scholarly journals Thinking Process of Concrete Student in Solving Two-Dimensional Problems

2020 ◽  
Vol 14 (2) ◽  
pp. 117-128
Author(s):  
Sri Adi Widodo ◽  
Ambar Dana Pangesti ◽  
Istiqomah Istiqomah ◽  
Krida Singgih Kuncoro ◽  
Tri Astuti Arigiyati

The purpose of this research was to find out the thinking processes of a concrete student in solving two-dimensional problems. The research method used is descriptive qualitative. The research subjects were two students taken using purposive sampling. The instrument used was the Test of Logical Operations and problem-solving tests. Stages of data analysis used are researching all data, making a cognitive classification of students, choosing concrete students to be used as research subjects, reviewing the results of concrete student work in solving mathematical problems, verify data and data sources that have been classified and transcribed in the presentation or exposure of data. The results showed that at the stage of understanding the problem and re-checking the answers, concrete students use the assimilation at the stage of planning to solve the problem of doing the disequilibration. At the stage of carrying out a plan to solve a problem, concrete students carry out the accommodation. During this study, it was found that students 'habits in mathematical problem-solving did not plan to solve problems, did not re-examine answers, and there were students' habits by interpreting the final results of problems. It can be concluded that the students' concrete thinking processes in solving two-dimensional problems vary according to the stages of problem-solving.

2016 ◽  
Vol 10 (1) ◽  
pp. 1 ◽  
Author(s):  
Jackson Pasini Mairing

Solving problem is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe the thinking process of naive problem solvers based on heuristic of Polya. The researcher gave two problems to students at grade XI from one of high schools in Palangka Raya, Indonesia. The research subjects were two students with problem solving scores of 0 or 1 for both problems (naive problem solvers). The score was determined by using a holistic rubric with maximum score of 4. Each subject was interviewed by the researcher separately based on the subject’s solution. The results showed that the naive problem solvers read the problems for several times in order to understand them. The naive problem solvers could determine the known and the unknown if they were written in the problems. However, they faced difficulties when the information in the problems should be processed in their mindsto construct a mental image. The naive problem solvers were also failed to make an appropriate plan because they did not have a problem solving schema. The schema was constructed by the understanding of the problems, conceptual and procedural knowledge of the relevant concepts, knowledge of problem solving strategies, and previous experiences in solving isomorphic problems.


Gunahumas ◽  
2020 ◽  
Vol 2 (2) ◽  
pp. 357-386
Author(s):  
Yomi Chaeroni ◽  
Nizar Alam Hamdani ◽  
Akhmad Margana ◽  
Dian Rahadian

ABSTRAK Penelitian ini dilatarbelakangi oleh fakta bahwa kemampuan pemahaman dan kemampuan pemecahan masalah matematis merupakan salah satu kemampuan matematika tingkat tinggi yang harus dimiliki oleh setiap peserta didik. Selain itu kemampuan pemahaman dan kemampuan pemecahan masalah matematis jarang diterapkan dalam pembelajaran matematika di sekolah. Salah satu model pembelajaran yang dapat menjadi alternatif bagi pembelajaran matematika dan kemampuan pemahaman dan pemecahan masalah matematis adalah model pembelajaran IMPROVE. Penelitian ini bertujuan untuk mengetahui penerapan i-spring suite 8 pada model pembelajaran IMPROVE untuk meningkatkan kemampuan pemahaman dan pemecahan masalah matematis peserta didik. Metode penelitian yang digunakan adalah quasi eksperimen karena penelitian ini menggunakan satu kelas eksperimen dan satu kelas kontrol sebagai subyek penelitian. Cara pengambilan subjek penelitian yang digunakan adalah purposive sampling. Subjek penelitian dipilih sebanyak dua kelas dari keseluruhan peserta didik kelas XI SMA Muhammadiyah Banyuresmi tahun pelajaran 2019/2020. Dari hasil penelitian dan perhitungan statistik diperoleh kesimpulan: 1) Terdapat peningkatan kemampuan pemahaman dan pemecahan masalah matematis peserta didik yang dalam pembelajarannya menggunakan i-spring suite 8 pada model pembelajaran IMPROVE; 2) Terdapat peningkatan kemampuan pemahaman dan pemecahan masalah matematis peserta didik yang dalam pembelajarannya menggunakan model pembelajaran konvensional/direct instruction; 3) Terdapat peningkatan kemampuan pemahaman dan pemecahan masalah matematis peserta didik yang dalam pembelajarannya menggunakan i-spring suite 8 pada model pembelajaran IMPROVE dibandingkan dengan peserta didik yang dalam pembelajarannya menggunakan model pembelajaran konvensional/direct instruction; 4) Tidak terdapat perbedaan kemampuan pemahaman dan pemecahan masalah matematis peserta didik yang dalam pembelajarannya menggunakan i-spring suite 8 pada model pembelajaran IMPROVE dan yang menggunakan model konvensional/direct instruction.Kata kunci: Kemampuan Pemahaman Matematis, Kemampuan Pemecahan Masalah Matematis, Model IMPROVEABSTRACT This research is motivated by the fact that the ability to understand and the ability to solve mathematical problems is one of the high-level mathematical abilities that must be possessed by every student. In addition, the ability to understand and the ability to solve mathematical problems are rarely applied in mathematics learning in schools. One learning model that can be an alternative for mathematics learning and mathematical understanding and problem solving abilities is the IMPROVE learning model. This study aims to determine the application of ispring suite 8 on the IMPROVE learning model to improve students' mathematical understanding and problem solving abilities. The research method used is quasi-experimental because this study uses one experimental class and one control class as research subjects. The method of taking the research subject used was purposive sampling. The research subjects were selected as many as two classes from all grade XI students of SMA Muhammadiyah Banyuresmi in the 2019/2020 academic year. From the results of research and statistical calculations conclusions: 1) There is an increase in the ability to understand and solve mathematical problems of students who in learning use the i-spring suite 8 on the IMPROVE learning model; 2) There is an increase in the ability of understanding and solving mathematical problems of students who in learning use conventional learning models / direct instruction; 3) There is an increase in students' mathematical understanding and problem solving abilities in learning using i-spring suite 8 in the IMPROVE learning model compared to students in learning using conventional learning models / direct instruction; 4) There is no difference in the ability to understand and solve mathematical problems of students who in learning use the i-spring suite 8 on the IMPROVE learning model and who use the conventional model / direct instruction.Keywords: Mathematical Understanding Ability, Mathematical Problem Solving Ability, IMPROVE Model


MATHEdunesa ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 211-220
Author(s):  
NILA NURCAHYANING KUSUMAWARDANI ◽  
RADEN SULAIMAN

Critical thinking is a thinking process in processing information logically starti from understanding, analyzing, evaluating and making precise conclusions. Critical thinking indicators are clarification, assessment, inference, and strategy that referred to Jacob and Sam. Mathematics is designed to improve students' critical thinking in a solving problem. One of the factors that affect students' critical thinking in solving a problem is AQ. This research is descriptive study with qualitative approach. The aim is to describe critical thinking profile of climber, camper, and quitter students in solving mathematical problems. The subjects were three students of VIII grade junior high school who represented each AQ category and had good communication skills. The instrument used was the ARP questionnaire, mathematics problem solving tests, and interview guidelines. The results shows that students’ critical thinking profile in understanding the problem is climber and camper student do all indicators of critical thinking in the clarification phase. Quitter student is only able mentioning known and asked information. In devising a plan, climber student implements all indicators of assessment and strategy phase. Camper student implements all indicators in assessment phase, but do not discuss the possible steps in strategy phase. Quitter student does not do both assessment and strategy phase. In carrying out the plan, climber and camper students do all indicators of inference phase, while quitter student does not. In the step of looking back, only climber student who carries out evaluating steps that have been done. Keywords: Jacob and Sam’s critical thinking, mathematical problem solving, adversity quotient


2021 ◽  
Vol 9 (2) ◽  
Author(s):  
Ahmad Talib

This research is a qualitative research with descriptive method. This study aims to describe the ability to think creatively based on the type of student personality, the type of choleric personality in solving mathematical problems. The research subjects were students in the odd semester of class XII IPA 1 SMA Negeri 22 Makassar, the 2019/2020 school year. This subject was chosen by giving a personality questionnaire to students. The data was collected using a mathematical problem solving test instrument on the number sequence material and interviews. The validity of the data was checked by using the triangulation method. The results showed: Students with choleric personality in solving mathematical problems. In question number 1, the subject had difficulty in finding the formula for the nth term. But the subject kept trying and the spirit of trying until finally found the correct formula for the nth term. The subject of the choleric personality type is also said to be able to fulfill the three indicators of creative thinking, namely fluency, flexibility, and novelty. In question number 2, the subject had difficulty finding many ways to solve the problem and only met one indicator of creative thinking, namely fluency.


2021 ◽  
Vol 9 (1) ◽  
pp. 1
Author(s):  
Alfiani Athma Putri Rosyadi

Berpikir kritis penting dalam kehidupan sehari-hari, karena dapat mengembangkan kemampuan untuk membuat keputusan dan menyelesaikan masalah. Tujuan dari penelitian ini adalah untuk mendeskripsikan proses berpikir kritis mahasiswa dalam menyelesaikan permasalahan kontroversial. Proses berpikir kritis dalam penelitian ini mengacu pada  (a) Identify, (b) Define, (c) Enumerate, (d) Analyze, (e) List dan (f) Self-Correct. Penelitian ini adalah penelitian deskriptif dengan pendekatan kualitatif. Instrumen penelitian terdiri dari peneliti, lembar kerja, hasil kerja mahasiswa dan hasil wawancara. Penelitian ini melibatkan 40 mahasiswa calon guru semester 6 ( 43% ) dan semester 8 (57%) di jurusan matematika di kota malang. Analisis data dilakukan melalui : (1) Reduksi dari data tes dan hasil wawancara ,(2) Analisis dari data hasil tes dan wawancara dan (3) menyajikannya. Hasil penelitian menunjukkan bahwa proses berpikir kritis dalam menyelesaikan masalah kontroversial melalui lima tahapan yaitu: Identify, Define, Enumerate, Analyze dan List serta Self-Correct. Hal ini menunjukkan terdapat penggabungan proses analyze dan list pada subjek penelitian saat menyelesaikan permasalahan kontroversial. Penguatan argumentasi muncul pada bagian enumerate, analisis dan list. Saran untuk peneliti berikutnya adalah diperlukan studi tentang kemungkinan penggabungan proses berpikir kritis. Selain itu kelemahan pada tahap analisis bisa menjadi referensi untuk dapat menggunakan metode lain untuk meningkatkan berpikir kritisnya. Kata kunci: Berpikir Kritis, Pemecahan Masalah, Masalah Matematika Kontroversial Abstract:  Critical thinking is essential in everyday life because it can develop the ability to make decisions and solve problems. The purpose of this study was to describe the critical thinking process of students in solving controversial problems. The critical thinking process in this study refers to (a) Identify, (b) Define, (c) Enumerate, (d) Analyze, (e) List, and (f) Self-Correct. This research is a descriptive study with a qualitative approach. The research instrument consisted of researchers, worksheets, student work results, and interviews. This study involved 40 student-teacher candidates in the 6th semester (43%) and 8th semester (57%) in the mathematics department in Malang. Data analysis was carried out through (1) reduction of test data and interview results, (2) analysis of test and interview data, and (3) presenting them. The results showed that the critical thinking process in solving controversial problems through five stages, namely: Identify, Define, Enumerate, Analyze, and List and Self-Correct. This shows that there is a combination of the analysis and list processes in research subjects when solving controversial problems. Argument reinforcement appears in the enumerate, analysis, and list sections. The suggestion for the next researchers is that studies on the possibility of incorporating critical thinking processes are needed. Besides that, the weaknesses in the analysis stage can be a reference to be able to use other methods to improve critical thinking. Keywords: Critical Thinking, Problem Solving, Controversial Problem


2021 ◽  
Vol 1 (1) ◽  
pp. 51
Author(s):  
Mochamad Jazim ◽  
Dinawati Trapsilasiwi ◽  
Randi Pratama Murtikusuma ◽  
Arifiatun Arifiatun

This study aims to describe and analyze students' mathematical problem solving abilities based on theory of APOS (Action, Peocess, Object, Schema) in terms of Field Dependent and Field Independent Cognitive Style. It is descriptive research with qualitative approach. The research subjects are 34 students in class XI MIPA 1 SMA Nurul Islam Jember, they are grouped on cognitive style, they are 24 students having field independent cognitive style and 10 students having field dependent cognitive style. The method of data collection use a GEFT (Group Embedded Figure Test), test of problem solving abilities, , and interviews. The results of the data analysis of the problem solving ability test and interviews showed that at the action stage, students with the independent field cognitive style (FI) tended to be able to explain the meaning and information on the questions even though they did not write down what they knew. Students with the field dependent cognitive style (FD) tend to be able to write down the information contained in the questions, but have difficulty explaining the meaning of the questions. At the process stage, FI and FD students are able to model and explain the stages well, but FD still has errors in the resulting mathematical model. At the object stage, FI students tend to work on questions freely, while FD students tend to work on questions in detail or are fixated on completely arranged steps, FD students also have difficulty in explaining back the results of their work. At the schema stage, FI and FD students tend to be able to explain how to use the information contained at the object stage to be used at the schema stage. In general, students with a field independent cognitive style in solving mathematical problems tend to be free or not fixated on complete and detailed steps, and have an analytical nature, so they are able to sort out the important information contained in the questions. Students with a field dependent cognitive style in solving math problems tend to be bound or fixated with steps that are arranged in a complete and detailed manner. Keywords: mathematics problem solving, APOS theory, cognitive style


2019 ◽  
Vol 4 (2) ◽  
pp. 175-189
Author(s):  
Nur 'Afifah ◽  
Ismail Hanif Batubara

Abstract. The research objectives are: (1) Knowing whether the approach to the mathematical investigation can improve the ability to solve open mathematical problems; (2) Knowing how the level of activity of students and lecturers in learning through a mathematical investigation approach. This type of research is Class Action Research. The research subjects were Students of Mathematics Education FKIP UMSU Academic Year 2018/2019. The object of research is the ability of lecturers to manage student learning and activities in the implementation of learning and the ability of students to solve open mathematical problems through an investigative approach to material numbers. The results of the study show that (1) The approach to the mathematical investigation can improve students' mathematical problem-solving abilities; (2) The approach to the mathematical investigation can increase the level of student activity. From the results of the initial test the ability to solve open mathematical problems an average value of 3.17, the average value of student cycle I tests is 10.73 (56.66%) students who have the ability to solve open mathematical problems and average test scores the second cycle was 12 (83.33%) students who had the ability to solve open mathematical problems. Based on the conclusions above, this study suggests that consider the application of a mathematical investigation approach in order to improve the quality of mathematics learning.Keywords: Mathematical Investigation, Problem-Solving, Open-Mathematics.


2017 ◽  
Vol 10 (2) ◽  
pp. 134-152
Author(s):  
Miftah Syarifuddin

[Bahasa]: Penelitian ini bertujuan untuk mendeskripsikan proses berpikir siswa bertemperamen choleric dan melancholic dalam menyelesaikan masalah geometri. Proses berpikir dalam penelitian ini adalah proses berpikir konseptual atau proses berpikir prosedural. Proses berpikir konseptual meliputi 5 (lima) kompetensi, yaitu menggunakan aturan dasar, melihat pola, menerapkan konsep, mengklarifikasi situasi, dan mengembangkan masalah. Proses berpikir prosedural adalah cara berpikir siswa yang terbiasa menghafal rumus dan menggunakan cara-cara rutin dalam menyelesaikan masalah. Penelitian ini merupakan penelitian deskriptif dengan pendekatan kualitatif. Subjek penelitian terdiri dari 2 (dua) siswa perempuan dengan kemampuan matematika tinggi dan setara di kelas IX Salatiga, Indonesia, terdiri dari 1 (satu) siswa bertemperamen choleric dan 1 (satu) siswa bertemperamen melancholic. Pemilihan subjek penelitian berdasarkan hasil tes temperamen dan hasil tes kemampuan matematika. Data penelitian diperoleh dari pemberian tugas penyelesaian masalah geometri dan wawancara kepada para subjek penelitian sebanyak 2 (dua) kali. Pemberian tugas penyelesaian masalah kedua dan wawancara kedua merupakan triangulasi data. Hasil penelitian menunjukkan bahwa proses berpikir siswa terungkap melalui tugas penyelesaian masalah geometri yang diberikan. Siswa bertemperamen choleric menggunakan proses berpikir prosedural dalam menyelesaikan masalah geometri, sedangkan siswa bertemperamen melancholic menggunakan proses berpikir konseptual dalam menyelesaikan masalah geometri. Kata kunci: Proses Berpikir; Choleric; Melancholic; Masalah Geometri [English]: This study aims to describe the thinking process of students with choleric and melancholic temperament in solving geometry problems. The thinking process in this research is conceptual thinking process or procedural thinking process. The conceptual thinking process includes 5 (five) competencies, i.e. using basic rules, seing patterns, applying concepts, clarifying situations, and developing problems. The process of procedural thinking is a way of thinking of students who are used to memorizing formulas and using routine ways of solving problems. This research was a descriptive research with qualitative approach. The subjects consisted of 2 (two) female students with high and equivalent mathematics abilities in the ninth grade in Salatiga, Indonesia consisting of 1 (one) choleric student and 1 (one) melancholic student. The selection of research subjects is based on temperament test and mathematical ability test. Research data obtained from geometry problem solving task and interview to the research subjects twice. The second task of problem solving and interview is triangulation of data. The results reveal the thinking process of students through the task of solving the geometry problem given. Student with choleric temperament used procedural thinking processes in solving geometry problems, while student with melancholic temperament used conceptual thinking processes in solving geometry problems. Keywords: Thinking; Choleric; Melancholic; Geometry Problems


Author(s):  
Ratumas Feby Purniance ◽  
Kamid Kamid ◽  
Jefri Marzal

Students have their own personality types which will ultimately affect their learning skills. This study aims to describe the critical thinking process of cholerist type students in solving mathematical problems. This type of research is a qualitative-descriptive study. The subjects of the study were students of SMK 5 Muaro Jambi who had participated in the district mathematics olympiad. The instruments used were personality test sheets, problem solving sheets and interview guidelines. The researcher directly observed the process of solving mathematical problems performed by the research subject. The researcher analyzed the results of the students' work in formulating questions, solving problems, and interviewing research subjects. The interview data was analyzed by means of data reduction, data exposure/categorization and subsequent conclusions. The results of this study indicate that during the problem solving process research subjects can solve problems casually, confidently and correctly. From the results of solving problems I and II it can be seen that the research subjects make decisions very quickly, directly and solve them with different steps according to the situation and the results of their thoughts on the problems faced. It can be concluded that the research subjects were able to solve the problem critically.


2018 ◽  
Vol 3 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Muhammad Irfan

Algebra is one of the most difficult material for students to understand, especially those experiencing math-anxiety. This study aimed to describe: (1) the thinking process of students who have high math-anxiety in solving mathematical problems according to Polya steps, (2) the thinking process of students who have low math-anxiety in solving mathematical problems according to Polya steps. Type this research is qualitative research with case study method. Sampling is done by purposive sampling technique. Subjects used in this study as much as two research subjects, namely: students who have high anxiety math, students who have low anxiety math. The instruments used to collect data are classification of anxiety level of mathematics learning, mathematics problem sheet, and interview guidance. The data validation test used is the triangulation test of time. In this study, researchers used a type of reflective and creative thinking to analyze the thinking process of the subject. The results show: (1) when understanding the problem, planning problem solving, running problem-solving plan, and re-examining answers, students experiencing high math-anxiety using reflective thinking process, (2) when understanding the problem and re-examining answers, students who experience low anxiety math using reflective thinking processes, while at the time of planning problem solving and running problem-solving plans, the subject engages in a process of reflective and creative thinking.


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