Carmelita Y. Ragasa
University of the East Manila
Journal of Statistics Education Volume 16, Number 1 (2008), jse.amstat.org/v16n1/ragasa.html
Copyright © 2008 by Carmelita Y. Ragasa all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the author and advance notification of the editor.
Key Words: Descriptive statistics; Multimedia; Learning.
The study of statistics can be tedious especially because of a lot of formulas to work with and computations that are long and difficult to use. Computerassisted instruction (CAI) could be of great help because of the drillandpractice, tutorial, or simulation activities offered either by themselves or as supplements to traditional teacher directed instruction. (Cotton, 2001). Cotton found in her study that computer software provides many instructional benefits and CAI can have a much greater impact on student learning.
In a classroom utilizing CAI, students often work independently or in pairs at computers around the room. Software effectively guides students through a series of interrelated activities and instruction, addressing a variety of learning styles.
Working in pairs could also facilitate learning. Davidson and Kroll (1991) found in their study that students in cooperative environments developed more positive attitudes towards mathematics than students in traditional environments. Johnson and Johnson (1985, 1986a, 1986b) advocate cooperative learning not only for the positive effect it has on student performance but also for the positive effect it has on motivation, classroom socialization, the student’s confidence in learning, and attitude toward the subject being learned.
Mathematical aptitude has a lot to do with successful performance in an introductory statistics course and together with aptitude is a positive attitude toward mathematics. A successful student must gain quantitative and graphical insights along with mathematical and analytical abilities (Härdle, Klinke, and Marron 1999).
Research in mathematics education has shown that the computer facilitated the learning of concepts and computations of statistical formulas (McCoy, 1996). Students of mathematics courses were more motivated, selfconfident, joyful and the subject became more meaningful with CAI (Rochowicz, 1996, Funkhouser, 1993).
The use of a CDROM tutorial is ideal to support traditional classrooms. The pedagogy of a teacher’s text extends into a highly visual, handson learning environment that is available any time. CDROM methods for teaching oral medication administration, Jeffries (2001) generate higher satisfaction and greater cognitive gains for the multimedia group.
In a study by Christopher L. Aberson et al. (2002) of Humboldt State University, he found out that students (n = 84) enrolled in introductory and intermediate statistics courses overwhelmingly rated the tutorial as clear, useful, and easy to use. Students who used the tutorial outperformed those who did not on a final examination.
Michael Szabo’s (2001) study showed that much research has been focused on the effectiveness of CAI, which is demonstrated through improved test scores (Williams & Brown, 1990). Effectiveness has also been measured through "heightened affective responses, or better attitudes, reduced learning time, higher course completion rates, an increased retention duration, and finally cost" (Williams & Brown, 1990, p. 214). Generally the effectiveness of CAI has been determined by comparing CAI with traditional classroom instruction (Clark, 1985).
Nickerson (1995) points out that while technology does not promote understanding in and of itself, it is a tool that can help students view learning as a constructive process and use simulations to draw students' attention. It provides a supportive environment that is rich in resources, aids exploration, creates an atmosphere in which ideas can be expressed freely, and provides encouragement when students make an effort to understand (delMas, et al 1999).
AndersonCook, C.M. and DoraiRaj, Sundar (2003) found in their study on the use of applets in statistics courses that students in introductory statistics classes react very positively to the applets, both in terms of enjoying being able to experiment with them as well as being better able to discuss the concepts relating to statistical power.
Researchers have also found that CAI enhances learning rate i.e., students learned the same amount of material in less time than the traditionally instructed students or learned more material given the same amount of time. (Cotton, 2001). Moreover, students receiving CAI also retain their learning better (Cotton, 2001)
Most researchers concluded that the use of CAI leads to more positive student attitudes than the use of conventional instruction. This general finding has emerged from studies of the effects of CAI on student attitudes as cited by Cotton (2001).
In what follows the treatment group consists of those who received the CAI and worked in teams and the control group received the traditional method of teaching some selected topics of basic statistics. The detailed description of the treatment and control groups is found in Section 3.
This paper aims to find out if teaching basic statistics with the use of computer assisted instruction helps students achieve better in the subject and have a better attitude towards mathematics. The objectives of the study are:
The CDROM prepared by Math Advantage (1997) served as the teaching medium for the experimental group. It is a selfpaced and individualized solution with easy stepbystep inter active tutorial courseware for students from high school to college levels.
Two students shared one computer. They discussed the text they read in the monitor. Solutions to the problems were clarified between the two of them. This is to say that the treatment involved collaborative work between two students. This combination of collaborative work and the CAI is what distinguishes the treatment group. When the two collaborating students did not understand the text of the CDROM or the solution to a given problem, they called the teacher for clarification. Aside from these group consultations there were three lecture hours out of the 12 hours of the whole experiment.
The first chapter of the CDROM consisted of descriptive and inferential statistics, population and sample, and random sample. The second chapter was on statistical representations of data: grouped data, frequency distributions: class limits, relative frequency distribution, percentage frequency distribution, cumulative frequency distribution, relative cumulative frequency distribution, percentage cumulative frequency distribution, graphs, bar chart, histogram, pie graph, ogive, frequency polygon, percentiles, deciles, and quartiles. In each of the subtopics there were 2 or 3 sample questions, which Math Advantage calls Practice. At the end of the chapter was an examination. Two students worked on the same quiz.
The traditional method consisted of lectures given by the teacher, recitation, and class activities involving the topics discussed during the class. The topics were the same as those given to the experimental group. A local textbook entitled "Basis Statistics" written by professors of the University of the East; Raymond Ang, Wilma Dechavez, Lotta Billones, and Ailene Diansuy was used by the students. Each one had a copy of this book. At the end of each lesson there were activities and practice problems that the students worked on. Some of these problems were done in class and the others were given as homework to be submitted the following day. The students were allowed to use hand held calculators.
The samples for this study were the 53 sophomore students of the University of the East who were enrolled in Basic Statistics in the first semester 20032004. 38 were in the experimental group and 15 in the control group. There were actually 20 students in the control group but only 15 took the pretest and the posttest. There were equal number of male and female in the experimental group while 60% were female in the control group and the other 40% were male. The students were grouped by the registrar’s office, the experimental group being a blocked section of information technology students while the control group was a free section consisting of a mixture of students from different courses. Because students were not randomly assigned to class, covariates were measured for subjects in order to allow adjustments for systematic factors that might also affect performance.
The 20minute achievement pretest was given on July 1, 2003. The test was to assure that both groups had the same knowledge, if any of basic statistics. Then the treatments were given for the two groups, the control group was taught using the traditional method of teaching and the experimental group the computerassisted instruction. After the treatment the 20minute achievement posttest was given on July 22. An attitude inventory was also administered as a pretest and a posttest.
The achievement pretest and the achievement posttest were one and the same test. The achievement test was a teacher made test. It was composed of 20 multiple choice test. The reliability index was computed by the researcher using the Kuder Richardson 20 (KR20) formula and the reliability index is 0.55. For hard tests the reliability index of 0.49 and above is reliable.
The mathematics attitude inventory was the questionnaire that Dr. Milagros Ibe validated and tested for reliability using the DOST Scholars as subjects. This same questionnaire was used in the thesis, "Some Factors Affecting the Ability to Solve Word Problems in Second Year High School Algebra" (Ragasa, 1987).
This study used SPSS 11.5 (Statistical Package for Social Sciences version 11.5) to compute for the multiple analysis of covariance (MANCOVA). Specifically the oneway MANCOVA was used because it involves 2 continuous dependent variables, ACHPOST (achievement posttest) and ATTPOST (attitude posttest), 1 categorical independent variable with 2 levels i.e., GROUP = 1(treatment group) and GROUP = 2 (control group) and 6 continuous covariates, ACHPRE (Achievement pretest), ATTPRE (attitude pretest), CETTOT (overall college entrance test), CETMATH (college entrance mathematics test only), HSGWA (high school general weighted average), HSMATH (grade in high school mathematics). The covariates were gathered to allow adjustment for prior differences among groups because random assignment was not possible. Means were adjusted for the influence of the covariate.
Table 1
BetweenSubjects Factors

N 

GROUPS 
1 
38 

2 
15 
Table 1 shows that there were 38 students in the experimental group (labeled Group 1) who were taught Basic Statistics using CAI and 15 students in the control group (labeled Group 2) who were taught basic statistics using the traditional method of teaching.
Table 2 Descriptive Statistics

GROUPS 
Mean 
Std. Deviation 
N 
ACHPOST 
1 
12.1053 
2.88322 
38 
2 
9.8667 
2.19957 
15 

Total 
11.4717 
2.87298 
53 

ATTPOST 
1 
90.5000 
16.29583 
38 
2 
94.4667 
17.80396 
15 

Total 
91.6226 
16.65975 
53 
Table 2 shows that the mean score of the posttest of the achievement test for the group taught using CAI was 12.1053 with standard deviation 2.88322 while the group taught with traditional method has a mean of 9.8667 with standard deviation of 2.19957. On the other hand the attitude posttest of the treatment group is 90.5000 while that of the control group is 94.4667, a difference of 3.9667.
The Multivariate Analysis of Covariance or MANCOVA (Table 3) was performed to determine if there are significant differences between the treatment and control groups, after adjusting for several covariates, with respect to their effect on both achievement posttest (ACHPOST) and attitude posttest (ATTPOST). If there is a significant difference, this means that there exists some linear combination of ACHPOST and ATTPOST for which the groups differ, after adjusting for covariates. Given that there is a significant difference, separate ANCOVAs (Table 5) are then run to determine which of the dependent variables (possibly both) differ across the two groups. The result (Table 5) shows that the groups differ with respect to ACHPOST but not ATTPOST.
MANCOVA assumes that the distribution of the errors is bivariate normal with mean 0 and the same covariance matrix for both the treatment and the control groups. Levene’s test in Table 4 is used to verify this assumption.
The multivariate tests section in Table 3 simultaneously tests each factor effect on the dependent groups. Hotelling's Trace for multivariate significance tests is commonly used for two dependent variables. In this study ACHPRE p(.026)<.05, ATTPRE p(.000)<.05, and GROUPS p(.006)<.05 have a significant effect on the dependent variables ACHPOST and ATTPOST.
Table 3 Multivariate Tests using Hotelling’s
Trace
Effect 
Value 
F 
Hypothesis df 
Error df 
Sig. 
Partial Eta Squared 
Noncent. Parameter 
Intercept 
.039 
.849(b) 
2.00 
44.00 
.435 
.037 
1.698 
ACHPRE 
.181 
3.975(b) 
2.00 
44.00 
.026 
.153 
7.950 
ATTPRE 
1.294 
28.459(b) 
2.00 
44.00 
.000 
.564 
56.919 
HSMATH 
.126 
2.768(b) 
2.00 
44.00 
.074 
.112 
5.536 
CETTOTAL 
.117 
2.564(b) 
2.00 
44.00 
.088 
.104 
5.129 
HSGWA 
.135 
2.977(b) 
2.00 
44.00 
.061 
.119 
5.954 
CETMATH 
.012 
.269(b) 
2.00 
44.00 
.765 
.012 
.539 
GROUPS 
.263 
5.797(b) 
2.00 
44.00 
.006 
.209 
11.593 
a Computed using alpha = .05
b Exact statistic
c Design: Intercept+ACHPRE+ATTPRE+HSMATH+CETTOTAL+HSGWA+CETMATH+GROUPS
Table 4, the Levene's test tests the assumption that each dependent variable has similar variances for the two groups. It is generally considered that if the Levene statistic is significant at the .05 level or better, then the null hypothesis that the groups have equal variances is rejected. In practice, people often consider pvalues below 0.01 as evidence of a serious assumption with the equal variance assumption. For this data the homogeneity of variances assumption between the two groups is met for ACHPOST, p(.583) > .05. However, for the ATTPOST, p(.015) < .05 but p is greater than 0.01. Hence the homogeneity of variances assumption is considered met.
Table 4 Levene's Test of Equality of Error
Variances(a)

F 
df1 
df2 
Sig. 
ACHPOST 
.306 
1 
51 
.583 
ATTPOST 
6.380 
1 
51 
.015 
Tests the null hypothesis that
the error variance of the dependent variable is equal across groups.
a Design: Intercept+ACHPRE+ATTPRE+HSMATH+CETTOTAL+HSGWA+CETMATH+GROUPS
The F test appears in the separate ANCOVAs computed on each of the dependent variables of Table 5. The F test tests the null hypothesis that there is no difference in the means of each dependent variable for the different groups formed by categories of the independent variables. This section gives the MANCOVA effects for each covariate. The univariate effects for ACHPOST that are significant are ACHPRE (p=.014)<.05, CETTOT (p=.033)<.05, GROUPS (p=.002)<.05 and the univariate effects that are significant for ATTPOST are ATTPRE (p=.000)<.05 and HSGWA (p=.043)<.05.
Table 5 Separate ANCOVAs on each of the Dependent Variables
Source 
Dependent Variable 
Type III Sum of Squares 
df 
Mean Square 
F 
Sig. 
Partial Eta Squared 
Noncent. Parameter 
Observed Power(a) 
Corrected Model 
ACHPOST 
150.571(b) 
7 
21.510 
3.474 
.005 
.351 
24.317 
.939 

ATTPOST 
9176.698(c) 
7 
1310.957 
11.224 
.000 
.636 
78.571 
1.000 
Intercept 
ACHPOST 
1.351 
1 
1.351 
.218 
.643 
.005 
.218 
.074 

ATTPOST 
191.180 
1 
191.180 
1.637 
.207 
.035 
1.637 
.240 
ACHPRE 
ACHPOST 
40.518 
1 
40.518 
6.544 
.014 
.127 
6.544 
.707 

ATTPOST 
283.237 
1 
283.237 
2.425 
.126 
.051 
2.425 
.332 
ATTPRE 
ACHPOST 
2.027 
1 
2.027 
.327 
.570 
.007 
.327 
.087 

ATTPOST 
6542.976 
1 
6542.976 
56.021 
.000 
.555 
56.021 
1.000 
HSMATH 
ACHPOST 
18.104 
1 
18.104 
2.924 
.094 
.061 
2.924 
.387 

ATTPOST 
241.408 
1 
241.408 
2.067 
.157 
.044 
2.067 
.291 
CETTOTAL 
ACHPOST 
29.935 
1 
29.935 
4.834 
.033 
.097 
4.834 
.576 

ATTPOST 
94.631 
1 
94.631 
.810 
.373 
.018 
.810 
.143 
HSGWA 
ACHPOST 
6.903 
1 
6.903 
1.115 
.297 
.024 
1.115 
.178 

ATTPOST 
509.005 
1 
509.005 
4.358 
.043 
.088 
4.358 
.533 
CETMATH 
ACHPOST 
2.965 
1 
2.965 
.479 
.492 
.011 
.479 
.104 

ATTPOST 
3.923 
1 
3.923 
.034 
.855 
.001 
.034 
.054 
GROUPS 
ACHPOST 
68.999 
1 
68.999 
11.143 
.002 
.198 
11.143 
.904 

ATTPOST 
22.431 
1 
22.431 
.192 
.663 
.004 
.192 
.071 
Error 
ACHPOST 
278.636 
45 
6.192 






ATTPOST 
5255.755 
45 
116.795 





Total 
ACHPOST 
7404.000 
53 







ATTPOST 
459352.000 
53 






Corrected Total 
ACHPOST 
429.208 
52 







ATTPOST 
14432.453 
52 






a Computed using alpha = .05
b R Squared = .351 (Adjusted R Squared = .250)
c R Squared = .636 (Adjusted R Squared = .579)
The results of the study show that the combination of computerassisted instruction and collaborative work improves learning without a significant effect on attitude. Due to some limitations of the study the results cannot be generalized. For one, the subjects of the study consisted of 35 mostly Information Technology majors in the treatment group who might be expected to respond favorably to CAI while the control group consisted of 15 students though a few in the computer science course the majority is a mixture of students from social sciences. Another limitation is the fact that it was conducted in one and a half months of one semester in one institution.
Nevertheless the following results could encourage other researchers to repeat the study taking care that the limitations mentioned above are eliminated. The univariate effects for achievement posttest that are significant are achievement pretest, the total score of the college entrance test, and the group effect. The univariate effects that are significant for attitude posttest are the attitude pretest and the high school general weighted average.
The Hotelling’s Trace for the multivariate test shows that achievement pretest, attitude pretest, and the two groups have significant effect on the dependent variables achievement posttest and attitude posttest. The Levene’s test shows that the homogeneity of variances assumption between the two groups is met for achievement posttest but not for attitude posttest.
It is interesting to note that in this study the mean score of the posttest of the achievement test of the treatment group is significantly higher than that of the control group. On the other hand there is no significant difference in the mean score of the attitude posttest of the treatment group and the control group.
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Unpublished Manuscript
Ragasa, C. Y. (1987). "Some factors Affecting the Ability to Solve word problems in Second Year High School Algebra". (A thesis requirement for Master of Arts in Teaching Mathematics, University of the Philippines, Diliman)
Carmelita Y. Ragasa
Department of Mathematics and Statistics
University of East Manila
2219 Claro M. Recto Avenue
Manila
cyragasa@yahoo.com
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