INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)
ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue X October 2025
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Programmed Instruction and Students’ Comprehension of the Concept of
Quadratic Equations in ITU Local Government Area
Edem, I. D., Abasi, A. U.
Department of Mathematics Education, Akwa Ibom State University, Ikot Akpaden
DOI: https://dx.doi.org/10.47772/IJRISS.2025.910000688
Received: 02 November 2025; Accepted: 08 November 2025; Published: 21 November 2025
ABSTRACT
This study investigated the effect of programmed instruction on secondary school students’ comprehension of
the concept of quadratic equations in Itu Local Government Area of Akwa Ibom State. The study adopted a
quasi-experimental, non-equivalent pre-test post-test control group design. A sample of 104 Senior Secondary
Two (SS2) students was drawn from two public co-educational schools using random sampling technique. The
instrument for data collection was the Quadratic Equation Comprehension Test (QECT), developed and
validated by the researchers with a reliability coefficient of 0.82 using the Kuder-Richardson formula (KR-20).
Two research questions and two null hypotheses guided the study. Data collected were analyzed using mean,
standard deviation, and independent t-test at 0.05 level of significance. Findings revealed that students taught
quadratic equations using programmed instruction achieved significantly higher comprehension scores than
those taught using the conventional method. Furthermore, there was no significant difference between the mean
comprehension scores of male and female students exposed to programmed instruction. It was concluded that
programmed instruction enhances students’ comprehension of quadratic equations irrespective of gender. It was
recommended that mathematics teachers adopt programmed instructional strategies in teaching algebraic
concepts to promote active learning, deeper understanding, and gender inclusivity in mathematics classrooms.
Keywords: Programmed Instruction, Quadratic Equations, Comprehension, Gender
INTRODUCTION
Mathematics is a science of magnitude and number as well as the science that sustains the daily practices of man.
It is the only core science subject that acts as a pivot on which national development and wealth of any nation is
created (Unodiaku, 2022). Competency in mathematics learning is vital and sustainable to every
individual’s meaningful and productive life. Mathematics learning is very important in enhancement and
sustainability of human existence because mathematics is all about finding solutions to human problems and
physical challenges. All these are indications that mathematics is useful in domestic and business deals, scientific
discoveries, technological breakthrough, problem-solving and decision making in different situations in life
(Usman &Nwoye, 2015; Unodiaku, 2017; National Council of Teachers of Mathematics (NCTM), 2018).
Mathematics is one subject that has generated interest consistently over the years as a result of its importance to
humanity. It is one of the subjects that is expected to bring about this national development. It is core subject at
all levels of education in Nigeria as such students are expected to excel in the subject. This is especially true
because the concept of Mathematics plays an important role to an individual day-to-day life and also to the nation
at large (Abasi & Ado, 2021). It is a precursor of scientific discoveries and inventions. Since 20th century,
mathematics has become the backbone of all scientific investigations and activities. This is to say that the only
route to effectively understand the modern world is through mathematics knowledge (D’Ambrosio, 2015;
Obodo, 2018).Among the many branches of mathematics that strengthen logical reasoning and problem-solving
skills, the study of quadratic equations holds a distinct place for its practical and theoretical importance.
Quadratic equations are polynomial equations of degree two, usually written in the standard form 𝑎𝑎
2
+ 𝑎𝑎 +
𝑎 = 0; they describe quadratic functions whose graphs are parabolas and whose algebraic solutions (roots) and
vertex carry geometric and analytic meaning (Smith, 2021). According to Johnson (2020), quadratics are central
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)
ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue X October 2025
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to algebra because they introduce students to nonlinearity, the relationship between algebraic expressions and
their graphs, and methods of solution such as factoring, completing the square, and the quadratic formula, which
are tools that build procedural skill and conceptual understanding. In the sciences and engineering, quadratic
relations model many everyday phenomena: the vertical position of an object under constant acceleration, the
shape of parabolic reflectors and suspension bridge cables, and simple optimization problems such as
maximizing area or profit (Davis & Lee, 2019). Mastery of quadratics therefore supports work in physics,
engineering, economics, architecture, and computer graphics, and it develops reasoning used in problem
formulation and interpretation. Because the topic links symbolic manipulation, geometry, and applied modelling,
it is a staple of secondary mathematics and a gateway to advanced study in STEM fields.
Despite its crucial role to man and the society, mathematics continues to be one of the most challenging subjects
in schools as perceived by students (Areelu, 2014; Ali & Jameel, 2016, Abasi & George, 2024). There is a
general impression that its nature is complicating, as such, students develop phobia in Mathematics that leads to
their poor achievement in the subject. Students’ dwindling achievement in Mathematics in public examinations
is so worrisome and this has led many researchers into investigating the factors that could be responsible for this
(Abasi, 2018). As reported by WAEC Chief Examiner report (2023), there has been an abysmal performance of
students in Mathematics in West African Senior School Certificate Examination (WASSCE) when compared
with other science subjects like chemistry, physics and biology.
Undoubtedly, many aspects influence students’ fear, lack of understanding and the resulting poor performances,
for example, the attitude of mathematics teachers towards students, the teaching strategies adopted by the teacher
and the attitudes and beliefs towards mathematics that are transmitted to them (Abasi & George, 2025;
Babayemi, Akpan and Abasi, 2023). These factors, very possibly influence inadequate learning of mathematics
and poor achievement in the subject (Cosgaya-Barrera & Castro-Villagrán, 2019). In addition, many researchers
are of the opinion that, problems associated with poor performance are due to factors such as poor method of
instruction/teaching strategies, lack of adequate qualified and experienced mathematics teachers and lack of
laboratory equipment among others are major recurring problems of teaching mathematics in secondary schools
(Sani & Salahudeen, 2016; Malik, 2017; Sharma, Fonolahi, Bali & Narayan, 2018).
Furthermore,thereisgreatconcernthatthelowacademicachievementofstudents is more prevalent in secondary
school settings where there is continuous use of the conventional lecture method by teachers at this level. This
system of teaching calls for the reforming of methods of teaching and application of innovative instructional
materials in teaching of Mathematics in order to make it more learner-centered and enhance successful
interaction among learners (Adesokan, 2023). To salvage the challenges of students’ poor achievement in
Mathematics there need for Mathematics teachers to employ innovative teaching strategies for effective teaching
and learning. Onose (2007) stated that the teaching and learning of the subject matter requires the discovery of
innovations that will promote knowledge retention, which in turn enhances better achievement. In the words of
Palin and Lassa in Onose (2007), the teaching of sciences should involve activities that give room for students
to think or reason about what they are doing in order to look for relationships, which may enlarge and build a
store of scientific techniques.
Programmed instruction is an strategy of presenting new subject matters to students in graded sequence of
controlled steps. Students work through the programmed material by themselves at their own pace and after each
step their comprehension is tested by answering test questions or filling in a diagram. Progression to the next
step in the instructional sequence is solely dependent on whether the students satisfactorily pass the test,
otherwise, that step is repeated (Ado & Abasi, 2021). Programmed learning strategy stems from the science of
behaviorology. The science addresses the interactive relation between behaviour and the milieu in which it
occurs. The typical educator assumes that if materials are well sequenced and well presented, the instructional
job has been done, and that when a student fails to learn, then the instructional model holds the student at fault.
Programmed instruction proposes just the opposite: If the student does not learn, then the instructional materials
need to be revised. But more than reworking of the materials is involved.
Programmed learning addresses the controls over the teacher as well as those over the student. The instructional
setting must be designed so that the teacher is also shaped to take the right actions. Programmed learning consists
of the teacher coming under control of the interaction of student behaviour with specific features of the
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)
ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue X October 2025
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instructional setting. The cybernature of programmed learning distinguishes it from other instructional
technologies. The student interacts with materials designed by an instructional designer, and the student's
success, or failure, at each step of the instructional process shapes the teacher's revision of materials or design
of future ones. The design effort is guided by the framework of the science combined with the effects of prior
engineering efforts. Programmed learning is believed to go a long way to help achieve the global aim of
Mathematics and science education in general, which is to enable learners acquire knowledge, skills and attitudes
that would be relevant to their future livelihoods.
Another issue that has continued to attract attention in educational research as a significant factor influencing
students’ learning outcomes, attitudes, and responses to different instructional strategies is gender. Gender could
be seen as all range of physical, biological, mental and behavioural characteristics which are naturally embedded
on individual and are used to make clarifications and distinctions between females and males (Aransi, 2019). It
may be associated with being masculine or feminine, including the construction of identities, expectations,
behaviours and power relationships derived from social interactions (Ambe-Uva, Iwuchukwu &Jibrin, 2018).
Gender issues could be linked with students’ academic performance in subjects since both males and females are
assumed to differ and as such their academic performances might as well differ. Some studies have shown that
there are distinguishing differences in the cognitive, affective, and psychomotor skill achievement of students
with respect to gender (Olowe, 2015), whereas some others provided reports that there are no distinguishing
differences in academic performance of students as a result of gender (Olaoye & Adu, 2015).In view of these
contrasting reports, this study sought to investigate the effect of programmed instruction on students’
comprehension of the concept of quadratic equations, considering gender as a moderator variable.
Statement of the Problem
Mathematics remains one of the most challenging subjects in the Nigerian secondary school curriculum, with
persistent evidence of students’ poor performance, particularly in algebraic concepts such as quadratic equations.
Despite their importance in scientific reasoning and practical problem-solving, many students still find it difficult
to comprehend the principles and applications of quadratic equations, resulting in low achievement and negative
attitudes toward mathematics. Traditional teaching methods, often dominated by verbal explanations and
teacher-centred delivery, have not effectively addressed these difficulties, as students continue to struggle with
abstract reasoning and comprehension. In response to this, programmed instruction, being a learner-centred
approach that presents content in a logical sequence with immediate feedback, has been advocated for improving
understanding and motivation. However, its effectiveness in enhancing students’ comprehension of quadratic
equations remains insufficiently explored, particularly within Itu Local Government Area. Also, gender
differences in learning outcomes continue to generate concern in mathematics education, raising the need to
determine whether male and female students benefit equally from programmed instructional strategies. This
study, therefore, sought to investigate the effect of programmed instruction on students’ comprehension of
quadratic equations in Itu Local Government Area, with gender as a moderating variable.
Purpose of the Study
The main purpose of this study was to investigate the effect of programmed instruction on students’
comprehension of the concept of quadratic equations in Itu Local Government Area of Akwa Ibom State. In
specific terms, the study sought to:
1. Compare students’ comprehension of the concept of quadratic equations when taught using programmed
instruction and conventionally.
2. Compare male and female students’ comprehension of the concept of quadratic equations when taught
using programmed instruction.
Research Questions
The following research questions were posed to give direction to the study:
1. What is the difference in the mean comprehension score of students taught the concept of quadratic
equations using programmed instruction and conventional methods?
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)
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2. What is the difference in the mean comprehension score of male and female students taught the concept
of quadratic equations using programmed instruction?
Hypotheses
The following null hypotheses were formulated to guide the study:
1. There is no significant difference in the mean comprehension score of students taught the concept of
quadratic equations using programmed instruction and conventional methods.
2. There is no significant difference in the mean comprehension score of male and female students taught
the concept of quadratic equations using programmed instruction.
METHOD
The study employed quasi-experimental non-equivalent group design. Area of study was Itu Local Government
Area of Akwa Ibom State. The population of this study comprised all the public Senior Secondary two students
in Itu Local Government Area for the 2024/2025 academic session numbering 2,728 from 8 schools. A sample
size of 104 SS2 students was involved in the study. Random sampling technique was used to sample two public
co-educational schools. Two intact classes were randomly sampled from each of the schools which were assigned
to the experimental group and control group respectively. The two groups were exposed to pre-test and post-test
respectively. The instrument for data collection was tagged Quadratic Equation Comprehension Test (QECT).
The QECT consisted of 30 multiple choice questions which have four options A, B, C, and D, scored one mark
each with a total of 30 marks. The test was developed by the researcher from the specified content “quadratic
equations” and also from past questions using Table of specification. The objectives of the topics served as a
guide in developing the questions. The QECT was validated and trial tested with the reliability index of 0.82
using Kuder-Richardson’s(KR-20) formula. After obtaining approval from the principals of the selected schools,
the researcher first administered the pre-test to the students in the two schools and obtained their scores to
ascertain their pre-entry ability before treatment. After the instructional process, post-test was administered to
the students to assess their comprehension after treatment. On completion, the instruments were collected and
appropriately parcelled for easy identification during scoring and collation.
RESULTS
The data generated from the retrieved instruments were analysed using mean and standard deviation to answer
the research questions and independent t-test statistics to test the hypotheses at 0.05 level of significance.
Answering the Research Questions
Research question one: What is the difference in the mean comprehension score of students taught the concept
of quadratic equations using programmed instruction and conventional methods?
Table 1:Mean and standard deviation of students’ pretest posttest comprehension scores on treatment
Methods
n
Pretest
Posttest
Mean Gain
Mean
SD
Mean
SD
Programmed Instruction
53
4.4
1.4
14.3
2.1
9.9
Conventional Method
51
3.8
1.4
10.1
1.7
6.3
Mean difference
0.6
4.2
3.6
Table 1 revealed that the mean gain comprehension scores (9.9) of students taught the concept of quadratic
equations using programmed instruction is greater than the mean gain comprehension scores (6.3) of those taught
using conventional teaching method with a mean difference of (3.6) between the two groups. This implies that
students taught using programmed instruction benefited more and scored higher than those that were taught using
conventional teaching method.
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)
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Research question two: What is the difference in the mean comprehension score of male and female students
taught the concept of quadratic equations using programmed instruction?
Table 2:Mean and standard deviation of male and female students’ pretest posttest comprehension scores on
treatment
Methods
Gender
n
Pretest
Posttest
Mean Gain
Mean
SD
Mean
SD
Male
23
3.5
1.1
14.2
2.3
10.7
Programmed Instruction
Female
30
4.0
1.6
14.5
1.9
10.5
As shown in Table 2, the mean gain comprehension scores (10.7) (10.5) of male and female students taught the
concept of quadratic equations using programmed instruction is approximately equal. This implies that both male
and female students that were exposed to the use of programmed instruction in teaching and learning quadratic
equations benefitted equally thereby performing at the same pace. Programmed learning strategy has shown to
be a gender friendly instructional strategy thus enhancing both male and female students’ comprehension
equally.
Testing the Hypotheses
Hypothesis one: There is no significant difference in the mean comprehension score of students taught the
concept of quadratic equations using programmed instruction and conventional methods.
Table 3: Independent t-test result on students’ mean comprehension scores in mathematics based on methods of
teaching (N = 104)
Methods
N
Mean
SD
df
Sig.
p-cal.
Programmed Instruction
53
14.3
2.1
102
.05
.000
S
Conventional Method
51
10.1
1.7
s = Significant at .05 level of significance
Analysis of independent t-test results in Table 3 revealed that there is a significant difference between the mean
comprehension score of students in taught the concept of quadratic equations using programmed instruction and
conventional method in favor of those taught using programmed instruction [p-cal = .000 @ p<0.05]. The null
hypothesis is therefore rejected. This implies that programmed instruction significantly enhanced students’
comprehension of the concept of quadratic equations when compared with conventional teaching method. Thus,
the mean difference earlier observed in Table 1 is statistically significant at .05 probability level.
Hypothesis two: There is no significant difference in the mean comprehension score of male and female students
taught the concept of quadratic equations using programmed instruction.
Table 4: Independent t-test result on male and female students’ mean comprehension scores in mathematics based
on method of teaching (N = 53)
Method
Gender
N
Mean
SD
df
Sig.
p-cal.
Male
23
13.6
3.2
Programmed Instruction
51
.05
.963
NS
Female
30
12.1
3.2
NS = Not Significant at .05 level of significance
Analysis of t-test results as shown in Table 4 revealed that there is no significant difference between the mean
comprehension scores of male and female students taught the concept of quadratic equations using programmed
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instruction [p-cal = .963 @ p<0.05]. The null hypothesis is therefore retained. This implies that there is no
significant difference in the mean scores of male and female students’ comprehension of concept of quadratic
equations when taught using programmed instruction. Hence, both gender benefited from the methods of
teaching.
DISCUSSION OF FINDINGS
The findings of this study in testing hypothesis one revealed a significant difference between the mean
comprehension scores of students in taught the concept of quadratic equations using programmed instruction
and those taught using conventional method of teaching. Hence, students taught using programmed instruction
had higher comprehension scores than their counterparts taught using the conventional teaching method. This
finding agrees with Ado and Abasi (2021) who found out in their study that students have higher interest and
performance in mathematics when taught using programmed instruction than their counterparts when taught
using conventional method of teaching. Also in support of this findings, Kurbanogbu, Taskesenligil and Sozbilir
(2018) reported that students become overwhelmed and satisfied when programmed instruction is employed in
teaching. The likely explanation for this outcome may be connected to the fact that programmed instruction
helped the learners to possess a meaningful in-depth knowledge of the content area when compared to the
conventional teaching method.
The findings of this study in testing hypothesis two revealed that there was no statistically significant difference
between male and female students’ comprehension of the concept of quadratic equations when taught using
programmed instruction. This implies that, programmed instruction is superior to the conventional method
irrespective of gender in fostering students’ comprehension. This finding also agrees with Igwe and Okoye
(2022) who found out in their study that there was no significant difference in the academic performance of male
and female students taught science using programmed instructional method.
CONCLUSION
This study revealed that using programmed instruction in teaching and learning the concept of quadratic equation
provides a better insight and deep comprehension for the students. The application of this method of teaching
has enhanced students’ comprehension in learning. It is also proved from the findings of this study that the use
of programmed instruction is more effective in facilitating and improving male and female students’
comprehension in mathematics than the conventional teaching method. By implication, this affirmed that
students’ comprehension in mathematical concepts depend on the method of instruction. Thus, programmed
instruction is significantly a very useful instructional method for increased meaningful learning and higher
comprehension for students regardless of their gender. It can be admitted that teachers’ frequent use of this
method will definitely enhance teaching output to a great extent.
RECOMMENDATIONS
Based on the findings of this study, the following recommendations are made:
1. Mathematics teachers should develop and use programmed instruction in teaching in senior secondary
schools since it has proven to be a viable option in enhancing students’ comprehension in mathematics
and it is not gender-biased.
2. Ministry of Education and professional bodies such as Teacher Registration Council of Nigeria (TRCN)
and Science Teachers Association of Nigeria (STAN) should organize conferences and workshops where
the use programmed instruction will be exposed to teachers for better application and to meet up with
the challenges and demands of the new curriculum.
REFERENCES
1. Abasi, A. U. (2018). Teachers’ instructional strategies and upper basic students’ academic achievement
in mathematics in Essien Udim Local Government Area of Akwa Ibom State. International Journal of
Educational Benchmark, 9(3) 76-83.
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)
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2. Abasi, A. U. & Ado, I. B. (2021). Effect of problem-solving method on secondary school students’
academic achievement and attitude in Mathematics in Uyo Local Government Area of Akwa Ibom State.
The Journal of Mathematical Association of Nigeria, 46(1) 342-352.
3. Abasi, A. U. & George, I (2025). Game-based instructional approach and mathematics students’ interest
and academic performance in Oruk Anam Local Government Area, Akwa Ibom State. International
Journal of Science Education, 6(1), 50-58.
4. Abasi, A. U., & George, I. G. (2025). Ethnomathematics and students’ interest, attitude and academic
performance in mathematics in Mkpat Enin Local Government Area, Akwa Ibom State, Nigeria.
International Journal of Research and Innovation in Social Science (IJRISS), IX(IIIS), 2430–
2444. https://doi.org/10.47772/IJRISS.2025.903SEDU0189
5. Adesokan, R. T. (2023). Investigating the effectiveness of geoboard manipulatives on JSS 1 students’
performance in plane geometry. A study of Katsina Metropolis. Sapientia Foundation Journal of
Education, Sciences and Gender Studies (SFJESGS), 5(4), 273 – 280.
6. Ado, I. B. & Abasi, A. U. (2021). Programmed-based instructional method and students’ academic
performance and retention in mathematics in Uyo Local Government Area of Akwa Ibom
State. International Journal of Education and Ethical Issues in Research, 2(1), 76-87.
7. Ali, H. H. & Jameel, H. T. (2016). Causes of poor performance in mathematics from teachers, parents
and student’s perspective. American Scientific Research Journal of Engineering Technology and Science,
15(1), 122–36.
8. Ambe-Uva, T. N., Iwuchukwu, O. & Jibrin, L. J. (2018). Gender Analysis in National Open University
of Nigeria (NOUN): Implications and policy issues in bridging the divide. Journal of Applied Sciences
Research, 4(7), 814-825.
9. Aransi, W.O. (2019). Psychosocial and economic variables as correlates of adults' participation into
sandwich educational programs in Osun State, Nigeria. Journal of Education and e-Learning Research,
6(3), 107-115.
10. Areelu, F. (2014). Effects of tiered lesson and group personalization instructional on senior secondary
school students’ interest and achievement in Mathematics in Lagos State. Unpublished Ph.D. Thesis,
University of Ibadan, Ibadan.
11. Babayemi, J. O., Akpan, I. F. & Abasi, A. U. (2023). Trainers’ attitude versus practices: a must for
revitalizing pre-service teacher education in Nigeria. Humanities, Management, Arts, Education & the
Social Sciences Journal, 11(1), 127-142.
12. Cosgaya-Barrera, B. R. & Castro-Villagrán, A. (2019). Creenciassobreel aprendizaje de las
matemáticasen estudiantes de ingeniería. Conciencia Tecnológica, (57), 1-15.
13. D’Ambrosio, V. (2015). Ethnomathematics, what it might be? International study Group on
ethnomathematics.News letter 3 (1) sept.
14. Davis, P. & Lee, H. (2019). Work applications of quadratic functions: Maximization and modeling. In
Intermediate Algebra for Science, Technology, Engineering and Mathematics (pp. 112-130).
LibreTexts. https://math.libretexts.org/Courses/…/Quadratic_Equations_and_Applications
15. Igwe, I. O. & Okoye, N. L. (2022). Effects of programmed instructional package on secondary school
students’ achievement in electrolysis. African Journal of Health & Environmental Sciences,
Entrepreneurship, Engineering & Agriculture, 8(1), 38–50.
16. Johnson, A. (2020). Why quadratics? Understanding variable rates of change. Oxford Education Blog.
https://educationblog.oup.com/secondary/maths/why-quadratics
17. Malik, N. A. (2017). Perceptions of teachers and pupils on use of Bridge IT mobile application for
Teaching Mathematics in Lagos State, Nigeria (Unpublished doctoral dissertation). University of Ilorin,
Ilorin, Nigeria.
18. NCTM, (2018). www.pat-thompson.net
19. Obodo, G.C. (2018). Mathematics: A language for computers in the new millennium implication for
Nigeria. Proceeding of Annual Conference of Mathematics Association of Nigeria.
20. Olaoye, O. & Adu, E. (2015). Problem-based learning strategies and gender as determinant of grade 9
students’ academic achievement in Algebra. International Journal of Education Science, 8(3), 485-492.
21. Olowe, T. T. (2015). Effect of computer animation and instructional models on the performance of
students in senior secondary school biology in Minna Metropolis. Unpublished Ph.D Thesis. University
of Ilorin.
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)
ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue X October 2025
Page 8469
www.rsisinternational.org
22. Onose, G. M. (2007). Problems of teaching mathematics for technological advancement in Nigerian
secondary schools. Journal of Teachers Perspective, 1(2), 197-204
23. West African Examinations Council (WAEC) (2023).Chief Examiner Reports, Nigeria
24. Sani, S. & Salahudeen, B. (2016). Effects of Geoboard and geographical globe on senior secondary
school students’ performance in mathematics in Kaduna state. ATBU Journal of Science, Technology &
Education, 4(1), 140-148.
25. Sharma, B., Fonolahi, A., Bali, A. & Narayan, S. (2018). The online mathematics diagnostic tool for
transformative learning in the pacific. In: A Singh, S Raghunathan, E Robeck, and B Sharma, editors.
Cases on smart learning environments. Hershey, Pennsylvania: IGI Global (2018). p. 63–80.
26. Smith, M. (2021). Defining the quadratic equation: From algebra to real-life modelling. Textbook
Mathematics Tutorials. https://testbook.com/maths/quadratic-equation
27. Unodiaku S. S. (2022). Effect of ethno-mathematics teaching materials on students’ achievement in
mathematics in Enugu State. Journal of Education and Practice, 4(23), 57-61.
28. Unodiaku, S. S. (2017). Development and validation of simultaneous linear equations assessment
instrument among junior secondary school Nigerian Students. International Journal of Education,
Science, Mathematics and Environmental Studies (IJESMES), 3(1), 49-64.
29. Usman, K. O. & Nwoye, M. N. (2015). Effect of graphical – symbol approach on the pupils’ achievement
in ratio at upper primary school level in Nsukka Central Local Government Area. Journal of
Mathematical Centre, Abuja, 1(1), 123 – 132.
