ISSN: 2548-0286
Journal of Research in
Education, Science and
Technology
Investigation of the Role of
Mathematics on Students’
Performance in Physics
Thomas Ojonugwa Daniel1, Ruth J. Umaru2, Kasali O. Suraju1, Abdulrahman O. Ajah1 1Alex Ekwueme Federal University, Nigeria 2University of Jos, Nigeria
To cite this article:
Daniel, T. O., Umaru, R. J., Suraju, K. O., & Ajah, A. O. (2020). Investigation of the
role of mathematics on students’ performance in physics. Journal of Research in
Education, Science and Technology, 5(2), 101-108.
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Journal of Research in Education, Science and Technology (JREST) is published biannual as an
international scholarly, peer-reviewed online journal. In this journal, research articles which reflect the survey with the results and translations that can be considered as a high scientific quality, scientific observation and review articles are published. Teachers, students and scientists who conduct research to the field (e.g. articles on pure sciences or social sciences, mathematics and technology) and in relevant sections of field education (e.g. articles on science education, social science education, mathematics education and technology education) in the education faculties are target group. In this journal, the target group can benefit from qualified scientific studies are published. The publication language is English. Articles submitted the journal should not have been published anywhere else or submitted for publication. Authors have undertaken full responsibility of article's content and consequences. Journal of Research in
Volume 5, Number 2, Autumn 2020, Page 101-108 ISSN: 2548-0286
Investigation of the Role of Mathematics on Students’ Performance in
Physics
Thomas Ojonugwa Daniel1*, Ruth J. Umaru 2, Kasali O. Suraju1, Abdulrahman O. Ajah1 11Alex Ekwueme Federal University
2University of Jos, Nigeria
Article Info
Abstract
Article History
Received: 5 March 2020
This study is aimed at investigating the role of mathematics in students learning, understanding and performance in Physics using senior secondary school science students. The study employed the use of design samples which were drawn through a simple random sampling technique. Structured questionnaires were used to collect data for the study, after which the data were analyzed using simple percentage and chi-square analysis. The result shows that there is a significant relationship between mathematics and physics, as insufficient mathematical skills such as analytical skills, algebraic process skills, geometry skills, calculation skills, tables and graph interpretation skills required to solve physics problems are the cause of the poor performance of students in physics, whereas the efficient application of mathematics to physics enhances students’ performance in physics. The study reveals that the cognitive tools involve in studying Physics are student’s expectation, thinking, knowledge, syntheses, application, memorization and remembrance of formulas and equations.
Accepted: 20 September 2020 Keywords Physics Students Mathematics Cognitive tool Performance
INTRODUCTION
Physics is a science-based analysis of matter, associated energy, detection and study of general physical laws and phenomena (Fuson, 1992; Freedman, 1996; Ogunleye, Awofala, & Adekoya, 2014). It is an understanding of the laws of nature (Chassy & Jones, 2019). Mathematics acts as a guide when teaching or learning physics, which helps one to incorporate problems dealt with in physics. Physical quantities are of interest among the concepts that make up the vocabulary of physics. Measurable properties or features of objects, phenomena and processes are physical quantities. In mathematical materials on which the teaching and study of physics is based, physical problems involving measurements play a fundamental role. The consequence of these measurements also allows certain relationships between physical quantities to be detected and calculated; taking the form of physical laws also formulated as mathematical relationships. Familiarity with these tends to challenge the problems, which in turn leads to theories that clarify the reasons for the relationships being established. Physical theories are hypotheses, confirmed by several experiments and covering a broad group, which make it possible to predict the result of several combined phenomena for which mathematics is essential as it relates to algebra equations, inequalities or formal rules, etc. (Abdurarahman & Madugu, 2014).
The insufficient promotion of the required application and comprehension of mathematics to help explain physical problems is a fundamental issue in physics education at secondary and tertiary institutions. A variety of studies have shown that learners of introductory physics courses have trouble using mathematics in both secondary and tertiary institutions (Akatugba & Wallace, 1999; Charles-Ogan & Okey, 2017; Mountcastel, Morgan, & Kaback, 2002). Fluency in mathematics has also been shown to be an important factor in physics conceptual learning (Meltzer, 2002).The basic laws of nature are represented in mathematical form. This fact makes physics a prototype of exact science and is primarily responsible for its predictive power (Chassy & Jones, 2019).
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Fluency in mathematics requires a full understanding of the concept of physics. However, on mathematical problem solving tasks in physics, many introductory physics students perform poorly. There are at least two potential explanations for these poor results, which are different. It is either that the student lacks the appropriate mathematical skills required to solve physics problems or that the students do not know how to apply the mathematical skills they have in physics to a specific problem situation. The poor performance of students on mathematical problem solving tasks in physics has led many departments of physics and instructors to introduce conceptual physics courses that dilute or simply exclude mathematical problem solving from the curriculum. This will not, in effect, allow students to further apply physics to other fields of study. To this end, this study is aimed at establishing the relationship between Physics and mathematics with a focus of finding the mathematical learning tools/skills that enhances students’ performance in Physics.
METHODS
Sample CollectionThe population for this study consists mainly of SS3 science students of senior secondary school who were selected from both public and private schools in Jos North Local Government Area of Plateau State, Nigeria as a case study. From amongst these schools, a sample of six secondary schools was randomly selected from the 127 secondary schools. Table 1 gives a breakdown of the total number of SS3 science student in each of the school and the sample drawn.
Table 1. Distribution of science students in selected schools Name of School Population of SS3
Science Students Sample
St. Paul’s Academy 72 31
Crown Basic Academy 10 9 Methodist High School 26 12
Bishop High School 36 14
G.S.S. Township 35 16
G.S.S. West of Mines 36 18
Total 215 100
Sampling Techniques
Randomization sampling was employed in this study for sample data selection since the data lent itself to an equal chance of being selected. Six (6) schools were selected for the population above by assigning a number to each school from among the 127 secondary schools after which six schools were picked at random one after the other. The following results were obtained as listed above:
1. St. Paul’s Academy 2. Crown Basic Academy 3. Methodist High School 4. Bishop High School 5. G.S.S Township 6. G.S.S West of Mines
Instrument for data collection
Questionnaire was used for the collection of data. It was designed to create a basis for the collection of data from students on the effects of mathematics on the success of physics students. The questionnaire was divided into two (2) sections namely:
a. Student’s personal data
b. Questions on the effect of mathematics on student’s performance in physics.
Section one consist of personal data of students, while section two consist of 10 research items which was made possible by using the modified Likert chart by the use of Research questions and hypotheses adopted as stated below:
SA Strongly Agreed A Agreed
D Disagreed
SD Strongly Disagreed
Research Questions
a. What are the cognitive tools involve in solving Mathematical problems in physics? b. Is there any relationship between Mathematics and Physics?
c. To what extend does mathematical skills relates to Physics learning? d. What kind of mathematical skills are require in studying Physics?
Hypothesis
The following hypothesis was meant to direct the study.
1. HO: There is no significant relationship between the study of mathematics and physics among secondary school students in Jos north.
HI: There is significant relationship between the study of mathematics and physics among secondary school students in Jos north.
2. HO: Effective application of mathematical knowledge in physics do not enhance students’ performance in physics.
HI: Effective application of mathematical knowledge enhance students’ performance in physics.
Procedure for Data Collection
The Questionnaires were distributed among the sampled students with the purpose of the research been explained to the students. A hundred questionnaires were administered. The format of the questionnaire is shown in the appendix.
Method of Data Analysis
The data was analysed based on the responses from the questionnaires administered. Simple percentage (%) and chi-square (X2) statistics were used for the data analysis. These are defined by equation 2 and 3:
Simple percentage (1)
Chi-square (2)
Where f0= observed frequency, fe= expected frequency, = Summation and X2 = chi-square
A 0.05 level of significance was taken as the probability of rejecting the null hypothesis. The observed frequency was obtained from students responses to questionnaires while the expected
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frequencies are those that would be expected if the groups of categories are equal. The expected frequencies were obtained using equation 3.
(3)
RESULT
Data Analysis of Gender Distribution
Table 2 shows the gender distribution of the sampled students. Table 2. Gender Distribution
Gender No. of Respondents Percentage (%)
Male 42 42%
Female 58 58%
Total 100 100%
Table 2 indicates that 42 percent of the total respondents reflected the male population, while 58 percent of the total respondents accounted for the female population.
Analysis of Age Group
Table 3 shows the age distribution of the sampled students Table 3. Age Group
Age No. of Respondents Percentage
Below 10 0 0
10 -14 19 19%
15 -19 78 78%
20 above 3 3%
Total 100 100%
From Table 3, it is observed that 19% of the population are within the age limit of 10 -14, 78% of the respondents are within the ages of 15 -19, while 3% of the respondents are within the ages of 20 and above.
Analysis of Research Question One
The answer to the research question "what are the cognitive tools involved in the resolution of mathematical problems in physics" is given in Table 4.
Table 4. What are the Cognitive Tools Involved in Solving Mathematical Problems in Physics? Response Frequency Percentage (%)
Agreed 79 79
Disagreed 21 21
Total 100 100
79% of respondents agreed to the declaration of cognitive methods used in physics to solve mathematical problems, although 21% disagreed with the declaration.
Analysis of Research Question Two
The answer to the research question is given in Table 5: Is there any relationship between mathematics and physics?
Table 5. Is There any Relationship between Mathematics and Physics? Responses Frequency Percentage (%)
Agreed 60 60%
Disagreed 40 40%
Total 100 100%
From the 100 responses on this question, 60% of the respondents agreed that there is a relationship between mathematics and physics while 40% of the respondents disagreed on the statement.
Analysis of Research Question Three
Table 6 gives the response to the research question- to what extent does mathematical skills relate to physics learning?
Table 6. To What Extent does Mathematical Skills Relate to Physics Learning? Responses Frequency Percentage (%)
Agreed 55 55%
Disagreed 45 45%
Total 100 100%
From Table 6, 55% of the respondents agreed to the statement of the extent to which mathematical skills relates to physics learning, while 45% of the respondents disagreed to the statement.
Analysis of Research Question Four
Table 7 give the response to the research question-what kind of mathematical skills are required in studying physics?
Table 7. What Kind of Mathematical Skills are Required in Studying Physics? Responses Frequency Percentage (%)
Agreed 84 84%
Disagreed 16 16%
Total 100 100%
From the 100 responses on the statement, 84% of the respondents agreed to the statement on mathematical tools required in studying physics, while 16% disagreed to the statement.
Test of Hypothesis One
H0: There is no relevant link between studying mathematics and physics. HI: There is relevant link between studying mathematics and physics. Table 8, show the summary of chi-square computation for hypotheses one.
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Table 8. Summary of Chi-Square (X2) Computation RC 1,1 60 57.5 2.5 6.25 0.11 1,2 40 42.5 -2.5 6.25 0.15 2,1 55 57.5 -2.5 6.25 0.11 2,2 45 42.5 2.5 6.25 0.15 Total 0.52 Degree of freedom = at (df) (r-1)(c-1) At 5% level of significance = 0.05 at df (2 -1) (2 -1) Critical value = 0.46
DECISION: If the calculated value (X2) is less than the critical value, the null hypothesis is accepted otherwise the null hypothesis is reject and the alternative accepted.
Test of Hypothesis Two
H0: Effective application of mathematical knowledge do not enhance students’ performance in physics.
HI: Effective application of mathematical knowledge in physics enhance students’ performance in physics.
Table 9, show the summary of chi-square computation for hypothesis two. Table 9. Summary Table of Chi-square RC 1,1 79 39.5 39.5 1560.25 39.5 1,2 21 10.5 10.5 110.25 10.5 2,1 84 39.5 44.5 1980.25 50.13 2,2 16 10.5 5.5 30.25 2.88 Total 103.01 Degree of freedom = at (df)(r-1)(c-1) At 5% level of significance = 0.05 at df (2 -1) (2 -1) Critical value = 0.46
DECISION RULE: If the calculated value (X2) is less than the critical value, the null hypothesis is
accepted otherwise the null hypothesis is reject and the alternative accepted.
DISCUSSION
From Table 4, a greater number of the respondents agreed to the statement of the cognitive tools involved in solving problems in physics. Therefore students require the cognitive tools of expectation, thinking, knowledge, synthesis, application and remembrance of formulas, equations and laws in solving problems in physics which is consistent with the reports of (Assefa, Ohijeagbon, Negash, & Melese, 2008; Chassy & Jones, 2019; Goldstern, 1998; Murphy, 2005; Tzanakis, 2001).
In Table 5, the greater number of respondents (60%) agreed that there is a correlation between mathematics and physics. This implies that there is a relationship between physics and mathematics and agrees with the study of (Abdurarahman & Madugu, 2014; Crowe, 1985; Charles-Ogan & Okey, 2017; Tzanakis, 2001).
In Table 6, the larger number of the respondents agreed to the statement of the extent to which mathematical skills relate to physics. This implies that inadequate mathematical skills needed to solve physics problems is the cause of student’s poor performance in physics, also the traditional instruction of mathematics skills in physics do not give enough emphasis to critical steps in solving physics problems. As such, students who perform poorly in mathematics will also perform poorly in physics which is consistent with the report of (Abdurarahman & Madugu, 2014; Assefa et al., 2008; Charles-Ogan & Okey, 2017; Murphy, 2005; Onah & Ugwu, 2012).
From Table 7, since a greater proportion of the respondents agreed to the statement of the mathematical skill required in studying physics, therefore the researcher agreed that students require the mathematical skill of Computation: formulation, number bases, numbers in standard form, subtraction, division, addition, multiplication, fractions, ratio, decimals and proportion; Algebraic process skills: common factors, factorization of simple algebraic and quadratic expressions, solving equations, simultaneous equations and word problems leading to equations and variation; Geometry and mensuration skill: areas of plane shapes, volumes of solids and areas and volumes of similar figures; Tables and graph Interpretations skill: interpretation of cost, travel, tables and graphs, interpretation of tables and graphs, etc in solving problems in physics (Assefa et al., 2008; Redish, 2005; Awodun, Omotade, & Adeniyi, 2013).
Furthermore, in test of hypothesis one, at 5% level of significance, calculated value (X2) is greater than the critical value which means that there is significant relationship between the study of mathematics and physics, which is also consistent with those of (Tzanakis, 2001).
In test of hypothesis two, at 5% level of significance, the evaluated value of (X2) is more than the critical value, which means effective application of mathematical knowledge in physics enhances students’ performance in physics (Awodun, Omotade, & Adeniyi, 2013).
SUMMARY AND CONCLUSION
To this end, the study revealed that there is a significant relationship between mathematics and physics (from the research questions and hypothesis). Students performance in mathematics determine their performance in physics. Effective application of mathematics in physics enhances student’s performance in physics. As such, mathematical knowledge, skill, memorisation of formula and effective application is essential for the excellent performance of students in physics. Mathematics teachers should ensure adequate and in-depth teaching of mathematical concepts to science students. Students should be encouraged to learn how to solve problems on their own and to know the required skills.
Teachers of physics should be individuals who have a firm grip of mathematical skills and concepts to avoid having issues of students who are only good theoretically but cannot solve mathematical problems which are basic and pivotal in the performance of the students in physics. Students should also learn to visualize the mathematical relation behind every physics theory and concept. Students should practice physics calculations regularly, starting easy and gradually getting harder. It will actually take time to become good at calculations. As such, students should persevere and don’t give up too soon. Once the student can do the basics quickly and easily, the student should pick challenges; stretch his/her abilities and aim to do calculations as quickly and accurately in physics.
In conclusion, since mathematics is related to physics, effective application of mathematical knowledge is basic and essential to the performance of students’ in physics. Since the study ascertains that there is a relationship between mathematics and physics, students are encouraged to give in their best in studying mathematics towards enhancing the student’s performance in Physics.
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REFERENCES
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APPENDIX
QUESTIONNAIRE FOR SSIII STUDENTS OFFERING PHYSICS AND MATHEMATICS SECTION B
PERSONAL DATA
Name of School: ……… Sex: Male ( ) Female ( )
Age: ……….……… SECTION C
INSTRUCTION: Kindly read the following questions carefully and give only one answer to every question by ticking any of these items
Strongly Agree - SA
Agree - A
Strongly Disagree - SD
Disagree - D
