INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)
ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue XI November 2025
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Students’ Competencies, Least Mastered Topics, and Performance in
Mathematics in the Modern World
Charina C. Gloria
Associate Professor V, Capiz State University Burias, Mambusao, Capiz, Philippines
DOI: https://dx.doi.org/10.47772/IJRISS.2025.91100119
Received: 10 November 2025; Accepted: 20 November 2025; Published: 02 December 2025
ABSTRACT
Students are expected to develop competencies in mathematics that integrate knowledge, skills, and values.
Exhibiting these competencies in mathematics is one of the goals of mathematics education. Despite the efforts
of the teachers to make students learn and acquire competence in the subject, difficulties are still encountered
by the students. This descriptive-correlational research was conducted at Capiz State University during the
Second Semester, School Year 2023-2024 to assess the level of acquired competencies, least mastered topics,
and performance of first-year college students in Mathematics in the Modern World. Data were gathered using
valid and reliable questionnaire, and were analyzed using descriptive and inferential statistics. Results of the
study revealed that first-year college students generally had a high level of acquired competencies in terms of
knowledge, skills, and values. However, there were topics identified as the least mastered topics namely, logic,
sets, inductive and deductive reasoning, measures of dispersion, probability, and correlation. Students had an
average level of performance in the subject. The acquired competencies by the respondents were significantly
related to their performance. This implies that the higher the competencies acquired by the students, the higher
the probability of getting high performance.
Keywords: knowledge, values, skills, least mastered topics, performance,
INTRODUCTION
One of the general education subjects offered during the first semester in the college curriculum is
Mathematics in the Modern World (MMW) with a 3-unit credit. Four mandatory topics in this subject are
mathematics in our world, mathematical language and symbols, problem solving and reasoning, and data
management, while two elective topics will be chosen depending to the need of the program to make a whole
course (CMO 20, Series 2013).
The course is intended to make students appreciate the nature and uses of mathematics in everyday life. The
competencies in MMW are not only focused on the cognitive aspect but also affective and psychomotor skills
which are significant in the achievement of the intended learning outcomes of the MMW.
According to Cabral (2022), the topics in MMW are very useful to students in their daily lives and by studying
the topics it would help them to go beyond the typical interpretation of mathematics as simply a bunch of
formulas, but as a source of aesthetics in patterns of nature.
In the study of Roman (2019), students experienced difficulties on the different topics of MMW with
satisfactory performance in the subject. In addition, Nabayra (2022), identified the least mastered topics in
MMW and found that mathematics learning in the new normal is challenging and difficult.
During the pandemic, and even in times of crisis up to the present, asynchronous classes and modular learning
have been widely implemented as alternative modes of instruction. In response, teachers were tasked to
develop instructional materials in mathematics and other subject areas to ensure continuous learning. These
materials are carefully designed to align with the students’ level of understanding, providing ample exercises
and activities that help learners acquire essential skills and knowledge from each lesson. Moreover, teachers
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)
ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue XI November 2025
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ensure that the objectives and learning outcomes of Mathematics in the Modern World (MMW) are effectively
achieved through well-structured and student-centered instructional materials.
Despite the efforts of the teachers to make students learn and attain the competencies in the subject, challenges
are still encountered by the students. The researcher believes that if students acquire the competencies intended
for MMW, students can perform well in mathematics. Hence, this study.
The objective of the study was to determine the acquired competencies, least mastered topics and performance
of students in Mathematics in the Modern World. Specifically, it sought answer to the following questions.
1. What is the level of competencies of the first-year college students in Mathematics in the Modern World
(MMW) as an entire group, in terms of its dimensions namely knowledge, values, and skills, and when
grouped according to sex and specialization?
2. What are the least mastered topics in Mathematics in the Modern World (MMW) by the respondents?
3. What is the respondents’ level of performance in Mathematics in the Modern World?
4. Is there a significant relationship between competencies and performance in Mathematics in the
Modern World (MMW) of the respondents?
Null Hypothesis:
1. There is no significant relationship between competencies and performance in Mathematics in the
Modern World (MMW) of the respondents.
METHODOLOGY
Research Design and Participants
This study employed a descriptive-correlational design to ascertain the relationship between the competencies
and performance of first-year college students in the College of Education of Capiz State University during the
Second Semester of School Year 2023-2024. The respondents of the study were selected through a simple
random technique. Cochran’s formula was used to determine the sample size using the criteria of 5% level of
precision, a 95% confidence level, and 0.5 variability. Then, the sample size was proportionately distributed to
different majors/specializations using the formula for allocation.
Data Collection Tool
The questionnaire was the primary instrument used in gathering data for this study. It was composed of three
parts. Part 1 gathered information about the respondent’s sex and major/specialization. Part II is a 5-point
Likert scale comprising 23 item statements adopted from the study of Roman (2019) that would measure the
competencies in math, namely knowledge, skills, and values. Part III is a 50-item multiple choice test adopted
from the study of Nabayra (2022) that would cover the four mandatory topics in this subject, namely
mathematics in our world, mathematical language and symbols, problem solving and reasoning, and data
management.
The researcher acknowledges the constraints and weaknesses of the instrument, although these are
standardized and adopted from other studies, and have been validated by experts. The competency data were
based solely on self-assessment, which is susceptible to bias due to respondents inaccurately assessing their
own abilities and may not accurately reflect their actual competency.
Data Gathering Procedure
Before administering the instrument, the researcher sought permission from the College Dean and the Campus
Administrator. After the permit was approved, coordination was done with the program chair and advisers to
administer the instrument to the students involved in the study. The researcher then personally administered
the questionnaires to ensure a 100 percent retrieval. The data were consolidated and coded for statistical
analysis.
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)
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Statistical Analysis
Data were analyzed using both descriptive and inferential statistics. Descriptive statistics such as frequency
count, percentage, mean, and standard deviation were utilized to describe the respondents’ competencies, least
mastered topics, and performance. For inferential analysis, Spearman’s rho was used to determine the
relationship between competencies and performance of the respondents. Results were interpreted at 0.05 level
of significance.
RESULTS AND DISCUSSION
Profile of the Respondents
The majority of the respondents were female (87.27%). Most of them were enrolled in the BSED program with
a specialization in English (20.9%), followed by Filipino (17.3%). A considerable number were from Social
Studies and Science (12.7% each), while the smallest group came from BSED Mathematics (7.3%).
Meanwhile, both the BEED and BPED programs had an equal number of respondents, each comprising 14.5%
of the total.
Level of Competencies of First Year College Students in Mathematics in the Modern World
Table 1 presents the level of competencies of the respondents. A majority of them were assessed to have a high
level of competencies (60.91%), while one-third (33.64%) of them attained a very high level. Only a small
proportion (5.45%) had an average level. The mean of 4.01 with a standard deviation of 0.41 indicates that, as
a whole, respondents' competencies are generally at a high level. The result of the study negates with the
findings of Gloria (2015) that students have low mathematical competence.
Table 1. Level of competencies of the respondents.
Level
Frequency
Percent (%)
Very High
37
33.64
High
67
60.91
Average
6
5.45
Total
110
100.00
Mean=4.01, SD=0.41 (High)
Note: Interpretation is based on the scale: 1.00-1.49 (Very Low), 1.50-2.49 (Low), 2.50-3.49 (Average), 3.50-
4.49 (High), 4.50-5.0 (Very High)
Shown in Table 2 is the mean score per item-statement indicator on the three dimensions of competencies. In
terms of knowledge, the respondents obtained a mean of 3.85, indicating a high level, with the highest rating
on the ability to analyze text critically (M=4.25, Very High). For values, the mean was M=4.10 (High),
highlighted by the very high ratings on taking responsibility for knowing and being Filipino (M=4.45) and
respect for human rights (M=4.39). Meanwhile, under skills, the mean was 3.97 (High), with the highest rating
on working effectively in a group (M=4.19, High). As a whole, these results suggest that respondents have
acquired competencies at a high level across knowledge, values, and skills reaching a very high level. This
result conformed with the findings of Roman (2019) that first-year college students have a high extent of
acquisition of knowledge, values, and skills as set in the curriculum mapping of the Mathematics in the
Modern World.
Table 2. Mean score per item statement-indicator on the three dimensions of competencies.
Mean
SD
V.I.
4.25
0.59
Very High
3.94
0.61
High
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ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue XI November 2025
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3.91
0.61
High
3.73
0.66
High
3.43
0.70
High
3.85
0.48
High
4.22
0.60
Very High
3.95
0.71
High
3.95
0.67
High
4.45
0.58
Very High
3.95
0.63
High
3.87
0.59
High
4.05
0.60
High
4.23
0.67
Very High
3.81
0.67
High
4.39
0.61
Very High
4.18
0.61
High
4.10
0.41
High
4.19
0.60
High
3.81
0.68
High
4.14
0.71
High
3.82
0.73
High
3.78
0.70
High
4.03
0.64
High
4.05
0.71
High
3.97
0.50
High
Note: Interpretation is based on the scale: 1.00-1.49 (Very Low), 1.50-2.49 (Low), 2.50-3.49 (Average), 3.50-
4.49 (High), 4.50-5.0 (Very High)
When the respondents were grouped according to profile variables (Table 3), in terms of sex, both male
(M=3.94) and female respondents (M=4.02) had rated at a high level, with females obtaining a slightly higher
mean. When classified according to specialization, the level of acquisition of the respondents ranged from a
high (3.68) to a “very high” level (4.23). The highest competency levels were noted among BSED Social
Studies (M=4.23, Ver High) and BSED Science (M=4.22, Very High). The BSED English (M=4.09) and
BPED (M=4.04) groups also reflected high competency levels, while the BSED Filipino (M=3.68) and BSED
Math (M=3.72) specializations had the lowest means, though still within the high category. Overall, the results
indicate that respondents across sex and specialization generally demonstrated competencies at a high level,
with notable strength in Social Studies and Science Specializations.
Table 3. Level of competencies of the respondent when grouped according to profile variables.
Variables
Mean
Sd
V.I.
Sex
Male
3.94
0.38
High
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Female
4.02
0.41
High
Specialization
BSED English
4.09
0.31
High
BSED Filipino
3.68
0.42
High
BSED Social Studies
4.23
0.31
Very High
BSED Science
4.22
0.36
Very High
BSED Math
3.72
0.40
High
BEED
3.99
0.35
High
BPED
4.04
0.42
High
Note: Interpretation is based on the scale: 1.00-1.49 (Very Low), 1.50-2.49 (Low), 2.50-3.49 (Average), 3.50-
4.49 (High), 4.50-5.0 (Very High)
Least Mastered Topics in Mathematics in the Modern World
Results show that there were seven (7) subtopics that were not mastered by the first-year college students, as
seen in figures 1 to 4.
These subtopics were logic (15.45%), four basic concepts (sets, functions, relations, and binary operations)
(35.64%) under Chapter 2-Mathematical Language and Symbols; inductive and deductive reasoning (11.87%)
and recreational Problems using mathematics (33.64%) under Chapter 3-Problem Solving Reasoning; and
measures of dispersion (15.00%), probability and normal distribution (18.18%), and linear regression and
correlation (25.23%) under the Chapter 4 - Data Management.
The least mastered topics were identified based on the mean percentage scores (MPS), calculated by dividing
the number of students who answered the topic correctly by the total number of respondents, and then
multiplying by 100.
The results imply that first-year students found these topics difficult, particularly in logic, reasoning, and data
management. This suggests that teachers should strengthen discussions and provide additional activities on the
least mastered topics to improve students' understanding. Likewise, implementing intervention programs such
as remedial instruction, module enrichment, or contextualized learning strategies would help address these
learning gaps.
According to Barlovits, S., Jablonski, S., Lázaro, C., Ludwig, M., and Recio, T., (2021), the new normal
learning environment may have also affected the results of the least mastered topics since it’s difficult for the
teachers to teach math concepts like statistics, problem solving, and logic in an online or even flexible learning
environment which limited personal communication unlike in personal face-to-face interaction. In addition, it
may also create key challenges for students, such as acquiring electronic devices for engagement, internet
connectivity issues, electricity outages, and adapting teachers and students to this new mode of learning (The
Gleaner, 2020).
Moreover, there is a need for teachers to incorporate 21st-century teaching tools, gadgets, and technology in
teaching mathematics. Technology offers additional opportunities for students to engage with and explore
mathematics concepts, fostering a positive attitude and perception toward the subject (Chand, S. et al. 2021)
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Figure 1. Percentage of Correct Responses of Freshmen Students per Topic in Chapter 1 – “Mathematics in
Our World”
Figure 2. Percentage of Correct Responses of Freshmen Students per Topic in Chapter 2 – “Mathematical
Language and Symbols”
Figure 3. Percentage of Correct Responses of Freshmen Students per Topic in Chapter 3 – “Problem Solving
and Reasoning”
Figure 4. Percentage of Correct Responses of Freshmen Students per Topic in Chapter 4 – “Data
Management”
62.50%
77.58%
61.59%
1
2
3
45.45%
35.64%
15.45%
1 2 3
11.82%
65.91%
72.73%
47.95%
33.64%
1 2 3 4 5
81.21%
43.33%
15.00%
40.91%
18.18%
25.23%
1 2 3 4 5 6
Legend:
1- Gathering, Organizing, Representing,
and Interpreting Data
2- Measures of Central Tendency
3- Measures of Dispersion
4– Measures of Relative Position
5- Probability and Normal Distribution
6- Linear Regression and Correlation
Legend:
1- Inductive and Deductive
Reasoning.
2- Polya's Four Steps in Problem
Solving
3- Problem Solving Strategies
4– Mathematical Problems Involving
Patterns
5- Recreational Problems Using
Mathematics
Legend:
1 - Expressions, Sentences and Variables
2 - Sets, Functions, Relations, and Binary
Operations
3 - Elementary Logic: Negation,
Connectives and Quantifiers
Legend:
1 - Patterns and Numbers in Nature and the
World
2 - Fibonacci Sequence
3 - Mathematics for organization, prediction,
control, and as an indispensable tool
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Level of Performance in Mathematics in the Modern World
Data in Table 4 shows that the majority of the respondents (65.5%) had an average level of performance in
MMW, thirty percent of them had a low level, while only a few (4.5%) reached a high level of performance. In
general, the mean of 23.40 with a standard deviation of 5.12 indicates that students had average performance in
math. It can be inferred that prior math exposure, attitude toward math, and other factors can influence math
performance. This is consistent with the findings of Roman (2019), which reported a satisfactory performance
among first year college students in Math in the Modern World. Furthermore, students demonstrate little
mastery of essential mathematical concepts, indicating a need for preparatory programs to enhance their
proficiency and performance in advanced mathematics courses (Santos et al., 2022).
Table 4. Level of performance in MMW
Level
Freq
Percent (%)
High
5
4.5
Average
72
65.5
Low
33
30.0
Total
110
100.0
M=23.40, SD=5.12 (Average)
Relationship between competencies and performance in MMW by the respondents
Table 5 reflects the relationship between competencies by the respondents and their performance in MMW.As
disclosed, the r-value of 0.264 with the probability value of 0.005 is lesser than 0.05 alpha. This indicates a
significant positive correlation between the two variables, though the correlation is weak. A positive r-value
suggests that an increase in one variable is generally associated with an increase in the other, but only to a
small extent. Key factors, such as students' prior math knowledge, their interest, and foundational skills, likely
contribute to stronger math performance. Instructional quality and access to learning resources can also play
crucial roles by supporting these mediating variables and further enhancing performance. Since the p-value is
statistically significant, the null hypothesis stating that there is no significant correlation between the students’
competencies and performance is rejected. These findings suggest that when students acquire essential
competencies in mathematics, their performance improves, while limited competencies are associated with
lower performance.
Table 5. Relationship between competencies and performance of the respondents.
Variables
Test
R-Value
Sig
Competencies and Performance
Spearman’s rho
0.264**
0.005
**. Correlation is significant at the 0.01 level (2-tailed).
CONCLUSIONS
Based on the findings of the study, the following conclusions were made.
1. The first-year college students have acquired a high level of competencies in terms of knowledge, values,
and skills. This implies that classroom activities are effective in enhancing their personal growth, which they
can apply to real-life situations.
2. The students have not mastered the topics, namely logic, inductive and deductive reasoning, measures of
dispersion, probability and normal distribution, and linear regression and correlation. This implies that
students have encounter difficulties in understanding these concepts suggesting the need for remedial
activities, and the use of more contextualized examples to address the gap.
3. The students enrolled in Mathematics in the Modern World (MMW) have demonstrated an average level of
performance in the subject. This implies that while students were able to meet the minimum expectation,
there are still challenges that hinder them in achieving higher levels of mastery. Hence, there is a need to
identify factors that affect their performance in the said subject.
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4. The acquired competencies of students are significantly related to their performance in Mathematics in the
Modern World (MMW). This implies that the lower competencies tend to have lower performance in
MMW, while those with higher competency levels perform better.
RECOMMENDATION
1. Teachers should encourage students to acquire and further develop knowledge, values, and skills in
mathematics, since these are the necessary requirements to make learning meaningful and applicable to
real-life situations.
2. Teachers should provide more contextualized examples, varied activities, and apply a variety of teaching
strategies and techniques to help students understand difficult topics, such as logic, reasoning, measures of
dispersion, probability, and regression. They should also encourage students to participate and ask
questions during class discussions.
3. Since students have demonstrated an average performance in MMW, teachers may devise a peer tutorial
program to assist those who have difficulty in mathematics.
4. Teachers should motivate and expose their students to the real world to gain more experience and
appreciate the beauty of Mathematics. With these, they would perform better in the subject.
Ethical Consideration
All data collected for this study were obtained through voluntary participation and with the informed consent
of each respondent. Participants were fully informed about the nature and scope of this research, how their data
would be used, and their right to withdraw from the study at any time. Confidentiality and privacy were strictly
maintained throughout the data collection and analysis process.
Conflicts of Interest
The authors declare no conflicts of interest regarding the publication of this paper.
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