Effects of Math Tutoring


 Ethelbert Martin
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1 Requestor: Math Deartment Researcher(s): Steve Blohm Date: 6/30/15 Title: Effects of Math Tutoring Effects of Math Tutoring The urose of this study is to measure the effects of math tutoring at Cabrillo College. This is an observational study in which we looked at student grades, success rates, and comletion rates for students who received tutoring and those who did not in all math classes in which at least one student was tutored. From a research oint of view, it would have been better to use an exeriment where we could examine the effects of tutoring while holding other variables constant. In order to erform an exeriment to measure the effect of math tutoring, we would need to randomly select students to be tutored from a ool of students who seek tutoring, while denying other students tutoring. However, due to ractical, ethical, and regulatory concerns about denying tutoring students to students, an exerimental aroach was not ossible. The direct comarisons between those receiving tutoring and those not receiving tutoring while useful are subject to selfselection bias. To hel control for bias from students selfselecting to articiate in tutoring, regression and roensity score matching (PSM) techniques were emloyed to equate articiants and nonarticiants on a variety of background variables. The results are of this study are consistent with the belief that tutoring is helful for students Samle: The samle analyzed consists of students who used tutoring at the MLC from summer 2009 through summer 2013 along with those who were enrolled in a course where at least one of the students used tutoring. We looked at six courses at Cabrillo where enrollment and tutoring use were both relatively high comared to other courses. The courses we looked at were Statistics (Math 12), Intermediate Algebra (Math 152), Basic Algebra (Math 154), Essential Mathematics (Math 254A), Precalculus (Math 4), and Calculus (Math 5A). Many students at Cabrillo have had difficulty succeeding in Intermediate Algebra. We look in detail at the relationshi between hours tutored and success in this course while controlling for other factors that are redictive of success. The following figure looks at the success rates in each class for these three grous 1. Students who did not log tutoring time or log time at the Math Learning Center (MLC)  Nothing 2. Students who used the MLC, but did not use tutoring MLC Only 3. Student who used some tutoring  Tutoring 1
2 Figure 1: Percentage of Math Students Earning a C or Better In every case, those who were tutored outerform those who were not. The samle sizes were large so even small difference would show u as significant. However, in many cases the differences are substantial. For examle, recalculus students who were tutored succeed 58% of the time and those who were not succeeded 48% of the time. Below we will investigate the effect of tutoring among secific among different gender, ethnic grous, and other secial oulations. 2
3 Figure 2: Percentage of Math Students Earning a C or Better by Gender Both female and male students erform better with tutoring than without. Female students tend to outerform male students in all cases excet for those not tutored in Calculus I. In every case other than Math 154, Elementary Algebra, the higher success rate for female tutored students was statistically significant at the 0.05 level of significance. For male students the higher success rate for tutored students was statistically significant in all cases other than Math 12 (Statistics) and Math 5A (Calculus). ChiSquare details are in Aendix A. 3
4 Figure 3: Percentage of Math Students Earning a C or Better by URM Status While underreresented minority students (URM) do tend to have lower success rates comared to other students, those URM students who receive tutoring erform better than URM students who do not receive tutoring. For Math 152, Math 254A and Math 5A the higher success rates are statistically significant at the 0.05 level significance. This information is based on a twotailed significance level where the hyothesis is whether or not success rates are different for tutored students. If we were to instead consider these onetailed tests where our hyothesis is whether or not tutored students have a higher success rate then the results would be significant for all six courses 1. ChiSquare details are in Aendix A. 1 While a chisquare test is generally only a twotailed test because the chisquare statistic is not symmetrical, in this case our chisquare is mathematically equivalent to a Zstatistic. We can therefor take half the value of the two tailed test and comare that to the 0.05 level of significance for a onetailed test. 4
5 Percent of Students Enrolled in Intermediate Algebra that Used Tutoring by Ethnicity 29.82% 23.68% 23.34% 25.63% 24.14% 18.68% 18.52% 13.45% 8.11% American Indian, Alaskan Nativ Asian Black Non Hisanic Filiino Latino Multile Ethnicities Pacific Islander Unknown White Non Hisanic Figure 4: Tutoring Use By Ethnicity Of the 8,082 Students enrolled in math 152 over the years studied, 1,757 (21.74%) used tutoring % of underreresented minority (URM) students used tutoring for intermediate algebra while 23.95% of nonurm students used tutoring. The table below shows tutoring use by ethnicity for Math 152, Intermediate Algebra. While URM students in general used less tutoring than other students, black students used tutoring at the highest rate. 5
6 Figure 5: roensity score matching analysis of tutoring use The above chart shows erformance differences between students who were tutored and a comarison grou of students who were not tutored but have similar attributes based on one to many roensity score matching (PSM). The criteria used for matching were gender, ethnicity (as a binary variable indicating URM or not), age, and rior overall grade oint average (GPA). The chart shows that on average those who were tutored had better success rates than those who were not. The chart also shows a 95% confidence interval for the difference. If the confidence interval does not include zero then we can be at least 95% confident that the difference did not occur by random chance. In every case excet for Math 154, Elementary Algebra the results were statistically significant. The largest difference in success rates between the two grous ids for Math 254, Prealgebra. 6
7 Figure 6: Distribution of Hours Tutored for Math 152 Intermediate Algebra For Math 152, Intermediate Algebra, the maximum number of hours someone was tutored for a semester was 72 hours and the minimum was less than an hour. The mean time for tutoring was about 3 hours er semester with a standard deviation of 5.5 hours. But as can be seen in the histogram above, the data are not normally distributed. The median for hours tutored was 1.15 hours; 50% of students tutored received 1.15 or less hours of tutoring in the semester. Seventy five ercent of students tutored received 3.16 or less hours of tutoring during the semester. Looking at these numbers searately for those who succeeded vs those who did not succeed we see the average number of tutoring hours for those who succeed was 3.58 and the average number of tutoring hours for those who do not succeed was This difference is statistically significant at <
8 Logistic Regression We used a Logistic Regression to estimate the number of tutoring hours required to succeed in Intermediate algebra and to attemt to at least artly control for selfselection bias. Below we estimate the ln(odds of succeeding) using hours tutored, gender, URM status, tutoring use and overall GPA. = robability of succeeding in Math ) = α + β 1x 1 + β 2 x 2 + β 3 x 3 + β 4 x 4 + β 5 x 5 + ε 1 ) = α + TutoringHoursx 1 + URMx 2 + Genderx 3 + GPAx 4 + UseTutorx 5 + ε Variables in the Equation Beta Std. Error Wald df PValue Constant P < Tutoring Hours P < URM (Y = 1) P < Gender (F = 1) P < Overall GPA P < Use Tutoring (Y = 1) P = Because we are looking at the log odds of succeeding, it is difficult to interret the Betas. However, ositive values mean that the variable has a ositive influence on succeeding and negative values mean the variable has a negative imact on succeeding. Of the variables coded dichotomously, URM status has the largest influence. We could use the equation below to redict the robability of success for a articular student that student s information for each of the variable in the equation. 1 ) = x x x x x 5 + ε 8
9 Alternatively we could use the equation to estimate the Number of Tutoring Hours Required to Succeed in Intermediate Algebra The equation below can be used to redict the ln(odds of succeeding) using hours tutored, gender, URM status and overall GPA as a covariate. = robability of succeeding in Math ) = α + β 1x 1 + β 2 x 2 + β 3 x 3 + β 4 x 4 + ε 1 ) = α + TutoringHoursx 1 + URMx 2 + Genderx 3 + GPAx 4 + ε Variables in the Equation Std. Error Wald df PValue Beta Constant P = Tutoring Hours P < URM (Y = 1) P < Gender (F = 1) P = Overall GPA P < ) = x x x x 4 + ε Note: Samle only includes those who used tutoring. 9
10 If we want to estimate the number of tutoring hours required for success for a grou, it is simler to exclude GPA (a continuous variable) as a covariate. Here we estimate the ln(odds of succeeding) using hours tutored, gender, and URM status. = robability of succeeding in Math ) = α + β 1x 1 + β 2 x 2 + β 3 x 3 + ε 1 ) = α + TutoringHoursx 1 + URMx 2 + Genderx 3 + ε Variables in the Equation Beta Std. Error Wald df PValue Constant = Tutoring Hours < URM (Y = 1) < Gender (F = 1) = ) = x x x 3 + ε Note: Samle only includes those who used tutoring. 10
11 Now we can estimate the number of tutoring hours required for success in Math 152 for a articular oulation of interest. For examle, if we want to know the number of hours of tutoring estimated for underreresented minority male success in Intermediate Algebra we could use the equation below. The equation for an underreresented minority male simlifies to: 1 ) = x 1 + ε Among the 1,467 Male URM students who were not tutored, 560 succeeded (38%) Among the 316 Male URM students who were tutored at all, 129 succeeded (41%) For = 0.5 we estimate that a URM male needs 8.3 hours of tutoring (about 0.5 hours er week) 29 Male URM students were tutored for at least 8.3 hours and 17 succeeded (59%) For = 0.75 we estimate that a URM male needs 29.5 hours of tutoring (about 2 hours er week) The two URM male students who had at least 29.5 hours of tutoring both succeeded. 11
12 English Placement Scores Other covariates such as English Placement scores could be used. However, comaring English Placement scores for those who used tutoring and those who do not use tutoring we see no significant difference. Used Tutoring N Mean English Placement Score Std. Deviation Std. Error Mean No 5, Yes 1, The difference of 0.37 is not significant ( = 0.149). Given that the samle size is over 6,000, this is evidence that English lacement scores are not related to the decision to use tutoring for Math 152, Intermediate Algebra. There is a significant difference between English lacement scores for those who succeed in Math 152, Intermediate Algebra vs those who do not succeed in Math 152; English lacement is a significant redictor of success in Math 152. Success in Math152 N Mean English Placement Score Std. Deviation Std. Error Mean No 3, Yes 3, The difference of 2.5 is statistically significant ( < 0.001) When we add English lacement scores to the equation it is a significant redictor of success. However, the fit of the equation does not change in any ractical way and the samle size is reduced by almost 1,700 students when we use this information. The rimary imlication is that more tutoring did aear to lead to greater success in math classes in general. Even those students who use tutoring tend to use very little. Encouraging students to use tutoring and to use it often would likely lead to greater success in math courses. Some of the underreresented minority grous used tutoring at a disroortionately lower rate than their white counterarts. In articular, Latino, Filiino, and Pacific Islander students used tutoring at less than 80% of the rate of use by White students. Other nonurm Asian students tended to use less tutoring as well. No more than 30% of any ethnic grou used tutoring and this seaks to the fact that all students, regardless of their background, could robably benefit by using more tutoring. 12
13 Aendix A Female Students Course Name ChiSquare N df Sig. (2sided) MATH , MATH , MATH , MATH254A , MATH MATH5A Table 1: ChiSquare analysis tutored vs nontutored female students. Male Students Course Name ChiSquare N df Sig. (2sided) MATH , MATH , MATH , MATH254A MATH , MATH5A , Table 2: ChiSquare analysis tutored vs nontutored male students. URM Students Course Name ChiSquare N df Sig. (2sided) MATH , MATH , MATH , MATH254A , MATH MATH5A Table 3: ChiSquare analysis tutored vs nontutored URM students. 13
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