The aim of this research is to find the difficulties of students in solving word problems in the three-variable linear equation systems subject. Before they took a mathematical problem-solving exam, the learners were given reinforcement of prerequisite knowledge of the intended subject. The problem-solving test indicators used in this study were taken from Polya's problem-solving steps consisting of (1) recognizing the question, (2) making a plan for problem-solving (developing a plan), (3) implementing the plan for problem-solving, and (4) looking back. The research method used in this study was a qualitative descriptive. The subject in this study was 15 students who were 10 th graders of senior high school. The data were obtained from a student performance who took mathematical problems solving test. The result obtained from this study can be seen from the number of students whose achievement indicators formulate a plan of 49.6%, achievement in completing plans 14.1%, and achievement in checking solutions 2.2%. However, the indicators of understanding the problem area in the good category, namely 80%. The result of this study showed that the students were only able to solve the word problems for understanding the problem (good category) and devising the plan steps (mediocre category), whereas they got difficulties in solving the word problems in carrying out the plan and looking back (low category).

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JTAM (Jurnal Teori dan Aplikasi Matematika)

http://journal.ummat.ac.id/index.php/jtam

p-ISSN 2597-7512 | e-ISSN 2614-1175

Vol. 5, No. 1, April 2021, pp. 254 -261

254

Senior High School Students' Mathematical Problem Solving

Of Three-Variable Linear Equation System

Abdul Nu'man Asok1 , A Hasanah2

1,2 Mathematics Education, Universitas Pendidikan Indonesia, Indonesia

1abdnumana@upi.edu, 2 aanhasanah@upi.edu

Received : 21-01-2021

Revised : 01-04-2021

Accepted : 03 -04-2021

Online : 17 -04-2021

The aim of this research is to find the difficulties of students in solving word

problems in the three-variable linear equation systems subject. Before they took a

mathematical problem-solving exam, the learners were given reinforcement of

prerequisite knowledge of the intended subject. The problem-solving test

indicators used in this study were taken from Polya's problem-solving steps

consisting of (1) recognizing the question, (2) making a plan for problem-solving

(developing a plan), (3) implementing the plan for problem-solving, and (4) looking

back. The research method used in this study was a qualitative descriptive. The

subject in this study was 15 students who were 10 th graders of senior high school .

The data were obtained from a student performance who took mathematical

problems solving test. The result obtained from this study can be seen from the

number of students whose achievement indicators formulate a plan of 49.6%,

achievement in completing plans 14.1%, and achievement in checking solutions

2.2%. However, the indicators of understanding the problem area in the good

category, namely 80%. The result of this study showed that the students were only

able to solve the word problems for understanding the problem (good category)

and devising the plan steps (mediocre category), whereas they got difficulties in

solving the word problems in carrying out the plan and looking back (low

category).

Mathematical problem

solving;

Three-variable linear

equation systems;

Qualitative.

https://doi.org/10.31764/jtam.v5i1.3929

This is an open access article under the CC– BY-SA license

—————————— ——————————

A. INTRODUCTION

Mathematics subjects are subjects that are given at every level of education from basic

education. But in reality, mathematics is often considered a difficult subject to understand

(Karso, 2019). According to the general public's opinion, one of the subjects that are considered

difficult at the primary and secondary education levels in mathematics. This is because

mathematics deals with abstract ideas and concepts (Herawati et al., 2010).

According Depdiknas (2006), learning mathematics has the goal of making students have

the ability (1) To understand mathematical concepts, to clarify the link between concepts and

to apply concepts or algorithms in problem-solving in a versatile, precise, successful and

precise manner. (2) Using reasoning on patterns and properties, making generalizations of

mathematical manipulations, compiling proof, or describing mathematical ideas and claims. (3)

Address cases concerning the ability to understand problems, develop mathematical models,

solve models, and interpret the solutions that have been obtained. (4) Expressing ideas in order

to explain the situation or problem through symbols, charts, graphs, or other media. (5) Having

an attitude of appreciating the value of mathematics in life, namely having an interest in

learning mathematics, enthusiasm, concentration and motivation, as well as being resilient and

Abdul Nu'man Asok, Senior High School Students' ... 255

confident in solving problems. This is focused on the learning goals set by the National Council

of Teachers of Mathematics(NCTM, 2000)such as learning to interact, learning to reason,

learning to solve problems, learning to relate ideas, and learning to represent ideas.Not much

different from the 2013 curriculum, which contains the goal of emphasizing the moder n

pedagogical dimension for learning using a scientific (scientific) approach where the activities

carried out to make learning meaningful, namely asking, trying, observing, reasoning,

presenting, and creating in mathematics learning (Kemdikbud, 2013). Therefore, to educate

students to be able to identify and solve issues they experience, learning must be created (Balım,

2009)

In learning mathematics so that it is easy for students to understand, it is hoped that

mathematical abilities can be mastered by students which are useful for facing challenges in the

era of globalization. These abilities include the ability to solve the mathematical problems

which everyone wants to solve the problems of life and face the industrial revolution(Sani,

2014). The ability to solve mathematical problems for Indonesian students can still be said

below. According to the 2015 Program for International Student Assessment (PISA) report,

Indonesia is in position 63 out of 70 countries, which means that it is ranked 8th from the

bottom and this is very concerning for the mathematical ability of students with an average

score of 386. While the international average score is 490, which means that Indonesia's

average score is still below the international average score(OECD, 2016). In addition, a survey

from the 2015 Trend in International Mathematics and Science Study (TIMSS) resulted in

Indonesia being ranked 6th from below, which means that Indonesia is in position 45 out of 50

countries with an average score obtained of 397 where the international average score is 500.

This means that Indonesia's average score is still far below the international average score

(Mullis et al., 2012).

The primary aim of mathematics learning is to improve different kinds of ability to solve

complex mathematical issues. The role of problem-solving in school mathematics is discussed

(Stanic & Kilpatrick, 1989) and demonstrates the rich history of the subject. Mathematics is

synonymous with problem-solving - creating word problems, making patterns, analyzing

numbers, designing geometries of construction, evidence theorems, etc.

Theoretically, "problem-solving" is usually defined as an effort to achieve some result when

there is no established method to achieve it (for people trying to achieve that result)(Schoenfeld,

2014). The core theoretical argument in MPS (Mathematical Problem Solving), described by

(Schoenfeld, 1989), states that there are four categories of problem-solving activities that need

to be done to analyze the success or failure of students in problem-solving efforts, which include:

(1) Individual awareness; (2) The use by individuals of problem-solving methods, known as

heuristic strategies; (3) Individual monitoring and self-regulation (aspects of metacognition);

and (4) Individual systems of belief (about themselves, about mathematics, about problem-

solving) and the interactions of students with their mathematical backgrounds.

The mathematical problem-solving ability of students can be described as the ability of

students to understand the problem, to prepare a strategy, to introduce the completion strategy,

and to check back later to solve the problem by other means (Kuzle, 2013). Fehr (1953) state

that a destination, the destination restrictions for individuals, and the individual's acceptance

of the intent must be to solve the issue. What matters to one student does not matter to another,

either because there are no limits or because targets are not recognized. (Schoenfeld, 2014)

also illustrates that it is often relative to the person to define a problem. According to Suratmi

& Purnami (2017), the problem-solving abilities that humans must have at school age (students)

include the ability of students to overcome any problems related to their education including

problems in learning activities. One of the fields of study or subjects in schools that require

problem-solving skills in mathematics.

256 | JTAM (Jurnal Teori dan Aplikasi Matematika) | Vol. 5, No. 1, April 2021, pp. 254-261

Problem-solving is very important in learning mathematics because problem-solving is

important in improving students' higher-order thinking skills to explore the knowledge and

skills they already have to solve problems that students rarely encounter. The use of

mathematical problem-solving abilities that are by the problem can make mathematical

ideas/ideas more concrete and help students to solve complex problems that are simpler.

Problem-solving abilities can provide students fluency in building concepts and thinking

mathematically and to have a strong understanding of the problem. Therefore, the ability to

solve mathematical problems needs to be owned by students because it can make it easier for

students to build a concept and think mathematically. This is certainly something to be worried

about amidst being left behind in the science and technology field compared to other countries.

Beigie (2008) also expressed the importance of problem-solving, stating that students will

learn to deepen their comprehension of mathematics by problem-solving by focusing on

carefully chosen problems using the application of mathematics to contextual problems.

Development of the capacity to solve mathematical problems in order to equip students to think

objectively, analytically, systematically, critically and creatively.

If there is an awareness of the significance of taking an action but can not immediately fulfill

it, a situation is called a problem (Ernest et al., 2016). Problems in mathematics present in the

form of a question. These concerns can come from inside mathematics itself and can also come

from real life (Foshay & Kirkley, 2003), which includes mathematical facts and cultural

environments. If students are ready to have a mathematical problem solving technique, then

the question is no longer a question, but an exercise (Schoenfeld, 2014). The mathematical

problem-solving abilities of students are still restricted in Indonesia. Results of teacher

interviews indicate that problems in math words are very difficult. It was also found that

mathematics is not preferred by many students because mathematics is too complex for these

students. Similarly, the poor mathematical problem solving capacity of students (Simamora et

al., 2017) while making observations at Pagaran Senior High School. The results of interviews

with school teachers showed that mathematics is a topic that most students find less appealing.

The results of observations by giving diagnostic tests to Pagaran Senior High School's tenth

graders, with tests in the form of explanations to explain the ability of students to solve math

problems, obtained the same information on the problem-solving abilities of other students,

were very low.

The material of the system of three-variable linear equations is very closely related to

problems in everyday life and is often encountered and experienced by students. Therefore,

this paper aims to describe students 'mathematical problem-solving abilities in solving three-

variable linear equation system problems and the causes of students' difficulties in solving

these problems at each problem-solving step based on Polya's steps. There are 4 stages of

problem-solving according to Polya (2004), namely: (1) Understanding the problem.

Understanding the problem means seeing the issue at hand and in what state. Students need to

decide and define what knowledge is known from the problem at this point, what to look for

and inquire about the problem in their language, and repeat it; (2) Devising a plan. Creating a

solution plan leads to the preparation of a mathematical model and the selection of strategies

that will be used, making estimates and reducing things that are not directly related or

simplifying the problem. Therefore, at this stage, students can build a mathematical model of

the problem and define the strategies and approaches that will be used to solve the problem;

(3) Carrying out the plan. Carrying out a settlement plan means implementing a plan that has

been prepared to solve a problem. So, the plans that have been drawn up and the strategies and

methods that students have chosen in the previous stage will be implemented at this stage; (4)

Looking back. Re-checking the results of the solution means that students look back at the

solutions or results obtained from the problem-solving steps so that there are no errors in the

answers that have been written. From some explanation above problems, the author aims to

Abdul Nu'man Asok, Senior High School Students' ... 257

describe students 'mathematical problem-solving abilities in solving three-variable linear

equation system problems and the causes of students' difficulties in solving these problems.

B. METHODS

The method used in this study is a qualitative descriptive case study approach so that

through this method and approach it is revealed the causes of student errors in solving

mathematical problem-solving problems. The subjects used in the study consisted of 15

students of class X IPA in a high school in Bandung Regency, while the object observed was the

results of student work related to students' problem-solving abilities on the topic of SPLTV.

Before being given a problem-solving ability test, they were given reinforcement of the

prerequisite material related to the topic of SPLTV.

The data used in this study were obtained from the results of a written test (essay)

consisting of five questions and the results of the interviews. The measurement/assessment for

the five written test questions was adopted from the problem-solving ability assessment sheet

used by (Akbar et al., 2018), where the assessment sheet refers to Polya's four stages of

problem-solving.

The interviews carried out were unstructured direct communication. However,

communication with students is still carried out by paying attention to aspects that are by the

data that has been collected. This direct communication is carried out to find out more deeply

about the causes of difficulties in solving problems experienced by students in solving problems

on student worksheets. Students who are selected to be interviewed directly are students who

have different abilities (heterogeneous) in their initial mathematical abilities. The teacher

divides the initial ability groups into three categories, namely students who have high abilities,

moderate abilities, and low abilities seen from the average daily tests of the students. The

average score for students in the high category is 86-100, the medium category is 70-85 and

the low category is less than 70. Of the three categories, some of the students who had difficulty

solving the story questions were the fewest and the most selected to be interviewed. In this

study, two high-ability students, two medium-ability students, and two low-ability students

were taken. Then the data obtained is analyzed to conclude.

C. RESULT AND DISCUSSION

From the data, the results of this study are in the form of student learning outcomes who

collect data using instruments in the form of essay test questions as many as 5 questions. The

following is the data on the results of the mathematical problem-solving ability test which is

presented in Table 1.

Table 1. Score indicators of mathematical problem-solving abilities

258 | JTAM (Jurnal Teori dan Aplikasi Matematika) | Vol. 5, No. 1, April 2021, pp. 254-261

Table 2. Percentage of problem-solving ability.

Problem Solving

Indicator

The following shows some examples of student answers given test questions.

Figure 1. Student answer number 1

In Figure 1 there is indicator 1 (Understanding Problem) where on average students can

complete mathematical modeling on SPLTV material.

Figure 2. Student answer number 2

Abdul Nu'man Asok, Senior High School Students' ... 259

In Figure 2. The answers to question number 2 have indicators 1 and 2 where on average

students can understand the problem, identify known elements, ask questions, and make

mathematical models.

Figure 3. Student answer number 3

In Figure 3. One student's answer to question number 3.There are indicators 3 and 4 where the

average student is only able to make a mathematical model.

Figure 4. Student answer number 4

In Figure 4. Response from one student to question number 4. Indicators 2 and 3 exist where

students can find alternatives to answer the questions on average.

Figure 5. Student's answer number 5

In Figure 5. There are indicators 3 and 4 for one student's response (S12) to question number

5. Students can create mathematical models that are incorrect.

Meanwhile, based on the results of the direct interviews, the information found in the questions

was not written by any students, as it was known to write down their linear equations, what

was the question in the question. Students often solve problems directly because students think

writing down the completion steps is not too important. After all, it is a waste of time. Students

260 | JTAM (Jurnal Teori dan Aplikasi Matematika) | Vol. 5, No. 1, April 2021, pp. 254-261

also often do not write about what they have to do at each completion stage, most students are

still confused in preparing the completion steps. The errors in planning are caused because

students do not know the completion strategy plan correctly. Students are not able to plan

because students are not used to and immediately work on the questions without making plans

in advance with sentences, other than that students have difficulty entering data in the formulas

that have been written down, and students are not careful in the calculations they do.

Meanwhile, the students' mistakes in indicator 4 (checking the solutions obtained) were caused

by the students not thinking they needed to double-check because they were sure that the

answer was correct. Besides, in checking the answers students are not accustomed to using

systematic steps on the worksheets used. These errors are also consistent with the findings of

the study carried out. (Hadi, 2018) that in general students do not have habits of mind to act

carefully or make definite steps in making strategies even students generally give up easily

when facing failure in executing the strategy so that they stop looking for other strategies when

the previous strategic plan failed to be executed.

D. CONCLUSION AND SUGGESTIONS

Based on the results and discussion above, it can be concluded that the cause of the low

achievement of the indicators of mathematical problem solving ability that students get is

because some students are not able to plan, students are not used to it and immediately work

on the questions without making plans in advance with sentences, other than that students

have difficulty in making plans. enter data in the formula that has been written, and students

are less careful in the calculations that are carried out. It can be seen in table 2 that the students'

mathematical problem solving abilities are included in the sufficient category on the indicators

of planning problems and low on the indicators of solving problems and checking This can be

seen from the number of students who have achieved the achievement indicators of preparing

plans 49.6%, the achievement of completing plans 14, 1% and the achievement in checking

solutions is 2.2%. However, the indicators of understanding the problem are in a good category,

namely 80%.

Therefore, researchers suggest that students are more often given contextual problems to

be solved by identifying the variables that are arranged into the correct mathematical model so

that their mathematical problem-solving abilities will increase optimally. Apart from that, it is

necessary to have habits of mind systematically, carefully, and thoroughly in solving problems.

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  • Suratmi Suratmi
  • Agustina Sri Purnami

The purpose of this research is to know about students problem solving ability between students who implemented metacognitive strategy and conventional strategy, to know about students problem solving ability between student who have high perception, medium perception dan low perception in mathematics, and to know about interaction between of strategy and perception. This research is quasy experimental. The population of this research were students of class VIII SMP Negeri 3 Karangreja year 2014/2015. The sample of this research were 2 class which is 63 students with cluster random sampling technique. Data analysis is used descriptive analysis dan two ways Anava or F-test. The result of this research showed that: The problem solving ability of experiment class better than control class that is ; The problem solving ability of student who have high perception is better than medium and low perception, the problem solving ability of students who have medium perception is equal with low perception that is , and there is no interaction between of strategy and level of perception in problem solving ability that is .

The purpose of this research are: (1) To know the improvement of problem solving ability of students, (2) To know the improvement of problem solving ability of mathematics students by applying Problem Based Learning Model on geometry topic. The approach of this research is a classroom action research. Subjects in this study were students of class X-6 of SMA (Tenth Year Senior High School) Negeri 1 Pagaran totaling 30 students. The result of data analysis after giving of action in cycle 1, it was obtained 70% classical completeness; medium problem solving ability category. In the second cycle obtained 90% classical completeness. The category of problem solving ability is very high. Based on the results of data analysis, it can be concluded that the problem-based learning model can improve mathematics problem solving ability.

This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of 'philosophical archaeology': the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.

  • Ana Kuzle Ana Kuzle

This paper describes the problem solving behavior of two preservice teachers as they worked individually on three nonroutine geometry problems. A dynamic tool software, namely the Geometer's Sketchpad, was used as a tool to facilitate inquiry in order to uncover and investigate the patterns of metacognitive processes. Schoenfeld's (1981) model of episodes and executive decisions in mathematics problem solving was used to identify patterns of metacognitive processes in a dynamic geometry environment. During the reading, understanding, and analysis episodes, the participants engaged in monitoring behaviors such as sense making, drawing a diagram, and allocating potential resources and approaches that helped make productive decisions. During the exploring, planning, implementation, and verification episodes, the participants made decisions to access and consider knowledge and strategies, make and test conjectures, monitor the progress, and assess the productivity of activities and strategies and the correctness of an answer. Cognitive problem-solving actions not accompanied by appropriate metacognitive monitoring actions appeared to lead to unproductive efforts. Redirection and reorganizing of thinking in productive directions occurred when metacognitive actions guided the thinking and when affective behaviors were controlled.

  • Darin Beigie

Problem solving is not a distinct topic, but a process that should permeate the study of mathematics and provide a context in which concepts and skills are learned. (NCTM 2000, p. 182)

  • Padillah Akbar
  • Abdul Hamid
  • Martin Bernard Martin Bernard
  • Asep Ikin Sugandi

Dalam penelnitian ini penulis menganalisis tentang kesulitan siswa dalam proses pemecahan masalah serta untuk mengetahui tingkat kategori disposisi matematik pada tiap butir pernyataan. Berdasarkan analisis, kesalahan yang dilakukan oleh siswa dalam mengerjakan soal pemecahan masalah matematik materi peluang dihasilkan dalam proses pencapaiandan kualifikasi dalam memahami masalah 48,75% (rendah), merencanakan penyelesaian 40% (rendah), menyelesaikan masalah 7,5% (sangat rendah), melakukan pengecekan 0% (sangat rendah). Instrumen soal yang digunakan adalah soal yang sudah diuji realibilitas, validitas, daya beda dan indeks kesukarannya juga telah divalidasi oleh validator ahli. Metode penelitian menggunakan analisis deskriptif kualitatif untuk mengetahui sejauh mana pencapaian indikator dari kemampuan pemecahan masalah serta mengetahui tingkat kategori disposisi matematik pada tiap butir pernyataan. Berdasarkan hasil penelitian secara keseluruhan bahwa pencapaian indikator dari kemampuan pemecahan masalah belum tercapai sepenuhnya serta kemampuan disposisi siswa yang tergolong rendah

  • Ali günay balım Ali günay balım

Problem Statement: In this study, the unit "If It Weren't for The Pressure?" in the Science and Technology course at the Elementary 7th grade was tackled in two different ways. The first way is the discovery learning method along with the daily plans and activities. The second is the traditional teaching method. This study particularly aims at answering the question: "How does teaching science through the discovery learning approach affect students' academic achievement, perception of inquiry learning skills, and retention of knowledge?" Purpose of Study: This study aims at identifying the effects of the discovery learning method upon the students' perceptions of inquiry learning skills, academic achievements, and retention of knowledge. This research also investigates whether there is a significant difference between the experimental and control groups in learning the subjects of the unit "If It Weren't for The Pressure?" from the point of cognitive and affective learning levels. Findings and Results: A quasi-experimental research design with a pre-test and post-test control group was used in this study. Fifty-seven seventh graders participated in this study during the spring term of the 2006-2007 academic year. The result of the study shows that there is a significant difference in favour of the experimental group over the control group regarding the average of academic achievement, scores of retention of learning, and perception of inquiry learning skills scores, both on cognitive and affective levels. Conclusions and Recommendations: The conclusions of the study showed that there is a significant difference in favor of the experimental group over the control group in terms of academic achievement scores, perception of inquiry learning scores, and retention of learning scores in both cognitive and affective levels. Thus, it can be stated that the experimental group students, who scored high in the post-achievement test, have high perception of inquiry learning skills scores. Using the discovery learning method, which is one of the various teaching methods in which the students are active and are guided by the teacher, is considered to increase students' success and inquiry learning skills more than the traditional teaching methods.