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1. AIP Conference Proceedings 2572, 050004 (2023); https://doi.org/10.1063/5.0119342 2572, 050004
© 2023 Author(s).
Analysis of mathematical problem solving
skill of fifth grade students on geometry
material
Cite as: AIP Conference Proceedings 2572, 050004 (2023); https://doi.org/10.1063/5.0119342
Published Online: 12 March 2023
Nur Habibah, Dadan Fitria Ramdhan, Inne Marthyane Pratiwi, et al.
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2. Analysis of Mathematical Problem Solving Skill of Fifth
Grade Students on Geometry Material
Nur Habibah a)
, Dadan Fitria Ramdhan b)
, Inne Marthyane Pratiwi c)
and
Muhammad Rifqi Mahmud d)
Teacher Education Islamic Elementary School, Faculty of Tarbiyah and Teacher Training, State Islamic University
Sunan Gunung Djati Bandung, Soekarno Hatta Street, Bandung City 40292, West Java, Indonesia
a)
Corresponding author: nurhabibahbdg11@gmail.com
b)
dadanramdhan74@uingsd.ac.id
c)
inne.mp@uinsgd.ac.id
d)
m.rifqi.mahmud@uinsgd.ac.id
Abstract. In mathematics learning, students have to master one of the mathematic's skills, which is problem solving skills.
The result of research of PISA in 2008 showed that the percentage of students' skills in finishing some high-level
mathematics questions only represented 1% from the average of OECD with 11%. The goal of this research is to identify
the students' problem solving skills in the subject of geometry in the fifth grade. This research uses qualitative and
descriptive methods. The subject of research is all students of fifth grade in one of the Bandung regency elementary schools,
including 39 people. The data acquisition is by giving a test of problem solving, an observation, an interview, and
documentation. The data analysis technique is based on Miles and Huberman's qualitative analysis of data, which entails
data reduction, data presentation, and data verification. According to the research findings, the average score for students'
ability to solve problems in the subject of geometry is 53,9. That information indicates that the students' problem solving
ability is lacking. There are 20% of students who belong to a perfect group, 10% who belong to a good group, 12.8% who
belong to a sufficient group, 33% who belong to a minus group, and 23.1% who belong to the least category. When it
comes to the approach used by students to complete the issue in solving the question, it is the strategy of drawing a picture,
creating a table, guessing and retesting, creating some sub-problems, and utilizing a formula.
INTRODUCTION
Education is an activity that supports human life to gain lessons, experience, and open insight. Education functions
to eliminate ignorance, develop skills, and build characters to educate the nation's life1
. Schools function as a center
for educational activities in the building, growing and developing the human potential to solve a problem for the
Indonesian nation2
. As an educational center, there is an interactive process to transfer knowledge between educators,
students, and learning resources called learning.
Learning in elementary school includes several subjects. One of the subjects is mathematics. Mathematics is known
as a subject related to numbers or calculations. Therefore, mathematics is a subject that has its peculiarities.
Mathematics is a scientific discipline that has abstract concepts and deductive reasoning3
. The standard content of
mathematics subjects from first grade to sixth grade is gradually given from easy material to difficult material, adapted
to the stages of development. The aim of mathematics since elementary is to prepare students to solve all kinds of
changes that develop in real life4
. Currently, mathematics has become a common science as the basis for the
development of modern technology5
. Therefore mathematics is found in everyday life. Often in everyday life, whether
or not there are problems related to mathematics are realized. The problems were found to require some level of
mathematical understanding, mathematical reasoning, and mathematical tools6
.
Students must possess several skills in pursuing mathematics. Problem solving skill is one of the skills that students
must possess. Halmos explained that problem solving is the center of mathematics7
. Problem solving includes high-
Education of Science, Technology, Engineering, and Mathematics International Conference (ESTEMIC 2021)
AIP Conf. Proc. 2572, 050004-1–050004-10; https://doi.org/10.1063/5.0119342
Published by AIP Publishing. 978-0-7354-4317-4/$30.00
050004-1

3. level intellectual activity so that students can work on High Order Thinking Skill (HOTS) problems by integrating
their knowledge with previously acquired knowledge8
. Halmos states that solving problems requires various
mathematical concepts to be organized7
.
Problem solving skill is very important for elementary school students because, with these skills, students can open
up space in finding and pursuing new things to achieve certain goals9
. Problem solving is not something separate from
mathematics but a process that must be taken in finding a solution to a problem. Without problem solving skills, the
usefulness of mathematics will be limited. In contrast, it will be more meaningful with the mathematical problem
solving skills because students can open up space in finding ways and making plans to find solutions to problems. The
Program for International Student Assessment (PISA) measures students from various skills, including reading,
mathematics, science, and problem solving10
. PISA measures students' skills to reproduce knowledge and assesses the
skill of students to apply knowledge in certain situations. Therefore, PISA uses questions related to everyday life that
are close to students and often encountered. The questions in it require students to answer questions that have a high
level and require good problem solving skills11
.
The results of the 2018 PISA research published by the OECD on December 3, 2019, showed that the average
score of Indonesian students in mathematics was 379 from the OECD average score of 487. This result shows that the
position of Indonesian students' skill in mathematics were below the average. In particular, the percentage of
Indonesian students' skills to solve high-level math problems is only 1% of the OECD average of 11%12
. Based on the
results of an interview with the fifth-grade teacher in one of the elementary schools of Bandung regency, the students
felt scared when learning mathematics. It has an impact on mathematical problem solving skills in fifth-grade students.
This is shown by the fact that the value of the Mid-Semester Assessment for odd semester mathematics for the 2020-
2021 academic year is below the average of 63.15 from the mathematics minimum completeness standard of 70.00.
Students have difficulty understanding the questions and are fixated on formulas. When the student given questions
that have different types, they will feel difficult to interpret the questions. The problems that arise in these schools
make researchers interested in analyzing elementary school students' mathematical problem solving skills. From a
mathematical point of view standpoint, in geometry, there is an approach to solving a mathematical problem13
.
Therefore, researchers interested in analyzing the problem solving skills of fifth-grade students on geometry.
METHOD
This research used a qualitative approach with a descriptive method to describe the problem-solving skill of
elementary school students in fifth grade on the material of the spatial structure. Data sourced from student answer
sheets on math problem solving tests that have been tested for validity by expert lecturers and other data sources,
namely the results of interviews with students. Data analysis techniques used were data reduction, data presentation,
and data verification. Data verification based on the interpretation table of mathematical problem solving skills as
follows.
RESULTS AND DISCUSSION
The research started from the distribution of test question sheets to students. The problem solving skill test contains
four questions about the description of the spatial material, tested for validity by a mathematician lecturer. The problem
solving skill test was done by students individually, corrected by researchers, and given back to the students for five
days. Nine students attended the first day, 10 students attended the second day, eight students attended the third day,
three students attended the fourth day, and on the fifth day was attended by nine students. The research started on
Monday, June 07, 2021 until Saturday, June 12, 2021. After giving the test, the researcher analyzes the students’
problem solving skill based on the indicators of Polya’s problem solving skill (understanding the problem, planning
strategies, implementing strategies and re-checking) then classifying students' skills based on scoring guidelines. The
researcher gave four questions, and it shown in Figure 1, 2, 3, dan 4.
FIGURE 1. Question Number One
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4. FIGURE 2. Question Number Two
FIGURE 3. Question Number Three
FIGURE 4. Question Number Four
Mathematical Problem Solving Skill
The recapitulation of students' problem solving skill scores can be seen in table 1.
TABLE 1. The Recapitulation of Students' Problem Solving Skill Scores
Data Score
Score Max 100
Score Min 0
Mean 53,9
Many Students 39
Based on table 1, from 39 fifth grade students, the average problem solving skill score was 53.9. The largest score
is 100, and the smallest score is 0.
The level of students’ problem solving skills based on the category shown in table 2.
TABLE 2. The Level of Students’ Problem Solving Skill
No Score Category Many Students Percentage
1 80,00 – 100 Excellent 8 20,5 %
2 65,00 – 79,9 Good 4 10,3 %
3 55,00 – 64,9 Sufficient 5 12,8 %
4 40,00 – 54,9 Low 13 33,3 %
5 00,00 – 39,9 Lowest 9 23,1 %
According to Table 2, the level of problem solving ability of fifth-grade students is 8 students or 20.5 percent in
the excellent category, 4 students or 10.3 percent in the good category, 5 students or 12.8 percent in the sufficient
category, 13 students or 33.3 percent in the low category, and 9 students or 23.1 percent in the lowest category.
The description of problem solving skills based on the category of mathematical problem solving skills taken from
the students' answer sheets on item number one.
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5. The Description of Students’ Problem Solving Skill in Excellent Category
FIGURE 5. Students' Answers in Excellent Category on Question Number 1
Based on Figure 5, it can be seen from the indicator of the first mathematical problem solving skill (understanding
the problem). Students understand the problems contained in the problem by writing the problem correctly. Students
wrote V = 630, p = 10 × height, l = 4 is longer than t, and t = 2. The second indicator (planning strategy), students
plan the search for length, width, and height, starting with drawing a cube, then changing it to a beam and writing
down the length and width based on their hypothesis. Then they proceed by guessing the height first and then proceed
with the third indicator (implementing the plan) by multiplying the length, width, and height that have been guessed
to find a volume of 630 m3. In the fourth indicator (re-check), students check when the calculation is processed. The
students found the multiplication of the length, width, and height to get a volume of 630 m3
. Then, they conclude that
the length of the building is 30 m (10 times the height), the width of the building is 7 m (4 m longer than high), and
the height of the building is 3 m (by guessing).
The Description of Students’ Problem Solving Skill in Good Category
FIGURE 6. Students' Answers in Good Category on Question Number 1
Based on Figure 6, students wrote the first indicator of problem solving skill, which is to understand the problem
by directly guessing the height of the building is 3 m. Students immediately write that the length of the building is 30
m, the width of the building is 7 m, and the height of the building is 3 m. Students in this problem devise strategies
either directly or through the use of logic. Then, they implement the strategy by determining the length of the building,
which is 10 times the height, which is 10 × 3 = 30, as well as the width. Students determine the width by calculating
4 m longer than the height, 4 + 3 = 7. Students did the fourth indicator, namely checking again. Nevertheless, students
are not complete in re-examining the results. It can be seen from the counting results that students only count 30 × 7
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6. employing repeated addition. Students did not complete the questions, and they did not find answers that matched the
volume listed on the questions.
The Description of Students’ Problem Solving Skill in Sufficient Category
FIGURE 7. Students' Answers in Suffucient Category on Question Number 1
Based on Figure 7, students understood the problem correctly. Students wrote the hypothesis based on the
questions correctly. Then in the second indicator (planning strategies), students used guessing and testing strategies.
Students' answers can be seen that students guess the height first by guessing the height of the building, which is 2 m.
Then proceed with the third indicator (implementing the strategy), determining the length with a height of 2, so the
length of the building obtained is 20 m, then the width of the building obtained is 6 m. After finding the length, width,
and height of the building, students multiply them to get the volume of a building. The volume obtained with a height
of 2 m is 240 m3
. Because the volume obtained is not the same as the volume in the problem, the students guess again
that the height of the building is 3 m. They continue to calculate the volume same as when calculating height = 2 m,
the length of the building is 30 m (10 × 3), the width of the building is 7 m (4 + 3), and the height is 3 m. Then they
multiply the length, width, and height of the building and get the volume of the building is 630 m3
. In the fourth
indicator (re-check), students check the results by multiplying the length, width, and height then they found a volume
of 630 m3
.
The description of students’ problem solving skill in low category.
FIGURE 8. Students' Answers in Low Category on Question Number 1
Based on Figure 8, students did not understand the problem. It can be seen that students determine the length of
the building to be 10 m while the problem about the length of the building is 10 times the height of the building.
Likewise, with the width, students wrote that the width of the building is 4 m. While in the problem, it is stated that
the width of the building is 4 meters longer than its height. Then, in the indicator of planning a strategy, students plan
the right strategy but lead to the wrong result. Students wrote the correct procedure and may write the correct answer
050004-5

7. in the indicator of implementing the strategy, but it was miscalculated. On the student's answer sheet, it can be seen
that students multiply 5 × 6 × 20 = 630m3
. While the result of multiplying these 3 numbers should be 600 instead
of 630. Therefore, students do not re-examine this question.
The Description of Students’ Problem Solving Skill in Lowest Category
FIGURE 9. Students' Answers in Lowest Category on Question Number 1
Based on Figure 9, students understood the problem. It can be seen that students wrote the length of the building
10 times more than the height, so students wrote p = 10 × t. The width of the building is 4 m longer than the height,
and students wrote l = 4 + t. Then in the indicators of planning strategies, students make plans that are correct but
not complete. It can be seen that students plan t + 2 while the results are not in line with the hypothesis before.
Students should continue by planning t = 3 or other numbers that will get volumes according to those in the problem.
Furthermore, in the indicators of implementing the plan, students wrote the correct procedure. They may write the
correct answer, but due to incomplete strategy planning, students did not find the answer to the problem on the
question. Then, the students did not do a recheck indicator.
Problem Solving Strategies
There is 12 problem solving strategies14
. Based on the 12 strategies, the observations obtained five types of
strategies used by students in solving the 4 questions given. The strategies whose students’ used are drawing pictures,
using formulas, guessing and testing, creating sub-problems, and drawing tables.
TABLE 3. Students’ Problem Solving Strategies
No Strategy of Problem Solving
Many Students (%) in number
1 2 3 4
1 Guesting and Testing 43,59% 0% 15,38% 0%
2 Using Formulas 0% 100% 0% 0%
3 Drawing Picture 0% 0% 10,26% 0%
4 Creating Sub-Problems 0% 0% 46,15% 15,38%
5 Drawing Table 0% 0% 0% 41,03%
Based on Table 3, there are five strategies that students used in answering the four questions. The guessing and
testing strategy was used by students in number 1 and number 3. In number 1, 17 students used the guessing and
testing strategy. In item number 3, six students use guessing and testing strategies. Furthermore, the strategy used by
students is using the formula shown on item number 2 only. Thirty-nine students use the strategy using formulas.
Then, four students used the strategy of drawing pictures in item number 3. Furthermore, 18 students used the strategy
of creating sub-problems in item number 3, and 11 students used it in number 4. Then, 16 students used the strategy
of drawing a table is used in item number 4.
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8. The problem-solving strategies contained in the student answer sheets are five types of strategies. The strategies
are guessing and testing, drawing, table making, formula, and subproblem strategies. The strategies used by these
students are described as follows.
Guessing and Testing Strategy
FIGURE 10. Guessing and Testing Strategy of Question Number 1
Based on Figure 10, students used guessing and testing strategies. It can be seen that the students guessed the
height of 3 m, so that the length obtained was 30 m and the width was 7 m. After guessing, students test their guess
by using the volume formula of the beam so that they find the answer that fits the question. This is generated from the
students’ estimates after understanding the questions. The students not only tested the 3 m high building, but also
guessed the 2 m high building but the answers produced did not match the problem in the question.
Using the Formula Strategy
FIGURE 11. Using the Formula Strategy of Question Number 2
Based on Figure 11, students used the formula for the volume of a cube and a beam. Students directly substitute
the numbers in the formula for the volume of the beam. Then, the volume of the beam is used to find the edge of the
cube because in the problem it is known that the volume of the beam is the same as the volume of the cube.
Drawing Picture Strategy
FIGURE 12. Drawing Picture Strategy of Question Number 3
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9. Based on Figure 12, students used a drawing strategy to determine the initial volume of water in the bath. It can
be seen that students use the picture to be a benchmark or illustration in determining the amount of water in the bathtub.
Students use the up and down arrows. The up arrow indicates that water is added, while the down arrow indicates that
water is used.
Creating Sub-Problems Strategy
FIGURE 13. Creating Sub-Problems Strategy Number 3
Based on Figure 13, students used the strategy of creating sub-problems in item number 3, namely, writing events
or things known in the question and then determining the proper arithmetic operation or following the events in the
question. Students wrote 30 + 80 because students create subproblems when water is added to the tub. Then students
wrote 110 + 50 because students create sub-problems again when water is used. These sub-problems result in a
subtraction number from the final volume of water in the tub, which is 420 − 60 = 360. Then, the students find the
answer to the initial volume of water in the bath, which is 360 liters.
Drawing Table Strategy
FIGURE 14. Drawing Table Strategy of Questions Number 4
Students employed the table-drawing method in response to Figure 14. Although students did not create tables,
the techniques or processes for obtaining answers are identical to the strategy for creating tables. Students can use the
table technique to deduce answers from the calculation or work process.
Referring to the research results, the mathematical problem solving skill of fifth-grade elementary school students
is still in the poor category. Based on the data analysis, it was found that the dominant students lacked the re-check
indicators. Similarly, Mulyani & Hanifah's research indicates that students had greater difficulty re-examining the four
Polya phases15
. Based on the results of observations and interviews, students did not check back was because students
did not know what to write at the re-check stage. Some students check the correctness of the answers with other
alternatives, namely by being careful in the third stage, namely completing the strategy. This is supported by
Sudirman's opinion that when solving the problem, it is necessary to check every step made from big steps then arrange
into small steps so that students get the right answer15
.
According to the findings of this research, the indicators that students most frequently mastered are indicators of
understanding the problem. This is the same as the results of research conducted by Argarini that students with auditory
and visual learning styles have understood the problem16
. However, it is different from the research results conducted
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10. by Mulyani & Hanifah, which resulted in 100% data of students having difficulty understanding the problem15
. Based
on the researcher's observations of the student answer sheets, most of the students understood the problem by writing
down the things that were asked and the things that were known. The students did not write down the known things
and asked on the answer sheet, but when interviewed, they could mention them orally. The researcher concluded that
students who did not write down the known and asked things did not necessarily understand the questions. The student
wants to abbreviate answers so that students do not write down known and asked17
.
The strategies seen and found on the student answer sheets were varied. There are strategies for drawing pictures,
strategies for guessing and testing, strategies for using formulas, strategies for creating sub-problems, and strategies
for drawing tables. Students do not mention the strategies used to answer the questions. Based on the fifth-grade
teacher, learning mathematics in elementary schools does not explain the various strategies that can be used to answer
problem-solving questions but is given several ways or alternatives to answer the questions. However, in this case,
the researcher analyzes the students' answers to be categorized into problem solving strategies. Another strategy found
is the strategy using formulas. This strategy is very familiar to the students. The fifth-grade teacher confirmed that the
students could work on questions if they used the formula. The next strategy is the strategy of drawing pictures. This
strategy is only found on answer sheet number 3. Based on the questions the researcher threw when the students were
working on the questions, the students answered the reason for drawing pictures, namely to give an idea when
determining the steps to be taken to get answers. The strategy of drawing pictures can make it easier for students to
understand problems such as problems story about volume size14
.
Another strategy is the strategy of creating sub-problems. Students used the strategy of creating sub-problems to
summarize the words and events in the questions so that questions or problems could be solved by creating sub-
problems. It is done by solving the sub-problems in succession and then solving the part of the problem14
. Finally, the
strategy used is the strategy of drawing a table. This strategy is used by students in item number 4. Students do this to
make it easier to get answers. Although there are no lines on the student's answer sheet to compose the table, the
process that students go through is the process of drawing table strategy. The strategy of drawing tables can help
students to get patterns in solving problems14
.
CONCLUSIONS
The problem solving skill of fifth-grade students in one of the elementary schools of Bandung Regency is still in
the low category, with an average problem solving skill score of 53.9. Eight students or 20.5% are in the excellent
category, four students or 10.3% are in a good category, five students or 12.8% students are in the sufficient category,
thirteen students or 33.3% are in a low category, and nine students or 23.1% are in the lowest category. Based on
problem solving indicators, 64% of students can understand the problem, 60% of students can plan strategies, 53% of
students can implement strategies, and 33% of students can re-examine the results.
The strategies used by students in solving problems are quite diverse. Although students do not write down the
names of the strategies used, it can be seen in the process of solving problems that there are five strategies used by
students, namely the strategy of drawing pictures, the strategy of drawing tables, the strategy of guessing and testing,
the strategy of creating sub-problems, and strategy using formulas.
ACKNOWLEDGMENTS
The researcher would like to thank the Principal who has allowed the researcher to conduct research at the school
he leads. Then, the teacher of fifth-grade students has been able to work together well in conditioning the students.
The researcher also would like to thank the guided lecture who always encourages and always give a recommendation
during the research.
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Mulyani Nani and Hanifah, in Pros. Semin. Nas. Mat. Dan Pendidik. Mat. (2018), pp. 469–477.
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F.D. Argarini, Matemaika Dan Pembelajaran 6, 91 (2018).
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