POLYA’S STRATEGY: AN ANALYSIS OF MATHEMATICAL
PROBLEM SOLVING DIFFICULTY IN 5TH GRADE ELEMENTARY
SCHOOL
Nunuy Nurkaeti1
Universitas Pendidikan Indonesia
Abstract
Problem solving is one of ways to develop higher order thinking skills. Strategy of problem
solving that can be developed in mathematics learning is Polya's strategy. This study aims to analyze
the problem solving difficulties of elementary school students based on Polya strategy. To support
this research,descriptive analysis is used on seven elementary school students . The results show
that, the difficulty of mathematical problems solving of elementary school students consist of the
difficulty of understanding the problem, determining the mathematical formula/concepts that is used,
making connections between mathematical concepts, and reviewing the correctness of answers with
questions. These happened because the problem presented is in a story problem, that is rarely studied
by the students. Students usually solve mathematical problems in a form of routine questions, which
only require answers in a form of algorithmic calculations.
Keyword: Problem Solving Difficulty, Polya’s Strategi, Word Problem.
Abstrak
Pemecahan masalah adalah salah satu cara dalam mengembangkan kemampuan berpikir
tingkat tinggi. Salah satu strategi pemecahan masalah yang dapat dikembangkan pada pembelajaran
matematik adalah strategi Polya. Penelitian ini bertujuan menganalisis kesulitan pemecahan masalah
siswa sekolah dasar berdasarkan strategi Polya. Untuk mendukung penelitian ini digunakan analisis
deskriptif pada tujuh orang siswa sekolah dasar. Hasilnya menunjukkan bahwa, kesulitan pemecahan
masalah matematik siswa sekolah dasar meliputi, kesulitan memahami masalah, menentukan
rumus/konsep matematik yang digunakan, membuat koneksi antar konsep matematika, dan melihat
kembali kebenaran jawaban dengan soal. Hal tersebut disebabkan, masalah yang disajikan berupa
soal cerita yang jarang dipelajari siswa. Siswa biasanya menyelesaikan masalah matematik berupa
soal rutin, yang hanya menuntut jawaban berupa perhitungan algoritmik.
Kata Kunci: Kesulitan Pemecahan masalah, Strategi Polya, Masalah Kata.
INTRODUCTION
Problem-solving is one of the
mathematical skills that should be had by
the student at the elementary school.
Polya's strategy can be used to solving a
problem. However, in reality, many
students are still struggling to solve
mathematical problems.
The result of PISA Indonesia test in
2015 shows the average score of
mathematics ability of 15-year-old students
is 386, the score is still at level two of math
ability (OECD, 2016). Such capabilities
have not yet reached the ability to conclude
and solve problems from diverse
information, and the use of diverse
algorithms in solving problems. In line with this, Suharta (2016) argues that students are
still weak in solving mathematical
problems, especially in solving realistic
problems, numerical operations, and
provide realistic reasons and
considerations.
Regardless the kind of realistic and
non-realistic problems used, students are
still weak to solve the word problem.
According to Nenden (Hidayat & Irawan,
2017) students difficulty in solving the
problem that a form of a word problem. In
addition, Amir (2015) argued that students
have difficulty in solving the word
problem. Students' difficulties in solving
problems can arise because of several
factors, such as the learning environment that includes learning approach used,
motivation, use of the problem type, as well
as teaching materials that do not support
students to develop problem-solving.
In
fact, important problem solving is owned
by students and accustomed by the teacher,
as one way in developing higher order
thinking.
Development of higher order
thinking skills such as communication,
collaboration, critical, and creative
certainly involves a problem-solving
context. Indirectly if students' higher order
thinking skills are developed, students will
be involved in a problem-solving. This is in
line with Kusuma's opinion, et al. (2017);
Abosalem (2016); Widodo & Kadarwati
(2013) higher order thinking activities can
one be developed through problem-solving.
Study of analysis mathematical
problem-solving analysis of elementary
school students is important, as a first step
in developing problem-solving skills. As
according to Ulya (2016) that the ability of
students in solving problems needs to be
studied by the teacher. This indicates that
when the teacher will develop problemsolving skills, the teacher must first
understand how far the ability of problemsolving students, through the analysis of
student difficulties in solving problems.
One of them in the context of word
problem.
Dari & Budiarto (2016) analyzed
mathematical problems based on Polya's
strategy in junior high school with various
levels of emotional intelligence and
mathematical ability. The results show the
various problem about difficulty of solving
problem. This is why students are wrong in
doing calculations, although the steps are
quite appropriate. Based on the above, there
needs to be an analysis also concerning the
problem of the mathematical problem of
students in primary school.
Problem-solving difficulties of
students in elementary schools can be seen
based on indicators of problem-solving
abilities. Indicators of problem solving
capabilities are described based on aspects
or steps problem-solving according to
Polya. Therefore, this study will answer the
question "How is the difficulties problem
solving to solve word problem in 5th grade
students of elementary school?" The
question will guide the analysis of
mathematical problem solving of 5th grade
elementary school students with Polya’s
strategy.
LITERATURE REVIEW
According to NCTM (Dari &
Budiarto, 2016 and Mustika & Riastini,
2017) that problem solving is an integral
part and not separate from mathematical
learning. The statement shows that in every
mathematical learning involves solving the
problem. Polya (Lidinillah, 2008) mentions
that problem solving is an important aspect
of intelligence, where problem solving can
be understood as an important character for
humans and can be learned by imitation or
experimentation. Imitation and experiment
activities can be facilitated by routine and
nonroutine problems. So it can be said that,
mathematical problems ability is the ability
of a person in solving mathematical
problems both routine and nonroutine
problems. As according to Lestari &
Yudhanegara (2017) that problem solving
ability is the ability to solve routine and non
routine problems both applied and non
applied in the field of mathematics. The
type of mathematical problem given will
lead the student to perform the problem
solving procedure. The routine and nonroutine procedure of solving the problem is
certainly different in its calculation
practice. The non-routine problem requires
planning problems that are not merely
applications of formulas, theorems,
propositions, as well as routine problems
that require more algorithmic calculation.
Problem-solving can be used as a
way to develop student problem solving.
Word problem is one form of presentation
problem solving on a words or a story.
According to Dewi, Suarjana, & Sumantri
(2014) in solving the word problem,
students required to think high order thinking, whereas student must determine
something known, asked, the mathematical
model used, and perform calculations
according to a predetermined mathematical
model.
The activity in solving the problem
is in line with Polya's strategy to solve the
problem. It is considered to be able to help
students in solving mathematical problems.
There are four steps of the problemsolving process that can be used as an
aspect of measuring/analyzing problemsolving according to Polya. Polya (Anglin,
2004) proposed four problem-solving steps:
understanding the problem, devise a plan,
carry out the plan, and look back over the
result. Understand the problem, can be a
reading problem, determine the
keyword/information/elements of the
problem. Devise a plan, can take the form
of drawing/form mathematics based on the
problem, determine the question, determine
the concept/formula/mathematical ideas to
be used in problem-solving. Carry out the
plan, can be a mathematical operation to get
the result of completion. Look back over
the results, confirm the answer with the
problem, check the problem with the given
solution, check the mathematical keywords
in the problem with the solution, and be
sure about the answer was given. Based on
the above description, the aspect and
indicators of problem solving difficulty
analysis refer to Polya's opinion, which is
arranged in table 1.
RESEARCH METHOD
This research is a descriptive study
on problem-solving analysis of difficulty
mathematical problem-solving in
elementary school students. Problemsolving difficulties were analyzed
according to Polya's steps. The sample of
this study is students of 5th grade at the
elementary school in Bandung, which
amounted to seven students. Data were
collected by tests and interviews.
Instrument test is arranged based on steps
Polya's strategy into an indicator, which is
poured in the word problem. After the test,
students are interviewed.
FINDING AND DISCUSSION
Analysis of problem-solving
difficulties was done in 5th grade
elementary school students. Some findings
of the analysis are related to solving
problem of the word problem, which
requires planning in solving the problem.
The analysis is based on the problem
solving aspect according to Polya.
Aspects of understanding the
problem, measured by three indicators are:
1) identifying the known aspects of a
problem; 2) mentions the questions asked
based on the given problem; and 3) connect
the issues with other mathematical topics.
The results of the analysis show that as
follows.
1) Students already understand the
problems in the matter and perform
mathematical calculation operations
appropriately.
2) Students do not understand the
problem in the matter but have been
able to perform mathematical
counting operations.
3) Students do not understand the
problem in the matter and have not
been able to perform mathematical
counting operations.
4) Students are able to understand
problems based on interrelationships between topics and perform
mathematical operations correctly.
5) Students have understood the
problem based on interrelationship
between topics but have not been able
to perform mathematical operations.
6) Students are not able to understand
the problem based on
interrelationship between topics and
unable to perform mathematical
operations.
In general, students have been able
to identify the known aspects of the
problem and mention the questions asked in
the problem, but the students have not
understood the intention/relationship of
every aspect known in the problem when
solving the problem .
In Figure 2 the students had
difficulties to identifying the mathematical
aspects of the problem. It looks at the
answer to the section "a" that the students
only answer the age, whereas what
expected is the meaning of the ratio about
ages of Dodi, Mother, and Father. In
addition, students have difficulty
determining the value of mother and
father's age ratio, because he does not
understand the problem. Finally, students
just counting the age of mother and father
based on Dodi's age.
Many students are unable to
determine the interrelationships between
math topics. So many errors occur when
working on problems related to the
difference in unit length. Where students
are not able to change the type unit of length
and change the type of fraction.
In Figure 3, students have difficulty
making conversions from units of meters
length to centimeters. In addition, students
have difficulty in the multiplication of
integers with decimals, so problem-solving
is less precise. It shows the connection
between the mathematics topic of students
is still lacking. The student's way of
determining the problem/question is also
still wrong, where the student should do the
sequence based on the number of flowers,
but it happens they sort by the length of
ribbon. It is clear that students'
understanding of problems in the word
problems is still get difficulties.
Aspects of devise and carry out the
plan, these two aspects into an integrated
entity. However, it is measured using two
different questions for the same problem.
The indicators include 1) create a
mathematical model based on the given
problem; 2) shows the mathematical
concepts to be used in problem-solving, and
3) describes the problem-solving process
based on the plan that have been made. The
results of the analysis show the following.
1) Students are able to make a plan and
implement problem-solving plans.
2) Students are able to make a problemsolving plan but not yet able to solve
the problem.
3) Students have not been able to make
a problem-solving plan and have not
been able to implement the problemsolving plan.
From the above, it can be seen that
students have difficulty in making a
problem-solving plan and do a good
problem-solving plan based on a word
problem. In general, students are able to
make interpretations in the form of models
/ drawings of mathematical concepts of the
problems given. However, students have
difficulty choosing and determining what
concepts/form should be used in solving the
problem.
From picture 4, already seen that the
students can be interpreted from the given
problem. However, students still have
difficulties in drawing up plans, which
students are still deformed when
determining the formulas to be used in
problem-solving. We have known from the
answer above "b" the student just
multiplying the problem without looking at
the mathematical context used (square).
The impact of these difficulties, students
also ger errors in problem-solving.
From the student answers in figure
4, the core difficulties gotten students in
solving problems is the difficulty when
making problem-solving plans and
understand the context of the problem. This
means that understanding aspects of the
problem is very influential in the problemsolving procedure.
An aspect of looking back at results,
measured by indicators checking the
accuracy of answers with questions. In this
aspect, almost all students are less precise
in determining the accuracy of the answers
to the problems presented. This is because
students do not understand the image
representation given and do not understand
the word problem described. Even some
students do not answer because there is no
number that can be operated. Their reason
that mathematics is identical with numbers.
Students are unable to look back on
the truth of answers with questions. When
looking back at the answers, word problem,
and the figure that have given, they think
that was no difference context between the
solution and the problem. Where in the
problem have a differences size of small,
medium, and large bricks, but students only
review the bricks are small and large only.
As stated in the following interview results.
A: What's the figure in number for?
B: Bricks.
A: With use the bricks. What is she want
make?
B: Create a small garden.
A: From that figure how many small
bricks?
B: It's still big, so I drew line to let me be
small.
A: Oh, you drew the line to make a small
bricks?
B: Yes, I drew the line from up to down, so
I get small bricks.
A: So, how many small bricks are there?
B: There are twenty for small bricks.
A: So, your solution is cut a big bricks to
get a small bricks?
B: Yes
From figure 5 and the conversation,
the results of the interview show the student
has not been able to assess the truth of the
answer given to the problem. This is
because students do not look back at the
context of the given problem, by
differentiating the size of the bricks in the
figure. In the problem described three are
sizes of bricks that are small, medium, and
large. So students should determine the size
of existing bricks into small, medium, and
large sizes. However, students only
determine small stone stones, then draw a
line to form the existing bricks into small
size. Whereas students should be able to see
the comparison of the size between small,
medium, and large bricks so that the
student's review of answers and questions is
appropriate and appropriate.
Referring to analysis problem
solving above, there are some difficulties
found based on the students' ability to solve
the problem. First, students do not
understand the problems given. This is
caused the given problem in a word
problem. The students rarely solve
problems in a word problem, so they are not
trained in reading and interpreting
problems. This is in line with the opinion of
Osterholm (Pratiwi, 2015) that students
have difficulty articulating in reading
comprehension, in this case, a matter of
word problem. This opinion is reinforced
by Dewi, Suarjana & Sumantri (2014) that
research results are students solve the word
problem with unstructured way, it is caused
by the lack of understanding of students
about how to do the word problem and
problem-solving model used by the teacher
is less precies.
Second, students have difficulty
determining problem solving plan. This is
because students are accustomed to work
procedurally, so when asked the right
concepts and mathematical formulas to
solve students' confusion problems.
Students tend to solve problems by
operating each number on the problem
algorithmically. This finding is confirmed
by research Suharta (2016) that students
tend to solve problems by taking into
account the numbers that exist, regardless
of the intent of the problem. Student
difficulties in determining the problem
solving plan are also supported by
Lidinillah (2008) opinion that teachers
usually provide the same strategy in solving
problems and often students ask about
"What is used formula to answer this
problem?". Frequently the question arises
indicating that students have difficulty
determining the mathematical formula /
concepts used in solving problems. In
addition, a relatively similar problemsolving strategy, showing less creative
students in solving problems.
Third, students have difficulty
making connections between mathematical
concepts. This difficulty has an impact on
problem-solving and the withdrawal of
wrong conclusions because students are not
keen on differences in mathematical
concepts. This is in line with the research
results of Mustika & Riastini (2017) that
students are not able to solve the story
problem about the conversion unit of the
length, although the problem is quite easy.
The results of this study clearly related to
the difficulties students make connections
between mathematical concepts.
Toward the connection of solving a problem and
mathematical concepts is very important,
especially in the word problem that requires
a lot of interpretation. As according to
NCTM (Dewi, Suarjana, & Sumantri,
2014) that the development of mathematics
necessarily involves various connections of
mathematical ideas, understanding
interrelated mathematical ideas in
constructing mathematical understandings,
and using mathematics in contexts outside
of mathematics.
Fourth, students have difficulty in
looking back to the truth of answers to
questions. Difficulty in looking back on the
truth of answers with problems gotten
students is caused by understanding,
planning, and implementing problemsolving erroneously. This means that the
difficulty in looking at the answer aspect
will not happen, if the student is correct in
understanding the problem, planning the
settlement, and solving the problem.
Alternative ways that can be done to
overcome student difficulties in solving
problems, one of them by using a problembased approach to learning. Presentation of
learning problems with different types of
problems can train students to solve
problems. As Arifin (2016) argued that
problem-based learning that presents
practical problems such as ill-structured or
open-ended can provide stimulus to
students in learning, so as to improve
learning outcomes. In addition, habits in
training skills in understanding and solving
problems need to be given to students
(Abdillah & Budiarto, 2017). With the
exercise and habituation of understanding
and solving the problem, will make
students familiar and understand problemsolving strategies.
Problem-solving difficulties also
cannot be separated from the way teachers
convey learning and use of teaching
materials. According to Mustika & Riastini
(2017), the results of his research shows the
rarity of teachers giving nonroutine
problems in learning to train problemsolving students and students tend to be
passive in learning. it is important to use
various problems mainly in the form of
non-routine questions. Non-routine
questions can encourage students to play an
active role in solving problems and building
knowledge. In line with that, the
development of LKS teaching materials
with Realistic Mathematics Education
approach can develop problem-solving
abilities (Hidayat & Irawan, 2017).
CONCLUSION
Mathematical problem solving of
fifth-grade elementary school students still
needs attention. Based on the problemsolving steps proposed by Polya, students
are still having difficulty in solving the
mathematical problem. Difficulties of the
students especially in understanding the
problem, determining the problem-solving
plan so that the settlement is also
wrong/difficulty, making connections
between mathematical concepts, and
reviewing the truth of the answers with
questions. The difficulties are caused by
several factors including, the students who
are not accustomed to solving problems in
a word problem, and learning does not
develop problem-solving. Therefore, in the
learning of students should be given a
variety of problems, especially that can
provide opportunities for students to
explore issues such as open-ended
problems. Alternatively, learning can use a
problem-based approach, an open-ended
approach, a mathematical realistic
approach, and other approaches that
provide students with opportunities to solve
mathematical problem.
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