The use of random, extra credit quizzes increased attendance by about 10%, and improved examination performance (Wilder et. al., 2001). A study by Haberyan (2003) found weekly quizzes did not improve student performance in a college-level general biology course, but student preferred quizzes as it helped in the preparation for examinations.
Student Aptitude and Application (SAT, and current class GPA)
Currently, some universities are debating the requirement of SAT scores as part of the application requirements, and making it optional for applicants with high GPA and class ranking (Daily Press, 2007). Eskew and Faley (1988) reported that SAT (math and verbal) score contributed significantly to student performance in the introductory accounting course. According to Brookshire and Palocsay (2005), the SAT math score has significant bivariate correlation with performance in the management science course. The SAT scores predicted academic performance for male students but not for female students (Kruck and Lending, 2003). The SAT math and verbal scores had significant influence on immediate accounting tests (Bernardi and Bean, 2002).
The influence of current class GPA on performance has been widely studied by researchers. Gracia and Jenkins (2003) found previous GPA earned had a significant effect on current GPA in the accounting and finance program. Kruck and Lending (2003) found a significant relationship between collegiate GPA and overall performance in an introductory information systems course. Eikner and Montondun (2001) concluded that college GPA to date was significantly related to performance in an intermediate accounting course. The GPA earned at the end of sophomore year strongly influenced performance in the complete accounting program (Al-Rashed, 2001). The overall GPA (excluding management science, calculus, and statistics course grades) was found to be most significantly related to the grade earned in the introductory management science course (Brookshire and Palocsay, 2005).
Student Preparation (prerequisites, transfer, and course repetition)
The prerequisite courses are generally scheduled during the freshman/sophomore year to prepare students for advanced courses. The usefulness of these courses has often been questioned. Bernardi and Bean (2002) have found that performance in Intermediate Accounting-I has a positive impact on the performance in Intermediate Accounting-II suggesting the importance of introductory courses as an indicator of success in more advanced courses. This was corroborated by Al-Rashed (2001) who found grades in introductory accounting and finance courses had a positive correlation with performance of graduating accounting students. The prerequisites generally required for an introductory management science course are one semester each of calculus and statistics. Brookshire and Palocsay (2005) found performance in the management science course was significantly correlated with quality points in the calculus and statistics courses. Eskew and Faley (1988) found college-level math and statistics courses do improve performance in introductory accounting course. Eikner and Montondon (2001) found that performance in the first intermediate accounting course was significantly related to the grade in the first accounting principle course. Surprisingly, Kruck and Lending (2003) found taking a similar course or programming classes did not improve the performance in the information systems course. Core courses taken by business students did not have a strong positive relationship with the final cumulative GPA (Alfan and Othman, 2005).
Often, prerequisite courses are transferred from high school AP program or from previously attended institutes of higher learning. Munro (2001) studied the performance of students in a Financial Accounting course who were granted transfer credits for a prerequisite first level accounting course. The results indicate that students who completed the prerequisite course in-house performed better than those who received transfer credits from other institutes. Eikner and Montondon (2001) studied the performance of student who transferred courses from other colleges and found no significant difference in performance between transfer and traditional students, and those repeating a course performed marginally better.
The relationship between the student performance and explanatory factors has been established in the past by researchers using multivariate analysis (Eskew and Faley, 1988; Miller and Westmoreland, 1998). This approach has been replicated by researchers from different disciplines to correlate multi-factors with performance. Kruck and Lending (2003) developed a multiple regression model that used five independent variables to predict grades in an introductory information science course. Eikner and Montondon (2001) identified eight independent variables as potential performance indicators in the first intermediate accounting course and found three to be significant: college GPA, grade in the first accounting principle course, and age. Garcia and Jenkins (2003) used multiple regression and principal component analysis to study the impact of around 20 independent variables on performance of a degree program in accounting and finance and found six were significant in explaining the variation in current performance. A multiple regression model was developed by Al-Rashed (2001) that related the final GPA of accounting students to 11 independent variables. After conducting a stepwise multiple regression analysis, Al-Rashed (2001) found a single variable (GPA) most significant, while the others had lesser degree of significance in predicting performance.
A few multivariate analyses have been conducted in the field of management science. Brookshire and Palocsay (2005) applied multiple regression analysis to determine significant factors that impact performance of students in an introductory management science course and found overall academic performance (GPA) had the strongest correlation with performance, while other variables included in the model (SAT math score, prerequisites, major, and instructor) had a lesser significance on the performance.
RESEARCH DESIGN AND RESULTS
The review of previous research across various fields identified a range of factors that could influence the academic performance in introductory business courses. As expected, the researchers differ on which factors are more important for the students' academic success. Furthermore, each research study considered different set of factors and used variety of measurements to assess the academic performance. In this study, we considered several previously reported along with some new factors together to investigate our basic research question "What factors determine academic performance in an introductory management science course?" Six different set of independent variables were considered that included student demographics, course structure, instructional methods, student motivation and effort, student aptitude and application, and student preparation. These sets are discussed later in this section.
The Course Details and Sample Size
The course studied for this research was a three credit hour introductory management science (Quantitative Methods) course required by all business majors and used as an elective by students from other majors. This sophomore level course is sequenced during the fourth semester and requires calculus and statistics prerequisites. The classes were taught by a single tenured professor on Monday, Wednesday, and Friday between 8:00 AM and 11:00 AM. A common course syllabus and grading scale was used covering deterministic and probabilistic models outlined in the sample course design by Borsting et. al. (1988). Powerpoint presentation was used as a teaching tool in all sections and made available electronically to students. The final score was complied as a weighted sum of three tests (45%), final examination (20%), homework (10%), quizzes (10%), class project (10%), and attendance/participation (5%). A course grade was assigned according to the University's grading system. The tests and final examination consisted of a combination of multiple-choice questions (30%) and numerical problems (70%). Homeworks and quizzes were assigned at the end of each chapter and were graded and returned back to students. The class project demonstrated an application of a management science technique covered during the course. The attendance/participation score was computed based on the number of unexcused absences.
The course was studied over a two-year period covering 333 students in 10 sections taught during the fall 2005 to spring 2007 semesters. Out of 333 students, 297 were assigned a letter grade from A through F. The remaining 36 students (around 11%) withdrew from the course, or did not take the final exam.
Preliminary Statistical Analysis
The methodology follows the approach of Eikner and Montondou (2001). The variables identified in the literature review were analyzed separately in relation to performance using the t-test, ANOVA, and/or simple regression, and significant variables were included in the multiple regression model. Instead of using the final grade for performance measure as suggested by Eikner and Montondou (2001), or the final examination score (Sugahara and Boland, 2006), this study used the simple average of the three tests and final examination scores (AVGT). The tests and final examination, from which the AVGT is computed, are conducted in class under supervision and hence, expected to reflect the true performance of students. Trautwein and Koller (2003) have also recommended the use of standardized achievement tests instead of grades to measure the performance of students.
Student Demographics (major, age, gender, and race)
The student population included largely business majors along with a few non-business majors. An ANOVA test showed no significant difference (F=1.638, df=296, p=.1499) in AVGT for the different majors presented in Table 1.
Most of the students in the study group were African-American sophomores or juniors residing on campus. Since the sample was largely homogenous with respect to age and race, these variables were not analyzed further. Table 2 provides a distribution of males and females in the study group. The females outnumber males (54% versus 46%) reflecting a national trend of higher enrollment of female college students. The AVGT scores for female and male differ significantly (t = 2.621, p = .009) suggesting that female students' performance was significantly better than male students in the course.
Based on the preliminary statistical analysis of student demographics, only the independent variable GENDER is included in the multiple regression model.
Course Structure (class size, duration, timing, and length)
The Table 3 presents a summary of descriptive statistics for each course section. Due to limited data sets, the class size was divided into two groups: small class ([less than or equal to] 30 students) and large class (> 30 students). The AVTG for small and large classes is not significantly different (t = -.994, p = .321). All the classes were held on Monday, Wednesday, and Friday at 8:00 AM, 9:00 AM, 10:00 AM, and 11:00 AM for a duration of 50 minutes each. The t-test for sample pairs of different class meeting timings show no significant difference (t = -0.009, p = 0.993 to t = -1.594, p = 0.118) in the AVTG. Similarly, there was no difference found between Fall and Spring semesters' AVTG (t= -.1965, p=.8442). The class length and semester duration variables could not be tested as all 10 sections considered in the study met for 50 minutes each in the regular 15-week semester.
Based on the preliminary statistical analysis of course structure, none of the independent variables in this set were significant; hence none of these variables were included in the multiple regression model.
Instructional Methods (instructor status, presentation style, and textbook)
All the sections were taught by a single tenured professor using Powerpoint presentation. The presentations were available electronically to students through the University website. Since, all sections were taught by same professor using similar presentation style, the instructor status and presentation style variables could not be tested. The prescribed text book for the course was changed in the Fall 2006. A t-test for the two sample courses using the old book in Spring 2006 and the new book Spring 2007 showed no significant differences in AVGT (t = - .639, p = .525.)
Based on the preliminary statistical analysis of instructional methods, none of the independent variables in this set were significant; hence none of these variables were included in the multiple regression model.
Student Motivation and Effort (attendance, homework, and quizzes)
Class attendance was required and constituted part of the final grade. A simple regression analysis conducted separately for the number of days absent and percentage of days absent showed a significantly high (p<.001) relationship on the AVGT. The percentage of days absent had a stronger relationship (r-square = 0.09) with AVGT.
Homework was assigned at the end of each chapter to strengthen learning of conceptual and quantitative materials. All homework were collected, graded by the instructor, and returned back to the students. A simple regression analysis conducted separately for the number of homework submitted, percentage of homework submitted, and the average homework score showed a significantly high (p<.001) relationship with AVGT. The average homework score had a stronger relationship (r-square =.238) with AVGT.
A short quiz followed the completion of each chapter. These were completed outside the classroom and were collected during the next class meeting, graded by the instructor, and returned back to the students. A simple regression analysis conducted separately for the number of quizzes submitted, percentage of quizzes submitted, and the average quiz score showed a significantly high (p<.001) relationship with AVGT. The average quiz score had a stronger relationship (r-square =.146) with AVGT.
As expected, all the motivation and effort variables were significant in the preliminary statistical analysis. Hence, the independent variables, percent of days absent (%ABS), average homework score (AHW), and average quiz score (AQZ) were included in the multiple regression model.
Student Aptitude and Application (SAT, current class GPA, and course utilization ratio)
As reported in many studies, the SAT scores are a good predictor of the performance during freshmen year of college. Since, the Quantitative Methods course is a sophomore level course, SAT scores were not included in this study. According to the business curriculum outline, all students must enroll in the Quantitative Methods course preferably during their sophomore year after completing at least 45 semester credit hours. An analysis of average hours attempted (96.65 hours) and the average hours earned (89.29 hours) up to completion of the course indicates that students were enrolling in this course much later in their curriculum, some even during their final semester. A number of students earned transfer credit hours that are included for total curriculum requirement but not included in the hours attempted and hours earned for class GPA computation. Hence, it was decided to compute the course utilization ratio of total hours earned to total hours attempted (HE/HA). This average value of HE/HA for this study was = 0.937 indicating a loss of hours due to withdrawal or failing grades. The current class GPA (including the Quantitative Methods course) and the course utilization ratio are reflective of the student's aptitude and application. A simple regression conducted separately for the current class GPA and course utilization ratio on AVGT, showed the former had a significant relationship (r-square =.404, p<.001) and the latter had a significant relationship (r-square = .119, p<.001). The GPA and course utilization ratio has significant relationship with AVGT indicating that higher values should lead to better performance. Hence, current class GPA (GPA) and course utilization ratio (HE/HA) were included in the regression model, and the SAT score was not included.
Student Preparation (prerequisites, transfer, and course repetition)
The curriculum requires two prerequisite courses in calculus and statistics to be completed prior to enrolling in the Quantitative Methods course. The AVGT for students who completed the Calculus and Statistics prerequisites earning a passing grade were significantly higher than students who did not complete the prerequisites (Table 4). The completion of Precalculus Mathematics I course which is a prerequisite for the Calculus as well as Statistics courses also had a significant impact on the AVGT.
The School allows students to transfer non-business course credits (not quality points) completed at any accredited institution of higher learning. The focus of this research was on students who obtained transfer of the prerequisite MAT 130--Calculus. There was no significant difference (t=-.821, p=.417) in AVGT between students who completed the calculus course on campus or at another institution. This contradicts results of Munro (2001).
Student repeating the course either withdrew from the previous course or received a lower grade than is necessary for their curriculum. There was no significant difference (t=1.186, p=.236) noted in AVGT between repeat and first time students. A similar analysis by Eikner and Montondon (2001) found marginal difference in performance.
Based on the preliminary statistical analysis of student preparation, the independent variables for completion of all direct and indirect prerequisites: Calculus (P1), Statistics (P2), and Precalculus Mathematics I (P3) were included in the multiple regression model.
Multiple Regression Analysis
Of the 22 independent variables analyzed by preliminary statistical methods, nine significant independent variables were included in the following multiple regression model.
AVGT = [[beta].sub.0] + [[beta].sub.1]GPA + [[beta].sub.2]GENDER + [[beta].sub.3]%ABS + [[beta].sub.4]AHW + [[beta].sub.5]AQZ + [beta]6HE/HA + [[beta].sub.7]P1 + [[beta].sub.8]P2 + [[beta].sub.9]P3 + [epsilon]
AVGT: the simple average of three tests and final examination scores.
GPA: a continuous variable representing the current class GPA up to completion of the Quantitative Methods course.
GENDER: a dummy variable, Male = 1, Female = 0.
%ABS: is a continuous variable representing the percentage of days absent (excused and unexcused) during the semester.
AHW: a continuous variable representing the average homework score out of 10.
AQZ: a continuous variable representing the average quiz score out of 10.
HE/HA: a continuous variable representing course utilization ratio (total hours earned by total hours attempted) up to completion of the Quantitative Methods course.
P1: a dummy variable for Calculus prerequisite. Completed = 1, not completed = 0.
P2: a dummy variable for Statistics prerequisite. Completed = 1, not completed = 0.
P3: a dummy variable for Precalculus Mathematics I prereq. Completed = 1, not completed = 0.
An analysis was conducted to determine the equation of the multiple regression model that best fits the data. The multiple regression results for the nine variables are shown in Table 5. The computed value of F = 34.214 and the P-value < 0.001 indicates that some of the independent variables have the ability to explain the variation in AVGT.
As shown in Table 5, only four out of nine variables have significant contribution to the regression model. It clearly shows that contribution of some variables is mostly explained by the other variable, as the regression model only considered variables which independently showed significant relationship with AVGT. For example, Precalculus Mathematics I (P3) is a perquisite for both Statistics (P2) and Calculus (P1). And the regression model shows that completion of P3 explained most of the variability as compared to the prerequisites P1 and P2. It is possible that a number of students who completed P3 had also completed P1 and P2 courses. Furthermore, a correlation matrix (Table 6) was developed showing the coefficient of correlation between pairs of independent variables. All the variables except GENDER and P2 appear to have a medium to strong correlation with AVGT. GPA has the strongest relationship and GENDER and %ABS have negative signs indicating an expected inverse relationship. A check for multicollinearity was conducted to determine if there was any correlation among the independent variables. With the exception of HE/HA and GPA (0.752), all the coefficients are between -0.70 and 0.70 and should not cause a correlation problem (Lind et. al., 2006).
The multiple regression output data was further analyzed by plotting the residuals versus predicted AVGT for each set of inputs. The scatter plot (Figure 1) shows the spread of residuals remains mostly constant except for few outliers at the lower AVGT values, thus fulfilling the homoscedasticity condition.
[FIGURE 1 OMITTED]
As described in the earlier section, not all nine variables are contributing significantly to multiple regression model. The stepwise multiple regression (SPSS, Inc., 2003) was used to find the better and concise regression model from the set of independent variables under consideration. The multiple regression model summary is shown in Table 7 along with the variable coefficients (Table 8).
The final multiple regression model (Mode 4) is:
AVGT = 67.847 + 13.303GPA + 1.213AHW - 40.721HE/HA + 3.666P3.
Out of nine independent variables in the multiple regression model, four appear to be significant in explaining the variation in the measure of performance in the Quantitative Methods course. The current class GPA is the strongest predictor of performance. Students who have a high current class GPA have the aptitude to perform well. This matches the results of recent research across different fields (Brookshire and Palocsay, 2005; Kruck and Lending, 2003; Gracia and Jenkins, 2003; Al-Rashed, 2001; Eikner and Montondun, 2001).
Homework plays an important role in understanding the course material presented in the class and contributes 10% of the overall grade. It has been observed that homework is not taken seriously and has an average computed score of 7.03/10.00 (C-). The 85% of homework submitted was mostly done hurriedly prior to submission with help from other students. Even with the deficiency in the quality of the homework, it is still a significant factor in assessing student progress. A decline in homework scores may be an early warning for instructor intervention.
The course utilization ratio measure the effectiveness of time spent at college. The average course utilization for this study was around 94% indicating a 6% loss in credit hours. Over the entire length of 125 hours needed to earn a degree, 7.5 hours were lost due to withdrawals or failing grades. It was hoped that the GPA variable would explain most of course utilization variability as lower course utilization generally meant lower GPA. However, course utilization is still a significant factor in explaining some of the variability in the AGVT despite GPA presence in the regression model.
The Quantitative Methods topics require application of basic math skills and some statistical background, and Calculus (P1) and Statistics (P2) are the recommended prerequisites. Out of the three prerequisites P1, P2, and P3 that were included in the multiple regression model, only Precalculus Mathematics I (P3) which is required for the Calculus (P1) and Statistics (P2) courses was found to significantly influence performance in the Quantitative Methods course. The Calculus (P1) and Statistics (P2) courses did not significantly influence the performance. It was observed that students did not take the prerequisites in the recommended sequence while many others repeated the Calculus (P1) and Precalculus Mathematics I (P3) courses several times to score the required grade (C or higher). Often, students have successfully completed the Quantitative Methods course without having the prerequisites.
Although GENDER was significant during the preliminary statistical analysis, it did not appear in the final multiple regression model (p = 0.1594). Past research has shown mixed results in performance between males and females. It is possible that the gender difference was also explained by either GPA or prerequisite Precalculus Mathematics I (P3).
The percentage of days absent (%ABS) is not significant (p = 0.7564). The average percentage of days absent was 12% of lecture meetings during the semester. Past research shows an impact of attendance on performance (Shimoff and Catania 2001; Marburger 2001; Devadoss and Foltz 1996). In this course, attendance accounted for 5% of the final course grade. Hence, some students with poor attendance record lost points on the course grade although they may have done fairly well at the tests and examination. Furthermore, students who missed classes have the opportunity to catch up during the instructor's office hours, homework application, and review sessions.
The average quiz score (AQZ) was not significant (p = 0.2841). The quiz score contributed 10% to the overall course grade. The objective was to provide an opportunity to learn the material by referring to the text and class notes while completing the quiz. But in actuality, students simple guessed the answers or sought help from others thereby diminishing effectiveness of the quiz. Hence, non submission of quiz did impact the overall course grade but did not influence the test and examination performance.
Can the final multiple regression model be used to predict student performance in the Quantitative Methods course? The scatter plot (Figure 2) of the predicted AVGT versus the actual AVGT shows most points fall very close to the line except for a few outliers at the lower AVGT values. It appears that the model provides a good fit and may be used to predict the performance of a student.
This study includes an exhaustive literature review of possible factors that could influence the performance of students in the management science (Quantitative Methods) course and identified around 22 such factors. After a preliminary statistical analysis, nine of these factors were included as independent variables in the multiple regression model. A stepwise regression analysis resulted in four significant (p < 0.001) variables: GPA, AHW, HE/HA, and P3. The remaining five factors although having influence did not independently contribute significantly to the predictive model.
An objective of this paper is to provide guidelines that may be used by faculty while advising students. Faculty teaching the Quantitative Methods course could do a prior analysis of student background to predict performance. The data for the independent variables could be drawn for the current semester and fitted to the final multiple regression model. The class GPA (GPA), course utilization ratio (HE/HA), and completion of prerequisite (P3) is available from student transcripts. The average homework score (AHW) will not be available at the beginning of the semester but a conservative estimate could be used. Student whose performance falls below normal could be advised to take appropriate action such as strengthening basic math skills, seeking tutorial help, improving study habits and class attendance, etc.
As part of the overall advising process, students must be urged to take courses in proper sequence to get the maximum benefit from their program. The Department may want to reconsider its prerequisite policy. Are Calculus (P1) and Statistics (P2) the necessary prerequisite courses, and if so, will a passing grade (D- or higher) be sufficient? Similarly, the instructor could review the grading policy with greater emphasis on homework as a means of increasing student participation. Since take home quizzes did not impact performance, it could be redesigned or eliminated. Class attendance was not significant for the multiple regression model, however, the correlation matrix (Table 6) shows somewhat strong correlation between attendance and homework as well as quiz grades. Therefore, a strict attendance policy may be necessary to ensure better performance.
This study has limitations. The final multiple regression model explains 51% of the variation in AVGT. Hence, additional factors may need to be included. For example, the current course load of student could possibly influence the performance. Students carrying a heavy course load may devote little or no time to this course. Although, no research was found that relates course load and performance in the management science course, studies in other subject areas have drawn inclusive results (Szafran, 2001 and Joy, 1981). Other factors that could influence student performance in the management science courses are students' utilization of faculty office hours and attendance of review or recitation session, if available. Additionally, a review of end-of-semester course evaluations may shed further light into course or instructor factors that may be related to student performance.
The sample size of around 300 students was drawn from classes taught by a single instructor and may not reflect the performance over a larger group taught by multiple instructors within the University, or among different colleges and universities. A larger study including multiple instructors from different institutions would be required to arrive at a general predictive model. In such a study, the dependent variable may be affected by different independent variables at the individual student level and university level. The individual students will be nested within universities thus requiring the application of Multilevel Regression Analysis (Bickel, 2007). Such large data sets could also be analyzed using data mining techniques (Han and Kamber, 2001).
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Kelwyn A. D'Souza, Hampton University
Sharad K. Maheshwari, Hampton University
Table 1. Student Major Groups. Semester Accounting Economics & Finance Entrepreneurship Spring 2007 10 6 9 Fall 2006 6 4 6 Spring 2006 17 10 14 Fall 2005 8 8 12 Total 41 28 41 AVGT 77.91 76.04 81.00 Semester Management Marketing Others Spring 2007 18 20 1 Fall 2006 21 11 2 Spring 2006 21 36 3 Fall 2005 34 20 0 Total 94 87 6 AVGT 76.74 79.59 76.50 Table 2. Gender Detail Gender Sample Size % Mean AVGT Std. Dev. Female 161 54% 79.82 8.35 Male 136 46% 77.00 10.15 Total 297 100% 78.53 9.31 Table 3. Class Size and Timing Section Semester Timing Class Size Mean AVGT Std. Dev. 1 Spring 2007 8:00 AM 31 78.133 7.016 2 Spring 2007 9:00 AM 33 77.508 11.563 3 Fall 2006 8:00 AM 20 77.981 10.457 4 Fall 2006 9:00 AM 30 77.846 10.226 5 Spring 2006 8:00 AM 33 79.311 7.725 6 Spring 2006 9:00 AM 31 80.00 7.539 7 Spring 2006 11:00 AM 37 79.980 10.617 8 Fall 2005 9:00 AM 27 76.111 8.113 9 Fall 2005 10:00 AM 27 76.778 7.673 10 Fall 2005 11:00 AM 28 80.839 10.987 Table 4. Statistical Test for Prerequisites Prerequisite Completed Not Completed Significance Calculus (P1) Mean AVGT = 80.34 Mean AVGT = 73.86 t=-5.626 Std. Dev. = 8.83 Std. Dev. = 8.94 p<.001 Statistics (P2) Mean AVGT = 79.40 Mean AVGT = 73.90 t=-3.806 Std. Dev. = 9.11 Std. Dev. = 9.08 p<.001 Precalculus Mean AVGT = 79.37 Mean AVGT = 72.23 t=-3.534 Mathematics Std. Dev. = 8.66 Std. Dev. = 11.53 p=.001 I (P3) Table 5. Multiple Regression Results Test of Significance of the Regression Model Coefficient R-square = ANOVA Standard N = 297 of multiple 0.518. F = 34.2141, Error = determination df = 296 6.5666 R2 = 0.5176. Significance <0.001. Test of Significance of the Intercept and Individual Variables Independent Variables Coefficients t Statistics P-value Significance Intercept 72.329 10.81 <0.001 Yes GPA 13.157 10.53 <0.001 Yes GENDER -1.118 -1.41 0.1594 No %ABS -1.482 -0.31 0.7564 No AHW 1.356 4.49 <0.001 Yes AQZ -0.471 -1.07 0.2841 No HE/HA -42.541 -5.17 <0.001 Yes P1 0.758 0.70 0.4846 No P2 1.285 1.17 0.2452 No P3 2.916 2.05 0.0416 Yes Table 6. Correlation Matrix AVGT GPA GENDER %ABS AHW AVGT 1 GPA 0.636 1 GENDER -0.155 -0.13 1 %ABS -0.301 -0.35 0.210 1 AHW 0.488 0.482 -0.147 -0.527 1 AQZ 0.382 0.486 -0.088 -0.519 0.676 HE/HA 0.345 0.752 -0.160 -0.354 0.391 P1 0.313 0.356 -0.049 -0.111 0.147 P2 0.216 0.268 -0.123 -0.054 0.098 P3 0.248 0.159 -0.065 -0.147 0.131 AQZ HE/HA P1 P2 P3 AVGT GPA GENDER %ABS AHW AQZ 1 HE/HA 0.384 1 P1 0.184 0.248 1 P2 0.127 0.228 0.223 1 P3 0.097 0.088 0.540 0.099 1 Table 7. Multiple Regression Model Summary Std. Error Adjusted of the Model Predictors R R-Square R Square Estimate 1 GPA 0.636 0.404 0.402 7.198 2 GPS, AHW 0.669 0.447 0.443 6.945 3 GPA, AHW, HE/HA 0.702 0.492 0.487 6.666 4 GPA, AHW, HE/HA, P3 0.713 0.508 0.501 6.574 Table 8. Variable Coefficients Unstandardized Standardized Model Variable Coefficients Coefficients T Sig. Std. B Error Beta 1 (Constant) 46.531 2.300 20.231 .000 GPA 11.498 .813 .636 14.148 .000 2 (Constant) 43.750 2.294 19.071 .000 GPA 9.436 .895 .522 10.545 .000 AHW 1.200 .251 .237 4.784 .000 3 (Constant) 70.782 5.733 12.347 .000 GPA 13.719 1.200 .759 11.429 .000 AHW 1.261 .241 .249 5.231 .000 HE/HA -41.998 8.223 -.323 -5.107 .000 4 (Constant) 67.847 5.734 11.832 .000 GPA 13.303 1.191 .736 11.165 .000 AHW 1.213 .238 .239 5.092 .000 HE/HA -40.721 8.120 -.313 -5.015 .000 P3 3.666 1.202 .127 3.050 .003
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|Author:||D'Souza, Kelwyn A.; Maheshwari, Sharad K.|
|Publication:||Academy of Educational Leadership Journal|
|Date:||Sep 1, 2010|
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