The study sought to find out the relative effectiveness of three classroom interaction strategies which are known to affect students' learning outcomes in Mathematics. 484 senior secondary school three (SSSIII) students randomly selected through judgmental and stratified random sampling from government-owned secondary schools in Ikere and Ado-Ekiti local government areas of Ekiti state participated in the study. The instrument was a self-constructed one, validated and used for collecting data and titled “Mathematics Achievement Test (MAT).” The experimental treatment lasted for four weeks, and the data collected were analyzed using one-way ANOVA, ANCOVA, two-way ANCOVA, and Tukey HSD post hoc pairwise comparisons analysis. The findings showed that the students' learning outcomes in Mathematics were better promoted by the cooperative and competitive strategies but rather minimally by both individualistic and conventional strategies.
The importance of Mathematics to human development attracted different comments, for instance, Cangiano [
Brown and Porter [
Considering the paramount importance such subject constitute to human life, the subject was made an essential choice of learners throughout their educational sojourn in Nigeria. In fact, it is an essential consideration for successful outing in certificate examinations like the Secondary School Certificate Examination (SSCE) conducted by the West African Examinations Council (WAEC) and the National Examination Council (NECO) as well as placement examinations like the Unified Tertiary Matriculations Examination (UTME) conducted by the Joint Admission and Matriculation Board (JAMB). Based upon reports from these examination bodies, performances of Nigerian learners in this subject have not been encouraging, making some curriculum and pedagogical pundits to beam their searchlights on teaching methods, curriculum contents, instructional materials, and other ancillary factors which they believe may influence the ability of the learners to want to learn more.
Different teaching techniques have been adopted by pedagogues in order to shore up students’ performance in Mathematics ranging from some teacher-centred techniques to other learner-centred methods. In this part of the world, the commonest type of teaching technique seems to be the teacher-centred whole-classroom teaching referred to in this study as conventional teaching strategy (CTS). This technique requires that the learners sit and listen to the teacher as he presents the content of the day’s lesson, with students asking few questions when necessary and supplying responses when asked to do so by the teacher.
Another popular approach used in teaching Mathematics is the cooperative learning strategy (CLS). Cooperative and collaborative learning are instructional contexts in which peers work together on a learning task, with the goal of all participants benefiting from the interaction. Cooperation and collaboration can be treated as synonymous, as a truly cooperative context is always collaborative [
In reciprocal peer tutoring (RPT), students work together to teach one another, and they alternate between the roles of student and teacher. This technique combines elements of both motivational and cognitive approaches to collaboration. The technique also promotes cognitive processing by using a structured approach to teaching and learning within a tutoring context. In contrast to scripted cooperation and reciprocal peer tutoring, guided peer questioning technique is explicitly intended to promote knowledge construction through higher-order thinking. It involves a process of question asking and answering, which is guided by the provision of question starters, students pick a few of the question starters, generate questions that fit the form of the starter, and then ask questions of their peers and answer their peers’ questions. Because these questions require complex answers, peers must probe their own understanding of material in order to answer.
Beachy [
Competitive learning exists when one student goal is achieved but all other students fail to reach that goal [
Individualistic learning exists when the learning or achievement of one student is independent and seperete from the achievements of the other students in the class [
Literature evidence concerning the relative effectiveness of and practical preferences of pundits among these teaching techniques have been varied and mixed. In a study carried out by Dowell [
In view of the varied and mixed findings about the relative effectiveness of the three classroom interaction approaches, this study would examine the classroom interaction strategies with a view to finding their relative efficiency and effectiveness at improving learners’ performance in Mathematics. As a result, the study looked at two research objectives. It sought to determine which of the interaction strategies will improve students’ performance in Mathematics. Specifically, this research investigated the following research hypotheses.
There is no significant difference in the posttest scores of students exposed to cooperative, competitive, and individualistic interaction strategies.
There is no significant difference in the mean score of students exposed to each of the experimental classroom interaction approaches and those exposed to the conventional approach.
There is no significant difference between the scores of male and female students exposed to each of the experimental classroom interaction strategies.
The research design used for the study is pretest-posttest experimental design with a control group. It involves the manipulation of independent variables to establish a cause-effect relationship of the independent variable (teaching strategies) on the dependent variables (Students’ academic performance in Mathematics). The sample consisted of 484 SSSIII students drawn through stratified random sampling technique from 4 secondary schools that have up to three classes of SSSIII offering Mathematics. In each of the four schools, the four interaction strategies (cooperative interaction strategy (CPIS), competitive interaction strategy (CMIS), individualistic interaction strategy (ILIS), and conventional interaction strategy (CNIS) were randomly assigned to the four intact SSSIII classes. CPIS, CMIS, and ILIS were the experimental groups while the CNIS served as the control group. The regular Mathematics teachers of these schools were the experimenters. They were trained on how to utilize the strategies using lesson plans prepared by the researchers. Before the treatment commenced, the pretest was administered to the participants. Eight lessons of one hour each were taught for four weeks.
The instrument used was a self-constructed 30-item multiple choice achievement test titled “Mathematics Achievement Test” (MAT). Judgmental content validity procedures were undertaken by two experienced Mathematics education experts in the Department of Special education and Curriculum Studies of the Obafemi Awolowo University, Nigeria to ascertain clarity of expressions, appropriateness to the class level, and readability. Item analysis of MAT gave average difficulty and discrimination indices of 0.51 and 0.64, respectively. The reliability index of MAT using Kuder Richardson formula-21 was 0.83 and Cronbach’s Alpha of 0.89.
Before the teachers started the treatment in each of cooperative interaction strategy group, the students were divided into mixed abilities subgroups. There were six students in each subgroup. Members of each subgroup were instructed to share ideas together, work towards mutual goals, render assistance to one another, work together as a team, provide answers to questions by consensus, and seek assistance primarily from the team mates whenever the teachers asked questions during the lesson or gave a take home assignment. Each student’s achievement in the lessons or assignments was evaluated based on the performance of his/her subgroup and not on individual contributions.
Students in the competitive interaction strategy group were divided into subgroup of eight students each. Members of each subgroup were instructed to compete with each other and seek to outperform others in any given task. They were told not to seek help from themselves but from the teachers as the best student in each of the subgroup will be rewarded. The students were evaluated based on their individual contributions and their scores were always compared in order to determine the best ones.
The students in the individualistic interaction strategy group were instructed to work on their own and seek help from the teachers when in difficulty. They were told that the performance of an individual will be independent of the other students. The teachers also made sure that the students sat widely apart.
In conventional interaction strategy group, the students were not given any special treatments. The teachers taught students the eight lessons with the conventional approach utilized by most of the secondary school teachers in Ekiti state. Thus, the lessons were predominantly teacher-centred with the teachers talking while the students paid attention, contributed minimally, and jotted points in their notebooks. The researchers occasionally supervised the lessons in each of the interaction groups to ensure that the teachers effectively implemented the instructions.
At the end of the treatment a posttest was administered to all the students. Pretest-posttest sensitization was controlled by renumbering the items used for the pretest and producing same for use in the posttest. Data were analysed using one-way analysis of covariance (ANCOVA) and Scheffe’s post hoc analysis test, all analyses were carried out at 5% probability level of significance that is,
There is no significant difference in the posttest scores of students exposed to cooperative, competitive, and individualistic interaction strategies.
In order to test this hypothesis the posttest scores of the students were subjected to a test of differences via analysis of variance and the result was as presented in Tables
Table
Table
Table
Descriptive analysis of posttest scores.
Classroom interaction strategies | Mean | Std. deviation | Maximum | Minimum | |
---|---|---|---|---|---|
Cooperative strategy | 120 | 59.4167 | 8.93730 | 40.00 | 75.00 |
Competitive strategy | 120 | 49.5333 | 11.64166 | 33.00 | 75.00 |
Individualistic strategy | 120 | 41.3417 | 12.44990 | 20.00 | 75.00 |
Total | 360 | 50.0972 | 13.32449 | 20.00 | 75.00 |
Test of difference in the posttest scores via ANOVA.
Sum of squares | Df | Mean square | Sig. | ||
Between groups | 19659.572 | 2 | 9829.786 | 79.614 | .000 |
Within groups | 44078.025 | 357 | 123.468 | ||
Total | 63737.597 | 359 |
Multiple comparison test.
(I) Exptalgrp | (J) Exptalgrp | Mean difference (I−J) | Std. error | Sig. |
---|---|---|---|---|
Cooperative | Competitive | 9.88333* | 1.43450 | .000 |
Individualistic | 18.07500* | 1.43450 | .000 | |
Competitive | Cooperative | −9.88333* | 1.43450 | .000 |
Individualistic | 8.19167* | 1.43450 | .000 | |
Individualistic | Cooperative | −18.07500* | 1.43450 | .000 |
Competitive | −8.19167* | 1.43450 | .000 |
There is no significant difference in the mean score of students exposed to each of the experimental classroom interaction approaches and those exposed to the conventional approach.
In order to test this hypothesis, the students’ scores under each of the teaching methods were subjected to test of difference via analysis of covariance. This is done in order to remove the effect of previous knowledge as measured by the pretest. The result was as presented in Tables
Table
Table
Descriptive analysis of students’ raw scores.
Exptalgrp | Mean | Std. deviation | |
---|---|---|---|
Cooperative | 59.4167 | 8.93730 | 120 |
Competitive | 49.5333 | 11.64166 | 120 |
Individualistic | 41.3417 | 12.44990 | 120 |
Conventional | 38.3500 | 13.62749 | 120 |
Total | 47.1604 | 14.32231 | 480 |
Test of difference after removing difference attributable to previous knowledge.
Source | Type III sum of squares | df | Mean square | Sig. | |
---|---|---|---|---|---|
Corrected model | 67276.605a | 4 | 16819.151 | 257.879 | .000 |
Intercept | 31443.459 | 1 | 31443.459 | 482.105 | .000 |
Pretest score | 35197.282 | 1 | 35197.282 | 539.661 | .000 |
Exptalgrp | 31794.532 | 3 | 10598.177 | 162.496 | .000 |
Error | 30980.043 | 475 | 65.221 | ||
Total | 1165827.000 | 480 | |||
Corrected total | 98256.648 | 479 |
aR Squared
Adjusted means for students’ scores on the basis of interaction strategies.
Exptalgrp | Mean | Std. error | 95% confidence interval | |
---|---|---|---|---|
Lower bound | Upper bound | |||
Cooperative | 59.462a | .737 | 58.013 | 60.910 |
Competitive | 49.295a | .737 | 47.846 | 50.743 |
Individualistic | 41.506a | .737 | 40.057 | 42.954 |
Conventional | 38.380a | .737 | 36.931 | 39.828 |
aCovariates appearing in the model are evaluated at the following value: pretest score = 37.9646.
There is no significant difference between the scores of male and female students exposed to each of experimental classroom interaction strategies.
To test this hypothesis the scores of the learners were subjected to a two-way ANCOVA to determine if there were difference on the basis of gender, teaching techniques, and on the basis of an interaction between gender and learning techniques to predict performance, after controlling for residual or previous knowledge. The result was as shown in Tables
Table
Table
Table
Table
Table
Raw means of student by interaction strategies and gender.
Descriptive statistics | ||||
Dependent variable: posttest score | ||||
Interaction strategies | Gender | Mean | Std. deviation | |
Cooperative | Female | 60.0392 | 9.91960 | 51 |
Male | 58.9565 | 8.18074 | 69 | |
Total | 59.4167 | 8.93730 | 120 | |
Competitive | Female | 47.7170 | 10.75135 | 53 |
Male | 50.9701 | 12.18789 | 67 | |
Total | 49.5333 | 11.64166 | 120 | |
Individualistic | Female | 40.5319 | 12.36554 | 47 |
Male | 41.8630 | 12.56131 | 73 | |
Total | 41.3417 | 12.44990 | 120 | |
Conventional | Female | 35.4000 | 13.78997 | 50 |
Male | 40.4571 | 13.20703 | 70 | |
Total | 38.3500 | 13.62749 | 120 | |
Total | Female | 46.0995 | 14.91845 | 201 |
Male | 47.9247 | 13.85373 | 279 | |
Total | 47.1604 | 14.32231 | 480 |
Test of difference and interaction between interaction strategies and gender.
Tests of between-subjects effects | |||||
Source | Type III sum of squares | df | Mean square | Sig. | |
Corrected model | 67496.035a | 8 | 8437.004 | 129.186 | .000 |
Intercept | 31062.698 | 1 | 31062.698 | 475.625 | .000 |
Pretest score | 34272.577 | 1 | 34272.577 | 524.774 | .000 |
Exptalgrp | 31048.428 | 3 | 10349.476 | 158.469 | .000 |
Gender | 202.226 | 1 | 202.226 | 3.096 | .079 |
Exptalgrp * gender | 16.715 | 3 | 5.572 | .085 | .968 |
Error | 30760.613 | 471 | 65.309 | ||
Total | 1165827.000 | 480 | |||
Corrected total | 98256.648 | 479 |
aR squared
Adjusted mean scores on the basis of interaction strategies.
Classroom interaction strategy | Mean | Std. error | 95% confidence interval | |
---|---|---|---|---|
Lower bound | Upper bound | |||
Cooperative | 59.365a | .746 | 57.899 | 60.832 |
Competitive | 49.218a | .743 | 47.759 | 50.678 |
Individualistic | 41.419a | .756 | 39.934 | 42.904 |
Conventional | 38.224a | .748 | 36.753 | 39.694 |
aCovariates appearing in the model are evaluated at the following value: pretest score = 37.9646.
Adjusted means of learners on the basis of gender.
Gender | Mean | Std. error | 95% confidence interval | |
---|---|---|---|---|
Lower bound | Upper bound | |||
Female | 46.397a | .571 | 45.276 | 47.519 |
Male | 47.716a | .484 | 46.764 | 48.667 |
aCovariates appearing in the model are evaluated at the following values: pretest score = 37.9646.
Test of interaction between interaction strategies and gender.
Classroom interaction strategies | Gender | Mean | Std. error |
---|---|---|---|
Cooperative | Female | 58.725a | 1.133 |
Male | 60.006a | .974 | |
Competitive | Female | 48.556a | 1.111 |
Male | 49.881a | .988 | |
Individualistic | Female | 41.021a | 1.179 |
Male | 41.816a | .946 | |
Conventional | Female | 37.288a | 1.146 |
Male | 39.159a | .968 |
This study was designed to determine which of the modern classroom interaction will best suit learners’ superlative achievement in Mathematics given the record of previous abysmal performance attributable to strategies adopted by its teachers. As soon as the posttest scores were obtained the researchers attempted to see if a significant difference existed between the performance of the students allocated to the experimental interaction strategy groups—cooperative, competitive, and individualistic. The result showed that a significant difference existed, giving the impetus to go on with the other stages of the study. Furthermore, the three experimental groups were compared to each other and the control group—the conventional interaction strategy. The result indicated that the learners in the experimental groups all performed better than those in the control group. Those in the cooperative interaction strategy gave the best result, followed closely by those in competitive and the individualistic groups. However, among the three groups, learners in the individualistic group performed far poorly than those in the remaining two experimental groups. It could therefore be stated that although this method is good, it is not well suited for good learners’ performance in mathematics. The researchers also investigated any possible interaction between the learners’ gender and the classroom interaction strategies. The study found that although significant difference existed in learners’ performance on the basis of the interaction strategies, no significant difference was found on the basis of gender. Also no significant interaction was found between gender and classroom interaction strategies.
This study showed that the cooperative interaction strategy brings about a significant difference in the achievement of students in mathematics when compared with those exposed to competitive, individualistic, and conventional interaction strategies of teaching and learning mathematics. This might be due to the interactiveness, friendliness, and teamwork that the cooperative strategy provides for the students. The competitive strategy when compared with the individualistic and conventional strategies yielded a better performance among learners. The reason for this may be due to the rewards attached and which might have motivated the students to perform better than their counterparts in the individualistic and conventional strategy groups. Individualistic interaction strategy and conventional strategy were found inferior to both cooperative and competitive strategies probably as a result of its teacher-centeredness, student’s minimal contribution to the instruction, and lack of interaction among students in the classroom.
It can therefore be concluded that although cooperative, competitive, and individualistic strategies can be used in teaching and learning processes, cooperative strategy was found to be the most effective because it facilitates the achievement of academic goals and is highly effective at producing harmony among students. It is therefore recommended that while satisfying the attempts to improve and develop appropriate classroom interactions, cooperative strategy should be adequately employed in Mathematics classrooms. The Mathematics curriculum should inculcate cooperative ideals that will allow meaningful classroom interaction patterns necessary for promoting academic achievement. Mathematics teachers should be exposed through conferences, seminars, symposium, and in-service training to the three strategies with special emphasis on cooperative strategy.