Empirical Research
Interaction Patterns in Mathematics Classrooms in Ogun State Secondary Schools
By Adebola S. Ifamuyiwa, Abisola Olusola Lawani
Aug 14, 2008 - 9:42:13 AM

Introduction

Interaction among people plays some vital roles in the life of individuals. This is evident in the way people relate with one-another at home, in the school, within the society, and among peer groups. In particular, the relationship between students and their teachers is expected to have a great effect on their lives. The way students learn any subject, Mathematics inclusive, will depend on the teacher’s pattern of classroom interaction. Teacher-student interaction in the classroom is a two-way process. Each participant influences the other’s behaviour; that is, the students condition their teachers’ behaviour and vice- versa. The concept of classroom interaction according to Oyedeji (1989) refers to the chain of events, which occur one after the other, each occupying a small segment of time. This includes what the teacher does that influences pupils’ learning. Study in classroom interaction is therefore a way to bridge the gap between the teacher’s good intentions for the class and the behaviour, which actually occurs in the classroom. The classroom interaction during a teaching-learning process can be verbal or non-verbal behaviours. The teacher may engage the pupils in verbal dialogue by asking questions, responding to pupils’ questions and so on. The interaction can be non-verbal like giving the pupils problems to solve, working problems on the chalkboard, or marking pupils’ work. It is a truism to say that during the teaching learning process, students’ personal and social problems in connection with their families and peer groups may hinder student-teacher interaction in the class. Meyers (1986) suggests the following basic rules for consistently encouraging student interaction in the classroom:

1. begin each class with a controversy or problem

2. use silence to encourage reflection

3. arrange & use classroom space to encourage interaction

4. create a friendly environment.

Peterson (2004) constructed a model of teacher communication styles, which he referred to as cooperation-opposition and domination-submission. He further added that observed classroom interactions could be divided into teacher talk and student talk. There seems to be three interpersonal goal structures through which students interact with one another and the teacher. Humphreys, Johnson and Johnson (1982) and Okebukola (1984) identified these as cooperative, competitive and individualistic interaction patterns. Interactions in Mathematics classrooms do employ all three at different times. According to Ifamuyiwa (2007), in the cooperative interaction condition, students learn together and have the opportunity to engage in interactions relevant to the accomplishment of the learning tasks. Cooperative interaction pattern offered the necessary aids for diagnosing students’ difficulties more easily than the competitive interaction pattern in which students study independently and a student tries to learn the material better than others in the group without discussing with other students but only seek assistance from the teacher. In the individualist condition, a student work on his or her own, avoiding interaction with other students, seeking assistance from the teacher alone. Ifamuyiwa (2007) further reported that the ability levels of the students involved in the various interaction patterns have been considered to be an important mediating variable by some researchers although no clear-cut pattern has emerged.

Osafehinti (1995) opined that the sex of a teacher have a great bearing upon classroom interaction. Male teachers are noted for tolerance and they are livelier in the classroom. They are also observed to be more mature, physically stronger and have broader perspectives of life than female teachers. On the other hand, female teachers are homely and could be motherly but are found to be stricter than their male counterparts. Tholander (2002) argued that girls usually take the role of a sub teacher in the classroom and that boys are usually the ones who break the rules of the classroom and use a wider spatial area. He further explained that males are generally dominant and that females are subordinate and that females traditionally have chosen predominantly humanistic fields while males have chosen science and technology. Phillip (2000) said a female teacher regards male pupils as one of her difficult pupils. Gordon, Holland and Lahelma (2000) reported that male teachers are better in maintaining discipline in the classroom. Harjunen and Tainio (2003) said the organization of classroom interaction and especially discipline management is interplay between the verbal and non-verbal activities as well as the visual and special resources used by teachers and pupils. Okebukola and Ogunniyi (1986) in their study found out that the relaxed and democratic atmosphere, which the indirect verbal influence foster enables students to feel free and be willing to interact with the teacher and materials of instruction. This is because when the class is free from tension, a student is free to offer his or her own views and actively participate in the class.

Interaction is a vital phenomenon that exists among people including secondary school students and their teachers in the classroom. Some specific factors have been speculated to be responsible for the type of classroom interaction pattern that exist between students and teachers in Mathematics classrooms. The classroom verbal interaction pattern created by a teacher has become an important factor in teaching-learning process, and therefore, it should be identified and utilized for optimal learning. Consequently, this investigation touched various aspects of interaction and behaviour exhibited by both students and teachers in Mathematics classrooms including pattern of instruction, questioning skills, and some other activities that takes place in the classroom.

Specifically, the study set out to provide answers to the following questions:

1. What is the general pattern of interaction in the observed Mathematics classrooms?

2. Is there any significant difference between the classrooms interaction behaviours of male and female teachers based on (a) Instruction, (b) Questioning skills, (c) Students responses and (d) Teacher’s feedback?

Methodology

Twenty Mathematics teachers from four secondary schools in Ijebu-Ode township of Ogun State Nigeria were purposively sampled to participate in the study. The teachers were selected based on their availability and readiness to participate in the study. The purposive sampling technique was thus considered appropriate for the study. The selected teachers comprised of 10 male and 10 female Mathematics teachers.

The main instrument used to collect data for the study is a section of the IEA Classroom Environment Study Instrument known as the Five Minutes Interaction (FMI). The FMI is an observational checklist and as reported by Ogunkola (2000), it was originally developed by the center for educational research, Stainford University. For the present study, the instrument was modified and used to measure the pattern of verbal interaction among secondary school students and their teachers during Mathematics lessons. Its inbuilt snapshot section, which is on the same page with the FMI was expunged as part of the modification process. The instrument consists of 34 items designed to elicit communication behaviour of teachers and students during Mathematics lessons. The IEA Classroom Environment Study Instrument was originally validated at the center for educational research, Stainford University. The category of the modified FMI instrument used in this study was scrutinized for clarity, adequacy, relevance and comprehensiveness by all the 2005/2006 Ph.D. students offering EVE 804 course in the University of Ibadan and the course lecturer. They found the instrument appropriate for observing secondary school classes. For the purpose of reliability, the scored interval (S.I.) method, which represents the most stringent method of determining reliability in an interval recording system, and recommended by Kawkins and Dodson (1975) and cited in Ogunkola (2000) was used. The result of the intra observer reliability using the scored interval method during the trial testing period gave Scott π of 0.91.

Twenty Mathematics teachers were observed, once each during their normal class teaching. The study lasted for four weeks during which the teachers taught topics selected from the school syllabus, and the verbal interaction during the lesson was recorded using the prepared coding sheet. The observation in each case lasted for 40 minutes. It should be noted that the categories on the IEA instrument are indicators of the type of verbal interactions that are taking place at a particular period of the lesson. Hence, for scoring the instrument, the frequency of a particular category in a period and the mean frequency in that particular category at the same period were considered. The resultant data were subjected to percentage analysis as well as the use of t-test statistical analysis at 0.05 significant level.

Results and Discussion

The results are presented below beginning with the first research question.

Question 1: What is the general pattern of interaction in the observed Mathematics classrooms?

This question was answered using the “who-to-whom section” of the FMI instrument (with codes 1-7). Table 1 clearly shows the observed frequencies, mean frequencies and the corresponding mean percentages for each observed behaviour category of the sampled male and female teachers and their male and female students.

Table 1: General Pattern of Interaction in the Observed Mathematics Classrooms

From the table, the male and female teachers differ slightly in initiating interaction in Mathematics classes.

The result in table 1 makes it obvious that total instruction initiated by the male teachers during the lesson was 82.9% while the female teachers in their own lessons initiated a total of 82.4% of the interaction in the class. This implies that the male and female teachers differ slightly in initiating interaction in Mathematics classes. However, out of the 82.9% total interaction of the male teachers, 70.6% was directed to the whole class, 4.8% to female student and 7.5% to the male student times respectively whereas the female teacher initiated a total of 82.4%, 70.6% was directed to the whole class, 7.2% to female student and 5.2% to the male student times respectively. Furthermore, the female student initiated 5.0% of the interactions in a male teacher taught class. This implies that the female students were freer to initiate interaction in a females’ teacher’s class than in a male teacher’s class. On the other hand, the male students initiated 6.5% of the interaction in the class taught by the male teacher while they initiated 5.2% of the interaction in a class taught by the female teacher. In essence, the male students can be said to be free both in the male and female teacher-taught classes despite the slight differences. Group initiated interactions in the class taught by the male teacher differ a bit from that of the female teacher. Group initiated to male teacher is 5% and group to female teacher interaction is 4.9%. The interaction between the teacher and non-members of the class were more in the classes taught by the female teachers than what was observed in the classes taught by male teachers. The trend was that male teacher concentrated more on their students than the female teachers. The percentage of the interaction recorded in category 1-7 for both the male and female teacher indicates that the two groups of teachers interact more with the whole class. This seems to be okay with the class since it has been suggested that thoughtful whole class instruction can produce as much discussion and appropriate problem solving as small group instruction.

To further answer the research question on the general classroom interaction pattern with respect to the teachers’ and students’ observed category of behaviour, the data obtained in the ‘what’ section of the FMI instrument (with codes 8-34), i.e. the section on instruction, question, response, feedback, and non-academic management of teaching behavior, was used. The result is presented in table 2.

Table 2: Observed Pattern of Teachers and Students Category of Behaviors

Table 2 reveals more information concerning mathematics classroom pattern of instruction with particular reference to gender disparity. For instance, the total pattern of instruction recorded by male teachers was 62.73% while female teachers recorded a total pattern of instruction of 62.33%. In terms of instruction, Mathematics classes were dominated by lecturing with very little ‘given of examples’ which recorded a mean of 5.03% by male teachers as against 5.53% by female teachers. It was quite disappointing that teaching was not supported with instructional materials in most Mathematics classrooms, however, it was better in the male teachers’ classes than in the female teachers’ classes (recording mean interaction of 6.93% and 3.93% respectively). During instruction, directives were more pronounced in the male teachers’ behaviours (5.59%) than in the female teachers’ behaviours (3.83%). In the responses category, it was observed that female students’ responses to female teachers’ questions (5.93%) was better than that of male teachers’ (5.61%). Surprisingly, this trend remained the same for male students’ responses to the questions and instructions of their teachers. A larger percentage of the female students (1.67%) gave “I don’t know the answer” response to female teachers’ questions more than male students (1.20%). This trend was also observed in male students’ response to male teachers’ questions. Male students were found to be more at ease in making statements than their female counterparts (1.50% and 0.96%) in male teachers’ classes while female students were found to be more at ease in making statements than their male counterparts (1.20% and 0.76%) in female teachers’ classes. In the feedback category, female teachers more positively acknowledged female students’ responses than male teachers (1.27% and 1.07%). The trend was however reversed in the positive acknowledgement of male students’ responses (1.17% and 1.07%) recorded by male and female teachers respectively. Effective teaching recorded higher mean frequency in the male teachers’ classes (3.0%) than in the female teachers’ classes (2.2%) during Mathematics instruction. Concerning the management of non-academic aspect of the class, female students were disciplined more in the female teacher’s class while male teachers disciplined their male students more than the female students during Mathematics classes. Male teachers recorded higher mean frequency (0.93%) in social interaction with the female students than with the male student (0.5%). The case is similar with female teachers who also interacted socially more with female students (0.4%) than with male students (0.2%).

Generally, the classroom snapshot instrument coded in the lower left hand corner of the first sheet of each FMI revealed the distribution and the involvement of the teachers and students in the activities that occurred simultaneously at the beginning of the five minutes coding sequences. It was generally observed that all the students were all the time involve in listening to lesson. The students, through handling of any equipment or apparatus, carried out no experiment. This pattern was found to be the same in both male and female teachers’ classes. This implies that the students were not presented with the opportunity to learn Mathematics through inquiry and discovery approaches.

Question 2: Is there any significant difference between the classroom interaction behaviours of male and female teachers based on (a) instruction, (b) questioning skills, (c) students’ responses and (d) teacher’s feedback?

Table 3: Result of Chi-Square (χ²) analysis of male and female teachers’ behaviours

The result in table 3 revealed significant outcomes. The computed chi-square values in the four cases were greater than the table values at the 0.05 significant level. This implied that there is significant difference between the classroom interaction behaviours of male and female Mathematics teachers with respect to instruction, questioning, students’ responses and teachers’ feedback.

This finding is surprising because one would expect that, since male and female teachers in Nigeria are exposed to similar training and working conditions, their classroom behaviour should be similar. The finding not only buttress the observation that most Mathematics classrooms in Nigeria used instructional strategies that are teacher-centered, but is opposed to the earlier findings of Long and Sato (1983) and Obanya and Osafehinti (1985) that practicing science and mathematics teachers in Nigerian schools tend to be only actors and talkers in the classroom. The Mathematics teachers involved in this study used mainly informational and memory questions during their classroom instruction with only a few leading and probing questions. The outcome of this study also lend support to the fact that although the new science and mathematics curricula encourages critical thinking and higher cognitive process, the type of questions used by both the mathematics and science teachers and their students do not lead them to the attainment of such objectives.

Summary and Conclusion

The following are the major findings in this study:

1. The instructional interaction initiated by the male teachers during the mathematics lessons was 82.9% while that initiated by the female teachers was 82.4% of the total interaction observed in the classes.

2. Out of the 82.9% interaction initiated by the male teachers, 70.6% was directed to the whole class, 4.8% to female students and 7.5% was directed to the male students whereas from the total of 82.4% interaction initiated by the female teachers, 70.3% was directed to the whole class, 7.2% to female students and 5.2% was directed to the male students.

3. The female students were freer to initiate interaction in female teachers’ classes than in male teachers’ classes.

4. The male students were freer to initiate interaction in male teachers’ classes than in female teachers’ classes.

5. Group initiated interactions in the classes taught by the male teachers’ was not better than that observed from classes taught by the female teachers.

6. There is significant difference between the interaction behaviours of male and female mathematics teachers based on instruction.

7. There is significant difference between the interaction behaviours of male and female mathematics teachers based on questioning skills.

8. There is significant difference between the interaction behaviours of male and female mathematics teachers based on the way the students respond to the teachers’ questions.

9. There is significant difference between the interaction behaviours of male and female mathematics teachers based on the teachers’ feedback.

Thus, the outcomes of this study represent the observed pattern of interaction in some mathematics classrooms in Nigeria. The findings that the classroom behaviours initiated by the teachers in the study is low may be attributed to limited opportunities resulting from inadequate equipment and facilities, inappropriate methodologies, paucity of instructional materials and the failure of teachers to design and formulate evaluation questions that will make the students more active participants in mathematics classroom and teaching. The findings in this study have important educational implications for mathematics teachers and mathematics teaching. Teachers of mathematics at the secondary school level need to engage their students in the teaching-learning process, use student-centered or interactive strategies and provide adequate feedback to their students after mathematics instructions. Mathematics teachers should endeavor to encourage group work among students. They should also ask questions that will encourage students’ participation in mathematics teaching.

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