A COMPARATIVE ANALYSIS BETWEEN STUDENTS COMPETENCE IN MATHEMATICS AND THEIR PERFORMANCE IN PHYSICS (A CASE STUDY OF SS2 STUDENTS)
ABSTRACT
The study investigated the effect of the knowledge of Mathematics on the Achievement of Physics students in secondary School in Lagos State. The study employed a pretest, posttest control group quasiexperimental research design, using school types and gender as moderator variables. A sample size of one hundred and ninetyfour (194) Physics students were purposively selected from five (5) senior secondary school (two Private, one Federal and two Public Senior Secondary School in Lagos State) from the population of 51 and 43 Senior secondary schools of Educational districts ii and iv in Lagos State respectively.
Two validated research instruments Mathematics Knowledge Test (MKT) r 0.74 and Physics Achievement Test (PAT) r 0.84 were used for data collection. The study lasted for five (5) weeks; in which both the experimental and control groups were pretested after which the experimental groups were exposed to Mathematics concepts relating to Physics concepts to be taught before exposing them to the Physics concepts, while the control groups were exposed to only the Physics concepts without prior exposure to Mathematics concepts simultaneously… (Scroll down for the link to get the Complete Chapter One to Five Project Material)
Introduction
Competence is defined as the capability to apply or use a set of related knowledge, skill, and attitude to complete a task according to its standards in a defined work area Ashworth, P. and Saxton, J. (2000) In addition, competence can be scored and is measurable Mansfield, B. (2003). The teachers or instructors can assess students’ competence through processes of observation and evaluation. Mathematics as a subject affects all aspects of human life at different levels.
Competence is an abstract construct. It describes the quality of being competent. It is the “habitual and judicious use of communication, knowledge, technical skills, clinical reasoning, emotions, values and reflection in daily practice for the benefit of the individual and community being served” (Epstein & Hundert, 2002).
In contrast, competency is a more concrete concept to include particular knowledge, a single skill or ability, and attitudes. It speaks to the quality of being adequately or well qualified, physically and intellectually. There is misuse and/or crossuse of the terms competence and competency. For example, competence is used as a synonym for performance, a skill, or personality trait (Bassellier, Reich, & Benbasat, 2001).
Not only is competence treated as performance, but it is also used indiscriminately to refer to either the observable performance or the underlying neural functions that support the observable behavior (Connell, Sheridan, & Gardner, 2003).
Schwandt (2008) drew attention to the different nature of competence and competency. He pointed out that to identify professional competence is “another” task than to identify competencies (Schwandt, 2008).
In addition, Epstein and Hundert (2002) and Eraut (2004) agreed that professional competence is more than a demonstration of isolated competencies… (Scroll down for the link to get the Complete Chapter One to Five Project Material)
Statement of the Problem
Teaching of science, especially mathematics and physics, and performance of students at the secondary school level have been the concern of government and parents. The challenges that might arise could be as a result of incompetency in the side of science teachers in the schools.
It could also be that there are no facilities to be used in the teaching and learning process in the schools… (Scroll down for the link to get the Complete Chapter One to Five Project Material)
Research Objectives
The main aim of the study is to examine a comparative analysis between student’s competence in math and their performance in physics. Other specific objectives of the study include;
 To determine the relationship between students competence in mathematics and their performance in physics… (Scroll down for the link to get the Complete Chapter One to Five Project Material)
LITERATURE REVIEW
Piaget’s cognitive theory of learning refers to the stage theory of cognitive development. According to Piaget, children develop knowledge by inventing or constructing reality out of the experience and thus mix their observation with their ideas about how the world works. Piaget observed that people of the same age level (especially children) have a similar line of reasoning.
For instance, children of the same age level have a similar line of reasoning or thinking. Children may make the same type of mistakes. They may have the same reasoning process. This indicates that cognition develops stage by stage. Piaget used the terms ‘Assimilation’ and ‘Accommodation’ to explain his views… (Scroll down for the link to get the Complete Chapter One to Five Project Material)
Students Performance Theory on Learning
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EMPIRICAL REVIEW
Adeyemi (2017), Awodun, and Ojo (2013), Odual (2013), and Redish (2005) affirmed the submission of Obafemi and Ogunkunle (2013) by acquiescing that Mathematics is the language of science in general and of Physics in particular. The researchers admitted that without Mathematics, there is no science and that without science, there is no technology, and without technology, there is no modern society.
This is the major reason why Mathematics is a compulsory subject for students in primary and secondary school levels in Nigeria. Mathematics is also, a requirement for admission into tertiary institutions of learning. Every subject, tribe, and society has its own language, Adequate and sound knowledge in a language of a particular subject is a requirement for success in the subject, sound knowledge in the language of a particular environment, tribe or society is a requirement for such a person to belong and flow well in such environment, tribe and society.
Hence, before one can be said to have understood a subject or belong to a particular society or environment one should be able to speak the language of that subject or speak the language of such society or environment… (Scroll down for the link to get the Complete Chapter One to Five Project Material)
The WAEC external examination of Physics students in secondary schools between the year 2004 and 2015 is showed in Table 1.1. The trend shows that the academic performance of Physics students in the external examination with grade Al — C6 is fluctuating between 41.50 and 68.74. The trend as such is not satisfactory.
Furthermore, from Table 1.1 below, the chief examiner’s report has showed that Physics students performed below average between 2004 and 2015 WAEC external exams.
Table 1.1: students’ performance in May/June SSCE (WAEC) Physics 2004 — 2015
Year 
Total Number of candidate 
Total pass A_{1 }_{–} 

Total Pass D_{7 }_{– } 

Total Fail (F)

Failed % 
2004  321499  158837  49.40  90012  27.99  61940  19.26 
2005  344111  142943  41.50  102036  29.62  89150  25.88 
2006  375824  218199  58.05  87025  23.15  62119  16.52 
2007  418593  180797  43.19  140172  33.49  88480  21.14 
2008  415113  200345  48.26  91116  21.95  116776  28.13 
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METHODOLOGY
The population for the study wasa ll Secondary School students in while the sample was 180 Secondary School Class II students selected from three schools. Purposive sampling was used to select two singlesex schools (one boys only and the other girls only) while simple random sampling was used to select one coeducational school.
60 students were selected from each singlesex school through simple random sampling while stratified sampling was used to select 30 boys and 30 girls from the coeducational school. The grouping of the students into experimental and control groups was also done through simple random sampling technique. However, 45 boys and 45 girls were allocated to each group. The sample size of the 180 SSII students was adequate for this kind of study according to Kiajcle, Robert, and Morgan (1970)… (Scroll down for the link to get the Complete Chapter One to Five Project Material)
RESEARCH FINDING AND DISCUSSION
What is the effect of Mathematics knowledge on the achievement of students in Physics?
Table 1 : Mean posttest achievement score of students (reflecting students competence) exposed to Mathematics before exposure to Physics (experimental) and those exposed to Physics (control)

TREATMENT 
Mean 
Std. Deviation 
Std. Error Mean 

EXPERIMENTAL
CONTROL 
102 92 
21.6863
12.6087 
4.28671
1.64388 
.42445 .17139 
Table I showed that the mean score of students in the experimental group is 21.6863 which is greater than 12.6087 mean scores of students in the control group. This showed that the knowledge of
Mathematics knowledge has the effect of 9.0776 on Physics achievement.
 What is the effect of gender on the achievement of students in Physics?
Table 2: Mean Post Test Scores of Male and Female Students in Physics
Group Statistics
GENDER 
Mean  Std. Deviation 
Std. Error Mean 

MALE
FEMALE 
133 61 
17.7669
16.5410 
5.57033
5.67031 
.48301 .72601 
Table 2 showed that the mean posttest scores of male students in Physics is 17.7669 which is greater than and that of female which 16.5410 is. The effect of gender on Physics achievement is 1.2259.
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CONCLUSION
From the results obtained in the study on mathematical competences on students’ performance in Physics, it was found that students taught Physics using improvised mathematical competences performed better than students taught using conventional material; male students did not perform better than their female counterparts in Physics. The results do not suggest the ordinal interaction effect between mode of method and gender on students’ achievement in Physics… (Scroll down for the link to get the Complete Chapter One to Five Project Material)
Study Implications
The findings of this study have implications for education particularly in teaching Physics in secondary schools in particular, and in Nigeria as a whole. The implications of this study border on the development of more virile mathematical competences for teaching Physics. In addition, the findings of this study have implications for Physics teachers… (Scroll down for the link to get the Complete Chapter One to Five Project Material)
REFERENCES
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