International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 1

ISSN 2229-5518

PERCEPTIONS OF PRIVATE SECONDARY SCHOOL TEACHERS IN PAKISTAN REGARDING THE EFFECTS OF STUDENT-CENTERED APPROACH ON THE

ABILITIES OF THEIR STUDENTS

Kaka Jan1

Abstract— the purpose of this causal comparative study was to investigate the perceptions of professionally trained versus untrained private secondary school teachers regarding the effects of student-centered approach on the abilities of their students. A cross-sectional research design was employed to conduct the study and a sample of 105 professionally trained and untrained private secondary school teachers were selected through convenience sam- pling technique and questionnaire was used as data gathering tool to collect the data. The nominal data were tabulated and tested statistically using Chi- square test to draw results about the null hypotheses. All the hypotheses were supported at P = 0.05 with df = 1. On the basis of this result, it is con- cluded that private secondary school teachers have the perceptions that student-centered approach contributes towards the enhancement of the stu- dents’ abilities in various domains.

Index Terms— Approach, student-centered, teacher-centered, professionally trained, untrained, private school, perceptions

——————————  ——————————

INTRODUCTION

HE role of school has changed from a passive transmitter of culture to an active leading agency of social reforms. Teaching has become more complex in today’s dynamic society and demands more innovative practices from the teachers to carry out it in its real sense than it was ever thought (Harreaves, Goodson, as cited in Lingard, Hayes, Mill
& Christie, 2003; Knight, 1998). Many global issues such as building relationship among the communities and maintain- ing global peace have drastically added new dimensions to the education regarding the social development of students and enhancing their critical thinking skills to enable them to un- derstand the world they live in a better way (Lingard et al.). The school in such situations needs to maximize academic and social learning of the young people by creating and sustaining the learning environment.
Dewey, a well-known progressive educational philosopher
of the twentieth century was a proponent of democracy in
education and emphasized the teachers to give freedom to the
students to learn on their own rather than imposing their own
learning on them. For this purpose he suggested the teachers
to provide the students with such learning environment where they can interact with each other and learn through social in- teractions (Chomsky, 2004). Dewey portrayed the classroom as a mirror of society and a laboratory for real life where the stu- dents develop their skills to solve their problems in practi- cal situations. The teacher’s responsibility is to facilitate the students’ learning based on democratic principles and enable them to make decisions for their own learning in the class (Ar- ends, 2004). The essence of pragmatic philosophy of education is to find ways to draw out the potential of the individuals. This idea is consistent with the psychodynamic view of Fraud, who stressed on the importance of students’ freedom to ex- press themselves in the working situations to release their im- pulsive energy in creative ways (Arends, 2004; Knight, 1998).
Rippa (1992) reports that Dewey was detested with the kind of students’ learning in which the teacher occupies the class- room and transfers information from the textbooks to the stu- dents. This type of classroom practice alienates the students from learning and acquaints them with the information, which is not sufficient to solve their problems in their practical lives. He simply replaces this narrow approach to education with a progressive thought and advocates that learning is a self- motivated, enjoyable and student-centered activity (Rippa,
1992). The student-centered approach to learning develops students’ abilities to cope with the challenges inside as well as outside of the school and stimulates students to think critically and reflectively (Sachs, 2003; Oser, as cited in Eggen & Kauch- hack, 1999; Rogers, as cited in Zimring, 1997).
Since the early 20th century, the trend of teaching all over the world has shifted drastically from providing information to students to develop their higher-order thinking abilities and problem-solving skills (Arends, 2004). Using these abilities and skills, students can solve their own problems and become self-directed learners.
Unfortunately the education system in Pakistan still rotates around transmission paradigm of teaching learning in which the students depend on the teachers to provide the infor- mation from the textbooks. The students copy down what the teacher writes on the blackboard in the classroom without any critique and they produce the same in the examination verba- tim (Rehmani, 2005). This traditional practice curtails the prob- lem-solving ability and creativity among the students.

TEACHING-LEARNING IN THE CONTEXT

Currently, the major concern of teachers and teacher educa- tors is the decline of students’ learning over time in which the

1 Kaka Jan is currently persuing his Master degree of Teaching (M.Teach)

and Master of Arts in Education ( Muslim Societies & Civilizations) from the Institute of Education, University of London, UK

email:kakandie2003@yah.com

IJSER © 2013 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 2

ISSN 2229-5518

students memorize the given information rather than creating meaning out of a situation on their own. The educational or- ganizations globally have set higher-order educational goals focusing on developing independent learners and these goals can be achieved through the active involvement of the stu- dents in their own learning (Eggen & Kauchak, 1999). The teacher-centered approach to teaching has failed to achieve such educational goals.
Education system in Pakistan does not provide education to the students according to the demands of the dynamic society and the teachers in Pakistani schools still use teacher-centered
or subject-centered approach of teaching rather than using student-centered approach. This out-dated model of teaching hampers students’ creativity and their ability of expression. They are considered as blank slates or sponge whose sole re- sponsibility is to absorb what the teacher delivers in the class- room (Siddiqui, 2007; Thomas, 2006). Most of the teachers in Pakistan admit the positive impact of student-centered ap- proach on the holistic development of the students but they are not motivated to implement it in their classes (Thomas,
2006). Consequently, the quality of education in Pakistan is not encouraging. Hoodbhoy (1998) reflects the educational
scenario in Pakistan and comments that:
Our [sic] education system produced the best breed of parrots in the world. These amazing creatures are able to reproduce staggering amount of information from their memory books. In an international compe- tition, these hafiz-e-science [italic added] produced by Pakistani school would surely walk away with all prizes (p.8).
This statement mirrors the educational philosophy of Paki- stan, which is disappointing. The process of schooling mostly starts from class 1 where the innocent minds are forced to learn the facts and figures through cramming. This ‘academic- minus-intellectual model’ (Siddiqui, 2007, p.117) prepares the students for examination rather than developing their prob- lem-solving skills (Bregman & Mohammad, 1998). Many chil- dren in schools memorize irrelevant facts, which their coun- terparts in other countries can simply look up in an encyclo- pedia or on a computer CD-ROM. The quantum of skills learned by a child is so small that after completing the fifth grade, they cannot meet the international standards of being literate (Hoodbhoy, 1998).
The researcher had a chance to work with both professional-
ly trained and untrained teachers in different schools in Paki-
stan. Observations and discussions with these teachers re-
vealed that both the trained and untrained teachers were fa- miliar with the student-centered approach to teaching- learning process but they did not implement it in their class- room teaching. To them this teaching approach gives much freedom to the students and they opined that it does not con- tribute towards the learning of the students. The researcher learned from these discussions that the teachers had limited their views of learning only to memorization of information and were not willing to see it as a process that develops inde-
pendent learners. To them developing critical and independ- ent learning skills is waste of time. The best teacher to them is the one who shows the best academic results. As a result, the children in these schools are reasonably competent in rote learning of facts and figures (Hoodbhoy, 1998; Siddiqui, 2007). The researcher investigated the perceptions of professional-
ly trained versus untrained teachers regarding the effects of students-centered approach on the abilities of their students to coin some contextualize and indigenous research driven rec- ommendations for the teachers and teacher educators to place student-centered approach in their schools. Thus the class- room will become a real learning place for the holistic devel- opment of the students, which will lead the schools to produce the problem-solvers and critical thinkers rather than the rote learners.

DIMENSIONS OF STUDENT-CENTERED APPROACH

Student-centered approach is a pedagogical framework that positions students at the heart of teaching learning process as an active constructor of knowledge rather than passive recipi- ent of information given in the textbooks. This approach de- fines teacher’s role as facilitator to create conducive learning environment for the students where they engage themselves in creating their own knowledge (Mahendra, Bayles, Tomoedo
& Kim, 2005). In the student-centered approach inquiry learn-
ing, discussion, cooperative learning, experiential learning and
individual learning strategies can be used. All these learning
strategies contribute towards the development of students’ abilities in various domains (Eggen & Kauchak, 1999; Lang- man et al., 1995).
The inquiry strategy improves students’ ability to do an in- depth investigation of a topic and enable them to take respon- sibilities for their own learning. In this way students can de-
velop their independent learning skills, analytical skills, ques- tion generating skills and problem solving skills which they use to solve their day to day problems as well as they con- struct their own knowledge (Arends, 2004; Eggen & Kauchak,
1999; Langman et al., 1995; Morris, 2004; Prasad, 1999; Wool-
folk, 2007).
In classroom discussions students are engaged in verbal
exchange and expression of thoughts on a particular topic
which help to develop the students’ skills of analytical think-
ing, interpretation of situations and decision making (Arends,
2004; Woolfolk, 2007). The students think critically and reflect on an issue under discussion, which stimulates their ability to pose questions and analyze the information to draw the solid conclusions (Rao, 2003).
Cooperative learning strategy is the arrangement of the stu- dents in such a way that they work with each other coopera-
tively for achieving the learning goals set by the teachers (Ar- ends, 2004; Langman et al., 1995). Cooperative learning aims at achieving two interrelated goals and the first goal is to im- prove students’ performance on the academic tasks. Both the low and higher achievers benefit out of it (Arends, 2004). The second goal of cooperative learning is to develop the attitudes of the students to tolerate and accept differing ideas in the groups and appreciate each other’s talents and skills used for

IJSER © 2013 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 3

ISSN 2229-5518

the accomplishment of the task. In this way they can develop their interpersonal skills, which is very critical for someone to relate himself/herself to the social system in his/her daily life (Arends, 2004).
Individual study is an independent learning strategy in which students study a problem individually and develop the independent learning skills, time management skills as well as it builds students’ confidence of working independently (Good & Brophy, as cited in Langman et al., 1995; Scott, Bu- chanan & Haigh, 1997).
Similarly in experiential learning, the students learn from
their experiences and subsequently from the reflection on their
experiences (Arends, 2004; Langman et al., 1995). These expe-
riences and reflections help students to develop their reflective and metacognitive skills (Santos, 2005).

RESEARCH METHODOLOGY

To conduct this research study, a questionnaire on the na- ture of Likert scale was designed to collect the data that was best suited to gather the perceptions of the research partici- pants (Burns, 2000). This was a five-point attitudinal scale in which the participants indicated their degree of agreement against each statement using Strongly Agree (SA), Agree (A), No Opinion (NO), Disagree (DA) and Strongly Disagree (SD). The teachers’ responses were later on converted into numeri- cal scale to test statistically.
The questionnaire had two parts. The part ‘A’ comprised of
a form related to the biographical profile of the participants
whereas part ‘B’ of the questionnaire was based on the state-
ments related to each null hypothesis used in the research study. There were seven statements regarding each hypothe- sis, which were taken from different research studies. Through this part of questionnaire, the perceptions of the teachers were investigated.
Using convenience-sampling technique (Gay & Airasian,
2003), seven private secondary schools in Karachi and five in
Gilgit-Baltistan were selected. These schools were run by dif-
ferent community organizations. The researcher developed a
list of the schools on the basis of his experience as a teacher in
some of the schools in Karachi and in the Gilgit-Baltistan
where he had observed that student-centered approach was used in some of these schools for teaching-learning interplay. On the basis of this observation, the researcher generalized that student-centered approach would be used in other schools run under the same administration. The teachers with professional qualifications such as Bachelor in Education (B.Ed) and Master in Education (M.Ed) were considered as professionally trained teachers and the teachers without such professional qualifications were considered as untrained teachers in this research study.
The questionnaire was distributed among the professionally trained and untrained teachers in these schools who taught English, Mathematics, Science subjects and Pakistan studies at the secondary levels. In Karachi, these schools were ap- proached with a letter requesting for the principals’ permis- sion to distribute the questionnaire in the schools. The consent
letter was attached with each questionnaire, which stated the purpose of conducting the research study in the school. The research participants read it and signed to show their consent to participate in the study.
Questionnaires were also administered in five schools in the Gilgit-Baltistan of Pakistan after taking permission from the principals through telephonic contact with them. The questionnaires were then sent to the principals via currier who returned them after completing with the teachers.

RESULTS OF THE QUESTIONNAIRE

The responses of the participants allowed categorizing the nominal data into high level of agreement and low level of agreement, which resulted in using Yates Correction formula to analyze and interpret the data. The degree of freedom (df) in each case was 1. The level of agreement above 50% was cat- egorized into high level and below 50% was categorized in low level of agreement. The Chi-square (2) value was inter- preted using Chi-square tables at P = 0.05 level of significance (Burns, 2000; Brown, 2004).

TEACHERS’ PERCEPTIONS REGARDING THE EFFECTS OF INQUIRY AS A STRATEGY

The perceptions of teachers regarding the hypothesis one was tested and analyzed as:

The calculated 2 value for this hypothesis was 0.101 which is not greater than the critical value of 3.841 at P = 0.05 level of significance (Gay & Airasian, 2003) with df = 1. (See appendix A for the procedure of 2 calculations) Therefore the null hy- pothesis there is no significant difference in the perceptions of professionally trained and untrained teachers regarding the effects of inquiry as a strategy to enhance the abilities of their students was not rejected but accepted. In this hypothesis 85% of trained and untrained teachers showed a high level of agreement to each statement of hypothesis and no significant difference exists between the perceptions towards the hypoth- esis.

TEACHERS’ PERCEPTIONS REGARDING THE EFFECTS OF DIS- CUSSION AS A STRATEGY

The perceptions of teachers regarding the hypothesis two was tested and analyzed as:

IJSER © 2013 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 4

ISSN 2229-5518

i

The calculated 2 value for this hypothesis was 0.157 which is not greater than the critical value of 3.841 at P = 0.05 level of significance with df = 1. Therefore the null hypothesis there is no significant difference in the perceptions of professionally trained and untrained teachers regarding the effects of discus- sion as a strategy to enhance the abilities of their students was not rejected but accepted. It was because 92% of both the trained and untrained teachers have shown high level of agreement to the hypothesis and no significant difference is exited in the perceptions.

TEACHERS’ PERCEPTIONS REGARDING THE EFFECTS OF COOP- ERATIVE LEARNING AS A STRATEGY

The perceptions of teachers regarding the hypothesis three
was tested and analyzed as:
The calculated 2 value for this hypothesis was 0.086 which is smaller than the critical value of 3.841 at P = 0.05 level of significance with df = 1. Therefore the null hypothesis there is no significant difference in the perceptions of professionally trained and untrained teachers regarding the effects of indi- vidual study as a strategy to enhance the abilities of their stu- dents was not rejected but accepted. It was because 81% of both the trained and untrained teachers have shown high level of agreement to the hypothesis.

TEACHERS’ PERCEPTIONS REGARDING THE EFFECTS OF EXPE- RIENTIAL LEARNING AS A STRATEGY

The perceptions of teachers regarding the hypothesis five was
tested and analyzed as:

The calculated 2 value for this hypothesis was 1.282 which did not exceed the critical value of 3.841 at P = 0.05 level of significance with df = 1. Therefore the null hypothesis there is no significant difference in the perceptions of professionally trained and untrained teachers regarding the effects of coop- erative learning as a strategy to enhance the abilities of their students was not rejected but accepted. It was because 92% of both the trained and untrained teachers have shown high level of agreement to the hypothesis

TEACHERS’ PERCEPTIONS REGARDING THE EFFECTS OF INDI- VIDUAL STUDY AS A STRATEGY

The perceptions of teachers regarding the hypothesis four was tested and analyzed as:
The calculated 2 value for this hypothesis was 0.648 which
is not greater than the critical value of 3.841 at P = 0.05 level of significance with df = 1. Therefore the null hypothesis there is no significant difference in the perceptions of professionally trained and untrained teachers regarding the effects of experi- ential learning as a strategy to enhance the abilities of their students was not rejected but accepted. It was because 93% of both the trained and untrained teachers have shown high level of agreement to the hypothesis.

DISCUSSION

The analysis of data for each hypothesis has shown that there is no significant difference in the perceptions of profes- sionally trained versus untrained teachers regarding the ef- fects of inquiry learning, classroom discussions, cooperative learning, individual studies and experiential learning strate- gies on the development of students’ abilities in various do- mains such as critical thinking, reflective thinking, analytical

IJSER © 2013 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 5

ISSN 2229-5518

thinking as well as developing the independent learning and problem-solving skills in the students of secondary schools.
The null hypotheses in each case was supported in this study may be due to ‘type II error’-a testing error occurs when the null hypothesis is supported due to some chance factors but in reality it should not have been supported (Fraenkle & Wallen, 2006). In this study all the hypotheses were support- ed because the sample size was very small. In this study 105 participants took part, which was actually a very small sample size. The biographical profile of the participants revealed that
47% of the trained teachers were involved in the classroom
teaching whereas 53% of the trained teachers were involved in management in their schools. Similarly 88% of the untrained teachers were classroom teachers. It is crystal clear that a small portion of the sample is the representative sample who teach in the classroom and it was very difficult to get the real picture related to the effects of different student-centered strategies towards the abilities of students.
The overwhelming majority of teachers indicated in their
biographic profile that they taught in the overcrowded classes.
In the true sense these student-centered strategies such as in-
quiry learning, classroom discussions, cooperative learning,
individual studies and experiential learning strategies can best be suited where there is limited number of students. All these strategies need teacher’s facilitation and in the classroom where there is larger number of students, the teachers cannot pay equal attention to every individual student. The responses of the teachers for each hypothesis indicate that they know about the importance of student-centered approach for the development of the students but they do not implement it in their schools due to overcrowded classrooms. The biographic profile also indicated that most of the schools organized short term training programs for both the trained and untrained teachers, which might have developed the conceptual under- standing of the teachers related to the importance of progres- sive nature of teaching learning processes and the teachers might have displayed their understanding about student- centered approach from their general knowledge which they developed from these short courses. This is highly consistent with the idea of Siddiqui (2007) who reflects that due to short training programmes teachers may learn several jargons about teaching learning but they cannot implement them in the ac- tual classroom setting.
Most of the teachers indicated that they have hardly one to two free periods a day and this confirms that they did not use any of student-centered strategy as these strategies need a lot of plans to implement them in their actual sense. In this case the teachers did not have time to plan and implement this progressive approach to teaching learning processes.

OUTCOMES OF THE STUDY

 Student-centered approach is not employed in the private secondary schools and teacher-centered ap- proach is still a dominant approach in these schools.
 In private secondary schools, the majority of the
trained teachers are involved in the school manage-
ment whereas the majority of untrained teachers are involved in classroom teaching.
 Both the professionally trained and untrained teach- ers understand the concept of student-centered ap- proach but overcrowded classrooms is the factor that inhibits the teachers from using this approach.
 The student-centered approach develops inquiry
skills, higher-order thinking skills, interpersonal skills, research skills and reflective skills of students, if implemented in the school.

CONCLUSION

The empirical evidence in the research study unveiled the reality that both the professionally trained and untrained teachers perceive that student-centered approach contributes towards the enhancement of students’ abilities in the second- ary school setting. Through this approach higher-order think- ing skills among the students can be fostered which the stu- dents would employ to solve their day-to-day problems with- in school as well as in their daily life. However, the descriptive statistics related to the biographic profile of the teachers re- vealed that they do not use this approach to teaching learning interplay in their schools due to their teaching in overcrowded classroom and their heavy workload which do not allow them to use this approach.
Teachers’ pedagogical skills related to the implementation
of this progressive approach can be fostered through school-
based teacher education programmes such as professional
development sessions, mentoring and conferences at the school level which will develop the teacher’s confidence to make classroom a real learning place for the students through employing innovative approaches to teaching learning. The school principals can ensure the effective use of this innova- tive approach to teaching learning through intensifying the follow-up mechanism.

References

[1].Arends, R. I. (2004). Learning to teach (6th.ed). Boston: McGraw Hill. [2].Bregman, J. & Mohammad, N. (1998). Primary and secondary education-

structural issues. In P. Hoodbhoy (Ed.). Education and the state: Fifty years of Pakistan (pp.68-89). Karachi: Oxford.

[3].Brown, J. B. ( 2004). Yates correction factor. JALT Testing & Evaluation,

18 (1), 19-22. Retrieved November 20, 2006 from

http://jalt.org/test/bro_19.htm

[4].Burns, R. B. (2000). Introduction to research methods (4th.ed). Australia: Longman.

[5].Chomsky, N. (2004). Democracy in education. Retrieved November 16,

2006 from http://www.zmag.org/chomsky/talks/9410-education.html.

[6].Eggen, P., & Kauchak, D. (1999). Educational psychology: Windows on classroom (3rd.ed). New Jersey: Merrill.

[7].Fraenkel, J. R. & Wallen, N. E. (2006). How to design and evaluate research in education (6th ed.). Boston: McGraw Hill.

IJSER © 2013 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 6

ISSN 2229-5518

[8].Gay, L. R., & Airasian, P. (2003). Educational research: Competence for analysis and application (7th.ed). New Jersey: Prentice-Hill.

[9].Hoodbhoy, P. (Ed). (1998). Education and the state: Fifty years of Pakistan. Karachi: Oxford University Press.

[10].Knight, G. R. (1998). Issues and alternatives in educational philosophy (3rd ed.).Michigan: Andrews University.

[11].Langman, H. R., McBeath, A., & Hebert, J. (1995). Teaching strategies and methods for student-centered instruction. Toronto: Harcourt Brace.

[12].Lingard, B., Hayes, D., Mills, M. & Christie, P. (2003). Leading learn- ing. Maidenhead: Open University Press.

[13].Mahendra, N., Bayles, K. A., Tomoeda, C. K., Kim, E. S. (2005). Diver- sity and student-centered education. The ASHA Leader, 18 (19), 12-13.

[14].Morris, M. (2004). Interacting in science in early childhood: A project approach. Teaching Science 50 (3), 11-14.

[15].Prasad, J. (1999). Practical aspect in teaching of science. New Delhi: Kanishka.

Professionally trained teachers:

Expected values for cell (a) = Row total  Column

Total Grand Total

5389

105

= 44.92

Expected values for cell (b) = Row total  Column Total

Grand Total

[16].Rao, V. K. (2003). Science education. New Delhi: APH.

[17].Rippa, S. A. (1992). Education in free society (7th ed.). New York: Long- man.

[18].Rehmani, A. (2005). Impact of public examination system on teaching and learning in Pakistan. Retrieved November 23, 2005 fromhttp://cc.msnscache.com/cache.aspx?q=2702170723898&lang en- US&FORM=CVRE3.

Untrained Teachers:

5316

105

= 8.08

[19].Sachs, J. (2003). The activist teaching profession. Philadelphia: Open

University Press.

[20].Santos, M. G. (1997). Portfolio assessment. Forum 35 (2), Retrieved February 6, 2006 from http://exchanges.state.gov/forum/vols/vol35/no2/p10.htm

[21].Scott, J. Buchanan, J. & Haigh, N. (1997). Reflection on student- centered learning in a large class setting. British Journal of Educational Technology 28 (1), 19-30.

Expected values for cell (a) = Row total  Column Total

Grand Total

5289

105

=44.08

Expected values for cell (b) = Row total  Column Total

Grand Total

[22].Siddiqui, S. (2007). Rethinking education in Pakistan: Perceptions, practic- es and possibilities. Karachi: Paramount.

[23].Thomas, M. (2006). Factors that inhibit middle and secondary school teach- ers in Pakistan from adopting a student- centered approach regarding the teach- ing and learning process. Paper presented at the international conference- Aga Khan University Institute for educational Development (IED), Kara- chi.

Woolfolk, A. E. (2007). Educational psychology (10th ed.). Boston: Pear- son.

Zimring, F. (1997). Carl Rogers. In J. C. Tedesco (Ed). Thinkers on educa- tion (pp.

411-422. India: Oxford University Press

Appendix A

Procedure for 2 calculations, which was used for testing all the null hypotheses

=7.92

105

5216

IJSER © 2013 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 7

ISSN 2229-5518

Untrained

Teachers

O E

43 44.08

(O-E) [O-E-0.5] 2 (43-44.08) [-1.08-0.5] 2

(0.58) 2

0.34

O E

9 7.92

(O-E) [O-E-0.5] 2 (9-7.92) [1.08-0.5] 2

(0.58) 2

0.34

df= 1, Yates Correction is applied to calculate 2 value (Burns, 2000 ; Brown, 2004).

Chi-square (2) = ∑ (O-E-0.5) 2

E

= 0.34 + 0.34 + 0.34 + 0.34

44.92 8.08 44.08 7.92

Adding 2 values = 0.008+0.042+0.008+0.043

= 0.101

IJSER © 2013 http://www.ijser.org