scholarly journals Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

2016 ◽  
Vol 10 (1) ◽  
pp. 1 ◽  
Author(s):  
Jackson Pasini Mairing
Keyword(s):  
Problem Solving ◽  
Procedural Knowledge ◽  
Mental Image ◽  
Research Subjects ◽  
Maximum Score ◽  
Mathematical Problems ◽  
Problem Solving Strategies ◽  
Thinking Process ◽  
Problem Solvers ◽  
Holistic Rubric

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.

scholarly journals PROFIL PENALARAN MATEMATIS SISWA SMP DALAM PEMECAHAN MASALAH ARITMETIKA SOSIAL BERDASARKAN KEMAMPUAN MATEMATIKA

MATHEdunesa ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 110-120
Author(s):  
YULIANA DWI RAHMAWATI ◽  
Masriyah Masriyah
Keyword(s):  
Problem Solving ◽  
Qualitative Data ◽  
Mathematical Reasoning ◽  
Research Subjects ◽  
Ability Test ◽  
Reasoning Abilities ◽  
Mathematical Abilities ◽  
Reasoning Problem ◽  
Mathematical Problems ◽  
Problem Solving Strategies

Mathematical reasoning is the ability to think about mathematical problems, namely by thinking logically about mathematical problems to get conclusions about problem solutions. There are several factors that can affect students' mathematical reasoning, including mathematical abilities. Dissimilarity of students' mathematical abilities allows for dissimilarity in their mathematical reasoning abilities. So, this research intends to describe students' mathematical reasoning abilities in solving social arithmetic problems based on dissimilarity in mathematical abilities. The purpose of this research was to describe qualitative data about the mathematical reasoning abilities of students with high, medium, or low abilities in solving social arithmetic problems. The instrument used was the Mathematical Ability Test to determine the three research subjects, followed by a Problem Solving Test to get qualitative data about students' mathematical reasoning abilities, then interviews to get deeper data that was not obtained through written tests. Thus, the research data were analyzed using mathematical reasoning indicators. From the result of data analysis, it was found that all students understood the problem well. Students with high and medium mathematical abilities are determining and implementing problem solving strategies properly, namely writing down the step for solving them correctly and making accurate conclusions by giving logical argumens at aech step of the solution. However, students with low mathematical abillities have difficulty in determining and implementing problem solving strategies because they do not understand the concept, thus writing the steps to solve the problems incorrectly and not giving accurate conclusions about the correctness of the solution. Keywords: mathematical reasoning, problem solving, mathematical abilities

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
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Two Dimensional ◽  
Research Subjects ◽  
Student Work ◽  
Logical Operations ◽  
Mathematical Problems ◽  
Thinking Process ◽  
Thinking Processes

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.

scholarly journals KEMAMPUAN MAHASISWA PENDIDIKAN MATEMATIKA DALAM MEMECAHKAN MASALAH DI AWAL DAN AKHIR SEMESTER PERTAMA

2017 ◽  
Vol 9 (2) ◽  
pp. 49
Author(s):  
Jackson Pasini Mairing
Keyword(s):  
Problem Solving ◽  
Confidence Level ◽  
Average Score ◽  
Research Subjects ◽  
Central Kalimantan ◽  
First Semester ◽  
Learning Mathematics ◽  
Mathematical Problems ◽  
Problem Solvers ◽  
Academic Year

Problem solving ability is main goal of students in learning mathematics. Lectures should be able to improve the ability. This reasearch aimed to describe ability ofstudents at the beginning and end of first semester academic year 2016/2017 in solving mathematical problems. The research subjects were 71 students of mathematicseducation program class of 2016 from one of the universities in Central Kalimantan, Indonesia. At the beginning and the end of first semester, each subject was given sixmathematical problems. The problems at the beginning and the end of semester were similar only differently in numbers. The result showed that average score of the students at the beginning and the end of first semester were 7.97 and 9.18 (scale 0 - 24), respectively. The scores increased significantly with a 95% confidence level. Theincreasng caused 8.4% of the students who were classified as naive problem solvers increased their ability becomed routine problem solvers. No students have improved their ability becomed good problem solvers.

Analisis Proses Berpikir Kritis Siswa SMK Tipe Koleris dalam Memecahkan Masalah Matematika

2018 ◽  
Vol 7 (1) ◽  
pp. 8-15
Author(s):  
Ratumas Feby Purniance ◽  
Kamid Kamid ◽  
Jefri Marzal
Keyword(s):  
Problem Solving ◽  
Personality Types ◽  
Personality Test ◽  
Research Subject ◽  
Research Subjects ◽  
Learning Skills ◽  
Mathematical Problems ◽  
Qualitative Descriptive ◽  
Thinking Process ◽  
Problem Solving Process

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.

scholarly journals Students’ Strategies in Solving PISA Mathematical Problems Reviewed from Problem-Solving Strategies

2021 ◽  
Vol 15 (1) ◽  
pp. 37-48
Author(s):  
Meryansumayeka Meryansumayeka ◽  
Zulkardi Zulkardi ◽  
Ratu Ilma Indra Putri ◽  
Cecil Hiltrimartin
Keyword(s):  
High School Students ◽  
Problem Solving ◽  
Descriptive Study ◽  
Dominant Strategy ◽  
Trial And Error ◽  
Research Subjects ◽  
School Students ◽  
Mathematical Problems ◽  
Problem Solving Strategies ◽  
Different Levels

This study purposes to describe the strategies used by students in solving PISA type problems seen from the strategy of problem solving according to Polya. The research methodology is qualitative type descriptive study. Research subjects were 6 high school students in Palembang who had different levels of mathematical ability. Data was gathered using observation, interviews, and student answer sheets on the type of PISA questions given. The results showed that the dominant strategy used by students in solving PISA type problems included making pictures when they solve problem related to geometry; looking for possible answers systematically when they try to solve problem within numeric; writing information stated and the question when the problem is in the form of storytelling; and using trial and error when the problem provide answer alternatives.

scholarly journals Kemampuan Komunikasi Matematis Siswa SMP dalam Menyelesaikan Masalah Matematika Berdasarkan Gaya Kognitif Reflektif dan Impulsif

2021 ◽  
Vol 4 (1) ◽  
pp. 22
Author(s):  
Nur Qomariyah ◽  
Rini Setianingsih
Keyword(s):  
Problem Solving ◽  
Cognitive Style ◽  
Communication Skills ◽  
Cognitive Styles ◽  
Research Subjects ◽  
Mathematical Communication ◽  
Mathematical Problems ◽  
Qualitative Descriptive ◽  
Problem Solving Strategies ◽  
Communication Differences

Abstrak — Komunikasi matematis merupakan cara penyampaian ide, strategi, maupun solusi masalah matematika secara tertulis maupun lisan. Gaya kognitif yang berbeda memungkinkan terjadinya perbedaan komunikasi dalam menyelesaikan masalah matematika baik secara lisan maupun tulisan. Penelitian ini bertujuan untuk mendeskripsikan kemampuan komunikasi matematis siswa dengan gaya kognitif reflektif dan impulsif dalam menyelesaikan masalah matematika. Penelitian ini merupakan penelitian deskriptif kualitatif. Subjek penelitiannya yaitu satu siswa bergaya kognitif reflektif (SR) dan satu siswa bergaya kognitif impulsif (SI). Hasil penelitian ini menunjukkan bahwa kemampuan komunikasi matematis tulis siswa yang bergaya kognitif reflektif dapat dikatakan tidak akurat, tidak lengkap, dan lancar pada tahap memahami masalah. Kemampuan komunikasi lisan siswa yang bergaya kognitif reflektif dapat dikatakan akurat, lengkap, dan lancar disetiap tahap penyelesaian masalah. Kemampuan komunikasi matematis tulis siswa yang bergaya kognitif impulsif dapat dikatakan tidak akurat, tidak lengkap dan lancar pada tahap memahami masalah. Selain itu, di tahap memeriksa kembali dapat dikatakan tidak akurat, tidak lengkap, dan tidak lancar. Kemampuan komunikasi matematis lisan siswa bergaya kognitif impulsif dapat dikatakan tidak akurat, tidak lengkap dan tidak lancar di tahap memeriksa kembali.Kata Kunci: Komunikasi Matematis, Gaya Kognitif Reflektif, Gaya Kognitif Impulsif  Abstract — Mathematical communication is a way to convey ideas of problem solving, strategies and mathematical solutions both in writing and verbally. The different cognitive styles allowing communication differences in solving mathematical problems both verbally and in writing. This study aims to describe the mathematical communication skills of students with reflective and impulsive cognitive styles in solving mathematical problems. This research is a qualitative descriptive study. The research subjects were one student with reflective cognitive style (SR) and one student with impulsive cognitive style (SI). The results of this study indicate that students' written mathematical communication skills with reflective cognitive style can be said to be inaccurate, incomplete, and fluent at the step of understanding the problem. The verbal communication skills of students who are reflective cognitive style can be said to be accurate, complete, and fluent at every step of problem solving. The students' written mathematical communication skills with impulsive cognitive style can be said to be inaccurate, incomplete and fluent at the stage of understanding the problem. In addition, the step of looking back can be said to be inaccurate, incomplete, and influent. The verbal mathematical communication skills of students with impulsive cognitive style can be said to be inaccurate, incomplete and influent at the step of looking back.Keywords: Mathematical Communication, Reflective Cognitive Style, Impulsive Cognitive Style

scholarly journals PROSES BERPIKIR SISWA YANG MENGALAMI MATH-ANXIETY DALAM MENYELESAIKAN MASALAH SISTEM PERSAMAAN LINIER DUA VARIABEL

2018 ◽  
Vol 3 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Muhammad Irfan
Keyword(s):  
Problem Solving ◽  
Creative Thinking ◽  
Math Anxiety ◽  
Reflective Thinking ◽  
Mathematics Learning ◽  
Planning Problem ◽  
Research Subjects ◽  
Mathematical Problems ◽  
The Subject ◽  
Thinking Process

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.

scholarly journals Proses Berpikir Mahasiswa dalam Memecahkan Masalah Fungsi Pembangkit

2018 ◽  
Vol 3 (1) ◽  
pp. 29-39
Author(s):  
Ninik Mutianingsih ◽  
Lydia Lia Prayitno ◽  
Agus Prasetyo Kurniawan
Keyword(s):  
Problem Solving ◽  
Generating Function ◽  
Procedural Knowledge ◽  
Think Aloud ◽  
Thinking Process ◽  
Low Ability

This study aims to describe students’ thinking process in solving the problems of generating function. This is a case study that classifies students into three categories: high, medium, and low. Subjects were asked to solve the problems then use think aloud to reveal their thinking process. The results show that in understanding the problem, using conceptual and procedural knowledge related to the problems, strategies, and experiences they have in solving similar problems between the three subjects is different. Subjects with high and medium capability are able to reveal the problem-solving component of Polya in detail, whereas low-ability subjects use only some of the problem-solving components of Polya.

scholarly journals PENERAPAN I-SPRING SUITE 8 PADA MODEL PEMBELAJARAN IMPROVE UNTUK MENINGKATKAN KEMAMPUAN PEMAHAMAN DAN PEMECAHAN MASALAH MATEMATIS PESERTA DIDIK PADA POKOK BAHASAN PROGRAM LINEAR DI TINGKAT SEKOLAH MENENGAH

Gunahumas ◽  
2020 ◽  
Vol 2 (2) ◽  
pp. 357-386
Author(s):  
Yomi Chaeroni ◽  
Nizar Alam Hamdani ◽  
Akhmad Margana ◽  
Dian Rahadian
Keyword(s):  
Problem Solving ◽  
Direct Instruction ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Learning Model ◽  
Mathematical Understanding ◽  
Learning Models ◽  
Research Subjects ◽  
Purposive Sampling ◽  
Mathematical Problems

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

Problem-solving strategies of sixth-grade students who are superior problem solvers

1980 ◽  
Vol 64 (2) ◽  
pp. 203-211 ◽  
Author(s):  
Joseph D. Novak ◽  
Alan Mandell
Keyword(s):  
Problem Solving ◽  
Sixth Grade ◽  
Sixth Grade Students ◽  
Problem Solving Strategies ◽  
Problem Solvers
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