Volume 17 Number 2
January 1978

George W. Cardell, William C. Cross and W. James Lutz

SCHOOL guidance programs traditionally consist of informational and administrative guidance activities. In addition, guidance personnel counsel in one-to-one or group counseling situations. Both of these guidance activities are an integral part of any school guidance program. However, they cannot continue to be the only thrust of the school counselor. In an age of increased accountability, counseling personnel must exert an even stronger influence throughout the learning process. More effective educative methodologies must be sought and found which will reinforce the particular learning processes that are significantly successful inside the classroom.

The purpose of the present study was to determine what effect peer learning among Indian children has with regard to: (a) learning of mathematical skills, (b) development of student attitudes toward mathematics, and (c) satisfaction reactions or attitudes with the interactive process of peer learning itself.

In New Mexico, the State Department of Education has long recognized that Indian students in New Mexico continue to be educationally disadvantaged to an even greater degree than Spanish-American and Black children! The scores of the elementary children at the school on the Mescalero Apache Reservation were profiled for pre- and post-tests and plotted for comparison with the scores of the non-Indian students in the elementary school at Tularosa. The results clearly indicate a consistent difference in the performance in favor of the non-Indian students, grades one through six. These results indicated a need for developing learning processes especially for these disadvantaged Indian children.

A review of the literature related to studies utilizing partner learning, matched pairs, cross-age tutoring, or other paired learning techniques did not reveal any investigations directed to discovering learning processes particularly effective for Indian children. The only study similar to this one was conducted by Sloan (see Note 3). His purpose was to test the effectiveness of training aides to counselors, as change agents for fellow students in the area of personal adjustment needs. At any rate, in view of the close-knit tribal structure, peer learning seemed to offer a viable methodology, providing a fairly unique and not too difficult approach for participants to master. Moreover, the methodology of peer learning could very well be beneficial to teachers and students alike by effecting a positive change. Harris (see Note 1) pointed out that "the ultimate value of research, whatever its form, lies in the production of information that enables people to change."

Arithmetic was selected as the area of concentration since it was found to be the area most prominent in lowering the composite battery stores of Indian children. Other factors were taken into consideration which resulted in the selection of sixth grade mathematics as the specific level of investigation. One advantage to the selection of mathematics is that it deals more directly with concepts and applications which are not necessarily dependent upon the English language. Secondly, if the process of learning can be systematically reinforced through peer interaction of this level, the need for students to adjust to the junior high level will be implemented. The specific need for the Indian students is to compete more successfully with their non-Indian peers in the junior high school. If the personal confidence of these students in their own number skills can be enhanced and also if they have had experience with a workable alternative to augment conventional classroom instruction, hopefully they will be in a better position to realize greater achievement. Moreover, the methodology of peer learning could very well be beneficial to teachers and students alike by effecting a positive change in classroom management.

The design of the study called for a specific eight-week period as the best continuous segment of time. Site of the study was the Mescalero Elementary School, northeast of Tularosa, on the Mescalero Apache Reservation. Peer learning with experimental and control groups was selected as the area of investigation for the study. The sample consisted of two sixth-grade classes in mathematics. The time block set for mathematics was between 9 and 11 a.m. on Mondays, Wednesdays, and Fridays. Two instruments, a work sheet and an attitude self-report, were prepared and utilized.

The Sample. Of the two intact sixth-grade mathematics classes of the Mescalero Elementary School, one class was designed the control group with 18 subjects, and the other was designated the experimental group with 17 subjects. The two groups were equated with regard to ability in mathematics and the difference proved to be not significant. Similarly, the two groups were compared for attitudes toward the peer learning process at the outset and again the difference between the two groups was not significant. Hence, the validity of the sample was substantiated.

The Instruments. The two instruments utilized in the study are described as follows:

1. The students’ arithmetic work sheet was cooperatively prepared by the sixth-grade participating teachers based upon objectives mutually acceptable and relevant to the skills measured by the California Test of Basic Skills.

2. The Attitude Self-Report was prepared especially for this study and for these children. The tone and wording of this instrument were carefully selected to maximize frank and realistic responses, providing a low anxiety level of participation.

The procedural operation with respect to the cluster partner learning process is best described by means of the operational phases.

Phase 1. The basic introduction for any concept-type learning objective, for instance, "whole numbers and fractional numbers," is presented by the instructor to the entire class in much the same manner as in the conventional classroom. The time involved is probably no more than the first hour of a two-hour mathematics time block per day.

Phase 2. After a break period of 10 or 15 minutes, the students reassemble and form casual, unstructured groups, and move to prepared learning stations which are under the supervision of learning leaders. All learning stations are supplied with different mathematics games, devices, or other visual motor, tactile, or auditory tasks to further clarify or reinforce the first learning session. The peer learning leader explains the task and provides sufficient time and direction for each individual student to complete the assignment.

The groups of students rotate from one learning station to the next, so that each student is exposed to all the learning devices. It should be pointed out again that in this phase the groupings are not specified, but are casual so that spontaneous grouping is encouraged. The learning leader, for the most part, remains at one station. The classroom instructor and/or the experimenter circulates from station to station without interrupting the activity or without intervening in any way except to make some brief reinforcing comments to individuals or groups. Replies are given to questions when they occur, but for the most part, the learning is group directed and oriented, led by the students who serve as learning leaders.

Phase 3. This step in the program is the one in which the peer learning process is effected. The students are allowed to group themselves according to their own preferences. In almost every case, the lower-scoring students selected the higher-scoring students as leaders.

The size of the groups varied ultimately from two to four students, with the most common being three in each learning cluster.

Each learning leader checked the work of each student in the learning cluster as the work sheets were completed, pointing out any errors and explaining the correct methods and answers. Everyone in the group was free to make other comments or explanations to each other, but the learning leader discouraged any student from merely copying the solution. Moreover, each learning leader was responsible for the maintenance of work folders for each student in the cluster.

Phase 4. At the end of each unit of work, a "checkup" review was administered by each learning leader to his group and was graded by the learning leader. These graded "checkup" reviews or tests were spot checked by the instructor and progress of each student was discussed with the learning leader.

Statistical procedures used for analysis of the data from this experiment were twofold. First, for the cognitive mathematics test, the basic procedure employed was the critical ratio of t. In the affective domain, five affective items were treated as tests and scaled from one to four. Thus, results on a total of five "tests" in the affective domain were available for analysis. Each test was treated independently and the statistical procedure was identical to that described for the cognitive mathematics test.

The straightforward one-tailed comparison of significance was applied to the following hypotheses:

1. Peer learners will demonstrate significantly more gain in mathematical concepts and skills than students in a conventional class during the same period. Hypothesis I was supported by data in Table 1 which showed that the t ratio for these two groups was significant at the .05 level. Therefore, this hypothesis was accepted.

3. Peer learners will show greater growth of positive attitude toward mathematics than will students in a conventional classroom in the same period of time. Data for this hypothesis, as shown in Table 3, showed no statistically significant support, but again positive directionality was indicated. Therefore, this hypothesis was also rejected.

p > * .05

Since the study provided evidence that the partner learning process did significantly and positively affect performance in the cognitive domain of mathematical skills among Mescalero Indian students at the sixth-grade level, teachers who are primarily concerned with content or subject matter mastery of the discipline might be motivated to experiment with the process in their own classrooms, regardless of grade level. Since attitudes are generally more difficult to change, especially in a short period of eight weeks, future experimentation in this respect might well be extended to a full 18 weeks, or one complete semester.

Finally, this study exemplifies the kind of contribution which guidance personnel can make to enhance and improve the educative methodology within the classroom.

1. Harris, T. A. I’m OK-You’re OK. New York: Harper and Row, 1969, p. 210.

2. New Mexico State Department of Education. Analysis of Statewide Testing Program Results, 1971-1972, Grades 1, 5 and 8 and ACT Report, 1972. Santa Fe: Research and Development Division, 1972 (a).

3. Sloan, N. E. "Students in Helping Roles." Personal Services Review Series 3: Human Resources in the Guidance Programs. Washington, D.C.: Office of Education, Bureau of Research, 1970.