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American Journal of  
Life Science and Innovation (AJLSI)

Exploring the Global Pupil’s Academic Performance in Linear Programming: A Glimpse 
on Literature Review

Mwambazi Chrispine Mulenga1*, Mubanga Lombe2, Francis Simui3 

Volume 2 Issue 2, Year 2023
ISSN: 2833-1397 (Online)

DOI: https://doi.org/10.54536/ajlsi.v2i2.1791
https://journals.e-palli.com/home/index.php/ajlsi

Article Information ABSTRACT

Received: June 20, 2023

Accepted: August 17, 2023

Published: August 29, 2023

The main objective of  this essay was to conduct an exhaustive literature review of  the pupil’s 
performance in linear programming. The study sample had 15 participants comprising 8 
females and 7 males purposively sampled. The study concerning students’ lived experiences 
of  their academic success in linear programming was conducted using a hermeneutics 
phenomenology design. The study was qualitative as the details were descriptive, led by the 
specified methodology, and used qualitative research methodologies and procedures. This is 
a result of  its stringent compliance standards for a variety of  processes, including sampling 
techniques and data analysis methodologies (Mulenga, 2015). The intent was to describe 
the pupil’s academic performance, explore pupils’ linear programming-related disablers, and 
explore techniques for enhancing pupils’ academic performance. The study was only carried 
out for six months. In light of  this, it has been noted that the performance of  pupils in 
linear programming is subpar as a result of  a variety of  complications, including lack of  
teaching and learning resources, incompetent teachers, pedagogy they use, pupils’ attitude, 
mathematical language, time and the usage of  subpar textbooks, among others. As a result, 
the existing difficulties have even led to pupils’ low morale, which is prevalent worldwide, 
especially in developing nations. In order to address the issue of  the topic being taught 
by incompetent teachers, it is advised that the government train and recruit qualified and 
competent mathematics teachers to teach the subject at senior secondary. Furthermore, 
additional time should be allotted to the challenging topics through collaboration between 
the MoGE and the Curriculum Development Centre (CDC). In order to support pedagogies 
among mathematics teachers, it is also advised that the MoGE strengthen Continuous 
Professional Development (CPD) initiatives in schools. Besides, the MoGE should receive 
more funding in order to purchase instructional materials for different schools across the 
nation. Teachers of  mathematics are commended to use a variety of  approaches, tactics, and 
strategies in order to enhance how they present the lesson they are teaching.

Keywords

Curriculum Development 
Centre, Emergence, Secondary 
School, Continuous Professional 
Development (CPD), Linear 
Programming, Academic 
Performance

INTRODUCTION 
The literature review in this article was based on 
the academic performance of  pupils learning linear 
programming, disablers leading to such performance, 
and mitigation to attain better results. The research 
design was based on a hermeneutic phenomenological 
study of  lived experiences of  former grade twelve pupils 
in mathematics, specifically linear programming. In 
using the hermeneutic approach, researchers accept the 
difficulty of  bracketing personal viewpoints as advanced 
through the transcendental phenomenology of  Edmund 
Husserl (Simui, (2018). The researchers’ decision to 
focus on grade twelve students’ performance in linear 
programming questions and related questions was 
justified based on the Examination Council of  Zambia’s 
examination analysis report from 2015 to 2016 question 
by question performance analysis in mathematics at the 
national level (ECZ 2015, ECZ 2016).
It is evidenced that pupils hardly perform well in linear 
programming and related problems during national 
examinations (ECZ, 2014, 2015, 2016). According to the 
Examination Council of  Zambia’s general performance 
reports, it has been highlighted that linear programming 
was one of  the topics in which learners have continued 

to underperform during examinations at the ordinary 
mathematics level (ECZ, 2012-2017).

Significance of  the Study
This study may be pertinent to those who create 
educational policy, especially those in the Ministry of  
General Education, subsequently it may help them 
implement strategies to lessen the challenges that pupils 
face when learning linear programming and to raise pupils’ 
academic achievement. Furthermore, it is anticipated 
that this work will help teachers of  mathematics better 
understand the challenges pupils face and develop 
strategies that will enhance their ability to teach. The 
review may also be pertinent to other scholars who 
wish to carry out additional studies in the area of  linear 
programming. Also, it will advance the comprehension of  
linear programming.

LITERATURE REVIEW 
Emergence of  Linear Programming
According to Luneta (2022), the history of  linear 
programming can be traced back to George Dantzig 
who developed it in 1947. He was studying proposed 
training and logistics for the United States military 

1 Munkuye Secondary School, Nkeyema, Zambia
2 Institute of  Distance Education, University of  Zambia, Lusaka, Zambia
* Corresponding author’s e-mail: mwambazicm@gmail.com



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training program, as a mathematical adviser to the US 
Air Force Controller in the Pentagon. His colleagues 
at The Pentagon, Hitchcock, and Wood, asked him to 
find a method that would rapidly compute a time-staged 
operation, training, and logistical supply program. 
Dantzig was motivated by the work of  Leontief, who 
developed the simplex method for tackling linear 
programming problems and offered a sizable but 
straightforward matrix structure known as the “inter-
industry input-output model” of  the American Economy 
(Evans, J.R. 2020). In the model, there was a one-to-one 
correspondence between the production processes and 
the items being produced by these processes. According 
to the study by Sun (2016), Dantzig also used ideas from 
a paper by UNEB (2020) on game theory together with 
his ideas on steady economic growth to formulate a 
highly dynamic model that could change over time. He 
realised that The Air Force needed a model with alternate 
activities which had to be computable; hence, he invented 
the simplex method. The simplex method can be 
described as dynamic linear programming with a staircase 
matrix structure. By repeatedly shifting the vertex of  the 
feasible region set to a nearby vertex with a lower, the 
approach creates a series of  feasible iterations. If  a better 
option cannot be found, the present optimal termination 
will take place. A realistic planning tool for huge complex 
systems is the simplex method (Boucher, C., 2023).

Pupil’s Academic Performance in Linear Programming
Low academic performance of  pupils worldwide in linear 
programming is a major concern. A number of  studies 
on the Pupil in secondary school have been conducted 
including European countries, where pupils are very 
successful academically (OECD. PISA, 2018). Mainly, the 
Pupil’s Academic Performance has been greatly affected 
by the size and location of  the school, infrastructure, and 
enrolment rates. Each pupil’s academic success is said to 
be greatly influenced by the availability of  resources as 
well as the provision of  teaching and learning aids. The 
aforementioned problems have a negative impact on 
pupils’ academic progress in developing countries like 
Zambia.

Pupil Comprehension Experiences with Linear 
Programming
The Pupil Comprehension Experiences with Linear 
Programming at various secondary school levels, as 
well as contexts, are worrying. Two levels with varying 
contexts are considered namely: Developed and Sub-
Saharan Africa contexts for easy comparative analysis of  
pupils in the current review. To this effect, this segment 
provides a context in which the current study is located as 
a way to contribute to the discourse on the performance 
of  students in linear programming progressions at the 
secondary level.

The Meaning of  Linear Programming 
According to Nakhanu (2015), linear programming is a 

mathematical technique for finding optimal solutions to 
problems that can be expressed using linear equations 
and inequalities. The term “linear programming” has the 
words programming and linear in it. The word “linear” 
describes a straight line that arises from the conditions 
between an independent variable (x) and a dependent 
variable (y). Programming is used to describe the 
methodical decision-making process in this manner. The 
mathematical equations for the relationships are y = ax + 
b, where a and b are constants. 
Applied mathematics (operational research) includes 
linear programming, where the mathematical modelling 
is done using linear equations or linear inequalities, which 
includes designing programs to solve various daily life 
problems (Idris, Sulfiaty,2015). 
Meanwhile, according to Zhe Bao, et al., (2020), linear 
programming is a program that can be applied to solve 
the optimization program.
The objective function and constraint equations are 
deterministic, and the Simplex approach can only be 
used to solve situations where there is no uncertainty 
in the variables or coefficients (Mohammed, A.R. and 
Kassem, S.S. 2020). Industries, including business, 
economics, telecommunications, manufacturing, 
transportation, agriculture, and the military, have adopted 
linear programming. In a real-world problem, it can 
be represented accurately by the mathematical linear 
equations, the method that can help to find the best 
solution to the problem. 

Global Performance of  Pupils in Linear Programming 
There are many factors that contribute to the good or 
poor performance of  novices in linear programming. 
The poor performance is due to teachers not being 
interested in teaching on topics that are contentious 
like linear programming, teachers’ incapacity to provide 
students with the support they require, to use different 
teaching methods during linear programming lessons, 
and substandard instructional materials coupled with 
time allocated. There is a belief  by some teachers of  
mathematics that linear programming could not be 
taught at the beginning of  learning and within the 
timetabled time. The importance of  promoting students’ 
preparation for learning activities, however, makes this the 
wrong move (Puteri, 2018). Thus, the teaching of  linear 
programming requires proper planning to ensure proper 
time management. In doing so, the pupils will have strong 
motivation and encouragement to absorb learning, so 
that it can attract pupils’ attention (Ahn, 2014). Similarly, 
the study conducted by (PISA, (2018), examined the 
pupil and teachers views on linear programming. pupils’ 
linear programming abilities were lacking as pupils were 
being taught in haste without taking into consideration 
the slow- learners. Additionally, when teaching the topic 
of  linear programming, secondary school teachers 
paid little attention to it due to limitations in terms of  
pedagogical content knowledge, consequently leading to 
poor performance.



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This collaborates well with the study by Lampert (2010), 
who asserted that a poor result in linear programming 
is resulting from the content provided to teachers 
throughout programs for teacher education, the 
methodologies used by some teachers, and the attitudes 
of  the pupils and teachers towards the topic.
Equally, the study by Ball and McDiarmid (2010), shows 
that teachers struggle with linear programming because 
they are given content from colleges and other academic 
institutions that bear little or no similarity to real-world 
classroom situations. 
In line with the aforementioned statement, the study by 
Stevenson, et al., (2020) reveals that the primary concern 
of  the American educational system today is that of  
raising the mathematics levels of  its pupils. However, 
cross-national studies reveal that American school 
children routinely underperform Chinese, Japanese, and 
Korean pupils in mathematics because of  discrepancies 
that become apparent due to cultural and familial 
influences. This means that culture contributes to pupils’ 
poor academic performance in mathematics where linear 
programming is a part.
Further, the study by Fan, W.; Williams, C. (2018), 
revealed that parenting and family factors contribute 
to American students’ poor performance than Asian 
pupils due to lack of  motivation, curriculum differences, 
parental involvement, time use, and pupils’ attitudes. 
Particularly, traditional Chinese views of  teaching and 
parenting contribute to pupils’ academic success (Ho, 
1994). Pupils from homes whose parents cannot afford 
to support their children tend to do bad at school. 
Pupils who get adequate learning resources and other 
essential requirements from parents are motivated. 
Failure to which pupil Performance who are demotivated 
will always perform poorly. The study in Indonesia by 
Kusmaryano (2014), revealed that pupils perform poorly 
as they are expected to memorise the content without 
fully comprehending the concept thereby failing to use 
it in practical situations. This revelation collaborated 
with Khafidah, W., et al., (2020) who postulated that the 
teacher-centred method compelled pupils to memorise 
the concept without fully understanding it. This was due 
to the failure of  the teacher to come up with activities that 
promote critical thinking among pupils, hence resorting 
to memorization of  material presented by the teacher. 
This is consistent with a study by Lasco and Raganas 
(2016), who discovered that pupil interactions in the 
classroom, teaching methods, and resources all had an 
impact on pupils’ performance and ability to learn linear 
programming. It has been proven that getting pupils 
involved in collaborative efforts can help them develop 
their mathematics abilities, which will help them do better 
in school.
In Indonesia, the study by Kumar & Vakkil, (2020), 
argues that good quality education is needed to achieve 
curriculum goals. The Educational Curriculum System 
strives to show that pupils have mastered a set of  skills 
that have been determined based on the unique qualities 

and characteristics of  the material from the disciplines 
that meet the Minimum Completeness. Pupils’ successes 
can take the shape of  abilities they acquire through 
teaching and learning activities. The other studies in 
Indonesia by Suyitno, (2015) using Newman procedures 
to analyse errors pupils make in linear programming 
reveal that pupils make mistakes when solving 
mathematical problems due to a lack of  reading skills, 
lack of  understanding of  questions, transformation, and 
process skills. The learning process depends on pupils’ 
understanding and mastery of  the material. 
A barrier that may prevent a pupil from performing 
better is when they can read the question but cannot 
understand the statements included inside. Due to 
their incapacity to understand mathematical concepts 
and develop innovative perspectives, pupils do badly 
academically and provide wrong answers. Pupils make 
transformation errors. Transformation errors occur when 
pupils are unable to identify the pertinent mathematical 
operations. Lack of  comprehension of  some concepts in 
linear programming contributes to a lacklustre academic 
record (Suyitno,2015). 
This coincides with a study by Herold (2014) who 
proposed that processing skill errors happen when 
students are unable to do mathematical operations 
correctly due to erroneous mathematical calculations 
and are unable to apply problem-solving techniques. 
The inability to comprehend and explain mathematical 
concepts in writing, locate the points where two axes 
cross, or resolve various types of  inequality are frequently 
to blame for students’ poor results in linear programming.
Similarly, a lack of  pupils’ ability to use mathematical 
language in linear programming affects pupils’ academic 
performance. This claim is supported by a study by 
Sukoriyanto (2021) that looked at how pupils’ use of  
mathematical language hinders their ability to comprehend 
the coordinates of  the corner points thereby causing them 
to use the incorrect determinant objective functions, 
which automatically produces the wrong optimum value. 
The learning approach is a crucial factor that must be 
considered in the teaching and learning process because 
the learning approach is a means to realising teaching 
goals. The more thoroughly the learning objectives 
are realised and the educational goals are achieved, the 
better the learning approach chosen. Facts are frequently 
ignored in favour of  knowledge and procedural learning 
(Olusegun S.,2015). By examining the facts, pupils truly 
gain a complete comprehension of  the problem, assisting 
them in learning and achieving the learning objectives.
According to Amir, Z. (2015), the terms in mathematical 
language can be defined carefully, clearly, and accurately. 
The process of  presenting mathematical concepts while 
developing concepts and understanding is known as 
mathematical communication. Abdullah (2018), did a 
similar study on the resources and teaching strategies 
utilised by teachers in Asia. The purpose of  the research 
was to assess the efficacy of  the study materials and 
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using ineffective teaching strategies and educational 
materials, which made it difficult for pupils to comprehend 
connected ideas and the core of  linear programming. The 
study also discovered that students did not think highly 
of  linear programming. 
Mariano Luque, Sandra González-Gallardo, and Ana B. 
Ruiz’s study (2019) used interval multi-objective linear 
programming to evaluate pupils in Finland and Spain. 
According to the study, the pupils’ subpar academic 
performance was caused by the teachers’ unstable 
methodological methods and the learning environment 
for the students (PISA, 2018). Pupils’ academic success 
in linear programming was negatively impacted by 
inadequate time organisation, insufficient lesson planning, 
and ineffective teaching and learning strategies.
This claim was corroborated by Willis & Judy, 
(2010), whose study on guide for learning and to love 
mathematics: teaching methods, pupils’ attitude and get 
results postulated that learners usually have a difficult 
perception of  linear programming as a topic and this 
affects their performance. The study in the Netherlands 
by Phakeng, M. S., N. Planas, A. Bose, and E. Njurai. 
(2018), on teaching and learning mathematics in 
trilingual classrooms from three different continents in 
Mathematical discourse that breaks barriers and creates 
space for marginalised learners, revealed that pupil’s 
academic performance was poor because pupils had a 
fear of  mathematics. 
This revelation was affirmed by Bell, S. et al., (2016), 
in the Republic of  Ireland, whose study revealed that 
pupil’s poor academic performance was a result of  many 
challenges pupils undergo such as social and mental. The 
study by Munawar (2014), examined how team teaching 
affected mathematical achievement among pupils in 
the eighth grade. The conceptual comprehension and 
procedural knowledge of  pupils in algebra and geometry 
were the main areas of  focus. Pupils struggled with 
graphing inequalities and had difficulties understanding 
the symbolic inequalities from the given word problems. 
They also misinterpreted the significance of  the inequality 
markings. Pupils had trouble comprehending complex 
ideas, and the worst reading-level mistakes were indications 
of  pupils’ poor knowledge of  mathematical language. 
Understanding concepts and procedural expertise is crucial 
for improving pupils’ academic performance.
The academic success of  pupils in linear programming 
is negatively impacted by their academic learning 
background. Early childhood education had a long-
term beneficial impact on academic achievement. 
According to Cortázar (2015), in his study on the long-
term impacts of  public early childhood education on 
academic achievement in Chile. However, this effect 
differed based on parental socioeconomic status, with 
middle-low socioeconomic status children benefiting the 
most. A strong educational foundation enables pupils to 
develop lifelong abilities that preserve and promote early 
entry into the educational community, aid in academic 
success, and lessen the likelihood of  academic failure. 

A comparative study conducted in China by Liu et al., 
(2015), on the predictors of  mathematics achievement 
of  migrant children in Chinese urban schools, concluded 
that among many variables, a strong education foundation 
has a strong impact on the mathematical achievement 
of  migrant children in Chinese urban schools. On the 
other hand, the study by Capraro and Joffrion (2006), 
in Liouaeddine et al., (2017) revealed difficulties students 
frequently encounter when solving equations, including 
a lack of  a symbolic understanding of  variables, no 
knowledge of  the representation of  equality, reliance on 
skills without conceptual understanding, and coefficients 
in an equation. Pupils must fill in this knowledge gap in 
order to do better in their academic work.

Developing Countries Pupils’ Academic Progress in 
Linear Programming
Pupils in Developing Countries have consistently 
performed below average in linear programming. 
According to a study by Pongsakdi (2020), the methods 
teachers employ to increase pupils’ knowledge have a 
substantial impact on how poorly pupils perform in linear 
programming. The review by UNEB (2016) revealed that 
mathematics has historically high failure rates, particularly 
in linear programming. The majority of  pupils struggle 
to respond to this question as most of  them struggle 
with this problem repeatedly; they frequently pick 
the wrong scale, forget to plot the inequalities they’ve 
constructed, name the axes improperly, neglect to specify 
integral solutions, and fail to maximise the viable region. 
Mathematics classes may also be impacted by the lack 
of  mathematics teachers in elementary and secondary 
schools. Poor academic performance is a result of  an 
unfavourable learning environment that isn’t furnished 
with enough instructional materials to support the 
teaching-learning process (Abijo, 2014). This finding is 
consistent with research by Abdullah (2014), who claimed 
that the absence of  an environment that is conducive 
to learning and furnished with sufficient educational 
resources to support the teaching-learning processes 
will result in ineffective teaching and learning, which will 
impair academic achievement. 
Distance is yet another factor that affects academic success.  
Distance might emotionally impact academic success. 
Being physically apart from a partner can cause emotional 
distress and emotions of  loneliness, grief, or anxiety. 
These emotional pressures might cause people to lose 
focus and get sidetracked from their academic goals.
Long-distance maintenance takes time and effort. It 
can be difficult to balance these duties with academic 
obligations, which puts pressure on time management 
abilities. If  not handled properly, it could lead to less 
study time and poorer academic performance.
It could be challenging to concentrate on studies or 
assignments when the thoughts and heart are on the 
distance to be travelled. This may cause frustration and 
have a detrimental effect on academic success.
Social isolation is another consequence of  distance. 



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Distance may limit social interactions and involvement in 
school activities. Having fewer social connections might 
negatively impact one’s welfare in general and subtly 
impact academic performance.
It’s important to keep in mind that long-distance travel 
frequently ends in hunger. Hunger is a factor that inhibits 
academic progress. This conclusion is consistent with 
Alordiah (2015), assertion that poor pupil performance is 
caused by a higher prevalence of  hunger in rural Tanzania 
and Nigeria. Mhiliwa (2015), discovered that long walking 
distances, exhaustion, and hunger all had a detrimental 
effect on pupils’ performance in school. This will lead 
to low performance from the pupils. In Morocco, 
the study by Liouaeddine et al., (2017), quantified that, 
several empirical studies have shown that low academic 
performance is closely correlated with the home 
environment. These studies generally tend to measure the 
home environment in terms of  Socioeconomic Status, 
which is influenced by the social class of  the family, the 
level of  parental education, and the material resources of  
the family. In agreement with this assertion Hair, et al., 
(2015), examined the link between poverty and children’s 
learning. The children from low-income households 
scored 4 to 7 points lower on standardised tests. Persistent 
low family income is associated with poorer attendance 
and low academic achievement in elementary school.

Zambian Perspective 
The Zambian pupils’ effectiveness in linear programming 
has fallen below expectations. According to the chief  
examiner report ECZ (2017), many pupils perform 
poorly because of  poor answering techniques. This is due 
to pupils not understanding the question properly as most 
teachers had not acquired the appropriate competencies 
for linear programming. Consequently, pupils are affected 
and struggle to apply the concepts of  linear programming 
to questions involving the creation and solution over time. 
This claim is supported by Koji Samuel’s (2016), whose 
study was to ascertain the difficulties encountered when 
learning. The study’s findings indicated that pupils perform 
poorly. These claims are strongly supported by the chief  
examiner’s annual reports for the mathematics section, 
which were produced by the Examinations Council 
of  Zambia (ECZ). It has been revealed that, despite 
admirable efforts, the issue has persisted. The teacher 
education curriculum has caused a decline in mathematics 
achievement. The study by Mbetwa (2016), emphasises 
that the mathematics teacher education curriculum too 
contributed to what the country is experiencing. The 
teacher’s lack of  expertise in the topic led to the pupil’s 
low efficiency in linear programming. Some teachers lack 
the expertise necessary to cover all mathematics topics 
(MOE, 2018). They do omit some topics that seem to be 
particularly difficult for them to impart to the pupils. For 
instance, certain teachers may find it challenging to teach 
linear programming, and their only option is to omit it 
from the curriculum while deceiving pupils into believing 
that the topic is not covered or that it won’t be on the test.

Disablers Affecting Academic Pupils Performance 
in Linear Programming
In their research, Mwambazi et al., (2023) revealed what 
influences pupils’ proficiency in linear programming 
globally.  Long periods of  time pupils had to spend 
travelling, dearth of  excellent teaching and learning 
resources like textbooks. Ineffective teaching strategies 
used by certain teachers have a poor impact on the final 
examinations for linear programming. According to 
Idris and Sulfiaty’s (2015) research, pupils have problems 
understanding the concept of  linear programming. 
Pupils have trouble comprehending and appreciating 
the concept because of  the prerequisite knowledge 
that must be learned, such as linear equations and 
linear inequalities. According to international research, 
American schoolchildren routinely do worse in maths 
than students in China, Japan, and Korea (Stevenson et 
al., 2020). Cultural and familial variables have a significant 
influence on the discrepancies because they can be seen 
as early as kindergarten. Parenting and family-related 
topics came up once more. According to research, 
American children perform worse than Asian pupils 
across a range of  domains, including curricular variances, 
parental involvement, time management, and teens’ 
perceptions of  their own comfort and competence in 
mathematics. The intellectual growth of  those children 
is severely hampered by traditional Chinese parenting and 
teaching techniques (Ho, 1994). An earlier analysis of  the 
literature found that students commonly have trouble 
solving linear programming issues because of  their poor 
comprehension and lack of  foundation knowledge.  
This poses a challenge and learning outcomes for the 
pupils. According to Skemp (1971), in order to properly 
study higher-order topics, pupils must have a thorough 
understanding of  the relevant lower-order concepts.
Munawar (2014) studied eighth-graders’ mathematical 
abilities in Pakistan. The main areas of  emphasis 
were students’ conceptual knowledge and procedural 
proficiency in algebra and geometry. Pupils had difficulty 
graphing inequality and failed to infer symbolic inequality 
from supplied word problems, and they misinterpreted 
the use of  inequality marks. Pupils struggled with wordy 
problems, and the worst reading-level errors were signs 
of  the pupils’ poor command of  mathematical language. 
Conceptual understanding and procedural knowledge 
are essential. Another difficulty is presented by the 
educational environment in which pupils are studying 
linear programming. This assertion is in line with research 
from Moschkovich (2018), who conducted research 
in the UK and found that students should participate 
in mathematical classroom discourse and meaningful 
written exercises, talks, or interactions when engaging in 
mathematical activities, all of  which can only occur in a 
supportive environment.  These in-class activities help 
teachers gauge how well their students have mastered the 
subjects under discussion and decide whether additional 
help may be required. Students should actively and 
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This claim is supported by Changwe and Mulenga’s (2018) 
findings, which show that most mathematics teachers lacked 
capabilities and expertise in linear programming. Similarly, 
it was discovered that the university did not offer a specific 
mathematics topic course for those pupils who intended 
to become teachers, indicating a lack of  the mathematical 
proficiency required for teaching. The revelation was 
supported by Iheanachor’s (2017) research in Lesotho on the 
effect of  teachers’ backgrounds, professional development, 
and teaching methods on pupils’ mathematics achievement 
in Lesotho, demonstrating a positive correlation between 
pupil mathematics performance and teaching methods. 
The years of  experience, and teaching methods of  teachers 
were all associated with the mathematical proficiency of  
their pupils.
According to Adino (2015), whereas a positive attitude 
is strongly correlated with success, a negative attitude 
is considerably linked to failure in all activities. It’s 
important to remember that when teaching and learning 
are interesting, entertaining, meaningful, and applicable, 
students are motivated to learn. As a result, they are eager, 
focused, attracted, and ready to absorb the information 
being offered. 
NCDC (2018) also carried out research in Uganda, 
and pupils had unfavourable opinions of  mathematics, 
particularly word problems. The eleventh graders in 
Uganda’s lower secondary schools are exposed to linear 
programming (using a graphical method). Despite this, 
the curriculum’s goal is to help them master linear 
programming. Pupils face a challenge because there isn’t 
any teaching or learning resources available for linear 
programming, leaving them without any books to use for 
their studies. Mulenga and Kabombwe (2019) bolster the 
assertion that there aren’t enough teaching and learning 
resources in Zambian schools. The current study’s findings 
therefore agree with Mwanza and Silukhuni (2020), who 
found that low student performance in the classroom was 
a result of  a variety of  factors including a lack of  suitable 
educational resources, large class numbers, unattractive 
classroom environments, and subpar desk quality. Poor 
arithmetic performance can be ascribed to a variety of  
factors, including teaching methods, student materials, 
problems with policy, and curricular changes. These factors 
collectively impact how effectively linear programming 
may be taught. Therefore, a lack of  resources is the main 
cause of  poor academic achievement. 
When teaching linear programming, pedagogy is crucial. 
According to Lee, et al., (2018), students’ ability to learn 
linear programming is influenced by the teaching approach. 
The teaching approach can either make pupils understand 
the material or not. The secondary school students’ 
conceptual understanding of  algebraic expressions and 
associated concepts, and the pedagogy used, are essential 
to their ability to learn linear programming. 
UNESCO’s (2018) report, found that teachers of  
mathematics must also be proficient in grasping the 
topic’s foundational ideas, concepts, and related abilities. 
This implies that teachers should understand how to 

inspire pupils. The perceptions and beliefs pupils bring 
to class must be taken into consideration by teachers. 
Before introducing new mathematical concepts to the 
class, the teacher must build on the information that the 
students currently have. The students shouldn’t be seen 
by the teacher as empty canvases ready to be filled with 
new knowledge.  
The difficulty of  word problems involving linear 
programming prevents pupils from understanding 
what is being taught. Pupils struggle to understand 
mathematical word problems, which impacts their 
procedural comprehension and competency. According 
to Pongsakdi et al., (2019), this is brought on by the 
academic backgrounds, prior conceptual knowledge, 
and attitudes of  the pupils toward mathematics. NCDC 
(2018) conducted a study in Uganda on the factors that 
predict s Learning Linear Programming word problems 
generally aims to improve students’ problem-solving skills, 
application of  prior algebraic conceptual knowledge, 
and comprehension of  writing models from word 
problems, as well as from real-life problems. Despite the 
learning difficulties, the goal of  the Linear Programming 
topic is to give students the necessary knowledge and 
abilities to complete advanced mathematics courses 
beyond the Uganda Certificate of  Education’s minimum 
mathematical proficiency (UCE).
The consistent reports (UNEB, 2020) on previous 
exams and candidates’ work demonstrate that students’ 
performance in mathematics, particularly at the distinction 
level, is not satisfactory. Previous examiners’ reports, 
in particular, highlight students’ subpar performance in 
word problems involving exams and also showed that 
many students had serious Linear Programming related 
deficiencies. The main difficulties that students encounter 
in Linear Programming are related to their creation of  
incorrect inequalities based on the given word problem in 
practical settings. Incorrect solutions can all result from 
incorrect models that were derived from the questions. 
As a result, these difficulties (and others) might make 
it difficult or impossible for students to build useful 
applications (Sudihartinih, E., 2019). 
Furthermore, while some pupils manage to avoid other 
learners consistently show cognitive barriers when 
responding to questions on Linear Programming. 
Factors that explain pupils’ weaknesses in learning Linear 
Programming and targeted interventions to address those 
weaknesses are conspicuously absent. UNEB (2020) 
reports a bad feeling about linear programming. However, 
a pupil’s attitude may have a direct impact on how well 
they learn and perform. Mbugua et al., (2012), showed 
that learner performance in mathematics, particularly in 
linear programming, was poor. 
The study by Koji (2016) looked into the difficulties 
faced by pupils. It was revealed that Pupils lacked the 
prerequisite knowledge necessary as well as inappropriate 
teaching strategies and techniques, which are just a few of  
the issues that have been identified. 
Another study by ECZ (2016) demonstrated that 



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understanding is necessary for learning linear 
programming. It uses mathematical symbols in its 
own vocabulary. During national exams, students had 
trouble completing the linear programming tasks that 
were required to develop a mathematical model. This is 
because mathematical models are made up of  inequalities 
that are derived from word problems (Nkhata et al., 
2018). Therefore, the ability to extract meaning from the 
word problem in order to construct the intended linear 
inequality system is necessary for the precise formation 
of  mathematical models. Nkhata et al., (2018) stressed that 
learners “should pay special attention to the expressions 
especially which change the sense of  the inequalities” 
because of  this. Such words include “at least,” “at most,” 
“not less than,” and “no more than,” to name a few. The 
inability of  learners to acquire the crucial comprehension 
skills for linear programming would mean that improving 
learners’ abilities would continue to be difficult. As a result, 
most Zambian students now consider mathematics to be 
a foreign topic that they merely need to master and pass 
in order to satisfy the criteria of  the nation’s educational 
system (Sakayombo, 2018).
In Zambia, the study by Mulenga, M. C., Lombe, M., 
& Simui, F. (2023), revealed that linear programming 
at the senior level was poorly performed due to a 
variety of  disablers due to the travel time required for 
pupils (distance), lack of  quality tools like textbooks, 
inefficient teaching methods employed by some teachers 
(pedagogy), lack of  parental support, pupils’ lack of  
prerequisite knowledge in linear programming (poor 
learning background), learning environment, pupils’ 
negative attitude, and lack of  a school library. Further, 
most of  the teachers who taught the component were not 
conversant with linear programming.

Strategies to Enhance Pupils’ Linear Programming 
Academic Performance
To help pupils do better in linear programming, teachers 
should use appropriate and efficient learning for 
conceptual and procedural understanding. González-
Gallardo, Ruiz, and Luque (2021) claim that thorough 
lesson planning with the pupil in mind can enhance 
pupils’ academic achievement. It is commonly accepted 
that for any test, they must understand the concept, 
which incorporates a related number of  concepts.
Academic success is frequently characterised by a 
thorough approach that enables pupils to quickly absorb 
subject matter, and the use of  effective teaching methods 
that encourage pupils to feel happy, connected, and 
perform well in school. A pupil’s performance in school 
is influenced by how well the teacher gets along with the 
pupils teaching they are given. Teachers should motivate 
pupils and use appropriate teaching and learning tools 
in order to foster accurate learning and a disciplined 
environment in the school learning context (Kern, M.L.; 
Waters, L.E.; Adler, A.; White, M.A. 2015). Similarly, the 
OECD’s 2019 study on how to simultaneously optimise 
for the best level of  pupil well-being found positive 

emotions, motivation, a sense of  belonging, and the 
teaching-learning environment elements that encourage 
pupils to perform well. This claim is consistent with a 
study by Ahdika, A. (2017), which stated that performance 
is enhanced by a supportive learning environment. A 
favourable learning environment increases the success of  
cognitive learning. 
Learning happens naturally when pupils engage in the 
activities and gain experience rather than just lecture 
(Fletcher, J., 2018). Andriyani, Karim, and S. Fahmi (2020) 
postulated that using an approach that is student-driven 
to instruction would help students improve their ability 
to solve issues, learn new material, build new thought 
patterns, and adopt a positive outlook. A study by 
Aizikovitsh-Udi E. and Cheng D. (2015), recommended 
that students should develop higher-order cognitive skills, 
such as critical thinking, throughout the progression of  
their education in schools.
According to Kosarenko N. N. et al. (2016), the purpose 
of  critical thinking is to actively work on understanding, 
applying, analysing, and synthesising (evaluating) 
knowledge by observing, gathering data, processing 
data by reasoning, reflecting, and expressing the results 
achieved. In light of  this, Fitria, R., Hairun, (2020), 
affirmed that still another definition of  critical thinking 
assesses fresh knowledge. If  appropriately used, critical 
thinking abilities can aid pupils in enhancing their 
academic success in linear programming. 
This is made obvious by the indicators utilised in problem 
solving, such as giving precise justifications, improving 
fundamental skills, coming to conclusions, offering 
further justifications, and developing means and tactics to 
reach findings (Paul, R., and Elder, 2012). Pradeep, M. D. 
& Aithal, S. (2015), when pupils are able to communicate 
their thoughts while solving a mathematical problem, 
academic achievement would only rise. Teachers should 
push slow learners to fulfil their maximum potential 
in comparison to their gifted counterparts for them to 
succeed academically even though they are slower than 
other pupils (Fitri R. M. et al., 2019). This is largely 
ignored by teachers. 
Since algebra provides an important basis while introducing 
algebraic topics to their pupils (Lee, Y., Capraro, R. M., 
& Capraro, M. M.,2018). However, Putranto S. and M. 
Marsigit (2018) argue that teachers should support 
sluggish students in developing their ability for critical 
thought by using the computational thinking method 
for students’ academic achievement. Pupils’ abilities can 
be enhanced through the Computational Thinking (CT) 
paradigm. The Computational Thinking (CT) method 
sharpens the minds of  pupils to become more acclimated 
to thinking in a structured, analytical, and logical manner. 
The learning process using a computational thinking 
method has its own allure because it is founded on a 
concept that seeks to address the difficulties encountered 
so that they may be resolved quickly in a constrained 
amount of  time and demand little resources, physical 
resources, and digital storage space (Painagoni K., 2018). 



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Therefore, according to Nixon, R. S., Toerien, R., &Luft, 
A. J. (2018), teachers must apply techniques and effective 
strategies to encourage pupil engagement and conceptual 
understanding. Based on the PISA (2018) dataset, this 
study focused on Spanish and Finnish pupils to examine 
the disparities in well-being that existed between these 
two populations. While Finland typically ranks in the 
top positions of  international rankings evaluating pupils, 
Spanish pupils have shown low educational performances 
in comparison with pupils from other European countries 
(González et al.,2021). 
The research by Opolot-okurut (2010), looked at the links 
between attitudes and performance of  Ugandan students. 
The study found a direct, significant, and favourable 
association between understanding mathematics and the 
adoption of  an appropriate teaching strategy. Therefore, 
pupils should adopt an optimistic mindset to enhance 
their potential to acquire concepts of  linear programming. 
Pupil’s mindset may change, which may impact their 
mathematics performance. 
The earlier empirical studies on how having the right 
mindset could improve student performance. Students 
should be motivated, excited, engaged in what they are 
studying, and enthusiastic about it (Mata, M., Monteiro, V., 
2015). Additionally, this will serve as a lens for improving 
students’ proficiency with both ordinary mathematics 
and word problems involving linear programming. 
Students’ academic progress will be improved by adopting 
techniques to teach linear programming. According to 
Juilus and Pongsakdi (2020), teaching methods are more 
effective in making sure that students understand what is 
being taught. Furthermore, according to Abreh, M. K., 
Owusu, K. A, & Amedahe, F. K. (2018), teachers should 
select instructional strategies that can improve students’ 
academic performance in all subjects taught in school, 
in both low and high grades. Dude, (2020), claims that 
using a clear and simple approach will help students learn 
more. Pupils’ performance in linear programming will be 
enhanced by learning that has a contextual focus and uses 
local resources. The contextual materials are beneficial 
for both teaching and learning. According to Damopolii 
et al., (2021), learning materials that have been updated 
using the Contextual Teaching and Learning approach 
improve student concept mastery. If  used properly, they 
can boost pupils’ academic performance. 
The primary tenet strategy is the development of  
students’ conceptual application skills. The argument is 
founded on constructivism theoretical paradigm, which 
contends that students should continuously reflect on 
previously learned knowledge (Smith and Johnson, 2018).
Budiman et al., (2020) reveal that Students’ ability to think 
logically while learning can be maximised by using suitable 
methods. Despite having varying levels of  motivation, 
students may read and comprehend text in a textbook well. 
The benefit paradigm is that students can investigate the 
phenomena in their immediate surroundings to strengthen 
their conceptual understanding. In applying Contextual 
Teaching and Learning model pupils appear active, 

motivated to solve problems, and increase concept mastery 
throughout their learning processes, (Ekowati et al., 2015). 
According to Martins et al., (2018), a learning process in 
linear programming should enable the pupil to detect a 
real problem and turn it into a sequence of  tasks that 
will finally be translated into a simple language. This 
assumption is consistent with their findings. According to 
Qian et al., (2020), teachers should motivate the students 
to keep up their hard effort in order to lower the implicit 
complexity of  linear programming. The teacher should 
also guide the pupils. Additionally, Dorn et al., (2018) claim 
that even though teachers are facilitators, understanding 
the challenges of  teaching programming can help them 
implement pedagogical strategies that benefit pupils 
during their learning process.
Significant results were presented by Gómez et al., (2020) 
and Zhang et al., (2018) to choose appropriate strategies 
using multi-criteria methods like Solutions in order to 
generate high-quality solutions. The TOPSIS technique 
considers the ideal and anti-ideal solution notions while 
choosing between different courses of  action. The 
observation that a certain alternative is located halfway 
between the nearest farthest negative ideal solution serves 
as its basis. Prior to beginning a new session, teachers 
should go over the prior one. Before beginning to teach 
the most recent lesson, the previous lesson should be in 
order. This will aid the pupil in making connections to the 
prior lesson. According to research by Blum, Galbraith, 
Henn, and Niss (2017), it is important for teachers to start 
classes by connecting concepts to past knowledge, such 
as linear inequality, and to give students incentives to learn 
the benefits of  or practical uses for linear programming. 
The teacher might, for instance, use the students’ prior 
knowledge to explain a linear inequality of  two variables 
before applying the innovative idea to linear programming. 
Students may find it simpler to comprehend the material 
and draw connections as a result. This will enhance pupils’ 
intellectual comprehension, their cognitive, and emotional 
grasp of  it. This is true because pupils’ affective domains 
may have an immediate cognitive and psychomotor 
domain. How the students approach word problems that 
require linear programming, and how successfully they 
can respond to them will be greatly influenced.  
According to Muis et al., (2015), changes in students’ 
attitudes and performance are greatly influenced by 
their epistemological views. Asempapa (2022) claims 
that teachers’ educational techniques that consider the 
particular qualities of  each pupil may result in a shift in 
the pupils’ attitudes, thereby promoting pupils’ active 
participation. 
Nakhanu, Shikuku, and Wasike (2015) explored whether 
problem-based learning can improve and encourage the 
teaching of  students in Kenya. This was an intervention 
measure for problem-based learning to enhance students’ 
understanding. The focus was instead on the methods 
teachers employed, with a specific focus on whether 
they used the extreme point and origin tests to include a 
problem-based learning strategy. Problem-based learning 



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is the most effective strategy for raising student-centred 
educational strategies known as problem-based learning, 
where students acquire knowledge by addressing 
problems in real life. Gained is critical thinking domain 
knowledge. The objectives of  problem-based learning 
(PBL) are to help pupils acquire adaptive information 
quickly. According to a study by Kenney (2020), teachers 
can successfully teach, tutor, and counsel pupils to 
overcome learning obstacles. 
Through seminars and workshops, seasoned teachers 
may be permitted to impart their best by developing and 
fostering pupils’ mathematical talents. Teachers should 
work together regardless of  gender disparities, school 
locations, and concerns to help pupils set and achieve their 
goals while facing linear programming problems. When 
teaching linear programming teachers should ensure that 
the fundamental ideas are understood, and pupils must be 
able to respond appropriately. Tsamir and Almog (2015) 
looked at how students were affected by active learning 
and a heuristic approach to problem-solving. According 
to research (STEM), linear programming and inequalities 
are related and effective optimization techniques. 
Pupils, overcome their struggles with algebra and linear 
programming in particular and consequently increase 
their skills, it is imperative to adopt or modify successful 
learning methodologies. Particularly, students should be 
given a sufficient introduction to and training as they are 
essential for their comprehension of  linear programming. 
Teachers should promote a constructive stance on 
teaching linear programming. This encourages a greater 
desire to understand it (Tumuti, 2015). The teacher 
should sufficiently include the class in the subject matter 
through the tactics used, as student engagement is crucial. 
For pupils to remain interested in learning about linear 
programming, they must devote an effort to the subject. 
Instead of  treating them like passengers, treat them 
like active participants. This demands that the teacher 
possess strong linear programming skills. Teachers must 
have pedagogical expertise. Additionally essential are the 
teachers’ continual, regular comments, and correction 
measures. Better academics is always the outcome of  
providing feedback to pupils and taking corrective 
measures. In order to catch up to other students, remedial 
work seeks to address students’ weaknesses. Pupils that 
actively participate in class are produced via interactive 
teaching approaches. The effectiveness of  project-based 
learning, group activities, and discovery methods has been 
established. Pupils perform better when humour-teaching 
approaches because humour makes a class interesting and 
pleasurable (Ngussa and Mbuta, 2017).
Pupils’ academics will be boosted by the availability 
of  instructional resources in schools, the decrease in 
overcrowded classrooms, as well as other additional 
factors. (Mulenga 2015). According to Tichapondwa 
(2017), another tactic that might improve pupils’ 
academic success is team teaching. How well students 
learn or approach learning is greatly influenced by the 
teaching strategies employed by their teachers. This 

implies that educators may apply a variety of  cutting-
edge instructional strategies to help address the learning 
challenges impeding pupils’ academic advancement. One 
of  these cutting-edge teaching techniques, among many 
academics, is team teaching. 
Another powerful technique for raising pupils’ interest is 
group discussion. Solehah et al., (2021) claim that group 
discussion helps the other students who listened to the 
instruction to understand the subject. The activities that 
students engage in and how they develop their thinking are 
related. Because they receive more scientific information 
from different groups, pupils’ thinking develops. The 
learning activities of  pupils are improved and reading 
material is increased when they actively participate in 
group discussions. The knowledge pupils gain from 
having conversations with peers in groups encourages 
them to talk clearly and communicate effectively when 
sharing information and helps them remember things 
when asked (Sudiyanto et al., 2020).

Strategies to Enhance Pupils’ Linear Programming 
Academic Performance 
Research on teachers’ methods for a few secondary 
schools in the Monze region, Kaabo (2019) found that 
understanding the concepts and symbols used in linear 
programming depends on teachers’ approaches used in 
secondary schools. In order to give essential contact with 
the concepts and symbols to improve their application in 
an interactive learning environment, attention should be 
applied to the teaching approaches that are created from 
the introduction to the finish of  the lesson.
The study further established the constraining factors in 
effective teaching hinged on the intervening measures 
that were suggested to overcome the constraints. The 
constraining factors were; the region to be shaded for 
linear in the equation and linear programming was not 
consistent, less learner interaction with a variety of  
linear programming questions/situational statements, 
and getting in equations to form linear programming 
questions to enhance the understanding of  terms and 
associated inequality symbols was inadequate.
Koji et al., (2016), in their study in Mufulira District, stated 
that before pupils are exposed to equations, the teachers 
need to arm themselves with more adaptable teaching 
strategies. By creating a supportive learning environment 
for pupils, these alternative teaching methods aim at 
these diverse learners. Teaching objectives and learning 
outcomes are no longer the only considerations when it 
comes to how to teach. To accommodate pupils’ varying 
abilities and help them excel in their studies, teachers are 
urged to adopt progressive teaching methods.

CONCLUSION 
Linear programming is faced with many challenges as 
emerged from the literature reviewed. These difficulties 
have contributed to pupils’ poor academic achievement, 
particularly in developing nations. The topic’s objective 
might not be achieved if  this situation continues. Therefore, 



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the Zambian government must work to mitigate the 
highlighted challenges not only to enhance the topic 
delivery but also to the pupil’s academic performance.

RECOMMENDATIONS 
The following are recommendations that can help 
improve performance: 

1. Mathematics teachers should use the right resources 
and instructional methods for better comprehension of  
mathematics concepts.

2. There must be extensive practice i.e., teachers 
should assign enough homework to keep their students 
practising.

3. The Zambian Examinations Council to examine the 
mathematics curriculum and make it more approachable 
because the current syllabus is excessively loaded.

4. There should be a manageable number of  pupils 
enrolled in class in order to give personalised education. 
Consequently, the official teacher-to-student ratio should 
be considered.

5. There should be enough textbooks and other 
teaching/learning resources available for students’ 
academic endeavours.

6. To address the issue of  incompetent teachers, it is 
advised that the government employ competent teachers 
of  mathematics around the nation. 

7. More time to be allocated to difficult topics like 
linear programming. 

8. The pedagogies used by maths teachers should be 
improved, and school administrators should strengthen 
monitoring systems in schools.

9. Mathematical instructors should employ a range of  
techniques, tactics, and strategies in the way they present 
their subject matter.

Chapter Summary 
The researcher reviewed pertinent literature to prevent 
repeating prior studies. It additionally enables the 
researcher to identify knowledge gaps in earlier studies. 
Additionally, the chapter covered the development 
of  linear programming, progression, and students’ 
performance on a worldwide level. It is sufficient to 
say that the study’s literature evaluation established the 
importance of  linear programming for any nation’s 
development. Additionally, it has come to light that there 
are a variety of  factors, such as lack of  resources and 
ineffective mathematics teachers, that contribute to poor 
performance in linear programming. Additionally, it has 
been noted in the literature that linear programming can 
drive economic growth if  it is well-connected.

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