scholarly journals Creativity in problem solving: integrating two different views of insight

ZDM ◽  
2021 ◽  
Author(s):  
Per Øystein Haavold ◽  
Bharath Sriraman
Keyword(s):  
Problem Solving ◽  
Research Problem ◽  
Mathematics Students ◽  
Analytic Thinking ◽  
Unconscious Processes ◽  
Creativity Research ◽  
Mathematical Problems ◽  
Productive Research ◽  
Problem Solving Process ◽  
Compare And Contrast

AbstractEven after many decades of productive research, problem solving instruction is still considered ineffective. In this study we address some limitations of extant problem solving models related to the phenomenon of insight during problem solving. Currently, there are two main views on the source of insight during problem solving. Proponents of the first view argue that insight is the consequence of analytic thinking and a sequence of conscious and stepwise steps. The second view suggests that insight is the result of unconscious processes that come about only after an impasse has occurred. Extant models of problem solving within mathematics education tend to highlight the first view of insight, while Gestalt inspired creativity research tends to emphasize the second view of insight. In this study, we explore how the two views of insight—and the corresponding set of models—can describe and explain different aspects of the problem solving process. Our aim is to integrate the two different views on insight, and demonstrate how they complement each other, each highlighting different, but important, aspects of the problem solving process. We pursue this aim by studying how expert and novice mathematics students worked on two ill-defined mathematical problems. We apply both a problem solving model and a creativity model in analyzing students’ work on the two problems, in order to compare and contrast aspects of insight during the students’ work. The results of this study indicate that sudden and unconscious insight seems to be crucial to the problem solving process, and the occurrence of such insight cannot be fully explained by problem solving models and analytic views of insight. We therefore propose that extant problem solving models should adopt aspects of the Gestalt inspired views of insight.

scholarly journals Level Of Math Problem Solving Proficiency Grade V SDN 2 Kalirejo On Fractional Story Problem

2019 ◽  
Vol 2 (1) ◽  
pp. 141
Author(s):  
Marita Cahya Purnama ◽  
Tri Yuniantari Redyoningrum ◽  
Liftahul Sekar Aji ◽  
Moh Salimi
Keyword(s):  
Data Analysis ◽  
Problem Solving ◽  
Quantitative Description ◽  
Fifth Grade ◽  
Mathematics Students ◽  
Math Problem Solving ◽  
High Category ◽  
Fifth Grade Students ◽  
Story Problem ◽  
Mathematical Problems

<em>In mathematics, students' ability to solve problems is very much needed. Every student has different abilities. For this reason, it is necessary to conduct a research in order to find out the students' abilities in solving problems in mathematics, especially in fractional material. In researching, quantitative description is the method chosen by the researcher. In this study using a research instrument in the form of a test to measure students' ability to solve mathematical problems and conducted interviews. Data analysis of the results of mathematical tests about solving fractions of fifth grade students at SD Negeri 2 Kalirejo is in the high category. This is evident from the results of tests at SD Negeri 2 Kalirejo that included in the high category were 61.29%, moderate were 23.80% and the low and very low categories were 12.89%.</em>

scholarly journals TEKNIK POLYA DALAM PENYELESAIAN MASALAH GEOMETRI

Sigma ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 114
Author(s):  
Rahma Wahyu
Keyword(s):  
Elementary Schools ◽  
Problem Solving ◽  
Qualitative Approach ◽  
High Ability ◽  
Story Problems ◽  
Story Problem ◽  
Study Results ◽  
Mathematical Problems ◽  
Problem Solving Process ◽  
Low Ability

This study aims to analyze the steps for solving mathematical problems by students' understanding of the geometric material in story problems based on the Polya technique. This research was conducted in one of the Islamic elementary schools in Batu City on six students in grade 6. The approach taken is to use a descriptive qualitative approach. The research was carried out using triangulation methods, namely observing the problem-solving process, interviews, and reviewing documents (students' work). Interviews in this study were conducted with several students, namely two high ability people, two low ability people, and two medium ability people. The analysis was carried out by concluding the data obtained based on the observations that have been made. The study results showed that the Polya technique showed different results on the results of solving the problems of each category of students in solving story problems about the area of squares and rectangles. Based on these results, it can be seen that students' understanding of the geometry material on the story problem.

The Prisoner Problem-a Generalization

2000 ◽  
Vol 93 (3) ◽  
pp. 192-193
Author(s):  
Gerald E. Gannon ◽  
Mario U. Martelli
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematics Teacher ◽  
Classroom Teachers ◽  
Mathematics Students ◽  
High School Mathematics ◽  
Classic Problem ◽  
Look Back ◽  
Problem Solving Process ◽  
Problem Solvers

Problem solving is generally recognized as one of the more important functions of mathematics, and producing “problem solvers” is one of the more important jobs of a mathematics teacher. In most problemsolving strategies, the final step is taking a look back after the problem has been solved to see whether the problem and the solution can be generalized. We believe that most classroom teachers would agree that this step is often the most difficult one in the problem-solving process. Hence, our purpose here is to suggest a possible generalization to a classic problem, one that is inherently interesting and that has a solution that is within the reach of most high school mathematics students.

scholarly journals STUDENT'S ABILITY TO SOLVE THE PROBLEM OF THE COMPARISON WITH MODEL PROBLEM BASED LEARNING IN THE CLASSROOM INSTRUCTION VII MTs NOORHIDAYAH DARUSSALAM

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Amin Paris
Keyword(s):  
Problem Solving ◽  
Design Research ◽  
Model Problem ◽  
Problem Based Learning ◽  
Field Research ◽  
Learning Model ◽  
Material Research ◽  
Mathematical Problems ◽  
Based Instruction ◽  
Problem Solving Process

This study aims to determine the ability of solving mathematical problems by using model Problem Based Instruction and the effect of problem based learning model Instruction on students' problem-solving abilities. The research method used experimental method to the type of field research and quantitative approaches. The sample in this study were students of class VII-B MTs Noorhidayah Darussalam in comparison with the material research design One-group pretest-posttest design. Design Research, the study was conducted only in one class as a class experiment. The data analyzed were taken from the value pretest and posttest study siswa.Hasil get the result that the problem solving process of students in the material ratio is in conformity with the learning pace of Problem Based Instruction, and there are significant learning model of problem-based instruction to the student's ability in problems solving on material ratio. Key Words : problem solving in mathematics, problem based instruction, comparasion

scholarly journals ANALISIS KEMAMPUAN BERPIKIR KRITIS MAHASISWA DALAM MEMECAHKAN MASALAH KALKULUS

2019 ◽  
Vol 8 (2) ◽  
pp. 279
Author(s):  
Yunis Sulistyorini ◽  
Siti Napfiah
Keyword(s):  
Critical Thinking ◽  
Problem Solving ◽  
Undergraduate Students ◽  
Thinking Skills ◽  
Critical Thinking Skills ◽  
Mathematical Abilities ◽  
Mathematical Problems ◽  
Problem Solving Process ◽  
Relationship Of ◽  
The Relationship

Berpikir kritis merupakan kemampuan yang dapat dipelajari dan dilatihkan agar mampu memecahkan masalah secara efektif. Penelitian ini bertujuan untuk mendeskripsikan kemampuan berpikir kritis mahasiswa dalam memecahkan masalah kalkulus. Jenis penelitian ini adalah penelitian kualitatif deskriptif. Subjek dari penelitian ini adalah tiga orang mahasiswa program studi Pendidikan Matematika IKIP Budi Utomo Malang yang berkemampuan matematika tinggi. Instrumen yang digunakan yaitu soal pemecahan masalah Kalkulus dan pedoman wawancara. Instrumen dibuat untuk menggali kemampuan berpikir kritis mahasiswa dalam memecahkan masalah. Hasil penelitian menunjukkan bahwa subjek mampu menunjukkan kemampuan berpikir kritis yang tinggi. Hal ini ditunjukkan dengan terpenuhinya seluruh indikator kemampuan berpikir kritis dalam memecahkan masalah matematika yaitu menggunakan penalaran pada tahap memahami masalah, menganalisis keterkaitan masing-masing bagian dari keseluruhan untuk menghasilkan sistem yang kompleks pada tahap membuat perencanaan, menganalisis dan mengevaluasi fakta-fakta pada tahap melaksanakan perencanaan, dan menarik kesimpulan berdasarkan hasil analisis pada tahap memeriksa kembali. Walaupun ketiga subjek memenuhi keseluruhan indikator berpikir kritis, namun masing-masing subjek menunjukkan proses pemecahan masalah yang berbeda. Masalah open-ended dapat dipertimbangkan dalam melatihkan kemampuan berpikir kritis sekaligus mengakomodasi berbagai tingkatan akademik mahasiswa.AbstractCritical thinking is an ability that can be learned and trained to be able to solve problems effectively. This study aims to describe students' critical thinking skills in solving calculus problems. This type of study was descriptive qualitative research. The subjects were three undergraduate students of the IKIP Budi Utomo Malang Mathematics Education with high mathematical abilities. The research instruments were calculus problem solving questions and interview guidelines. The instruments used to explore students' critical thinking skills in solving problems. The results showed that subjects were able to demonstrate high critical thinking skills. This is indicated by the fulfillment of all indicators of critical thinking skills in solving mathematical problems, namely using reasoning at the stage of understanding the problem, analyzing the relationship of each part of the whole to produce a complex system at the stage of devising a plan, analyzing and evaluating the facts at the stage of carrying out the plan, and draw conclusions based on the results of the analysis at the stage of looking back. Although all three subjects fulfill all indicators of critical thinking skills, each subject shows a different problem solving process. Open ended problems can be considered to develop critical thinking skills while accommodating various academic levels of students.

scholarly journals ANALISIS KEMAMPUAN PEMECAHAN MASALAH MATEMATIKA MAHASISWA CALON GURU SEMESTER VI IKIP-PGRI PONTIANAK

2017 ◽  
Vol 7 (1:) ◽  
pp. 49-52
Author(s):  
Nurmaningsih Nurmaningsih
Keyword(s):  
Problem Solving ◽  
Prospective Teachers ◽  
Mathematical Problem ◽  
Mathematics Students ◽  
Word Problem Solving ◽  
Problem Solving Skills ◽  
Written Information ◽  
Key Word ◽  
Mathematical Problems

Abstrak Penelitian ini bertujuan untuk mendekripsikan kemampuan pemecahan masalah matematika mahasiswa calon guru semester VI IKIP-PGRI Pontianak. Secara khusus, penelitian ini bertujuan untuk mendeskripsikan kemampuan pemecahan masalah matematika mahasiswa calon guru semester VI IKIP-PGRI Pontianak pada masing-masing aspek pemecahan masalah matematika. Dalam penelitian ini digunakan metode deskriptif dengan bentuk penelitiannya adalah studi kasus. Berdasarkan analisis data dapat disimpulkan bahwa: (1) Pada aspek memahami masalah, mahasiswa sudah menuliskan informasi yang ada pada soal namun masih terdapat kekurangan dan kesalahan dalam menentukan apa yang ditanyakan pada soal, (2) Pada aspek merencanakan penyelesaian, mahasiswa masih belum menuliskan rencana penyelesaian secara sistematis dan detail pada tiap langkah-langkahnya, (3) Pada aspek melaksanakan rencana penyelesaian, masih terdapat kesalahan dalam perhitungan sehingga menghasilkan jawaban yang kurang tepat, (4) Pada aspek memeriksa kembali hasil yang diperoleh, masih terdapat kesalahan dalam kesimpulan akibat dari kesalahan dalam memahami masalah dan juga kesalahan dalam perhitungan. Kata kunci: pemecahan masalah, program linear Abstract This study aims to decrypt the problem solving skills of mathematics students prospective teacher semester VI IKIP-PGRI Pontianak. Specifically, this study aims to describe the mathematical problem solving skills of prospective teachers of semester VI of IKIP-PGRI Pontianak in each aspect of solving mathematical problems. In this study used descriptive method with the form of research is a case study. Based on the data analysis, it can be concluded that: (1) In the aspect of understanding the problem, the students have written information on the problem but there are still deficiencies and mistakes in determining what is asked on the question, (2) In the aspect of the plan of settlement, the student still has not written the plan (3) In the aspect of executing the settlement plan, there are still errors in the calculation so as to produce a less precise answer, (4) In the aspect of re-examining the results obtained, there is still a mistake in the conclusion of the result of Error in understanding the problem and also the error in the calculation. Key word: problem solving, linear programming

scholarly journals Kemampuan Pemecahan Masalah Matematis Peserta Didik yang Diajar Dengan Model Pembelajaran Missouri Mathematics Project (MMP) Disertai Strategi Think-Talk-Write (TTW) di SMP Negeri 2 Lengayang Pesisir Selatan

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Andi Susanto ◽  
Rara Anggun Syaveta
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Mathematics Students ◽  
Problem Solving Skills ◽  
Average Value ◽  
8Th Grade ◽  
Mathematical Problems ◽  
Class Viii ◽  
Skills Learning

This research is driven by the low level of problem solving ability of 8th grade students of SMPN 2 Lengayang. This study aims to determine the problem-solving ability of mathematics students taught by matrix Missouri mathematics project with a strategy of Think-Talk-Write better than students who use the scientific approach. This research is a quasy experiment research. The population of this research is all students of class VIII SMPN 2 Lengayang, and sampel is this research class VIII.A and class VIII.E. Based on the results of this study obtained the average value of mathematical problem-solving skills of learners who were taught by MMP method with TTW strategy is 76 and the usual learning is 68. After hypothesis testing using t-test, known ttable = 1,64 and tcount = 2,23 with 95% confidence level, this means that this indicates that the accepted hypothesis means the ability to solve mathematical problems of students with MMP with scientific approach.Keyword : Mathematical Problem Solving Skills, Learning Model Type Missouri mathematics project (MMP), and strategy of Think-Talk-Write (TTW)

scholarly journals Assessment of the Research on Problem Solving and Insight

2017 ◽  
Vol 6 (1) ◽  
pp. 126-132
Author(s):  
Amanda Volkamer ◽  
Kathy Sexton-Radek,PhD
Keyword(s):  
Problem Solving ◽  
Literature Review ◽  
Strong Evidence ◽  
Probabilistic Reasoning ◽  
Unconscious Processes ◽  
Unconscious Process ◽  
Integral Role ◽  
Problem Solving Process ◽  
Problem Solving Task

This literature review explores the extent of research on problem solving and insight, as well as the roles of conscious and unconscious processes.  This paper looks at the research on the structure of how insight develops and in general the problem solving process.  Next, the type of problems are examined as to which type of problem solving task work best using either conscious or unconscious processes.  Then, this paper covers research on probabilistic reasoning as this may be an unconscious process and the role of memory and sleep may have in problem solving and insight.  To conclude, there are areas that still need further research but there is strong evidence of an integral role of unconsciousness processes in problem solving.

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.

Visual thinking profile of mathematics students in graph theory problem solving process

2020 ◽  
Author(s):  
Sapti Wahyuningsih ◽  
Abd Qohar ◽  
Darmawan Satyananda ◽  
Noor Azean Atan
Keyword(s):  
Graph Theory ◽  
Problem Solving ◽  
Visual Thinking ◽  
Mathematics Students ◽  
Theory Problem ◽  
Problem Solving Process
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