ii

THE HEURISTIC APPROACH IN PROBLEM-SOLVING

AND STUDENTS' LEARNING IN LOGIC
AND SET THEORY
Joana Joy A. Bauyon; Erica A. Condicion, and Melody C. De Sosa.
College of Teacher Education, Batangas State University TNEU ARASOF- Nasugbu
20-72362@g.batstate-u.edu.ph 20-71287@g.batstate-u.edu.ph 20-7092@g.batstate-u.edu.ph

ABSTRACT

This study seeks to determine the effects of problem-solving heuristic approach on students' learning
in Logic and Set Theory. Furthermore, the study identifies the heuristic strategies used by the students; the
extent of heuristic strategies in improving students' performance in terms of motivation and interest,
knowledge acquisition, and attitude and behaviour; the effects of the heuristic approach in a student's
ability in solving Logic and Set Theory problems in terms of pre-test and post-test result; and the
significant difference between the pre-test and post-test of students under experimental groups. The study
employed a quantitative and descriptive research design wherein respondents were selected through
purposive sampling. Data was collected through pre-test and post-test from 38 BSEd Mathematics students
enrolled in the course and survey-questionnaires from 126 BSEd Mathematics students in BatStateU TNEU
ARASOF across all years.
The results were treated using scoring, weighted mean, ranking, and z-test. The study reveals that
commonly used heuristic strategies, such as systematic listing, tabulating data, careful problem reading, and
breaking down complex problems, significantly enhance students' performance in the course. These
strategies positively influence motivation, interest, knowledge acquisition, and attitude, with an overall
weighted average considered satisfactory. Additionally, experimental pre-tests yield notably better results
than post-tests, signifying a substantial impact of heuristics on problem-solving ability. Moreover,
integrating Singaporean Mathematics heuristics, including representation, simplification, generic, and
pathway heuristics specified by Sage, T. R. (2022), provide a significant mean difference between pre-test
and post-test scores, highlighting a noteworthy improvement in academic achievement before and after
instruction.
Keywords: Heuristic Strategies, Logic and Set Theory, Problem-Solving, Students’ Learning
1. INTRODUCTION them strategies that allow them to think critically
and solve mathematics problems at a high level.
Education is inevitably one of the vital
factors in developing the human resources that is K to 12 Basic Education Curriculum,
crucial for a nation’s progress on all fronts. In a identified problem-solving as one of the twin goals
broad sense, education refers to any activity that of mathematics education. With this in line, by
significantly influences how someone’s cognitive, emphasizing their persistent re-use in numerous
skill, and attitude are developed. It is made up of contexts, many concepts and techniques’ broad
many disciplines that everyone should be taught applicability is shown. One of these contexts is the
and trained in. Mathematics is one of the oldest use of mathematical languages and reasoning in
academic fields or disciplines that is taught in the application of problem solving in Logic and
every school curriculum worldwide (Guinocor et Set Theory. (Wolfgang, R. 2010). It was then
al., 2020). supported by CHED Memorandum Order no. 75 s,
2017, allowing Higher Education Institutions
In any educational system, teaching and offering the Bachelor of Secondary Education
understanding mathematics are considered as a (BSEd) Program to exercise flexibility in their
significant concern. The Trend International curricular offering. The order issued specified all
Mathematical Science Study Advanced (TIMMS) the curriculum components for each program
examined patterns of students’ achievement in under Article V, Section 9.1 where the course
mathematics and discovered a consistent decline in Logic and Set Theory was identified.
students' math performance over 20 years,
prompting more proactive math guidance strategies Heuristic as a strategy can be applied in
in many Asian countries. The Philippines, as an teaching logic and set theory class. In this setup,
Asian country, embraces mathematics as a general the students will be able to construct their own
education integrated from primary to higher knowledge and create their own representation of
education where students are expected to acquire the problem to solve it heuristically (Singh et. Al
and apply specific skills including knowing and 2018). Heuristics offer the advantage of allowing
understanding, estimating, computing, and solving students to draw conclusions without exhaustive
problems, visualizing and modeling, representing information or complex calculations. This stems
and communicating, conjecturing, reasoning, and from the recognition that humans often seek
making decisions (K to 12 Basic Education acceptable conclusions when unable to grasp all
Curriculum). relevant information. This idea was guided by the
belief that there are alternative ways in solving a
However, issues with mathematical mathematical problem. Based on this premise, the
proficiency are still present, not just in the researchers decided to provide an investigation that
Philippine context but also in other nations. In the will examine the effectiveness of utilizing heuristic
2018 Programme for International Student approaches in solving mathematical problems
Assessment (PISA), Filipino students were specifically in logic and set theory. The four
identified to have low performance levels among categories of Singaporean mathematics heuristic
all the student participants across all participating strategies specified by Sage, T. R. (2022), such as
nations. The results indicate that less than 20% representative heuristics, simplification heuristics,
reached the required proficiency level, with over pathway heuristics and generic heuristics will be
50% displaying very low proficiency. This places utilized to determine the techniques' significant
Filipino students behind their international impact on increased students’ motivation and
counterparts, as evident from PISA scores. In interest in mathematics, knowledge acquisition,
accordance with this, the Department of Education and attitude and behaviour.
(2019), claimed that the poor performance in
mathematics also varied in degree between the
2. OBJECTIVES
students in public and private schools, where the
means were 343 and 395, respectively. For Erif This study investigates the effects of the
Ahdhianto et. Al, (2020), teaching strategies and problem-solving heuristic approaches on the
techniques are a significant component that learning of BSEd Mathematics Major Students of
promote student’s mathematics achievement and Batangas State University TNEU ARASOF
open doors for learners to the development of their Nasugbu in Logic and Set Theory.
mathematical thinking, which is the cornerstone
Specifically, the study sought answers to the
and the basis for a long-term sustainability in
following questions:
mathematics. In order to address these issues, the
1. What are the heuristic strategies used
instructor can aid in students’ learning by offering
by the students in solving Logic and
Set Theory problems?
 2. To what extent does the heuristics survey questionnaires where the number of
approach contribute to improving a respondents is 126 BSEd Mathematics students
student's performance in Logic and taking and taking the course Logic and Set Theory.
The survey was conducted through Google Forms.
Set Theory in terms of:
The survey was used to determine what are the
2.1 motivation and interest in heuristics strategies that they are using and to
Mathematics; gather data with regards to their perception of the
2.2 knowledge acquisition; and effectiveness of the application of heuristic
2.3 attitude and behavior? strategies to problem-solving in their Logic and Set
3. What are the effects of the heuristic Theory class in terms of motivation and interest,
approach on a student's ability to knowledge acquisition and attitude and behaviour.
solve Logic and Set Theory problems 3.3 Data Gathering Instrument
in terms of pre-test and post-test The researchers used survey
results? questionnaires, pre-test, and post-tests to gather the
4. Is there a significant difference necessary information for this study. The
between students' pre-test and post- questionnaire consisted of well-designed questions
test results under the experimental to obtain valuable data. Additionally, the Pre-Test
groups? and Post-Test were developed and validated to
evaluate students' perceptions of the notable
5. What mathematics learning material
changes in their learning before and after
applying the heuristic approach can implementing heuristic problem-solving
be prepared by the proponents? approaches in Logic and Set Theory.
3.4 Data Gathering Procedure
3. MATERIALS AND METHODS
Researchers obtained permission to gather
3.1 Research Environment information through an information consent form,
ensuring adherence to the Data Privacy Act. This
The study was directed at the Batangas study centres on applying heuristic strategies to
State University, the National Engineering mathematical problem-solving, employing
University ARASOF - Nasugbu Campus, Nasugbu methods such as examining examples and creating
Batangas. The proponents chose this school to diagrams to link mathematical notions
make their data-gathering procedure convenient as systematically.
the respondents could give them enough time and
sincerity to fill in the information needed for the The study involved regular first-year
study. students pursuing a Bachelor of Secondary
Education Major in Mathematics at Batangas State
3.2 Participants of the Study University - TNEU ARASOF Nasugbu. The
The study focused on First Year College research included administering pre-tests on
students pursuing a Bachelor of Secondary Boolean Algebra, followed by a two-week
Education Major in Mathematics at Batangas State instructional period on heuristic strategies. The
University - TNEU ARASOF Nasugbu. These instruction focused on Singaporean mathematics
students were chosen because they are the only and covered representation, pathway, generic, and
ones currently enrolled in Logic and Set Theory, simplification heuristics. A post-test was
which is a program under the College of Teacher conducted after the teaching period, and the results
Education (CTE). were recorded. The gathered data were used to
supplement SOP 3 and 4.
The researchers utilized purposive
sampling in choosing the subject of this study Additionally, a survey questionnaire,
since they used their discretion when selecting another data-gathering instrument, was used to
individuals from the population to participate in complete the data needed for the study. The
their surveys. In this study, the data gathering was researchers distributed the crafted and validated
divided into two phases. The first phase is the pre- questionnaire to students taking Bachelor of
test and post-test, where 38 students from first-year Secondary Education Major in Mathematics from
Bachelor of Secondary Education major in the first year to the fourth year. The number of
Mathematics students currently taking logic and respondents is a total of 126 BSEd Mathematics
set theory class participated in a class instruction students.
where the application of heuristic strategies was
OPTION RANGE VERBAL
highlighted. INTERPRETATION
The second phase is the distribution of 4 3.51 - 4.00 Strongly Agree
3 2.51 - 3.50 Agree
2 1.51 - 2.50 Disagree
1 1.00 - 1.50 Strongly Disagree
 Table 3.2 Likert Scales Theory-Related Problems
3.5 Statistical Treatment of Data
The above table revealed that the
The data collected in the study was
statement “I solve part of the problem by splitting
subject to various statistical treatments. The data
complex problems into smaller parts.”, “I read the
was coded, tallied, and tabulated for better
problem carefully and restate it in my own words,”
presentation analysis and interpretation of the
“I systematically list and tabulate data to solve
result. The statistical method includes:
Logic and Set Theory related problems
heuristically’’ ranked first, having the most
Frequency presents the number of actual
significant number of frequencies which are in
responses of the respondents to a specific question
total of 116 students who answered yes from the
item in the questionnaire.
list of Heuristic Strategies.
Weighted Mean is used to determine the
average responses of the research participants in This can be attributed to the fact that a
the different parts of the survey questionnaire. problem seems to be easier if the given data are
Ranking is used to assess the order or listed and tabulated, as well as if it is translated and
responses to the items from the need’s assessment interpreted in its own words depending on how the
questionnaire, with rank one as the highest. students understand, and also by splitting complex
Z-test the means of two groups are problems into smaller parts. The statements
compared using this method. It is frequently discussed how the students used drawing
employed in hypothesis testing to ascertain diagrams/models to illustrate problems with a rank
whether a procedure or treatment genuinely affects of 4, with a frequency of 114.
the population of interest or whether there is a
Using equations to solve the problems
meaningful link between the two groups.
and looking for pattern/s or relationships falls in
the rank of 5.5 and gives a frequency of 109 yes
4. RESULTS AND DISCUSSION answers. Trial and error or guess and check also tie
5. Table 4.1: Heuristic Strategies Used by in with the strategy of making problems more
the Students in Solving Logic and Set straightforward by reducing the value of the
numbers in the situation in the rank of 7.5 with 105
Heuristic Strategies Frequency Rank frequencies. The second least used heuristic of the
students in the rank of 9 and frequency of 98 is
I drew a diagram/model to 114 4 making suppositions and assumptions. The least
illustrate the problem.
used heuristic strategies of the students revealed
I systematically list and 116 2 with the 95 frequency and rank of 10 is looking at
tabulate data to solve Logic the results and working backward towards the
and Set Theory related beginning.
problems heuristically.
This was relevant to the study conducted
I use equations to 109 5.5 by Nokhatbayeva (2020), where he used a Likert
heuristically solve the
problems. scale questionnaire composing the Heuristics
strategies specified by the Curriculum Planning
I look for the pattern(s) or 109 5.5 and Developing Division (CPDD) within the
relationships. Ministry of Education Singapore (MOE). With
I do trial and error or guess 105 7.5
these findings, a study, according to Guzman
and check. (2018), shows the relevancy of heuristics as a
method or strategy for solving mathematical
I make suppositions and 98 9 problems that are methodical and free of context.
assumptions. Additionally, by looking at exceptional examples,
I look at the end results and 95 10 creating a diagram, specializing in the solution,
work backward towards the and generalizing the solution, a heuristic approach
beginning. can link mathematical notions. It is connected to
non-standard mathematical issues like looking
I read the problem carefully 116 2
and restate it in my own
backward or forward. The study recommended that
words. heuristic techniques be used regularly in
mathematics lessons to teach students how to
I make problems simpler by 105 7.5 obtain the information they need from problems.
reducing the value of the
numbers in the situation.

I solve part of the problem by 116 2 2. To what extent does the heuristics
splitting complex problems approach contribute to improving a student's
into smaller parts.
performance in Logic and Set Theory in terms of
(1) motivation and interest in Mathematics, (2) I want to get good 3.89 Strongly 1
knowledge acquisition, and (3) attitude and grades on tests, Agree
behaviour? quizzes, assignments
and projects.
2.1. Motivation and Interest in
Mathematics
General Weighted 3.55 Strongly
Table 4.2.1. Extent of heuristics approach Mean Agree
effects in improving the student's
performance in Logic and Set Theory in
terms of Motivation and Interest in The above table revealed that the
Mathematics Heuristic Approach of problem-solving
dramatically improves the student's performance in
Motivation and Weigh Verbal Logic and Set Theory – mathematics subjects
Interest ted Interpre Rank regarding motivation and interest. It is apparent
Mean tation that most respondents strongly agreed that they
want to get good grades on tests, quizzes,
I actively participate 3.26 Agree 10 assignments, and projects, which have an average
in the discussion, of 3.89. Next, the statement, "I am aware that I
answering exercises need mathematics in the future," – has a weighted
and/or clarifying mean of 3.71. The idea of Heuristic Strategies' role
things I did not in improving students' performance was supported
understand. as well by the fact that First Year BSEd
Mathematics students strongly agreed with the
I am interested in 3.53 Strongly 5 statement, "I feel comfortable working on
doing Mathematics Agree Mathematics problems," which have a weighted
activities. mean of 3.60 and the statement" I make myself
prepared for the mathematics subject," which had
I am aware that I need 3.71 Strongly 2 gained an average of 3.59 and the statement "I am
Mathematics in my Agree interested in doing Mathematics
future. activities" that gained a weighted mean of
3.53. The substantial agreement of the students
I make myself 3.59 Strongly 4 that they are motivated when they answer
prepared for the Agree mathematics equations correctly is evident as the
mathematics subject. majority of them favored the claim with a
weighted mean of 3.52, together with the statement
I feel comfortable 3.60 Strongly 3 that they are aware that Mathematics helps them to
working on Agree understand the importance of other subjects. Also,
Mathematics they are interested in learning Mathematics and
problems. have a passing grade which has all gained a
weighted mean of 3.49. In connection to this, the
I listened attentively 3.45 Agree 9 respondents also showed their utmost agreement to
to the lecture of my the statement that they listened attentively to the
Mathematics lecture of their Mathematics Professor, had a
Professor. weighted mean of 3.45, and lastly, to the statement
where their responses got the lowest rank and least
I am interested in 3.49 Agree 7.5 weighted mean of 3.26 stating that they do agree
learning Mathematics that they participate in the discussion, answering
and having a passing exercises and clarifying things they do not
grade. understand. All in all, the students' responses
revealed that Heuristics strategies of problem
I am aware that 3.49 Agree 7.5 solving significantly improve students'
Mathematics helps me performance in motivation and interest, with a
to understand the general weighted mean of 3.55, verbally
importance of other interpreted as they strongly agreed.
subjects.
These findings are relevant to the study
I am motivated when 3.52 Strongly 6 entitled "The Use of Problem-Solving Heuristics
I answer Mathematics Agree Approach in Enhancing STEM Student's
equations correctly. Development of Mathematical Thinking" by Singh,
Parmjit et al. (2022). The previous study aimed to
evaluate how a problem-solving heuristic I am aware 3.58 Strongly 7.5
application technique affects students' growth in that Agree
mathematical thinking. The mathematics Mathematics
curriculum for primary school places a strong deals with
emphasis on high-interest, career-related themes. situations and
By engaging in activities mapped to the standards ideas that
of the pertinent academic areas, students will come from the
explore cross-disciplinary topics, encourage real world.
creativity, and build higher-order thinking skills. I know the 3.68 Strongly 2.5
Students will apply what they have learned through fact that it Agree
exploration activities, mathematical challenges, provides an
and real-world connections. Singh, Parmjit, et al. understanding
(2022) study came up with the conclusion that a of the world
heuristic approach must be used in order to foster around us.
students' growth as mathematical thinkers; thus, it
plays an essential role in dealing with the student's I am aware 3.69 Strongly 1
that when Agree
motivation and interest to learn more about solving
mathematics. With these relevant findings, the Mathematical
researchers, therefore, concluded that Heuristic tasks, I need
strategies of problem-solving greatly enhance to know the
students' performance in Logic and Set Theory in correct
terms of motivation and interest. procedure.

I understand 3.59 Strongly 6

2.2. Knowledge Acquisition that Agree
Mathematics
Table 4.2.2: Extent of heuristics approach
involves the
effects in improving the student's
remembering
performance in Logic and Set Theory in
and
terms of Knowledge Acquisition
application of
definitions,
Knowledge Weighted Verbal Rank formulas,
acquisition Mean Interpretation mathematical
facts and
procedures.
I know that 3.66 Strongly 4
Mathematics Agree I am familiar 3.58 Strongly 7.5
emphasizes with Agree
argument, mathematics
reasoning and which
logical requires much
analysis. practice,
correct
I know that 3.68 Strongly 2.5
application of
Mathematics Agree
non-routine
improves my
and problem-
thinking
solving
capacity.
strategies.
I am familiar 3.55 Strongly 9
I believe that 3.63 Strongly 5
with the fact Agree
Mathematical Agree
that
problems can
Mathematics
be solved
is important to
correctly in
other subjects.
many ways.
I believe that 2.47 Disagree 10
getting the General 3.51 Strongly
right answer Weighted Agree
is more Mean
important than
understanding The table above expresses the substantial
why the agreement of the first-year students of BSEd
answer works. Mathematics to the idea that Heuristic Strategies of
problem-solving are, to a great extent improving
their performance in terms of knowledge
acquisition. The tabulation revealed that with a Mathematics is not
weighted mean of 3.69, the students strongly confusing.
agreed that they know that when solving
Mathematical tasks, they need to know the correct I like Mathematics, 3.38 Agree 6
procedure. The students showed their strong but I like other
agreement with the idea that they know that subjects just the
Mathematics improves their thinking capacity and same.
that they know the fact that it provides an
understanding of the world around them. These I don’t believe that 3.42 Agree 5
two statements all got an average of 3.68. Mathematics is
Garnering an average of 3.66, the students also boring.
strongly agreed that they know that Mathematics
emphasizes argument, reasoning, and logical I enjoy doing 3.71 Strongly 1
analysis. problems when I Agree
know how to work
Additionally, students showed a firm them out.
agreement that they believe that Mathematical
problems can be solved correctly in many ways,
with a weighted mean of 3.63, and the statement I enjoy the 3.21 Agree 8.5
challenge of hard
that they know that Mathematics deals with
Mathematics
situations and ideas from the real world. They are problems.
familiar with Mathematics, which requires much
practice, and correct application of non-routine and
problem-solving strategies that gained a 3.58 I am proud to say 3.51 Agree 2
that Mathematics is
mean/average. Students also favoured the idea that my favorite, and I
they are familiar with Mathematics as it is essential like it better than
to other courses, gaining an average of 3.55. any other subject.
However, the students disagreed with the statement
concerning their beliefs that getting the correct
I think I am good at 3.45 Agree 3
answer is more important than understanding why Math.
the answer works, wherein their responses
accumulated only a 2.47 weighted mean that tells
that they disagree with the statement. To sum up, I am eager to 3.44 Strongly 4
participate in Agree
students of BSEd Mathematics – first year strongly
discussions that
agreed that Heuristic Strategies of solving involve
contribute to their academic performance in Mathematics.
knowledge acquisition, having a general weighted
mean of 3.51 that falls under the level of
I have confidence 3.37 Agree 7
agreement – strongly agree.
when taking a
The study by Hardi Tambunan (2018) and Mathematics
another study found that heuristic strategies problem.
significantly improve students' mathematical
abilities in high-order thinking, conceptual I am aware that 3.21 Agree 8.5
understanding, creativity, communication, learning
problem-solving, and reasoning. These strategies Mathematics is not
significantly enhance students' performance in frustrating.
Logic and Set Theory knowledge acquisition.
General Weighted 3.51 Strongly Agree
2.3. Attitude and Behaviour
Mean
Table 4.2.3: Extent of heuristics approach
effects in improving the student's
performance in Logic and Set Theory in The table above presented the level of
terms of Attitude and Behaviour agreement and disagreement of the respondents to
the idea that Heuristic Strategies contribute to
Attitude and Weighted Verbal Ran student's academic performance in terms of
Behaviour Mean Interpre k attitude and behavior. The tabulation revealed that
tation students strongly agreed that they enjoy doing
problems when they know how to work the
I believe that 2.37 Disagree 10 problems out. The statement garnered 3.71
weighted mean and a rank of 1. It was also a total mean of 21.47. After a two-week teaching
revealed that they strongly agree that they are period, the researchers administered another set of
proud to say that Mathematics is their favorite, and exams: the post-test. Upon checking their post-test
they like it better than any other subject, which got examination, the researchers found out that
a 3.51 average. Also, students agreed that they students' performance in Logic and Set Theory had
think they are good at Math. This statement was increased significantly, with a mean of 40.08 in
found to have a 3.45 average. Students also agreed their post-test. Comparing the pre-test and post-test
to the statements — they are eager to participate in results with the mean of 21. 47 and 40.08, it is
discussions that involve Mathematics problems identified that students performed well in their
garnering a mean of 3.44, and the idea that they do post-test as it gives a mean difference of 18.61.
not believe that Mathematics is boring with a mean The findings suggested that the
of 3.42. Revealing a 3.38 average, students experimental group who received a treatment
expressed that they like mathematics but other wherein various heuristic problem-solving
subjects the same. Also, students believed they had strategies were introduced significantly improved
confidence when taking a Mathematics problem, their performance. The result showed a significant
gaining a 3.37 average. Also, students agreed with increase in their Logic and Set Theory class
the idea that they enjoy the challenge of hard performance, apparent in the mean difference
Mathematics problems, and the statement that they between the student's pre-test and post-test scores.
are aware that learning Mathematics is not The results of the findings expressed that
frustrating resulted in a 3.21 accumulated weighted the mean difference between the general mean of
mean. However, the first-year students disagreed the experimental group test scores was 18.61,
with "I believe that Mathematics is not confusing," indicating that applying heuristic strategies in
with a weighted mean of 2.37 and a rank of 10. To solving logical problems was practical.
sum up, students from BSEd Mathematics first
year at BatStateU TNEU ARASOF-Nasugbu
clearly showed their agreement that problem- df = 37, α =
0.05
solving heuristic strategies are accurate to a great
extent in improving students' academic
Experiment n Mea Var z Criti P- Resul
performance in terms of attitude and behavior as al Group n (n) ianc cal Valu t
the overall mean responses resulted to 3.31 which e Valu e
falls under the level of agreement — agree. (V) e
(CV)
The study by Pramita & Rusmayadi
(2018) found that heuristic learning techniques Pre-test 3 22.6
enhance students' understanding of concepts and 8 21.47 3
problem-solving, leading to improved learning
results and increased self-efficacy. Both studies Post-test 3 8.62 8. 1.96 0.000 Signif
suggest that heuristic strategies are crucial for 8 40.08 0 881 icant
4
improving students' performance in Logic and Set
Theory in attitude and behavior.
The researchers' findings align with
3. What is the effect of heuristic approach Singh, Parmjit et al.'s (2022) study, which
on the student's ability in solving Logic evaluated the impact of problem-solving heuristics
and Set Theory problems in terms of pre- on students' mathematical thinking. Both studies
test and post-test results? used pre-test and post-test data. Both studies found
that students who applied heuristics outperformed
Table 4.3. Mean of Individual Pre-test,
Post-test of First Year BSEd Mathematics
those who did not, suggesting the use of heuristics
Students to enhance mathematical thinking skills.4. Is there
a significant difference between the pre-test and
post-test of students in the experimental group?

Pre - Post - Difference Table 4.4. Output for Independent Z-

Test Test test based on the Pre-test and Post-test
(Mean) (Mean) Results of Experimental Group
The thirty-eight (38) students who
received experimental treatment in their class
Experimen 21.47 40.08 18.61
tal Group acquired an increased performance (Pre-test =
21.47) (Post-test = 40.08) after they undergo on
The table above shows the mean/average two-week instruction utilizing various problem-
scores obtained by students in the experimental solving heuristic approaches. This means student
group. The pre-test of an experimental group gives performance improvement was significant since,
based on the findings, the researchers failed to 4. Utilizing heuristic strategies can boost
accept the null hypothesis for t = 8.04 p (0.000881) students' confidence and positivity when
< 0.05. After receiving the experimental treatment, solving logical problems. It is believed
the class performed better in their Logic and Set that these strategies can cultivate a better
Theory class than when they were taking a attitude and behavior towards Logic and
conventional method of instruction. The findings Set Theory class.
also revealed the significant difference between the 5. The study revealed that Heuristics had a
mean of the experimental groups' pre-test and post- significant impact on the student’s ability
test scores. The 18.61 mean score difference to solve problems in logic and set theory.
clearly explained that students' increased class The experimental groups showed
achievement. Since the z-value (z=8.04) was significantly better post-test scores
higher than the critical value (CV=1.96), compared to their pre-test scores.
proponents claimed that the problem-solving 6. The comparison of the scores of the
heuristic approach implemented during the students from the two different sets of
instruction with the experimental group effectively examinations revealed a significant
solves logical problems quickly. Therefore, the relationship. Thus, the problem-solving
results were statistically significant, and the heuristic approaches implemented during
proponents rejected the null hypothesis. the instruction with the experimental
group is an effective strategy for solving
The study's findings align with Abraham D.
logical problems easily.
Cacay's (2022) experimental study, which used
pre-test and post-test methods. Both studies found
improvements in learning performance and student 7. RECOMMENDATIONS
retention with the heuristic strategy, with a From the results and assumptions of the study,
significant difference between pre-test and post- the following recommendations were
test results in the experimental groups. recommended:
1. Researchers recommend that teachers should
introduce problem-solving heuristic approaches
6. CONCLUSIONS
to students so they can use them as a means to
Based on the above-stated summary of the enhance their learning in Logic and Set Theory
findings, the following conclusions were classes.
crafted: 2. Researchers recommend that teachers use a
1. The researchers found that the most developed learning plan for Logic and Set
commonly utilized heuristic strategies for Theory courses to integrate heuristic strategies
solving Logic and Set Theory problems to further address the learning challenges in-
were (1) systematically listing and class instruction.
organizing data, (2) restating the problem 3. Teachers should practice applying heuristic
in one's own words after careful reading, approaches to their innovative teaching
and (3) breaking down complex problems strategies to help students improve their
into smaller parts. To develop their performance in class.
mathematical thinking, students should 4. Future researchers may use this study as an
employ these strategies in problem- additional and supplementary reference to
solving. However, the least utilized serve as a foundation for developing new
strategy was working backward from the research related to the topic.
end results to the beginning. 5. For further validation, future researchers may
2. Many students recognize the importance work on similar studies investigating the effects
of mathematics for their future and strive of problem-solving heuristic approaches on
to achieve high grades in their Logic and students' learning with a larger sample of
Set Theory classes. By utilizing problem- respondents.
solving heuristic strategies, they are able
to maintain their motivation and REFERENCES
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ACKNOWLEDGEMENT
The researchers, with much sincerity and deep appreciation, would like to convey their heartfelt
thanks and gratitude to the following persons who inspired them and helped them in the preparation and
completion of this research:

First of all, the researchers would like to thank the Almighty God for giving them the wisdom,
courage, and guidance to go beyond all the hardships that they encountered to make this study possible and
worthwhile;

Dr. Tirso A. Ronquillo, University President, for upholding the University’s vision, mission, as well
as for granting researchers the opportunity to pursue this study;

Dr. Enrico M. Dalangin, Executive Director of Batangas State University TNEU ARASOF -
Nasugbu Campus, for the support to the Department’s research endeavours;

Dr. Anania B. Aquino, Dean College of Teacher Education, for her substantial support and
encouragement in the success of this study;

Mr. Joselito S. Arquiza, the researchers’ thesis adviser, for his thorough analysis, suggestions, and
criticism that motivated the researchers and for his willingness to share his expertise to guide the proponents;

Dr. Anania B. Aquino, Mrs. Marilou A. Romarate, and Asst. Prof. Gliceria R. Quizon, the Panel
Members of the Thesis Committee, for the direction and assistance, which allowed the researchers to complete
the study;

The respondents for giving time and effort in answering their survey questions; and

The researchers’ families and friends who served as their source of inspiration and encouragement
and by giving them financial support, which was a great help in pursuing this study.

J.J.A.B

E.A.C

M.C.D