1. E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 2, 2010161THE EFFECTS OF PEER TEACHING IN THE PERFORMANCEOF STUDENTS IN MATHEMATICSDr. Editha T. VasayDirector, Institute of Computer ScienceAgoo, La Union, PhilippinesIntroductionThe teaching of Mathematics is enjoyable. This is true when the performance of the students issatisfactory or better. Otherwise, it is frustrating.Inspite of the researcher’s long years of teaching experience, exposure to trainings andseminars, giving pieces of advice and motivations to students, using simple language anddifferent techniques and strategies, still many students have poor performance.Based from quizzes and examinations, it is observed that students have poor performancewhich may be due to weak foundation. Students have no mastery on the operations of wholenumbers , integers, decimals, and fractions. Techniques were conceived to improve thesituation and peer teaching was used.Peer teaching is a technique in helping students perform better in understanding the differentconcepts, developing computational skills and their moral, social and emotional values mostespecially their ability to express their ideas.Statement of the ProblemThis research activity is composed of two parts: Phase I and Phase II.Specifically, it aimed to find out the effects of peer teaching inPhase I
2. Improving the foundation of students in the operations of while numbers, integers, decimals,and fractions.Phase IIThe performance of the students in College Algebra.Research HypothesesThis study tested the following hypotheses:Phase I (Fundamental Operations of Whole Numbers, Integers, decimals, and Fractions)1. There is no significant difference between the pre-test and post-test mean scores ofthe experimental group.2. There is no significant difference between the pre-test and post-test mean scores ofthe control group.3. There is no significant difference between the pre-test mean scores of theexperimental and control groups.4. There is no significant difference between the post-test mean scores of theexperimental and control groups.5. There is no significant difference between the mean gain of the experimental andcontrol groups.Phase II (College Algebra)1. There is no significant difference between the pre-test and post-test mean scores ofthe experimental group. E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 2, 20101622. There is no significant difference between the pre-test and post-test mean scores ofthe control group.3. There is no significant difference between the pre-test mean scores of the
3. experimental and control groups.4. There is no significant difference between the post-test mean scores of theexperimental and control groups.5. There is no significant difference between the mean gain of the experimental andcontrol groups.Scope and Delimitations of the Study:This study was conducted during the first semester of the school year 1994-1995.Two classes of college freshmen students of the Don Mariano Marcos Memorial StateUniversity, institute of Science, Agoo, La Union, were involved in the study. The B.S.Biology I was used as the experimental group and the control group was the B.S. Math I. Theexperimental group was composed of 41 students while the control group was composed of 40students.Instruments Used:Phase ITwo sets of similar 45-item tests on the fundamental operations of whole numbers, integers,decimals, and fractions was the main instrument used. The first set was administered todetermine the foundation of every student on the fundamental operations of the different kindsof numbers. The second set was administered to determine the effects of per teaching on theirfoundations of the operations. The second set was administered after two weeks of peerteaching.Phase IITwo sets of 50-item achievement test of the multiple choice type was the main instrumentused. The first set was administered during the midterm and the second was administered
4. during the finals. This served to determine the performance of the two groups of studentstaught with and without peer teaching.Questionnaire was also prepared and answered by the students in order to know where theyfinished their elementary and secondary education, their favourite and least-liked subjects.Observation and interview were also used to gather data. There were used to find out thebackground of the students and to determine the effects of peer teaching on the moral values ofthe students.Research Design:This study made used of the Pre-test-Post-test Control-experimental group design using twogroups of freshmen college students. One group was taught with peer teaching while the othergroup was taught without peer teaching. E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 2, 2010163Treatment of Data:Frequency counts and percentages were used to describe students’ variables based on theresults of the pre-test.The t-test for correlated means was utilized to determine the significant differences in the pretest ofeach group and also the significant differences in the post-test mean scores of eachgroup.The t-test for uncorrelated means was used to determine the significance of the variation of theperformance of the two groups of students, both in Phase I and Phase II.Review of Related Studies:A review of related studies was done to construct, refine, and evaluate the present study.Celino (1987) conducted a study on the comparative effectiveness of instructional tools in theachievement of high school students in Algebra. Same as the present study, he also used the
5. pre-test - post-test control-experimental group research design. It was found out that the mosteffective combination of instructional tools in improving achievement of students is review,test, and assignment followed by test and assignment and review and test in that order. Theleast effective combination of instructional tools in enhancing achievement is review andassignment, and test.Mangubat (1980), in his research work, made sample modules on ratio, proportion and percent.The study made mention that one teaching strategy that could possibly help solve our problemregarding low performance of student is modular instruction. It is one of the many strategiesaimed at individualized instruction. It also uses philosophy of programmed instruction and themastery learning strategy.Hermosura (1990) compared the performance of students taught with and without workbook inMath 1. She found out that students taught with and without the workbook performed equally.There was no significant difference between the performance in an achievement test in Math 1of the students taught with and without the workbook with respect to their sex.De Leon (1973) worked on the effect of grouping on achievement, classroom participation andinteraction of students in Modern Geometry. Subjects of his study were two groups of highschool juniors with a total of 82 high school students. The findings revealed that there was asignificant difference in the achievement of the students in the specific ability group from thatof the general ability group. The specific ability group referred to the group of students of nearhomogeneous abilities based on their achievement in a particular branch of subject area. Onthe other hand, the general ability group was based on their general average computed from thefinal ratings in all academic subjects in the curriculum. While De Leon made used of groupingon achievement, classroom participation and interaction, the researcher of the present studymade used of peer teaching.Emphasizing the importance of grouping, Hyman (1973) clearly expressed the following:
6. With the isolation of students in the individualization program comes the loss of camaraderie.This loss is significant beyond measure. The very essence of democracy is the feeling of E-InternationalScientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 2, 2010164responsibility to all fellows. This feeling evolves from participating together on commonactivities.The individualizing of program and the loss of interaction also leads to the minimizing of peerteaching. Much of what each of us learns is learned from peers. When student works in groupson common projects, each pupil learns from his classmates in a significant way.Flores (1990) conducted a study on the mathematical readiness of first year high schoolentrants during the SY 1989-1990. The study revealed that the first year entrants performed“low” in Elementary Mathematics. Out of the 335 respondents, one hundred fifty-fourperformed “high” and one hundred eighty-one performed “low”. In other words, less than onehalf ofthem were ready for first year mathematics. Flores was able to determine that highschool entrants were not ready while the present investigator determined that many collegefreshmen are not also ready for their college mathematics.Procedure:Phase 1Phase 1 aimed to find out the effect of peer teaching in improving the foundation of studentson the operations of whole numbers, integers, decimals and fractions.The first year B.S.Math was used as the control group. It is composed of forty students. TheB.S. Biology 1 was used as the experimental group. It is composed of forty-one students.Both groups are heterogeneous in nature.The experimental group was divided into six groups. The top six students were chosen as littleprofessors. They were numbered 1-6. The remaining students were also numbered 1-6. All
7. number 1’s were the students of little professor’s no. 1. All number 2’s were the students oflittle professor no. 2, and so on.Two sets of 45-item test on the four operations of whole numbers, integers, decimals andfractions were prepared and administered before and after peer teaching. Scores on the pre-testwere announced to the students for them to know their performance in the foundations ofmathematical operations. Both groups were advised, motivated and encouraged to improvetheir skills on the operations because a similar test shall be given to them after two weeks.The advantages and disadvantages of doing and not doing the peer teaching were explained tothe students in the experimental group. Schedule of peer teaching was arranged in such a waythat there will be no disruption of the regular schedule and professor’s meeting. The peerteaching handled by the little professors was scheduled during Fridays. A day after thestudents underwent peer teaching, they approached the researcher and asked if they could dothe peer teaching everyday during their vacant time. The researcher approved it providedclassrooms are vacant.During the peer teaching, the researcher observed the activities done by each group. The littleprofessors were asked to interview their respective students why they are weak on theoperations or computational skills in mathematics. They were asked to report to the researcherthe results of their peer teaching and their interviews.A questionnaire was also prepared and answered by the students in order to know their favoriteand least-liked subjects and the schools where they finished their elementary and secondaryeducation.After two weeks the post-test was administered to both experimental and control groups.Frequency counts and percentages were used to describe students’ variables based on theresults of the pre-test. E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 2, 2010
8. 165After the second set was administered it was found out that peer teaching was very effective inimproving the foundation of every student as evidently shown by the results (see results ofPhase 1) that the two groups were already comparable since the t-value obtained showed nosignificant difference between their performance.Phase IIA 50-item achievement test of the multiple choice type was administered during the midtermexamination to the B. S. Math I and B. S. Biology I. The result showed that the B. S. Biologystudents were very far behind the B. S. Math students. Most of them got very low with a meanscore of 36.66 while the mean score of the B.S. Math was 47.32. Out of the 41 B.S. Biologystudents 11 or 27 % got scores of 10 and below. Eighteen or 44% got scores between 10 to 20.The lowest score obtained by the B.S. Math students was 20.Based on the results of the achievement test, phase I was conducted and after it was found outthat the two groups were comparable, peer teaching was done in their lessons in CollegeAlgebra.The same grouping was utilized but the researcher instructed the little professors to submitnames of their students in their respective groups who could do the job of the little professoralready. The original little professors became the supervisors/ evaluators during the peerteaching of the chosen little professors by the original little professors. This activity went onuntil the last member of every group was able to cope up with the classroomdiscussion/activities.A similar 50-item achievement test was administered during the final examination. That wasafter two months of peer teaching.Results and Analysis:
9. The results in Phase I was analyzed and interpreted as follows:Table 1Students with Weak Foundation on the operations of Whole NumbersOperations F %AdditionSubtractionMultiplicationDivision71513469191656Table 1 shows that 7 or 9% out of 81 students are weak in addition of whole numbers.Fifteen or 19% are weak in subtraction. Thirteen or 16% are weak in multiplication and 46 or56% are weak in division. E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 2, 2010166Table 2Students With Weak Foundation on the Operations of IntegersOperations F %Addition
10. SubtractionMultiplicationDivision1436171417442117Table 2 evidently shows that subtraction is the most difficult among the operations ofintegers. Thirty-six or 44% are weak in subtraction while 14 or 17% are weak in addition anddivision. Seventeen or 21% are low in multiplication.Table 3Students With Weak Foundation on the Operations of DecimalsOperations F %AdditionSubtractionMultiplicationDivision5291829
11. 6362236Table 3 shows that only 5 or 6% out f the 81 students are weak in addition of decimals but 29or 36% are weak in subtraction and division while 18 or 22% are weak in multiplication.Table 4Students With Weak Foundation on the Operations of FractionsOperations F %AdditionSubtractionMultiplicationDivision1524271519303319Table 4 presents how weak are the students on the operations of fractions. Fifteen or 19% outof the 81 students are weak in addition and division while 24 or 30% are weak in subtraction.Twenty-seven or 33% are poor in multiplication.Based on the results of the pre-test and the questionnaire it was found out that the top 25% of
12. both the experimental and control groups graduated from central schools, national high schoolsand private schools particularly Montessori school. The bottom 25% came from the barangayschools and lower sections of national high schools from the different towns of La Union andPangasinan. E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 2, 2010167Students were very much interest in the peer teaching especially those little professors assignedto teach. But after one day, most of the students taught by the little professors became moreinterested. They asked for tutoring even at noontime and during their vacant periods.Through observation, students were very noisy conversing and doing unnecessary activitiesbefore peer teaching was started but when they were doing the peer teaching, noises werelessened. Through peer teaching, therefore, students learned to develop so many values suchas time management, sense of responsibility, sharing, self-discipline, self-reliance, ability toexpress their ideas, and others.The fast learners became more developed especially in expressing their own ideas. They hadmastered the lessons. The slow learners improved their classroom participation and were ableto cope up with the different classroom activities.Through interviews done by the little professors, it was known that many students were weakin their foundation because their teachers, when they were in the elementary, oftentimesattended to faculty meetings. They just assigned their students to clean the classroom andgrounds. Some students said they were handles by teachers who are not so good inmathematics. Students also said they even had teachers who were sleeping during class hoursassigning their students some other activities.Many of the students, through their conversations with their little professors, admitted that theywere learning to, love mathematics. These students hated math all their lives from elementary
13. to high school. They considered Math as the most difficult subject and that’s why theyconsidered it as their least-liked subject.Table 5Results of the Pre-test and Post-test on the Fundamental OperationsExperimentalGroupMeanControlGroupMeanMeanDifferenceT-ratioPretest Mean 24.33 29.82 5.49 2.52 *Posttest Mean 32.28 32.53 0.25 0.995Mean Gain 7.95 2.71 5.24 4.33 *T-ratio 8.76 * 3.37 **significant at .01 levelBased on the data above, it is inferred that both groups registered marked increase in the posttestmeans (t-ratio for experimental groups is 8.76 while the t-ration for the control group is3.37, both significant at the .01 level). The t-test applied in each group was that of thecorrelated means.It is also noted that the difference in the mean gain between the two groups (5.24) alsoregistered a significant t-ration (4.33 at .01 level) with the use of the independent t-test. This E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 2, 2010
14. 168indicates that the experimental group had a significantly greater gain in their performance withthe use of peer teaching while the control group did a very slight improvement.There is significant difference between the pre-test and post-test mean scores of theexperimental group.There is significant difference between the pre-test and post-test mean scores of the controlgroup.There is significant difference between the pre-test mean scores of the experimental andcontrol groups.There is significant difference between the post-test mean scores of the experimental andcontrol groups.There is significant difference between the mean gain of the experimental and control groups.Table 6Results of the Pre-test and Post-test College AlgebraExperimentalGroupMeanControlGroupMeanMeanDifferenceT-ratioPretest Mean 36.66 47.32 10.66 2.50 *Posttest Mean 48.27 48.98 0.71 0.84
15. Mean Gain 11.61 1.66 9.95 4.40*T-ratio 5.26 * 1.18*significant at .01 levelTable 6 evidently shows that the experimental group registered a great increase in the post-testmean (t-ratio is 5.26, significant at .01 level) while the control group did not. The t-testapplied in each group was that of the correlated means.The difference in the mean gain between the two groups (9.95) also registered a significant tratio (4.40at .01 level) using the independent t-test. This means that the experimental grouphad a significantly greater gain in their performance with the use of peer teaching while thecontrol group did not.There is significant difference between the pre-test and post-test mean scores of theexperimental group.There is no significant difference between the pre-test and post-test mean scores of the controlgroup. E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 2, 2010169There is significant difference between the pre-test mean scores of the experimental andcontrol groups.There is no significant difference between the post-test mean scores of the experimental andcontrol groups.There is a significant difference between the mean gain of the experimental and control groups.Implications:1. The Studentsa. Fast LearnersPeer teaching helps the fast learners to have mastery on the different concepts.Through this technique they develop their ability to express their ideas. They also
16. develop values such as sharing, sense of responsibility, self-confidence, self-discipline,time management, etc.b. Slow LearnersThe slow learners can improve their performance through the help of other students likethose chosen as little professors. They gain better understanding of the lessonsdiscussed. They also develop values similar to the bright students.2. The TeachersThe use of the technique, peer teaching, helps the teachers in the teaching-learningprocess. But the teachers should see to it that motivating and inspiring their studentsmust not be taken for granted, otherwise the technique will be a failure. They must seeto it that the students will be enlightened on the advantages of doing it. They must bealert in checking the activities through the little professors. Every problem that arisesin the peer teaching must be solved immediately.3. The AdministratorsAdministrators must be very careful in giving teaching loafs to teachers. They shouldnot assign teachers who were not trained to teach mathematics handle classes inmathematics especially when students are still developing their foundation otherwisethe whole educational system will be affected. They must be alert in supervisingwhether their teachers are teaching or sleeping. They should schedule faculty meetingsin such a way that classes are not disrupted. They must schedule remedial teaching forthe slow learners.Summary of Findings and Conclusion:1. It was found out that the top 25% of students graduated from central schools, nationalhigh schools and Montessori school while the bottom 25% came from the barangayschools and from the lower sections of national high schools from the different towns
17. of La Union and Pangasinan.2. Peer teaching greatly affected the intellectual and moral values of the students such asthe ability to express their ideas, mastery of the different concepts, time management, E-InternationalScientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 2, 2010170sense of responsibility, sharing, self-discipline, self-reliance. Self-confidence,resourcefulness, cooperation, obedience, etc.3. Majority of the B.S. Biology students were found out to be very weak in theirfoundation on the fundamental operations of whole numbers, integers, decimals andfractions.4. There was a significant difference between the pre-test and post test mean scores of theexperimental group on the fundamental operations of the different kinds of numbers.5. There was a significant difference between the pre-test and post-test mean scores of thecontrol group on the fundamental operations of numbers.6. There was a significant difference between the pre-test mean scores of the experimentaland control groups on the fundamental operations of numbers.7. There was no significant difference between the post-test mean scores of theexperimental and control; groups on the fundamental operations of numbers. Meaningtwo groups were already comparable after peer teaching had improved the performanceof the experimental group.8. There was a significant difference in the mean gain between the experimental andcontrol groups in their performance on the fundamental operations of numbers whichmeans that the experimental group had a significantly greater gain with the use of peerteaching while the control group did a very slight improvement.9. There was a significant difference between the pre-test and post-test mean scores of the
18. experimental group in (their performance in ) College Algebra.10. There was no significant difference between the pre-test and post-test mean scores ofthe control group in College Algebra.11. There was a significant difference between the pre-test mean scores of the experimentaland control groups in College Algebra.12. There was no significant difference between the post-test mean scores of theexperimental and control groups in College Algebra.13. There was a significant difference in the mean gain between the experimental andcontrol groups which means that the experimental group had a significantly greatergain in their performance in College Algebra with the use of peer teaching while thecontrol group did not.Recommendations:In view of the findings and conclusive statement, the following recommendations aregiven: E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 2, 20101711. Teachers in the elementary and secondary schools must help their students developtheir computational skills, master the four fundamental operations of the differentkinds of numbers and apply these knowledge in simple problem solving.2. Teachers can make use of peer teaching to help their students in improving theirperformance in the acquisition of knowledge and in developing their moral values.3. Administrators should assign math majors to teach math in the elementary andsecondary schools or those with trainings in the area.4. It is also recommended that peer teaching be used in all academic subjects to helpstudents in their studies.
19. References:Celino, Manuel C. (1987). “ The Comparative Effectiveness of Instructional tools in theAchievement of High School Students in Algebra.” DMMMSU-CAS, Agoo, La Union.De Leon, Lorenzo. (1973). “ The Effects of Grouping on Achievement, ClassroomParticipation and Interaction of students in Modern Geometry at the Manuel Luis QuezonUniversity.” U.P.Diliman, Quezon City.Flores, Herminia K. (1990). “ The Mathematics Readiness of First Year High School EntrantsDuring the School 1989-1990.” DMMMSU-CAs, Agoo, La Union.Hermosura, salvacion B. (1990). ; The Use of Mathematics I Workbook: A ComparativeStudy.” .” DMMMSU-CAs, Agoo, La Union.Hyman, Ronald. (1973). “Individualization: The Hidden Agenda.” The Education Digest.XXXIX,2.Mangubat, Emmanuel . (1980). “ How to Write Master-Based Teaching Modules.” ThePhilippine Journal of Education. 57, No. 7Ang website:http://www.slideshare.net/jennilynbalbalosa/final-na-final-thesis
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