Analysis of Student Difficulties in Mathematics Problem Solving Ability at MTS SWASTA IRA Medan

Abstract

This study aims to describe the analysis of student difficulties in solving math problems class VIII MTS
SWASTA IRA Medan. Research instruments used tests and interviews. The type of research is qualitative
descriptive. The subjects of this study are students of class VIII MTS SWASTA IRA Medan academic year
2016/2017 which amounted to 39 people. The results showed that the percentage of problem-solving ability of
students in the indicators of problem understanding of problem-solving was 84.62%, indicator planning was
61.54%, the indicator of performing the plan was 39.74%, and the confirmation of the answer indicator was
32.05%. And students' difficulties in solving such problems 1) students have difficulty solving mathematical
problems in reading text or questions, 2) students always misinterpretation the problem, 3) If students don’t
understand the problem then they will guess the answer from the problem, 4) the students do not want to find
out the solution of the problem given, 5) the students have difficulty in understanding the problem so can’t
interpret it into symbol form.

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International Journal of Sciences:
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(IJSBAR)
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63
Analysis of Student Difficulties in Mathematics Problem
Solving Ability at MTs SWASTA IRA Medan
Milda Rizky Novriania*, Edy Suryab
a,bMathematics Education Post Graduate Program Study,State University of Medan, Jl. Willem Iskandar Pasar
V, Medan 20221, Indonesia
aEmail: milda.rizky669@gmail.com
bEmail: edy_surya71@yahoo.com
Abstract
This study aims to describe the analysis of student difficulties in solving math problems class VIII MTs
SWASTA IRA Medan. Research instruments used tests and interviews. The type of research is qualitative
descriptive. The subjects of this study are students of class VIII MTs SWASTA IRA Medan academic year
2016/2017 which amounted to 39 people. The results showed that the percentage of problem solving ability of
students in the indicators of problem understanding of problem solving was 84.62%, indicator planning was
61.54%, the indicator of performing the plan was 39.74%, and the confirmation of the answer indicator was
32.05%. And students' difficulties in solving such problems 1) students have difficulty solving mathematical
problems in reading text or questions, 2) students always misinterpretation the problem, 3) If students don’t
understand the problem then they will guess the answer from the problem, 4) the students do not want to find
out the solution of the problem given, 5) the students have difficulty in understanding the problem so can’t
interpreted it into symbol form.
Keywords: Mathematical difficulties; mathematical problem solving.
------------------------------------------------------------------------
* Corresponding author.

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1. Introduction
Education is a human need throughout life, without human education will be difficulties to develop and
education plays an important role in life. According to [1] the purpose of mathematics education is surely to
make students actualize learning in the highest level. However, the fact that the vast majority of the students
experience difficulties while a few of them actualize learning is considered a reality of life. That is the
importance of mathematics education, so that the knowledge gained makes it easy to apply it into the life of the
day.
Reference [2] States that mathematics is a way of expressing certain ideas, opinions, and concepts that math can
be said as a communication tool, or a tool to make it easier for someone to convey ideas, opinions, and concepts
to be understood by others. Some students claim that mathematics is a difficult subject to the statement Cooney
& Cotton [3] Say some students view mathematics learning as interesting, others may believe that it is a form of
tedious and monotonous work. Students who like mathematics and have a high ability must say mathematics is
an interesting lesson, otherwise low ability students say mathematics is a tedious and difficult job in solving the
problems. Reference [3] Say some student see mathematics as a subject that causes their fear, anxiety, and anger
during lesson. Students who say mathematics as a subject that makes them afraid, anxious and even hate
mathematics that this is because the students are not able to follow the lessons of mathematics or have a low
ability and do not want to dig the low ability in order to improve the lessons of mathematics, especially in
solving the question problem solving.
Mathematics is an important science but in fact mathematics lessons are less desirable, feared, and boring for
students. This can be seen from the students' weak math skills. One of the weaknesses among students is the
weakness of students in solving math problems. Where students complain and find difficulties in solving
problems in math so that students look less able to solve math problems.
According to [4], Problem is a work in which an individual who is facing it feel the need for solving or want to
solve it, she/he does not have a way how to solve it and she/he tries to solve it. It is therefore very important as a
human being to solve the problem. Likewise with students, every student must have certain problem solving
skills in solving problems or questions given by the teacher. Because in mathematics is very synonymous with
the problem and in the process of completion needed problem solving skills. But most of what happens in the
field, students are not able to solve math problems in everyday life. Students find it difficult to solve them if
given a problem. Students always say that the problems in mathematics are difficult to resolve, so there is no
effort to solve them.
Though the development of problem solving mathematics students at the school level into educational goals.
However, the students' skills in developing problem solving are so low that they become a major dilema in
education.
Therefore, this study was conducted to analyze students' difficulties in math problem solving skills in schools.
Solving mathematical problems is essential to the general purpose of learning mathematics, even as the heart of

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mathematic, it is prioritized rather than the process and as a result the focus of school mathematics and aims to
help develop mathematical thinking.
2. Mathematic Problem Solving Ability
The ability to solve problems is needed by students in understanding concepts, relationship between concepts,
and relationship between concepts and other fields [5]. According to [6] That good problem solving generally
builds representations of problems to facilitate understanding. This is confirmed by [7]. Assertion that problem
solving is the basic skills required by today's learners and problem solving to be the main focus of the
mathematic curriculum.
Reference [8]. Defined mathematical problem solving as the process of interpreting a situation mathematically,
which usually involves several iterative cycles of expressing, testing, and revising mathematical interpretation
and of sorting out, integrating, modifying, revising or refining clusters of mathematical concepts from various
topics within and beyond mathematic. Reference [9] Defined problem solving as one as the effort to find out
from difficulty to achieved one aim which is not easy to achieve.
In solving problems, students are expected to understand the process of solving the problem, identifying relevant
conditions and concepts, seeking generalizations, formulating a plan of completion and organizing previously
owned skills. It will be seen that mathematical problem solving has an important function in teaching and
learning activities in mathematic. The teacher presents the problem, because through problem solving students
can practice and interpreted the concepts that have been learned.
Step known mathematical problem solving proposed by [9], in his book "How to Solve It". Four step
mathematical problem solving by [9] are: "(1) Understanding the problem, (2) Devising a plan, (3) Carrying out
the plan, (4) Looking Back". Problem solving is categorized into two aspects; i) how the problems are delivered
linguistic (using words) or non linguistic (using graphic or problem based); ii) the illumination of the problem
structure information, objective and action plan (Zhining and his colleagues [10]). Reference [11] Stated that
problem solving is a process starting from the minute students is faced with the problem until the end when the
problem is solved. There are many problem solving models (Table 1).
Table 1: Problem solving models
Polya (1981)
Krulick & Rudnick (1996)
Zalina (2005)
4 - hierarchy phase
5 - hierarchy phase
3- hierarchy phase
i)
nderstanding problem;
ii)
lanning;
iii)
erforming the plan;
iv)
onfirmation the answer.
i)
eading and thinking;
ii)
nalyze and planning
iii)
rganizing strategy;
iv)
etting the answer;
v)
onfirmation the answer.
i)
nderstanding problem;
ii)
olving the problem;
iii)
tating the answer.

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Reference [12] Suggests that problem solving is a process that uses certain measures (heuristic) that help in
resolving the problem. Furthermore, NCTM added that the term refers to problem solving mathematical tasks
that have the potential to provide intellectual challenge and improve the understanding of students' mathematical
development.
From the opinions above, can be concluded that the mathematic problem solving ability is ability of the student
to solve problems by observing the process of finding answers based on the step by step problem solving: 1)
understand the problem, 2) planning, 3) performing the plan, and 4) confirmation the answer.
3. Difficulties in Mathematics Problem Solving
In school students learn mathematics as a useful knowledge for life, but in learning mathematics students not
only learn to count but also students also learn mathematics related to everyday life, but students often have
difficulty. (Martin and his colleagues [13]) Suggests that children who have difficulty actually have the potential
for success, but because an academic achievement of children's performance may decrease on certain subjects
such as reading or learning mathematics. According to [14]. Mathematical difficulties in elementary school will
continue into secondary school, even affecting subsequent adult life. Mathematical difficulties have certain
characteristics, namely difficulties in processing information, difficulties related to language and reading skills,
and mathematical anxiety [14].
Reference [15] Difficulties affecting mathematical problem solving can be classified as:
1. Students can’t understand the whole or some parts of the problem due to the lack of imagination and
experience needed to consider the problem.
2. Students have difficulties in reading and comprehension, unable to understand what important
information is in a problem and organize it accordingly. Thus they cannot invert the text into
mathematical symbols.
3. Students lack interest in solving mathematical problems due to the length and complexity of the
problems, which is demotivating.
4. Teachers do not present daily life matters as problems very often.
5. Teachers are likely to make students memorize "keywords" in the problems to use in formula.
6. Teachers focus on following examples given in textbooks rather than teaching the principles behind
each problem.
7. Teachers teach without concern with thinking process orders.
Lack of many mathematics skills caused difficulties in solving problem. Garderen [16] Stated deficiency in
visual spatial skill might cause difficulty in differentiating, relating and organizing information meaningfully.
There are five types of math skills:
i. number fact skill (proficiency of number facts, tables and mathematics principal);
ii. arithmetic skill (accuracy and logarithm in computational and mathematical working procedure);
iii. information skill (expertise to connect information to a concept, operational, and experience as well the

International Journal of Sciences: Basic and Applied Research (IJSBAR)(2017) Volume 33, No 3, pp 63-75
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expertise to transfer information and transform problems into mathematical sentence);
iv. language skill (proficiency of terms and relevance of mathematical information)
v. visual spatial skill (skill to visualize mathematical concepts, manipulate geometrical shape and space
meaningfully).
Theoretically, lacked in mathematics skills that could caused difficulties in mathematics especially in
problem solving might be due to interference in cognitive abilities [17,18].
4. Research Methods
This research is a qualitative descriptive. Reference [19] Said that a qualitative descriptive research is the basic
types of research that major purpose is description of the state of affairs as it exists at present. The type of this
research is qualitative descriptive to see the description student difficulties in problem solving ability of student
math. Subjects in the study of students of class VIII MTs SWASTA IRA Medan amounted to 39 students.
Technique of collecting data is written test and interview. Problem solving ability tests in the form consisted one
problem cube with four questions. The scoring techniques used in this study using the following guidelines:
Table 2: Grid of problem solving
Indicators of Mathematic Problem
Solving Ability Indicators of Cube
Number of
Test
Understanding problem
Resolving problems related to calculate the
area of the cube
1a
Planning
Resolving problems related to calculate the
area of the cube
1b
Performing the plan
Resolving problems related to calculate the
area of the cube
1c
Confirmation the answer
Resolving problems related to calculate the
area of the cube
1d
To calculate the percentage ot the total score for each indicator of problem solving ability (
) used :

=     − 
     −  ×100% (1)
= 1, 2, 3, 4

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Table 3: Test scoring guidelines mathematical problem solving
Rated Aspect
Reaction To The Problem
Score
Understanding problem
The completion is based on a wrong process or
argument, or no response at all
0
Completion is not resolved in its entirety but there is the
correct argument
1
Completion of the problem completely and correctly
2
Planning
There is no completion strategy plan
0
The planned strategy is not quite right
1
The strategy used is correct and leads to the right answer
2
Performing the plan
There is no completion
0
There is completion but the plan is not clear
1
Make a completion using a specific plan and leads to the
right answer 2
Perform a completion using a specific plan that is correct
but incorrect in calculating 3
Perform a completion using a specific plan that is true
and the results are correct 4
Confirmation the answer
No checking of answer
0
Inaccurate examination only on the process
1
An examination of the process and the answer to the
truth 2
With the qualification such as table 4 below:
Table 4: The qualification of total score percentage
Percentage
Qualification
85 ≤ 
≤100
Very Good
70 ≤ 
≤84,99
Good
55 ≤ 
≤69,99
Good Enough
40 ≤ 
≤54,99
Not Enough
0≤ 
≤39,99
Very Less
Arikunto [20]

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5. Result and Discussions
5.1 Result
From the research data showed the test results of mathematical problem solving ability of students are presented
in table 5 as follows:
Table 5: Students’ score of indicators of problem solving ability
Code of
Student
Score of Indicators
Understanding
Problems
Planning
Performing the plan
Confirmation the
answer
S1
2
1
2
1
S2
2
1
2
0
S3
2
2
4
2
S4
1
2
1
1
S5
2
1
3
0
S6
1
1
2
1
S7
1
1
3
1
S8
2
2
1
0
S9
1
1
1
1
S10
1
2
2
0
S11
2
1
2
1
S12
2
2
4
2
S13
2
1
2
0
S14
1
1
2
1
S15
2
1
2
0
S16
2
1
2
0
S17
2
1
0
0
S18
2
1
2
1
S19
2
2
2
0
S20
2
1
0
0
S21
1
1
2
1
S22
1
1
0
0
S23
1
2
2
1
S24
2
1
0
0
S25
2
1
0
0
S26
2
0
0
1
S27
2
1
2
1
S28
2
1
2
0
S29
1
2
0
1
S30
2
1
2
1
S31
1
2
2
1
S32
2
1
1
0
S33
2
2
4
2
S34
2
1
2
1
S35
1
1
2
1
S36
2
1
0
0
S37
2
1
1
0
S38
2
1
1
1
S39
2
1
0
1
Here is examples of students' answers on problem solving abilities test:

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Problem:
Anggi makes a cube shaped cake with a rib length of 20 cm. Anggi will put the cake into cardboard. Anggi will
make his own cardboard using cardboard. What to do Anggi?
a. What data is obtained from the problem?
b. How Anggi puts the cake into the box?
c. Calculate the surface area of the cube shaped cake that will be inserted into the box?
d. Check back the results of the question c! Is the surface area of the cake 2.400 2? What to do Anggi?
Explain!
Table 6: Problem solving ability percentage based indicators of problem solving
Indicators of Problem Solving
Score of
Students
Total Score
Percentage
Category
Understanding problem
66
78
84.62%
Good
Planning
48
78
61.54%
Good Enough
Performing the plan
62
156
39.74%
Very Less
Confirmation the answer
25
78
32.05%
Very Less
Student’s answer sheets:
Figure 1: Student ’s answer sheet

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Figure 2: Student ’s answer sheet
Figure 3: Student ’s answer sheet
From the picture above can be obtained as:
• Student on Figure 1 can answer the questions well. He can understand the problem and can make a
planning too, then he can solve the problem well. Only 3 of 39 students can solve the problem well,
they are S3, S12 and S33.
• Student on Figure 2 can’t understand the problem well. She also can’t make a planning, the she can
performing the plan well.
• Student on Figure 3 are not able to plan and solve the problems at the same time in checking result
from the answer, students just multiply the number contained in the problem.

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The result of mathematics difficulty analysis of the students in solving the problem is obtained based on the
result of the interview on the mathematics teacher that is 1) the students have difficulty solving mathematical
problems in reading the text or questions, 2) the students always misinterpreted the problem, 3) If the students
don’t understand the problem then they will guessed the answer from the problem, 4) the students don’t want to
find out the solution of the problem given, 5) the students have difficulties in understanding the problem so can’t
interpreted it into a symbol form.
Teacher A: "Not all students can read and understand the problem well so don’t know the intent and purpose of
the problem can’t even write it into a symbolic form. And also there are some students who don’t know where to
start in solving math problems because they only know the formula but don’t know to use the formula ".
Teacher B: "Students find it difficult to understand math problems so they can’t solve the problem. And
sometimes students don’t have the will to try to understand the purpose of the problem because they assume that
the math problem is very difficult. Students also can ‘t interpreted the problem so that its use into symbolic form
is wrong.
5.2 Discussions
Based on the results of the research shows that most students MTs SWASTA IRA Medan class VIII are not able
to solve the problems that well provided with meet the level of indicators of problem solving ability. Percentage
of students' ability to understanding problem reached 84.62% and classified in the category good, the percentage
of problem solving ability of students to planning 61.54% and classified in the category good enough, the
percentage of problem solving ability of students to performing the plan 39.74% and classified into categories
very less, the percentage of the student's ability to confirmation the answer the results obtained 32.05% and
classified in the category very less, while the average percentage reached 54.48% and classified not enough
category. This indicates that the class was not finished in solving problems. Reference [11] Stated that problem
solving is a process starting from the minute students is faced with the problem until the end when the problem
is solved with four indicators of problem solving: understanding problem, planning, performing the plan, and
confirmation the answer.
This research is relevant to research conducted by Phonapichat and his colleagues [15] States that students have
difficulty in understanding the mathematical problems that affect the problem solving process. Student
difficulties in problem solving namely 1) Students have difficulties in understanding the keywords appearing in
problems, thus can’t interpret them in mathematical sentences. 2) Students are unable to figure out what to
assume and what information from the problem is necessary to solving it, 3) Whenever students don’t
understand the problem, they tend to guess the answer without any thinking process, 4) Students are impatient
and don’t like to read mathematical problems, and 5) Students don’t like to read long problems. Likewise with
research (Lubis and his colleagues [21]) Said that the average percentage reached 50% and classified in the not
good category. It shows class in solving problems unresolved.
Based on the above explanation, the researcher analyzed the students' difficulties in problem solving ability and

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obtained the result of the research based on the indicator that the students of MTs SWASTA IRA Medan class
VIII can’t solve the problem given with the problem solving indicator.
6. Limitations
This research is a qualitative descriptive research to know how to describe students’ difficulties in math
problem solving ability class VIII MTs SWASTA IRA Medan in cube material. The mathematic problem
solving is analyzed by it’s four indicator. The indicators are understanding problem, planning, performing the
plan, and confirmation the answer.
7. Conclusions and Recommendations
7.1 Conclusions
Based on the analysis and discussion of the results of research conducted can be concluded that percentage of
students’ ability to understanding problem reached 84.62% and classified in the category good, the percentage
of problem solving ability of students to planning 61.54% and classified in the category good enough, the
percentage of problem solving ability of students to performing the plan 39.74% and classified into categories
very less, the percentage of the student’s ability to confirmation the answer the results obtained 32.05% and
classified in the category very less, while the average percentage reached 54.48% and classified in the not
enough category. This indicates that students have difficulty in solving problems obtained based on interviews
with teachers in the field of mathematics studies such as 1) students have difficulty solving mathematical
problems in reading text or questions, 2) students always misinterpret the problem, 3) If students don’t
understand the problem then They will guess the answer from the problem, 4) the students don’t want to find out
the solution of the problem given, 5) the students have difficulty in understanding the problem so can’t interpret
it into symbol form.
7.2 Recommendations
Based on these results, the recommendations can be submitted by researcher are:
• For teacher, it’s better to give more practicess to solve non routine problem to increase student’s ability
to solved student’s math problems.
• For students, must to practice more and study math to have a good result and not having any difficulty
in doing test that has to do with math solving problem
• For researcher, can use this as reference to do some research to know more about student’s difficulty in
math problem solving.
Acknowledgements
The authors acknowledge support from State University of Medan. The authors thank for Mathematics
Education Program Study of Postgraduate School for support.

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