1
Chapter 1
INTRODUCTION
Background of the Study
Algebra is one of the subjects that students often find the most challenging. Solving
algebraic problems requires a learners’ logical reasoning and critical thinking skills.
Mastering these skills is not simple and cannot be acquired overnight. Furthermore, algebra
is centered on using problem-solving skills rather than mere memorization. It is essential
to understand the concepts thoroughly to improve one’s performance in algebra.
Numerous studies have highlighted the challenges students encounter in mastering
algebraic concepts. For instance, Sugiarti (2019) found that seventh-grade students struggle
with understanding and processing these concepts. Additionally, Mokhtar et al. (2019)
reported that students often have difficulty comprehending the language used in
mathematical problems, which leads to failures in grasping basic concepts. They also tend
to avoid reading lengthy questions, particularly in mathematics. Specific challenges
include solving numerical problems, placing unit numbers correctly, tackling word
problems, and distinguishing between different symbols for mathematical operations
(Sakilah et al., 2018).
Recent assessments, particularly from the Program for International Student
Assessment (PISA), have revealed that the Philippines ranks as one of the weakest
countries in mathematics, coming in third in the world. The latest test scores indicate no
significant improvement compared to prior years. This continuing issue is concerning,
2
especially given that, similar to findings in 2018, there has been no progress in enhancing
students' problem-solving abilities in mathematics and science.
Mathematics in 7th Grade is not just about computations and numbers, it is a tool
for understanding structures, relationships, and patterns needed to solve complex real-life
problems. It is connected in all fields of endeavor. High school math is taught to help
students to develop their critical thinking skills and problem-solving skills.
The Institute of Science Education – Science High School is renowned for its junior
high school courses, not only in Marawi City but also among other institutes in the country.
It also implemented the science curriculum in their teaching. The school implements a
comprehensive science curriculum in its teaching. One of the core subjects offered at all
grade levels includes various areas of mathematics, such as Algebra, Geometry,
Trigonometry, and Calculus. The researcher selected the first-year high school students at
Mindanao State University – Institute of Science Education to evaluate their problemsolving skills in Algebra. This study aimed to investigate the problem-solving performance
levels of these science high school students and to determine if there was a significant
relationship between the students' demographic profiles and their performance in Algebra.
Statement of the Problem
This study aimed to investigate the problem-solving performance of science high
school students at Mindanao State University – Institute of Science Education in the subject
Algebra for the year 2024-2025. The study sought to answer the following questions:
1. What is the demographic profile of respondents in terms of:
a) age
3
b) sex
c) average grade
2. What is the problem-solving performance level of the respondents?
3. Is there a significant relationship between the respondent’s demographic profile
and their problem-solving performance in Algebra?
Null Hypothesis
H0: There is no significant relationship between the respondent’s demographic
profile and their problem-solving performance in Algebra.
Significance of the Study
This study aimed to investigate the problem-solving performance of science high
school students at Mindanao State University – Institute of Science Education in the subject
Algebra. This would benefit most individuals including:
Students. This would let students become aware of their problem-solving level and
understand their strengths and weaknesses in algebra, allowing them to focus their efforts
on areas that need improvement.
Teachers. Conducting this study would allow teachers to use the results to adjust
instructional strategies to better address students' problem-solving difficulties and to
modify teaching methods to make learning more accessible and effective.
School. This study would help the school identify students' strengths and
weaknesses in Algebra, serving as a guide for refining teaching strategies to better meet
4
students' needs. Additionally, the school could develop and implement strategies to support
all students' success.
Future Researchers. The findings of this study would serve as a reference for
future researchers conducting similar studies.
Scope and Limitations of the Study
The study only focused on the problem-solving performance of students. The
respondents included all the enrolled Grade 7 students of Mindanao State University –
Institute of Science Education from the school year 2024-2025. The researcher used a
survey type in order to gather data and necessary information for this study.
The subject areas were only limited to the second quarter topics that were discussed
for the Grade 7 students. This study only obtained data from the respondent’s test scores.
The research will be conducted by the researchers with the help of books, textbooks, and
references taken from the internet for the tests that will be given to the students.
Theoretical Framework
This section presents the theory used by the researcher to support and better
understand the objectives of the study.
Mathematical Problem-Solving Theory. This study is supported by George
Polya’s theory of Mathematical Problem Solving, that first existed in the year 1945 through
his book entitled How to Solve It: A New Aspect of Mathematical Method. It stated some
cognitive activities involved in problem-solving and these activities are isolation,
mobilization, organization, and combination (Polya, 1945). In this theory, there are four
5
activities that an individual undergoes while doing problem-solving. These activities are:
understanding the problem, devising a plan, carrying out the plan, and looking back or to
reflect and check the results.
This theory supported the present study due to its relevance to the research problem
– the students’ problem-solving in algebra based on their performance on a given test.
Polya’s theory suggests that the performance of the students only differs depending on how
effectively they apply the problem-solving steps.
Furthermore, this theory provided a strong basis for proving concepts similar to this
study, particularly involving the relationship between students’ problem-solving skills and
their academic performance.
Conceptual Framework
To understand the concept of this research, the researcher provided a schematic
diagram of this study to support the explanation of its framework.
Figure 1
Research Paradigm
Independent Variable
Dependent Variable
Student’s Demographic
Profile:
Problem-Solving
Age
Sex
Average Grade in Math 1A
Performance in Algebra
6
Figure 1 shows the conceptual framework of the study. It is composed of two inputs;
these are the independent variable and dependent variable. The figure illustrates the flow
of the study during its conduct.
The following scale was used to describe the students’ problem-solving
performance in Algebra: high (31-40), moderate (21-30), and low (0-20).
Definition of Terms
For a clearer understanding of this research paper, the following terms were defined
both conceptually and operationally.
Algebra. This word is a branch of mathematics in which arithmetical operations
were generalized by using alphabetic symbols to represent numbers (Collins Dictionary,
2023). In this study, Algebra is one of the main courses in the first-year high school level.
It tackled the topics of laws of exponents, factoring, special products, polynomials,
equations, and some basic topics in trigonometry.
Mathematics. This refers to the science and study of quality, structure, space, and
change (Tennessee Tech University, 2024). In this study, it referred to the ability of the
students to apply algebraic concepts, procedures, and strategies to solve mathematical
problems.
Problem-solving. It refers to the act of defining a problem, determining the cause,
identifying a solution, and implementing it (American Society for Quality, 2024). In this
study, problem-solving meant the skills and capabilities of Grade 7 students from
Mindanao State University – Institute of Science Education.
7
Chapter 2
REVIEW OF RELATED LITERATURE AND STUDIES
This chapter presents the relevant literature and studies that were considered in
strengthening the importance of the present study. The majority of the subjects were taken
from online articles and publications.
Related Literature
This section includes publications and articles from a variety of sources that were
published before the study. The subjects covered by the selected materials were predicated
on the central concepts of the study.
Algebra
Algebra is considered to be one of the oldest components in the history of
mathematics. Muhammad ibn Musa Al-Khwarizmi, known as the father of mathematics,
was a Persian mathematician who wrote a book named Kitab Al Muhtasar fi Hisab Al Gabr
Wa I Muqabala in Arabic, which was later translated into English as The Compendious
Book on Calculation by Completion and Balancing, from which the word Algebra was
derived (CUEMATH, 2023).
Algebra is recognized as a challenging course for students, particularly at the
secondary level. According to Kilpatrick and Izsak (2021), algebra served as the gatekeeper
for advanced mathematical and scientific learning, providing students with the ability to
generalize, recognize patterns, and reason logically. However, these cognitive skills could
not be acquired easily. Students often experienced significant struggles when they were
introduced to algebraic concepts.
8
Problem-Solving Performance of Students in Mathematics
Mathematics serves as an important tool in our life, but unfortunately, many
students encounter significant difficulties in learning Mathematics subjects, which often
leads them to disliking the subject. It needs attention because many countries have
problems regarding the students’ performance in Mathematics. By addressing this
challenge, the researcher can help students to overcome their difficulties with mathematics
and develop the skills and confidence needed to succeed in this field (Brezavscek et. al,
2020; Bringula et al., 2022).
Research over the past few years has highlighted that the most probable cause why
students tend to have low performance in Math is because they lack reading comprehension
skills. They cannot comprehend the problem hence; they cannot answer the problem.
According to Malibiran and Aplaon (2019), reading comprehension of students should be
developed in early grades for the students to have better performance in Mathematics.
Before the students’ have to solve, they must know how to comprehend the problem so that
they won’t struggle when it comes to understanding each question.
Bernardo (2022) stated that grade 7 is a critical period where students transition
from concrete operational thinking to more abstract reasoning. Since they are transitioning
or they have just become high school students, they might have a problem with
Mathematics especially since there are various fields introduced including Geometry and
Algebra.
To be able to move forward to a higher level of problem-solving in Algebra,
students' need to know the basic knowledge in Algebra and for that matter, the researchers
aimed to determine the problem-solving performance level of the Grade 7 students in
9
Algebra. Sullivan and Mornane (2014), stated that the ability to solve problems effectively
at this stage influences students' future academic performance, particularly in mathematics.
Problem- Solving in Mathematics
Problem solving helps improve students’ understanding of mathematical concepts,
it also equips them to use their systematic and logical thinking skills that are useful in
various aspects of life (Nurmeidina et al., 2021). This can be solved through several steps;
(Krulik & Rundick, 1995) reading and thinking, exploring and planning, choosing a
strategy, finding an answer, and then reviewing it.
Every student has their own way of analyzing and solving a problem. While some
students make sense of mathematics on their own, some also struggle to analyze simple
expressions on their own, so they require help from others. Because of this, many people
tend to get frustrated with Mathematics because they don’t understand its concepts.
(Pacaña, 2017).
In order for students to solve problems relating to math, they need to acquire
problem-solving skills. Problem-solving skill is an important aspect especially in
Mathematics education. This skill is defined as the ability of a person to engage in cognitive
processes when understanding and solving problems for which the method of solving is
not readily available (Ismael et.al., 2020). All mathematical problems require problemsolving skills and for that, it is important to understand each concept for you to solve each
problem in Mathematics.
Overall problem-solving in Mathematics remains relatively low, with one study
reporting an average score of 42% (Tafari et al., 2024). Problem-Solving is hard for
10
students, that is why they develop their own strategies when it comes to solving algebraic
problems, including changing perspective, logical reasoning, and working backwards
(Sa'adah & Faizah, 2022). They may have difficulty when dealing with algebra problemsolving, particularly understanding variables and constants, applying division concepts,
and performing operations like addition, subtraction, and multiplication with algebraic
forms (Sugiarti & Retnawati, 2019).
Cognitive development in early adolescence significantly affects academic
performance, especially in higher-order thinking subjects like mathematics. This stage
involves improvements in attention, working memory, and problem-solving skills (Berk,
2013). Although adolescents start to develop abstract reasoning, individual differences can
lead to challenges in applying logic to complex tasks. This variability is particularly evident
in mathematics, where effective problem-solving requires both computational skills and
logical thinking, explaining why some students find subjects like algebra difficult.
Related Studies
This section contains a review presentation of previously written studies related to
the study.
Problem-solving of Students in Mathematics
Problem-solving is needed not just in class but in everyday living as well. Students’
need fundamental knowledge so that they can answer problems that require high critical
thinking skills. Many of the students tend to be anxious when they hear problem-solving.
According to Mokhtar et al. (2019), students have difficulty understanding the
words, students fail to comprehend mathematical problems, mathematics comprehension,
11
basic concepts, and they tend to not read long questions when it comes to mathematics.
Even in some countries like Indonesia, students’ performance in mathematics is low. They
face challenges in solving numeracy problems, placing unit numbers, word problems, and
distinguishing the symbols of counting operations (Sakilah et al., 2018). Several studies in
the Philippines said that students have difficulty when it comes to word problems,
comprehension, selecting a strategy, computing numerous problems, and students tend to
have careless solving skills which in return led to poor performance in mathematics as a
whole (Mangulabnan, 2016; Preclaro, 2016).
Sekaryanti et al. (2022) found that students with high emotional intelligence
understand problems better and use effective strategies, while those with lower emotional
intelligence struggle to connect information and often guess answers. Additionally, Rico
and Baluyos (2020) emphasized the need for better teaching methods, suggesting that
teachers should undergo training and use interactive strategies to enhance students'
problem-solving abilities.
Garinganao (2022) highlighted that algebra skills significantly impact students’
math performance, with stronger algebra foundations leading to better academic
achievement. These studies showed that students' problem-solving ability is closely related
to their habits of mind. There are some students who have their styles when it comes to
solving a problem. This just shows that the higher their attitude towards mathematics, the
better their performance will be.
12
Demographic Profile and Problem-Solving Performance in Mathematics
The performance level of High School students is low. A study by Alave and
Rodrigo (2021) aimed to investigate the Academic Achievement of High School Students
in Algebra. The researchers concluded that the academic achievement level was low, no
significant difference and relationship between sex and academic achievement level
however, there was a significant difference and relationship between parent’s highest
educational attainment and achievement level. Additionally, the researchers stated that
students seemed to have failed mastering the basics which could have been a factor as to
why they failed to analyze the problems that were given to them.
A study by Alpuerto & Sales, 2016; Peteros et al. (2019) showed that there is a
positive correlation between students' math grades and their performance on standardized
tests or diagnostic assessments. While some studies report no significant gender differences
in math performance (Bhowmik & Banerjee, 2016), others find variations in attitudes
towards mathematics between genders (Bhowmik & Banerjee, 2016). Factors such as
gender and grade level may influence problem-solving understanding and mathematics
learning results, though findings vary across studies (B. Sinaga et al., 2023; Kalaivani J &
Dr. N. Amutha Sree, 2024). Common challenges in problem-solving include difficulties in
representing mathematical statements as algebraic symbols and formulating equations
(Alberto R. Sia, 2020).
Recent studies explored problem-solving skills in algebra among secondary school
students. A study about mathematically gifted high school students showed that problemsolving abilities are not influenced by gender or ethnicity (Lukmana, 2022).
13
A study by Cai et al. (2019) investigated the impact of gender on students'
mathematics performance. Their findings challenge the common belief that gender
significantly influences mathematical ability. Instead, the study highlighted that personal
attitude, self-confidence in learning, and the quality of teaching are more critical factors
affecting students' academic success. Additionally, the researchers discovered that when
students are provided with equal learning opportunities and a supportive educational
environment, the performance gap between boys and girls tends to diminish. This
emphasizes that the learning context and students’ mindset play a more significant role in
mathematical success than gender-based differences.
Most of the studies showed that the Performance of the students when it comes to
Mathematics, specifically in areas like algebra and geometry, is fairly satisfactory or low.
Many of the researchers have been trying to improve the quality education of Mathematics
here in the Philippines. To summarize, previous studies have shown that many students are
struggling to have problem-solving skills and most high school students have low
performance when it comes to Mathematics. This gave the researchers an idea on how poor
the performance of the students when it comes to problem-solving in Mathematics.
The PISA report published by Organisation for Economic Co-operation and
Development (OECD, 2016) highlights key factors associated with academically
underperforming students in mathematics. It indicates that low self-efficacy, ineffective
learning strategies, and lack of motivation contribute significantly to poor academic
outcomes, which are influenced more by students' perceptions of their competence than by
intellectual capacity. The findings also show that students lacking foundational skills and
struggling to apply mathematical concepts tend to underperform. This aligns with the
14
current study's results, emphasizing the need for educational interventions that focus on
developing core mathematical skills and enhancing student motivation and confidence.
15
Chapter 3
RESEARCH METHODOLOGY
This chapter discusses the methods and procedures that were used by the researcher
in the conduct of the study. It includes the research design, locale of the study, research
participants, and the research instruments.
Research Design
This study utilized a descriptive correlational method to investigate the
performance of grade 7 students of Mindanao State University – Institute of Science
Education – Science High School in the subject algebra. The descriptive correlational
method was applied to examine the relationships between the dependent variable (the
demographic profile of the students) and the independent variable (levels of problemsolving performance in Algebra). This method also uses any method of collecting data
which can yield quantitative data such as tests and forms (Fraenkel et al. 2012).
Locale or Setting of the Study
This study was conducted at Mindanao State University – Institute of Science
Education specifically for grade 7 students during the school year 2024-2025. The Institute
of Science Education of Mindanao State University was formerly known as Mindanao
State University – Science Training Center (STC).
The historical background of MSU Science Training Center (STC), which is now
known as the Institute of Science Education (ISED), was established on March 28, 1974,
by Prof. Fortunato F. Portugaleza, its founding director. The director proposed the
16
establishment of the MSU – STC as a training laboratory of the STC programs which was
for the elementary and secondary elementary teachers. A four-year curriculum was
approved by the University Council for consideration, which was implemented during the
S.Y. 1975-1976.
Figure 2
Location Map of Mindanao State University – Institute of Science Education
Source: https://earth.google.com
17
Research Participants and Sampling Technique
The respondents of the study were selected through purposive sampling, ensuring
that participants met specific criteria relevant to the research objectives. The participants
of the study were taken from the Grade 7 students who are officially enrolled in Mindanao
State University – Institute of Science Education during the school year 2024-2025. Grade
7 level of the Science High School is composed of two sections, namely, Dirichlet and
Lagrange. Section Dirichlet is composed of 31 students, with 19 female students and 12
male students. On the other hand, section Lagrange also consists of 31 students, 19 of
whom are female students and 12 of whom are male students. Overall, there are a total of
62 students.
Research Instrument and its Validity
The said instrument was adopted to collect the necessary data:
Problem-Solving Performance Test
The Problem-Solving Performance Test (PSPT) was developed by Anda and Aman
(2021) and consisted of ten (10) open-ended questions. This assessment focused on
domains such as solving problems related to linear equations and inequalities in one
variable. To ensure its effectiveness, the test underwent validation and reliability testing,
allowing for the identification of any weaknesses before administration to respondents. The
highest possible score for each problem-solving question was four (4) points. The points
of distribution were reflected on the scoring rubrics with the following criteria shown in
Table 1.
18
To determine the problem-solving performance level of the respondents, a
corresponding basis was used shown in Table 2.
Table 1
Scoring Rubrics on Problem-Solving Test
Score
Descriptors
4
Used an appropriate strategy to come up with the correct solution
and arrived at the correct answer.
3
Used an appropriate strategy to come up with a solution, but a part
of the solution led to an incorrect answer.
2
Used an appropriate strategy but came up with an entirely wrong
solution that led to an incorrect answer.
1
Attempted to solve the problem but used an inappropriate strategy
that led to the wrong solution.
0
No attempts, problems are left unanswered.
Adopted from the Grade 7 Teacher’s Guide of DepEd
The students' problem-solving performance levels were measured using the raw
scores obtained in the PSPT. The categorization of problem-solving performance was based
on the study of Tawantawan (2017). The scores were divided into High, Moderate, and
Low categories, as presented in Table 2.
Table 2
Categorization of Problem-Solving Performance Levels
Conceptual Understanding
Levels
High
Score Range
31 – 40
Moderate
21 – 30
Low
0 – 20
19
Table 2 shows the performance levels and the ranges of the scores. The high level
ranges from 31 to 40, the moderate level ranges from 21 to 30, and the low level ranges
from 0 to 20. These performance levels were used to determine the students’ performance
in algebra.
Methods of Data Gathering
The researchers requested permission and approval from the Institute Principal of
Mindanao State University – Institute of Science Education before the study was
conducted.
The study was conducted during the Math 1A class of the grade 7 students. The
study utilized a survey as its primary method of data collection. The researchers were given
access to conduct the research and to have the grades of the grade 7 students. Both sections
of the grade 7 were given an hour to answer the questionnaire. All 62 students were present
on the day the study was conducted.
After the study was conducted, the researchers collected the papers. After recording
the results of the study, a one-on-one interview was conducted. To further support the
results of the study, eight students were interviewed.
Ethical Considerations
Ethical issues must be considered in accordance with research ethics.
Voluntary Participation
Participation in this study was completely voluntary. Participants were informed
that they were not obligated to take part in the study and that their decision to accept or
20
decline would not lead to any negative consequences. Their choice regarding participation
would not affect their academic standing, grades, or relationship with the institution in any
way.
Confidentiality and Anonymity
It was crucial to protect the privacy of participants. All collected information
remained confidential, including demographic details and responses from participants or
interviewees. Any names, ages, or identifying information that could reveal a participant's
identity were anonymized. Access to the securely stored data was limited to the research
team only. This ensured that participants’ responses could not be traced back to them and
that no personal details were disclosed.
Statistical Treatment
The data gathered in the study was subjected to the following statistical tools.
Descriptive statistics such as Mean, Frequency, and Percentage were used in analyzing the
demographic profile of the respondents in terms of their age, sex, and average grade, as
well as to determine their problem-solving performance level. To determine if there is a
relationship between the demographic profile of the respondents and their performance in
Algebra, the Pearson Correlation was used.
21
Chapter 4
PRESENTATION, ANALYSIS, AND INTERPRETATION OF DATA
This chapter presents the data collected from the study, provides an analysis of the
findings based on statistical methods, and the interpretation of the data. This chapter also
aimed to answer the questions from the statement of the problem.
Demographic Profile of the Respondents
Table 3
Distribution of Respondent’s Age
Age (in years)
Frequency
Percentage
12
20
32.26
13
29
46.77
14
11
17.74
15
2
3.23
Total
62
100
Mean Age = 12.92  13
The distribution of the respondent’s age in Table 3 shows that majority are 13 years
in age. 46.77% of the respondents are 13 years old and 32.26% of the respondents are 12
years old. 17.74% are 14 years old respondents and there are only two respondents who
are 15 years old.
Table 3 showed that the majority of the respondents were 13 years old. This
suggested that most respondents were in early adolescence. Berk (2013) described this
developmental period as marked by gradual cognitive changes in attention, working
22
memory, and problem-solving abilities. While adolescents began to develop advanced
thinking skills, such as abstract reasoning, these abilities did not emerge uniformly. Many
students at this stage struggled with applying logical reasoning to complex tasks. This was
reflected in the study's findings, where a significant number of respondents demonstrated
low problem-solving performance, as seen in Table 6. Berk's insights highlighted that
younger adolescents might have lacked the cognitive skills necessary for effective
mathematical problem-solving, particularly in algebra, which required higher-order
thinking.
Table 4
Distribution of Respondent’s Gender
Sex
Frequency
Percentage
Female
38
61.29
Male
24
38.71
Total
62
100
The distribution of the respondent’s gender in Table 4 shows that majority are
female. There is a total of 61.29% indicating that the respondents are female and a total of
38.71% showing that the respondents are male.
Cai et al. (2019) contended that gender by itself did not determine a student's ability
or performance in mathematics. Their study emphasized that personal attitudes, selfconfidence in learning, and the quality of teaching experiences exerted a more significant
impact on student achievement than biological sex. They discovered that when students—
regardless of gender—received equal learning opportunities and nurturing environments,
the differences in performance often lessened. This indicated that the educational setting
23
and student mindset were more significant determinants in comprehending academic
success in mathematics than gender alone.
Table 5
Distribution of Average Grade
Average Grade
Frequency
Percentage
1.75 to 1.50
3
4.84
2.25 to 2.00
8
12.9
2.75 to 2.50
8
12.9
3.25 to 3.00
18
29.03
Below 3.25
25
40.32
Total
62
100
The distribution of the Average grade in Table 5 shows that the majority have a
lower average grade. 40.32% of the respondents have below 3.25 average grade and
29.03% of the respondents have 3.25 to 3.00 average grade. 12.9% of the respondents have
2.75 to 2.50 average grade, as well as those that have an average grade of 2.25 to 2.00.
There are three respondents whose average grade is 1.75 to 1.50.
According to the OECD (2016) PISA Report, students who performed poorly
academically often shared certain traits, including low self-efficacy, ineffective learning
strategies, and diminished motivation, especially in mathematics. The report highlighted
that underachievement was not merely a reflection of ability but was often associated with
students' perceptions of their competence, the strategies they employed in learning, and the
level of support they received in their educational settings. Additionally, the PISA findings
indicated that students lacking fundamental skills and who had difficulty applying
mathematical concepts usually showed consistently low performance across various
24
assessments. These insights correlated with the findings of the current study, emphasizing
the need to cultivate a stronger foundational understanding and effective learning practices
to enhance academic achievement.
Problem Solving Performance
Table 6
Problem-Solving Performance Level
Performance
Level
High
Score Range
Frequency
Percentage
31-40
2
3.23
Moderate
21-30
13
20.97
Low
0-20
47
75.81
62
100
Total
Mean Performance = 16.81
Table 6 shows the distribution of the performance level in problem-solving. The
score range is shown in the second column and the performance level description is in the
first column. The majority have low performance levels with 75.81% of the respondents.
Those who got a moderate performance level are 20.97% of the respondents. Only two
among the 62 respondents have high-performance levels. This result in Table 4 has a similar
result to the average grade shown in Table 3 where the majority have a lower average grade.
The result of the study is parallel to the study of Alave and Rodrigo (2021) in which
they studied the academic achievement in algebra of public high school students in the
Philippines. The study showed that the academic achievement of students when it comes
to Algebra is low. They stated that they failed to master the basics which could be the reason
why they can’t answer the problems given to them. Additionally, students have difficulty
25
understanding the words, students fail to comprehend mathematical problems and
mathematics comprehension, and they tend to not read long questions when it comes to
word problems (Mokhtar et.al., 2019).
Relationship between the respondent’s demographic profiles with their problemsolving performance in Algebra
To determine whether there is a significant relationship between demographic
profile and problem-solving performance in algebra, Pearson correlation analysis was used.
Table 7 shows the correlation analysis result between the variables, age and performance
level and average grade and performance level.
Table 7
Correlation Analysis Result
Pair of Variables
p-value
Interpretation
Age vs. Performance Level
Correlation
Coefficient*
-0.0662
0.6094
Not significant
Average Grade vs. Performance Level
0.4719
0.0001
Significant
*Pearson Correlation Coefficient (p-value < 0.05 is significant)
The correlation analysis result in Table 7 shows that average grade and performance
level have a significant correlation with a coefficient value of 0.4719. This implies that as
average grades increase the performance level also increases. The age and performance
level has negative correlation with a coefficient of -0.0662 but is not significant. This result
is further verified by the regression analysis result in Table 8.
The study showed that there is no significant relationship between age and
performance level. Congruent to the study (Lukmana, 2022) where the researchers
investigated the skills of math-gifted students in high school to solve math problems with
26
factors of gender and ethnicity showed that problem-solving abilities are not influenced by
gender or ethnicity.
Additionally, a study by Alpuerto & Sales, 2016; Peteros et al. (2019) supported
these findings and showed that there is a positive correlation between students' math grades
and their performance on standardized tests or diagnostic assessments. This indicates that
the performance level of the students is connected with their average grade.
Interview with Some of the Respondents
To support the study further, the researchers interviewed some of the respondents
after recording the results from the Problem-Solving Performance Test that was given to
them. These interviews were done through calls via the Messenger app. A total of 8
interviewees were interviewed, with respect to the scores they acquired from the given test:
two students who obtained high score from the test, three students coming from the
moderate-level and 3 students coming from the low-level. The researchers assigned
nicknames to each of the interviewees in order to keep the study confidential. Anna and
James had a score belonging to the high-level, Daniela, Marvin, Sam had a score belonging
to the moderate-level, and Trisha, Mae, and Livy had a score belonging to the low-level.
The following were the statements that the researchers obtained:
Researcher:
Based on the test that we gave you, do you find it difficult to answer? If yes,
what made it difficult? If not, why do you think it was easy for you?
Anna:
Even though I love solving math problems, I still am not sure of how well I
answered it. Most of the questions are hard and are difficult to answer
considering we are not always exposed to these kinds of concepts. But I’m
confident that I answered problem 1 correctly.
Daniela:
I think for me the test is hard but from what I can recall, there are some
problems which I had fun solving because it’s basic math. However, I found
the problem that involved distance or time hard or the most challenging, it
27
took me some time to fully grasp the problem. I didn’t think money
questions were easy for me but I still enjoyed it. I answered the questions
the way I understand it.
Marvin:
When I was answering the test, I mostly used my common sense because I
really couldn’t understand the problems, especially those questions that
were in the last part. So, I think I found the test hard because I am not sure
of my own answers.
Trisha:
It was harder than I thought it would be. It’s basic math but I couldn’t seem
to find the right formula to use in the problems. For me, numbers 5 and 6
were particularly challenging because I had a hard time thinking of ways on
how to solve it. Only Numbers 1 and 2 are what I think I answered correctly.
Mae:
I had a hard time answering the tests, especially numbers 4 and 5 since I
didn’t have prior knowledge of these kinds of problems and when I was
answering the test, I couldn’t analyze what formula I would use.
Sam:
Wala po akong naintindihan sa problems na sinagutan namin. Ang maalala
ko lang po na na answer ko na yung number 1, the rest po na super hirap. (I
didn't understand the problems from the test. From what I remember, the
only problem that I answered is number 1. The test was super hard)
Livy:
Honestly, I don't know po if I answered it correctly. From all the test na na
answer ko na dito po talaga ako na challenge. I don't like solving word
problems. (Honestly, I don’t know if I answered it correctly. From all the
test I have encountered, this test is by far, the most challenging. I don’t like
solving word problems.)
James:
The test is quite hard but I enjoyed answering the problems. The numbers I
think I answered right are numbers 1, 9, and 10. The rest of the problems
are quite challenging and difficult to solve. I don't know, maybe I'm not
smart and I just don't know how to solve it.
Students who were interviewed said that most of the questions were hard. They said
that they were answering the questions the way they understand it, they used their common
sense to answer the problem, and they didn’t know what formula they’d use on a specific
problem. The result is parallel to the study of Pacana (2017) students struggle to analyze
the problems and students make sense of the problems on their own. This factor may
contribute to the reason why students have poor performance when it comes to problemsolving in mathematics.
28
After carefully checking the test answers of the students, almost all of them got
problem 1 correct. However, as the problem question progressed, the answers were blank
some of them tried to answer the question but stopped because they didn’t know how they
to the formula they wrote. They had strategies in mind but since they are not able to know
the basic concepts, they tend to get the answers wrong. Figure 3 shows problem 1 in the
test. Figures 4, 5, and 6 show the sample answers of the students from the test.
29
Figure 3
Problem 1
Figure 4
Extracted Answer of Student 13 from the Test
Student 13 was able to find the correct answer, identifying that the man received
₱1,000 for the mobile phone. However, the student's work shows that the solving process
was messy and disorganized. The student began by writing random operations and crossing
them out several times, suggesting trial-and-error thinking rather than a clear plan.
Although the student knew that the total amount was ₱1,250, the path to arrive at the correct
breakdown between the mobile phone and the watch was not systematic. This indicates
that the student may rely heavily on common sense rather than structured problem-solving
strategies.
30
Figure 5
Extracted Answer of Student 5 from the Test
Student 5 demonstrated a much more organized and logical approach to solving the
same problem. The student first assumed that the price of the watch was ₱250 and then
correctly multiplied this by 4 to find the price of the mobile phone, which is ₱1,000. After
calculating both, the student checked that the total was ₱1,250, matching the given
information in the problem. The student labeled or analyzed the problem clearly in his own
way. Compared to Student 13, Student 5 not only arrived at the correct answer but also
presented the solution with logical sequencing and explanation.
Figure 6
Extracted Answer of Student 22 from the Test
Student 22 displayed an even more advanced approach by using algebra to
represent the problem. By letting p represent the mobile phone's price and w represent the
31
watch's price, the student set up two equations based on the information: p + w = 1250 and
p = 4w. Solving these led to the correct amounts: ₱1,000 for the phone and ₱250 for the
watch. Furthermore, Student 22’s solution was neatly written, with clear steps shown for
substitution and elimination. This structured method shows that the student not only
understood the relationships in the problem but could also organize their thinking into a
formal mathematical process, which is a higher-order skill important in secondary
mathematics and beyond
Their answers on Problem 1 followed the Mathematical Problem-Solving theory of
Polya. According to Polya, there are four activities that an individual undergoes while
doing problem-solving. These activities are: understanding the problem, devising a plan,
carrying out the plan, and looking back or to reflect and check the results. The extracted
answers from the test of the interviewee showed that they understood the problem because
they answered it correctly. They created their own method or approach as to how they will
solve the given problem. Their answers are correct which means that in this area and type
of problem, they are knowledgeable. They also looked back and checked the result if their
answer was correct. The three of them used addition to verify if they got the amount 1,250.
Almost all the students answered problem 1 correctly, however the majority of them
failed to analyze the problems below 4. Most of the interviewees stated that problems
starting from problem 5 up to 7 is hard. After seeing the results of their answers from the
test, some of them did not answer or didn’t have an idea on how to solve problem 5. In
addition, they all had a common answer that problem 5 is what they found hard.
32
Figure 7
Problem 5
Figure 8
Extracted Answer of Student 6 from the Test
Student 6 was able to identify and record the important details of the problem: the
total distance (130 km), the two speeds (55 kph and 40 kph), and the total time (2.5 hours).
The student even correctly labeled each speed and the time. However, the student did not
proceed to connect these pieces of information into a full solution. There were no attempts
to form equations or calculate partial distances or times. This suggests that the student has
a basic skill in reading and organizing given information but lacks confidence or
understanding in setting up between distance, speed, and time. The answer of the student
shows that they might struggle when the problem involves two different stages or when
two variables (speed and time) must be managed together.
33
Figure 9
Extracted Answer of Student 35 from the Test
Figure 10
Extracted Answer of Student 58 from the Test
Students 58 showed that instead of setting up equations relating speed, time, and
distance, the student simply subtracted the two speeds (55 - 40 = 15) and divided this by
the total trip time of 2.5 hours. This led to a final answer of 0.15 hours, which does not
make sense in the context of the problem. This approach suggests confusion about how
speed and time interact; the student appeared to think that the problem was about the
difference between speeds rather than about covering different distances at different
speeds. It shows that the student did not fully understand the structure of the problem and
did not recognize that each stage needs separate treatment.
34
Figure 9 shows that the student came up with a strategy to answer the problem;
however, the strategy that he used led him to answering incorrectly. While in Figure 10,
the student tried to solve the problem but because the student does not know what formula
to use, the only thing that the student wrote is the given. This also suggests that students
cannot answer the question because they cannot comprehend the problem, and because
they cannot comprehend it, they don’t know which formula they’ll use or apply.
As seen in Figure 8 and 9, the respondents came up with ways or strategies on how
to solve problem 5. However, both of their answers were wrong. According to a study by
Aplaon and Malibiran (2019) the reason why the students cannot answer the problem is
because they cannot comprehend the problem. They can devise a plan and had unique
strategies on how to solve the problem but they tend to conclude with the wrong answer
because they did not understand the problem
Therefore, the scores they got is based on how they understood the problems. They
had a hard time answering the test; hence, their scores will reflect on how they answered
the test. Almost all the responses are negative. They answered the test based on their
understanding, their common sense, and analyzed it with their own strategy.
35
Chapter 5
SUMMARY, CONCLUSION, AND RECOMMENDATIONS
This chapter comprises the summary of findings, the conclusion drawn based on
the data presented, and the recommendations for consideration and future research.
Summary
This study aimed to determine the problem-solving performance of Mindanao State
University – Institute of Science Education Grade 7 Students in Algebra. A total of 62
students were given a 10-items test with a total of 40 points.
The findings are summarized as follows:
1. The respondents of the study had an age ranging from 12 to 15. Majority of the
students were 13 years old, 32.6% were aged 12, 17.74% were aged 14. 2 out
of 62 students were aged 15.
2. Majority of the respondents were female with a percentage of 61.29. The
remaining 38.71% were male respondents.
3. The average grade of the respondents ranged from 1.50 to below 3.25. Most of
the respondents had an average grade below 3.25 with a percentage of 40.32.
18 of the students had a grade of 3.25 to 3.00. 8 of the respondents had 2.75 to
2.50 average grade, as well as those that had an average grade of 2.25 to 2.00.
Only 3 of the respondents had an average grade of 1.75 to 1.50.
4. The study showed that 47 respondents had a low performance level having a
percentage of 75.81 out of 100%.
36
5. There was no significant relationship between the respondent’s demographic
profile in terms of their age with their problem-solving performance in Algebra.
On the other hand, there was a significant relationship between respondent’s
demographic profile in terms of their average grade with their problem-solving
performance in Algebra.
Conclusion
The results showed that most of the students had a low performance level when it
came to problem-solving in algebra. The study revealed that there is no significant
relationship between the demographic profile in terms of their age with their problemsolving performance in algebra. On the other hand, there is a significant relationship
between the demographic profile of the students in terms of average grades with their
problem-solving performance in algebra.
Recommendations
Based on the results and conclusion of the study, the following recommendations are
presented:
1. It is recommended for a similar study to have more respondents in order to
guarantee a more reliable result.
2. The school should conduct activities that would enhance the mathematics problemsolving performance of the students.
3. Another study should be conducted to discover the factors influencing the
mathematics performance of the students in problem-solving.
37
4. It is recommended that future studies compare the problem-solving performance
of students from other schools or institutions for broader findings.
5. Researchers may investigate other topics related to mathematics, like how teaching
methods or learning preferences affect students' problem-solving performance.
38
REFERENCES
Alpuerto, M. D., & Sales, E. L. (2016). Mathematics grades as correlates to performance
in Asian Psychological Services and Assessment (APSA). University of Bohol
Multidisciplinary
Research
Journal,
4,
63–71.
https://doi.org/10.15631/ubmrj.v4i1.62
American Society for Quality. (2024). Problem solving ASQ. https://asq.org/
Anda, A. S., & Aman, J. P., (2021). Effects of Concept Scaffolding Teaching Approach on
Grade 7 Students’ Conceptual Understanding and Problem Solving Performance
in Mathematics. ResearchGate.
Bakar, M. a. A., & Ismail, N. (2020). Exploring Metacognitive Regulation and Students’
Interaction in Mathematics Learning: An Analysis of Needs to Enhance Students’
Mastery. Humanities & Social Sciences Reviews, 8(2), 67–74.
https://doi.org/10.18510/hssr.2020.82e07
Berk,
L. E. (2013). Child Development (9th ed.). Boston, MA: Pearson.
https://www.scribd.com/document/791018265/Child-Development-9th-Editionpdf
Bernardo, A. (2020). Understanding Filipino Students’ Mathematical Thinking.
ResearchGate.
Bhowmik, M., & Banerjee, B. (2016). A study on relationship between achievement in
mathematics and attitude towards mathematics of secondary school students. IRA
International Journal of Education and Multidisciplinary Studies, 4(3), 402.
https://doi.org/10.21013/jems.v4.n3.p7
Brezavšček, A., Jerebic, J., Rus, G., & Žnidaršič, A. (2020). Factors influencing
mathematics achievement of university students of Social Sciences. Mathematics,
8(12), 2134. https://doi.org/10.3390/math8122134
Bringula, R. P., & Atienza, F. a. L. (2022). Mobile computer-supported collaborative
learning for mathematics: A scoping review. Education and Information
Technologies, 28(5), 4893–4918. https://doi.org/10.1007/s10639-022-11395-9
Cai, J., Wang, T., Moyer, J. C., Nie, B., & Garber, T. (2019). Mathematical problem solving:
What do we know and what are we learning?. International Journal of Educational
Research, 95, 167–176. http://dx.doi.org/10.1016/j.jmathb.2019.02.006
Collins Dictionary. (2023). Algebra. https://www.collinsdictionary.com/
39
Cuemath. (2021). Introduction to Algebra. Cuemath. Retrieve April 30, 2025, from
https://www.cuemath.com/learn/maths-olympiad-introduction-to-algebra/
Fraenkel, J. R., Wallen, N. E., Hyun, H. H. (2012). How to Design and Evaluate Research
in Education. McGraw-Hill Companies, Inc.
Garinganao, N. S., & Bearneza, F. J. D. (2021). Algebraic skills and academic achievement
in mathematics of Grade 7 students in a Philippine Chinese school. Philippine
Social Science Journal, 4(3), 57–64. https://doi.org/10.52006/main.v4i3.396
Kalaivani, J., & Amutha Sree, N. (2024). Influence of problem-solving ability, learning
style and home environment upon achievement in mathematics of high school
students. Journal of Emerging Technologies and Innovative Research, 11(9), 324–
331. https://www.jetir.org/papers/JETIR2409364.pdf
Kilpatrick, J., & Izsak, A. (2021). A contemporary view of Algebra. In Meaning in
Mathematics Education (pp.97-115). Springer. https://doi.org/10.1007/978-3-03052371-2_4
Kusdinar, U., Sukestiyarno, S., Isnarto, I., & Istiandaru, A. (2017). Krulik and Rudnik
model heuristic strategy in mathematics problem solving. International Journal on
Emerging
Mathematics
Education,
1(2),
205.
https://doi.org/10.12928/ijeme.v1i2.5708
Lukmana, D. A. (2022). Gifted students’ skill in solving mathematics problems: A study
used gender and ethnicity as differentiating factors in senior high school.
International Journal of Trends in Mathematics Education Research, 5(1), 19–28.
https://doi.org/10.33122/ijtmer.v5i1.108
Malibiran, H. M., Candelario-Aplaon, Z., & Izon, M. V. (2019). Determinants of problemsolving performance in Mathematics 7: A regression model. International Forum,
22(1), 65–86.
Nurmeidina, R., Zaqiyah, N. N., Nugroho, A. G., Andini, A., Faiziyah, N., Adnan, M. B.,
& Syar’i, A. (2024). Analysis of students’ problem-solving abilities in solving
contextual problems of Linear Equations with Three Variables in terms of Habits
of Mind. Indonesian Journal on Learning and Advanced Education (IJOLAE), 7(1),
117–135. https://doi.org/10.23917/ijolae.v7i1.23550
OECD. (2016). PISA 2015 results (Volume I): Excellence and equity in education. OECD
Publishing. https://doi.org/10.1787/9789264266490-en
40
Polya, G. (1945). How to solve it: A new aspect of mathematical method. 3rd Ed., New
York. Macmillan publishing.
Rico, C. O., & Baluyos, G. R. (2021). Level of implementation of spiral progression
approach in relation to students’ performance in algebra. United International
Journal for Research and Technology, 2(11), 1–8. https://uijrt.com/paper/levelimplementation-spiral-progression-approach-relation-students-performancealgebra
Rodrigo, D. B., & Alave, A. D. (2021). Academic achievement in algebra of the public high
school students in the new normal. Philippine Social Science Journal, 4(3), 65–74.
https://doi.org/10.52006/main.v4i3.381
Sa’adah, N., Faizah, S., Sa’dijah, C., Khabibah, S., & Kurniati, D. (n.d.). Students’
mathematical thinking process in algebraic verification based on crystalline
concept. https://eric.ed.gov/?id=EJ1391469
Sekaryanti, R., Darmayanti, R., Choirudin, C., Usmiyatun, U., Kestoro, E., & Bausir, U.
(2023). Analysis of Mathematics Problem-Solving Ability of Junior High School
Students in Emotional Intelligence. Jurnal Gantang, 7(2), 149–161.
https://doi.org/10.31629/jg.v7i2.4944
Sia, A. R., Jr. (2020). Strategies and attitude in problem solving. Test Engineering &
Management,83,8630–8637.
https://www.testmagzine.biz/index.php/testmagzine/article/view/8630
Sinaga, B., Sitorus, J., & Situmeang, T. (2023). The influence of students’ problem-solving
understanding and results of students’ mathematics learning. Frontiers in
Education, 8. https://doi.org/10.3389/feduc.2023.1088556
Sugiarti, L., & Retnawati, H. (2019). Analysis of student difficulties on algebra problem
solving in junior high school. Journal of Physics Conference Series, 1320(1),
012103. https://doi.org/10.1088/1742-6596/1320/1/012103
Sullivan, P., & Mornane, A. (2014). Exploring teachers' use of, and students' reactions to,
challenging mathematics tasks. Mathematics Education Research Journal, 26(2),
193–213. https://doi.org/10.1007/s13394-013-0089-0
Tafari, N., A., & Roza, Y. (2024). Analysis of Students’ Ability to Solve Mathematical
Problems on Contextual Problems Involving Algebraic Forms. Jurnal Pendidikan
Matematika dan IPA.
41
Tennese Tech University. (2024). Mathematics Department. Tennessee Technological
University. https://www.tntech.edu/
Tawantawan, J. C., & Aman, J. P., (2018). Bilingual medium of instruction: Effects on
students’ conceptual understanding, problem solving performance, and interest in
mathematics. International Journal on Humanities and Sciences (IJHSS), 10(2),
95-111.
42
APPENDICES
43
Appendix A
Letter of Permission to the Dean
January 21, 2025
SONNY M. MAGNO
Institute Dean
MSU Institute of Science Education – Science High School
Dear Prof. Sonny M. Magno,
I hope this letter finds you well.
We, the undersigned, are requesting permission to conduct a research study entitled
“Problem-Solving Performance of Mindanao State University – Institute of Science
Education Grade 7 Students in Algebra” in partial fulfillment of the requirement for
Research II. The research will involve the Grade 7 ISED students, Lagrange and Dirichlet,
during Prof. Teofista A. Aringa’s class time today, January 21, 2025 at 1:00 PM – 2:00
PM for Lagrange and 2:00 PM – 3:00 PM for Dirichlet.
We kindly ask for your approval with this research plan during the specified times.
We are looking forward to your response and approval. Thank you very much for your time
and consideration.
Respectfully yours,
JASHRYN D. ABAD
RAHAF A. AMPUAN
Researchers
Noted by:
PROF. ASGAR M. ANDA
Research Adviser
Approved by:
PROF. SONNY M. MAGNO
Dean, MSU-ISED Science High School
44
Appendix B
Problem-Solving Performance Test
Name:
Age:
Sex:
Grade level & Section:
Average Grade:
Instructions: Answer the problem according to what is asked. SHOW YOUR
SOLUTIONS NEATLY AND LEGIBLY. Use the space provided to write the solutions.
1. A man needs money so he sold his used mobile phone and watch for P1,250 to his
friend. If he received four times money for mobile phone than the watch, how much
money he received for the mobile phone?
2. A student cuts a 912 cm piece of rope into two pieces for his math project. One piece
is 120 cm longer than the other. How long are the pieces?
912 cm
3. Bashit is planning to fence his rectangular backyard for ducks and chickens. He has 26
m of wire to enclose the backyard. What should be the dimensions of the fence if the
length is 3 m longer than the width?
4. The perimeter of a triangle ABC is 76 cm. Side a of the triangle is twice as long as side
b. Side c is 1 cm longer than side a. Find the length of each side.
45
5. On a 130 km trip, a car travelled at an average speed of 55 kph and then reduced its
speed to 40 kph for the remaining hours of the trip. The trip took 2.5 hours. How much
time did the car travel for 40 kph?
6. Romina and Daniela start from the same point and walk in opposite directions. Romina
walks 20 km per hour faster than Daniela. After 3 hours they are 300 km apart. How
fast did each walk?
7. Jehan goes to school by walking instead of riding a tricycle after learning that it is also
good for health. If the time she spent walking from her house to reach her school at 4
kph is 30 minutes longer than taking the tricycle which requires 5 kph. Find the distance
between her house and her school.
8. The sum of ages of two children is 16 years. Four years ago, the age of the older child
was three times the age of the younger child. Find the present age of each child.
9. Ali and Abdul are teachers from Pagalamatan National High School. They spent at most
P1,100 native products at Saguiaran public market for their coming visitors. Ali spent
P473. How did Abdul spend?
10. The principal’s list includes the names of students who got an average grade of at least
90 in five academic subjects. Leo has grades 89, 90, 88, and 92. What must he get in
5th academic subject to be included in the list?
46
Appendix C
Problem-Solving Performance Levels
Conceptual Understanding Levels
Score Range
High
31 – 40
Moderate
21 – 30
Low
0 – 20
47
Appendix D
Score in Problem-Solving Performance Test of the Grade 7 Students
Respondent
Student 1
Student 2
Student 3
Student 4
Student 5
Student 6
Student 7
Student 8
Student 9
Student 10
Student 11
Student 12
Student 13
Student 14
Student 15
Student 16
Student 17
Student 18
Student 19
Student 20
Student 21
Student 22
Student 23
Student 24
Student 25
Student 26
Student 27
Student 28
Student 29
Student 30
Student 31
Student 32
Student 33
Student 34
Student 35
Student 36
Student 37
Student 38
Student 39
Student 40
Score
18
16
13
24
13
22
15
13
10
21
25
30
15
16
14
11
24
33
18
18
18
6
21
18
11
16
14
16
32
19
11
10
12
14
7
27
24
13
19
10
Performance Level
Low
Low
Low
Moderate
Low
Moderate
Low
Low
Low
Moderate
Moderate
Moderate
Low
Low
Low
Low
Moderate
High
Low
Low
Low
Low
Moderate
Low
Low
Low
Low
Low
High
Low
Low
Low
Low
Low
Low
Moderate
Moderate
Low
Low
Low
48
Student 41
Student 42
Student 43
Student 44
Student 45
Student 46
Student 47
Student 48
Student 49
Student 50
Student 51
Student 52
Student 53
Student 54
Student 55
Student 56
Student 57
Student 58
Student 59
Student 60
Student 61
Student 62
16
22
12
19
8
17
9
14
17
13
15
17
12
12
11
15
22
30
14
26
16
18
Low
Moderate
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Moderate
Moderate
Low
Moderate
Low
Low
49
Appendix E
Documentation of the Respondents Taking the Test
50
51
Appendix F
Statistical Software Analysis Results
. import excel
"C:\Users\admin\Downloads\Softcopydatasopconceptualframework\RESEARCH DATA.xlsx", sheet("data") firstrow clear
. tab Sex
Sex |
Freq.
Percent
Cum.
------------+----------------------------------F |
38
61.29
61.29
M |
24
38.71
100.00
------------+----------------------------------Total |
62
100.00
. summarize
Variable |
Obs
Mean
Std. Dev.
Min
Max
-------------+--------------------------------------------------------StudentNo |
62
31.5
18.04162
1
62
Age |
62
12.91935
.7954458
12
15
Sex |
0
AverageGrade |
62
4.516129
2.622362
1
11
Score |
62
16.80645
6.056669
6
33
-------------+--------------------------------------------------------Scode |
62
1.274194
.51754
1
3
s |
62
.3870968
.4910624
0
1
s2 |
62
4.036252
.7235791
2.44949
5.744563
. pwcorr Age AverageGrade Score, sig
|
Age Averag~e
Score
-------------+--------------------------Age |
1.0000
|
|
AverageGrade | -0.0662
1.0000
|
0.6094
|
Score | -0.0339
0.4719
1.0000
|
0.7935
0.0001
|
. swilk Score
Shapiro-Wilk W test for normal data
Variable |
Obs
W
V
z
Prob>z
-------------+-----------------------------------------------------Score |
62
0.95176
2.692
2.139
0.01623
52
. generate double s2 = Score^(1/2)
. swilk s2
Shapiro-Wilk W test for normal data
Variable |
Obs
W
V
z
Prob>z
-------------+-----------------------------------------------------s2 |
62
0.98436
0.873
-0.294
0.61567
. pwcorr Age AverageGrade s2, sig
|
Age Averag~e
s2
-------------+--------------------------Age |
1.0000
|
|
AverageGrade | -0.0662
1.0000
|
0.6094
|
s2 | -0.0392
0.4584
1.0000
|
0.7626
0.0002
|
. tab s
s |
Freq.
Percent
Cum.
------------+----------------------------------0 |
38
61.29
61.29
1 |
24
38.71
100.00
------------+----------------------------------Total |
62
100.00
. regress s2 Age s AverageGrade
Source |
SS
df
MS
-------------+---------------------------------Model | 8.28558107
3 2.76186036
Residual | 23.6519911
58 .407792951
-------------+---------------------------------Total | 31.9375722
61 .523566758
Number of obs
F(3, 58)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
62
6.77
0.0005
0.2594
0.2211
.63859
-----------------------------------------------------------------------------s2 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------Age |
.0057629
.1032545
0.06
0.956
-.2009235
.2124492
s | -.3517944
.179201
-1.96
0.054
-.7105043
.0069155
AverageGrade |
.1506004
.0336049
4.48
0.000
.0833329
.2178678
_cons |
3.417847
1.352248
2.53
0.014
.7110286
6.124666
-----------------------------------------------------------------------------.
53
Appendix G
Certificate of Proofreading
This is to certify that the research paper entitled,
“PROBLEM-SOLVING PERFORMANCE OF MINDANAO STATE UNIVERSITY
INSTITUTE OF SCIENCE EDUCATION – SCIENCE HIGH SCHOOL
STUDENTS IN ALGEBRA”
conducted and submitted by JASHRYN D. ABAD and RAHAF A. AMPUAN, in partial
fulfillment of the requirements in Research II of the Science High School Curriculum for
the school year 2024-2025, has been edited and proof read based on the standard rules of
the English language, grammar, punctuation, spelling, syntax, and overall composition,
issued on May 2025.
SITTIE AYENA H. CAYE
Editor / Proofreader
54
RAHAF A. AMPUAN
Dimalna II, Housing, MSU, Marawi City
rahaf.ampuan@msumain.edu.ph
Date of Birth
Gender
Citizenship
Civil Status
:
:
:
:
October 22, 2008
Female
Filipino
Single
Educational Background
Secondary:
Junior High School:
Mindanao State University - Institute of Science Education- Science High
School (MSU- ISED-SHS)
MSU Main Campus, Marawi City, 9700 Lanao Del Sur
(2020 - 2024)
Elementary:
Mindanao State University - Integrated Laboratory School (MSU - ILS)
MSU Main Campus, Marawi City, 9700 Lanao Del Sur
(2014-2020)
55
JASHRYN D. ABAD
GMA New Capitol, Marawi City
jashryn.abad@msumain.edu.ph
Date of Birth
Gender
Citizenship
Civil Status
:
:
:
:
February 06, 2009
Female
Filipino
Single
Educational Background
Secondary:
Junior High School:
Mindanao State University - Institute of Science Education- Science High
School (MSU-ISED-SHS)
MSU Main Campus, Marawi City, 9700 Lanao Del Sur
(2020 - 2024)
Elementary:
Ibn Siena Integrated School Foundation (ISISF)
Biyaba, Marawi City, Lanao Del Sur, Philippines
(2014-2020)