Effect of Two Teaching Methods of Teaching Quadratic Equation on Secondary School Students’ Performances
CHAPTER ONE
Objective of the Study
The purpose of this study was to determine the effect which problem-solving teaching method would have on students‟ achievement in Mathematics.
Specifically, this study is intended to address the following issues:
- The effect of problem-solving teaching method on SSII students‟ achievement in mathematics.
- The influence of gender on students‟ achievement in mathematics when taught using problem-solving teaching
- The influence of location of schools on students‟ achievement in mathematics when taught using problem-solving teaching
CHAPTER TWO
Review of Related Literature
Conceptual Framework
The Role and Importance of Mathematics
Mathematics is a very important subject in any society (Salman, 2005). There can be no question about the importance of mathematics both in general and specific education. The need for mathematics increases because of technological advancement.
Mathematics is among the core subjects at both Junior and Senior Secondary School levels of our educational system. According to National Policy on Education (F.R.N., 2004) “the core subjects are the basic subjects which will enable students to offer arts and sciences in higher education”. International Association for Evaluation of Educational Achievement (I.A.E.E.A, 1998), has associated the learning of mathematics with basic preparation for adult life. Similarly, the Nigerian nation recognizes this association between mathematics and preparation for adult life when the (F.R.N. 2004) included the inculcation of permanent and functional numeracy as one of the general objectives of primary education.
Mathematics, according to Aminu, (1995) is not only a Language of the Sciences; it is also the essential nutrients for thought, logic, reasoning and therefore, progress. Science is the foundation of technology and technology is the bedrock of modern development. Therefore, mathematics is the foundation of science, technology and modern development. For any nation to survive and develop, it has to improve its technology, which can be achieved through effective teaching and learning of Mathematics in the schools.
The application of Mathematics spans almost the entire ramifications of human endeavours. On account of this, Skemp (2000) observed that the application of Mathematics to the bottlenecks of natural science, of technology and of commerce is a powerful weapon that has gained enough ground. It serves as a solid metal tool which man employs in dealing with his physical environment. In the area of technology, for instance, the design and construction of physical and structural projects received a tremendous support of elaborate Mathematical principle and method.
Skemp (2000) further stated that mathematical methods have strongly penetrated many fields of knowledge, changing them both in substance and power and have actually brought new disciplines into being or existence. Skemp went further to say that Mathematics is currently playing a dominant role in physics, Computer Science, Engineering, Economics and Chemistry. The layman‟s idea of Mathematics has been that it is the abstract study of quantity alone. But from the above point of view, it is apparent that apart from the theoretical and abstract treatment of quantity, mathematics encompasses the use of the knowledge gained in solving real life predicaments. It constitutes a language which gives an exact and accurate way of representing certain ideas and relationships which exist in physical phenomenon or systems.
In support of the above, Obioma (1996) expressed that learners of the subject should be able to discover the extensive applicability of the subject in other subject areas like Physics, Chemistry, and Sociology etc. Obioma further stated that mathematics helps to generate and sustain curiosity motives of learners and to develop academic skepticism. In the same vein, Fakuade (1997) writing on mathematics as a service subject stated that the choice of science subject at certain level is very much related to ability in mathematics. This is because proficiency in mathematics is of basic importance to the study of Physics, Chemistry, and Integrated Science etc and in understanding elementary principles of science subject generally.
Nwichi (2001) said that mathematics, being one of the cultural components of any society have played diverse roles in both human developments and material developments like textile industries, engineering, food processing, housing, motor production, prediction, designing etc. Nwichi finally stated that mathematics has affected changes for the better. In support of this, Iwuoha (1993) in his paper titled “mathematics in everyday life” presented at the academic staff seminar of Alvan Ikoku College of Education, Owerri maintained that:
“If there were no mathematics there would be no salary, no speed limit, no measurement, no time, no building, no buying and selling, no houses, no education, we cannot quantify the amount and size of food we eat, the doctors cannot prescribe the doses of medicine, the banks will fold-up, all scientific institutions will cease to function and indeed life will come to a stand- still (Iwuoha, 1993:92)
In relation to the above, Arnold (1990) stated that the role of mathematics in physics is conspicuously seen. The essential ingredient of inductive reasoning is deduction. Deduction is familiar to us in the various processes of mathematics which are used extensively in physics without which we should not be able to progress very far. Mathematics may be regarded as a highly organized form of reasoning employing certain agreed-upon symbols and conventions to the aim of partly improving on the reasoning powers with which we are endowed by nature.
One can conclude that mathematics has an important role to play in a wide range of applications, so long as we are realistic about what it cannot do, as well as what it can do. But the issue is on how to motivate students at their early stages to develop interest and increase their performance in this important school subject.
CHAPTER THREE
Research Method
In this chapter, the researcher presents the method and procedures adopted in the study. The chapter is organized under the following sub-headings: design of the study, area of the study, population of the study, sample and sampling technique, instrument for data collection, validation of the instruments, reliability of the instrument, experimental procedure, and control of extraneous variables and method of data analysis.
Design of the Study
The design for this study is a quasi-experimental study of the non-equivalent control group design. In this type of design, there is no randomization of subjects since this may disrupt school organization, hence intact classes were randomly assigned to experimental and control groups respectively.
Area of the Study
The study was carried out in Nsukka Education Zone of Enugu State. The zone was chosen because it is made up of urban and rural settings. The zone was also chosen because it has been found out that most of the students in the zone fail their SSCE in mathematics yearly (Exam and Records Unit, PPSMB Zonal Office Nsukka).
The indigenes of Nsukka Local Government Area are mostly Christians and therefore worship the Almighty God. Very few of them are pagan and practice traditional religion. These pagans also marry many wives and practice farming as their occupation. Many of the indigenes are civil servants and traders. Schools available are mostly government secondary schools and few missionary and private secondary schools.
Nsukka local government is bounded by the East by Udenu Local government area, by the West by Uzo-Uwani local government, by the North by Kogi State and by the South by Igbo-Etiti local government area.
Population of the Study
The population of the study is made up of the SSII students in all the thirty-one co-educational secondary schools in Nsukka Education Zone. SSII was chosen because the concepts covered (quadratic equations and longitude and latitude) are embodied in their
Sample and Sampling Technique
The sample for the study comprised of 168 SSII students made up of 84 male and 84 female students selected through purposive sampling technique.
The purposive sampling technique was used to select the co-educational schools in Nsukka Education zone. Co-educational schools were chosen for the study because gender is a factor in the study. Four (two from urban and two from rural) out of the thirty-one (31) co-educational schools in Nsukka education zone were used for the study. Two out of the four secondary schools were rural schools because location is a factor in the study. In each of the four schools, two intact classes were randomly selected and used for the study. A total of eight intact classes were used for the study (four experimental groups and four control groups) to avoid contamination of the experiment by exchange of ideas between the experimental groups and the control groups. The researcher used Head/Tail of a fair coin thrown up in determining which of the eight intact classes from the four schools would be experimental groups and which ones would be the control groups.
CHAPTER FOUR
RESULTS
This chapter presents the results of the analyses of the data obtained in the study. The results are presented according to the research questions and the corresponding hypotheses of the study. The hypotheses were all tested at 0.05 level of significance.
Research Question One: What is the effect of problem-solving teaching method and conventional method on the mean achievement of students in mathematics?
Table 4 shows that the mean achievement score (22.05) for the experimental group was higher than the mean achievement score (11.71) for the control group in the post PSAT.
Hypothesis One: There is no significant difference in the mean achievement scores of students taught mathematics with problems solving teaching method and those taught with conventional method.
From Table 5, the null hypothesis one is rejected since the probability value associated with the calculated value of F-ratio (205.246) is 0.000 which is less than the 0.05 level of significance. Therefore, there is a significant difference in the mean achievement scores of students taught mathematics with Problem-Solving Teaching Method and those taught with conventional method in mathematics in favour of the students taught using Problem-Solving method.
CHAPTER FIVE
DISCUSSION, CONCLUSION AND RECOMMENDATIONS
In this chapter, the researcher presents discussion, conclusion, implication and recommendations.
Discussion of Findings
The findings of this study revealed that problem solving teaching method had significant effect on students‟ achievement in mathematics. The experimental group had higher mean achievement score (22.05) than their control group counterparts (11.71) in the posttest, as shown in table 4. Results in table 5 further confirmed this finding by indicating statistically significant effect of problem solving teaching method on students‟ achievement in mathematics. The observed probability value
- which was significant at 0.05 level of significance testifies to the result. This implies that the efficacy of problem solving teaching method was more positive in enhancing and facilitating students‟ achievement in mathematics. Other researchers Alio and Harbor Peters (2000) and Galadima (2002) had similar
Secondly, on the influence of gender on students‟ achievement in mathematics as a result of the use of problem solving teaching method, table 6 shows that the mean achievement of males in experimental group in the posttest PSAT 22.95 is higher than that of females of 21.05. However, the analysis of covariance (ANCOVA) of table 7 shows that the difference in mean achievement of males and females in experimental group is not statistically significant. This is because the observed probability value of 0.126 is not significant at 0.05 level of significance. This implies that problem solving teaching method is effective for teaching male and female students alike. This result is in line with the findings of Olagunju (2001) that there is no significant difference between the general performance of boys and girls in mathematics when a good method is used in teaching. In support of this finding also Aliyedum (2000) stated that the cognitive power necessary for mathematical ability correlates with the general intelligence and not on any particular sex. Hence, students‟ performance in mathematics is dependent on teaching method irrespective of sex.
On the influence of location on students‟ mean achievement in mathematics using problem solving teaching method, table 8 revealed that urban students had higher mean achievement score of (23.91) than their rural counterparts with mean score (19.79) in the posttest. Results of table 9 further confirmed this finding by indicating statistically significant effect of problem solving teaching method on students‟ achievement in mathematics. The observed probability value (0.001) which was significant at 0.05 level of significance testifies to the result. This implies that urban students perform better than their rural counterparts in mathematics when taught with problem solving teaching method. Other researchers Akukwe and Obioma in Ugwoke (2008) had similar results.
Conclusion
Based on the findings, the following conclusions were drawn:
- Problem-solving teaching method fostered students‟ achievement more positively than the conventional method used in teaching their counterparts mathematics.
- Gender had no influence on students‟ achievement in mathematics when taught with problem solving teaching
- Location had influence on students‟ achievement in mathematics when taught with problem solving teaching
Educational Implications of the Findings
The findings of this study have implications on the teachers, students, school principals, curriculum planners and the government.
The use of problem-solving teaching method in teaching would make mathematics cease to be mere recall of theories, rules, facts and formulas. Since practice makes perfect, students would be able to use their own initiatives to solve some mathematical problems correctly as the use of the method promote understanding.
There is need for the mathematics teachers to be trained by Teacher Education Institutions on how to prepare different lesson notes on different concepts in mathematics using the problem-solving teaching method. This would make the teaching and learning of mathematics very interesting which in turn leads to high achievement in mathematics.
Curriculum planners, school principals and government should see the need to provide and equip mathematics laboratories where teachers and students could do mathematics practical. This would make for active participation of learners in the classroom, generate interest and enhance understanding thereby leading to high performance in mathematics by both male and female students.
Since, there is no significant difference in the mean achievement scores of boys and girls, it follows that the problem solving teaching method is not gender biased. It should, therefore, be employed in teaching to develop critical and creative thinking in the minds of both boys and girls in our secondary schools.
Recommendations
Based on the findings of this study and their implications, the following recommendations are made by the researcher:
- Teachers should adopt problem-solving teaching method in our school system since this has been proved to be an effective method of teaching difficult concepts in
- Government and schools should provide and equip mathematics laboratories where teachers and students could do mathematics practical. This would make male and female students to be actively involved in the teaching/learning processes which would in turn lead to a better understanding of the concepts in mathematics.
- Teachers should be encouraged to teach in the rural schools. Government should encourage qualified teachers to be in the rural areas by giving them some form of
- Government and curriculum planners should make provisions for in-service training/workshop/conferences for their mathematics teachers to enable them develop competence in their choice and use of various teaching methods.
- Authors of mathematics textbooks should write their texts to be child centered and activity based as in problem solving teaching
Limitations of the Study
- Complete randomization was not possible because of the use of intact
This may have affected the results of this study.
- The regular mathematics teachers used as research assistants for the study were considered in terms of qualification. Other factors such as personality, tribe, age and classroom environment could also have affected the results of the
- The use of the same achievement test for both pretest and posttest without disguise may have affected the results of the
Suggestions for Further Research
The findings of this present study have made the researcher to suggest the following:
- Parallel studies could be conducted which would include other difficult concepts in
- Similar studies could be conducted in single sex schools instead of co- educational schools.
- Another teaching method could be used in teaching quadratic equations and longitude and latitude for SSII students and the effectiveness of the two be compared in enhancing students‟
Summary of the Study
The study found the effect of problem-solving teaching method on the achievement of students in mathematics. The study employed a non-equivalent quasi- experimental design. The sample for the study was comprised of 168 SSII students drawn from four co-educational schools out of 31 co-educational schools in Nsukka Education Zone of Enugu State. A total of eight intact classes were randomly selected and four assigned to the experimental group while the other four intact classes were assigned to the control group. The experimental group comprising of 84 students were taught quadratic equation and longitude and latitude using problem solving teaching method and the control group comprising of 84 students were taught quadratic equation and longitude and latitude without problem solving teaching method (conventional method).
Data were collected using Problem Solving Achievement Test (PSAT) for both pre-testing and post-testing. Three research questions were asked and three null hypotheses were formulated for the study. The research questions were answered using mean and standard deviation while the null hypotheses were tested at 0.05 level of significance using analyses of covariance (ANCOVA). It was revealed from the study that problem solving teaching method increased the achievement of students in mathematics. There was no significant difference in the mean achievement scores of boys and girls in mathematics. There was significant difference in mean achievement scores of urban and rural students in the direction of urban students.
Based on the findings, the researcher recommended among other things that problem solving teaching method should be used in teaching difficult concepts and that government should encourage qualified mathematics teachers to be in the rural areas by giving them some form of incentives.
REFERENCES
- Abakporo, J.E. (2005). Effective problem solving in mathematics: challenges and prospects. Journal of issues on mathematics. The Annual Publication of Mathematics Panel of Sciences Teachers Association of Nigeria, 8(1):19- 33.
- Agwagah, U.N.V. (2004). Sustaining development in secondary schools mathematics through constructivist Framework. Page 29 of the. Journal of Mathematical Association of Nigeria (MAN), volume 29 Number 1, Mathematics Education Series, September 2004.
- Agwagah, U.N.V. (1993). Instruction in mathematics as a factor in students‟ achievement and interest in word problem solving. Unpublished PhD Thesis, University of Nigeria Nsukka.
- Aiyedun, J.O. (2000). Influence of sex difference of students on their achievement in secondary school mathematics. Journal of Mathematics Association of Nigeria. ABACUS 25(1) 102 -112.
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- Ale, S.O. (2006). Address presented during opening ceremony of the 4th Zonal Workshop on the use of the Federal Government Sponsored Primary Mathematics kits (PMK) Project. Held on Federal College of Education (Technical) Omoku, Rivers State. 4th April, 2006.
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