Posing Mathematical Problems: An Exploratory Study

1996 ◽  
Vol 27 (3) ◽  
pp. 293-309 ◽  
Author(s):  
Edward A. Silver ◽  
Joanna Mamona-Downs ◽  
Shukkwan S. Leung ◽  
Patricia Ann Kenney
Keyword(s):  
Problem Solving ◽  
Prospective Teachers ◽  
Initial Conditions ◽  
Mathematical Problem ◽  
Problem Posing ◽  
School Teachers ◽  
Written Responses ◽  
Task Setting ◽  
Mathematical Problems ◽  
Mathematical Problem Posing

In this study, 53 middle school teachers and 28 prospective secondary school teachers worked either individually or in pairs to pose mathematical problems associated with a reasonably complex task setting, before and during or after attempting to solve a problem within that task setting. Written responses were examined to determine the kinds of problems posed in this task setting, to make inferences about cognitive processes used to generate the problems, and to examine differences between problems posed prior to solving the problem and those posed during or after solving. Although some responses were ill-posed or poorly stated problems, subjects generated a large number of reasonable problems during both problem-posing phases, thereby suggesting that these teachers and prospective teachers had some personal capacity for mathematical problem posing. Subjects posed problems using both affirming and negating processes; that is, not only by generating goal statements while keeping problem constraints fixed but also by manipulating the task's implicit assumptions and initial conditions. A sizable portion of the posed problems were produced in clusters of related problems, thereby suggesting systematic problem generation. Subjects posed more problems before problem solving than during or after problem solving, and they tended to shift the focus of their posing between posing phases based at least in part on the intervening problem-solving experience. Moreover, the posed problems were not always ones that subjects could solve, nor were they always problems with “nice” mathematical solutions.

scholarly journals PROBLEM POSING SEBAGAI KEMAMPUAN MATEMATIS

2018 ◽  
Vol 6 (1) ◽  
pp. 163-180 ◽  
Author(s):  
Ekasatya Aldila Afriansyah
Keyword(s):  
Prospective Teachers ◽  
Mathematical Problem ◽  
Present Problem ◽  
Problem Posing ◽  
Good Teacher ◽  
Quality Of Learning ◽  
Mathematical Problems ◽  
Mathematical Problem Posing ◽  
Mathematical Skill

Perlunya kemampuan dalam membuat permasalahan/persoalan matematis sangat diperlukan oleh seorang guru. Hal tersebut berguna agar guru tidak hanya memberikan soal yang ada di buku saja. Guru dituntut kreatif; guru perlu memiliki kemampuan dalam membuat soal yang dibutuhkan oleh siswanya. Selama ini, kemampuan yang terus disoroti adalah kemampuan dalam menyelesaikan berbagai tipe soal dilihat dari daya pikir siswanya. Untuk kali ini, kita coba lihat dari sudut pandang perlunya kemampuan seorang guru untuk memiliki kemampuan pengajuan permasalahan matematis (mathematical problem posing) ini. Seiring dengan meningkatnya kemampuan membuat soal yang baik tentunya dapat meningkatkan kualitas pembelajaran di kelas. Kemampuan mathematical problem posing ini masih menjadi kendala bagi beberapa mahasiswa calon guru matematika, padahal kemampuan ini sangat diperlukan bagi mereka yang akan menjadi seorang guru yang baik. Oleh karena itu, pada kesempatan ini, kita akan coba paparkan problem posing sebagai suatu kemampuan matematis yang diperlukan oleh seseorang, terutama calon guru.The need for the skill to create mathematical problems/issues needed by a teacher. It is useful for teachers to provide problems that exist in books only. Teachers need to be creative; teachers need to have the skill to create questions that needed by their students. During this time, a skill that continues to be highlighted is the ability to resolve various types of problems seen from the intellect students. For this time, we look from the perspective of the need for the skill of a teacher to have the skill of mathematical problem posings. Along with the increased mathematical problem posing skill can certainly improve the quality of learning in the classroom. Mathematical problem posing skill is still an obstacle for some mathematics prospective teachers, but this skill is very necessary for those who would become a good teacher. Therefore, on this occasion, we will try to present problem posing as a mathematical skill needed by someone, especially prospective teachers.

scholarly journals Prospective elementary school teachers’ ways of making sense of mathematical problem posing

2012 ◽  
Vol 6 (4) ◽  
pp. 135-146
Author(s):  
Olive Chapman
Keyword(s):  
Elementary School Teachers ◽  
Prospective Teachers ◽  
Mathematical Problem ◽  
Problem Posing ◽  
Knowledge For Teaching ◽  
Making Sense ◽  
Mathematical Problems ◽  
Mathematical Problem Posing ◽  
The Impact ◽  
Futuros Maestros

The study tackled prospective teachers’ sense-making of mathematical problem posing and the impact of posing different contextual problems on their learning. Focus was on the generation of new problems and reformulation of given problems. Participants were 40 prospective elementary teachers. The findings provide insights into possible ways these teachers could make sense of problem posing of contextual mathematical problems and the learning afforded by posing diverse problems. Highlighted are five perspectives and nine categories of problem posing tasks to support development of proficiency in problem-posing knowledge for teaching. Modos en que futuros profesores de primaria dan sentido a la invención de problemas matemáticos El estudio indagó sobre los modos en que futuros profesores de primaria dan sentido a la invención de problemas matemáticos y el impacto de plantear diferentes problemas contextualizados en su aprendizaje. El foco fue la invención de nuevos problemas y la reformulación de otros dados. Los participantes fueron 40 futuros maestros de primaria. Los resultados proporcionan elementos sobre posibles modos en que estos maestros dan sentido a la invención de problemas matemáticos y el aprendizaje que ofrece plantear diversos problemas. Se destacan cinco perspectivas y nueve categorías de tareas en la invención de problemas para apoyar el desarrollo de la competencia de plantear problemas en la enseñanza.Handle: http://hdl.handle.net/10481/20053Nº de citas en WOS (2017): 6 (Citas de 2º orden, 4)Nº de citas en SCOPUS (2017): 7 (Citas de 2º orden, 7)

Assessing Students' Mathematical Problem Posing

2005 ◽  
Vol 12 (3) ◽  
pp. 129-135
Author(s):  
Edward A. Silver ◽  
Jinfa Cai
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Scientific Investigation ◽  
Problem Posing ◽  
Intellectual Activity ◽  
Mathematical Inquiry ◽  
Mathematical Problem Posing ◽  
Mathematics Research

Posing problems is an intellectual activity that is crucially important in mathematics research and scientific investigation. Indeed, some have argued that problem posing, as a part of scientific or mathematical inquiry, is usually at least as important as problem solving (Einstein and Infeld 1938; Hadamard 1945).

scholarly journals MENINGKATKAN KEMAMPUAN PEMECAHAN MASALAH DAN KOMUNIKASI MATEMATIK MELALUI PENDEKATAN PROBLEM POSING DALAM PEMBELAJARAN MATEMATIKA DI SMA

2018 ◽  
Vol 6 (1) ◽  
pp. 93-104
Author(s):  
Deddy Sofyan ◽  
Sukanto Sukandar Madio
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Mathematical Problem ◽  
Problem Posing ◽  
Mathematical Problem Solving ◽  
School Students ◽  
Problem Solving Skills ◽  
Quasi Experimental ◽  
Mathematical Problem Posing

Tujuan penelitian ini adalah untuk meningkatkan kemampuan siswa SMA dalam pemecahan masalah dan komunikasi matematik melalui pendekatan problem posing dalam pembelajaran matematika. Metode penelitian yang digunakan adalah metode kuasi eksperimen. Populasi penelitian ini adalah siswa di salah satu SMA Negeri di Kabupaten Garut. Sampel penelitian dipilih secara acak berdasarkan kelas, sampelnya adalah kelas XII IPA 1 yang mendapat pembelajaran menggunakan pendekatan problem posing dan siswa kelas XII IPA 3 yang mendapat pembelajaran konvensional. Simpulan hasil penelitian ini adalah bahwa dalam pembelajaran matematika di SMA: 1. Kemampuan pemecahan masalah matematik siswa yang mendapatkan pendekatan problem posing lebih baik dibandingkan dengan konvensional, 2. Tidak terdapat perbedaan kemampuan komunikasi matematik antara siswa yang mendapatkan pendekatan problem posing dengan konvensional, 3. Tidak terdapat kaitan yang signifikan antara kemampuan pemecahan masalah matematik dengan kemampuan komunikasi matematik pada siswa yang mendapatkan pendekatan problem posing. The purpose of this research is to improve the ability of high school students in problem solving and communication of mathematics through problem posing approach to learning mathematics. The method used is a quasi-experimental method. The study population was one of the students in high schools in Garut. Samples were selected randomly based on the class, the sample is a class XII IPA 1 gets learning using problem posing approach and class XII IPA 3 students who received conventional learning. Conclusion The results of this study is that the study of mathematics in high school: 1. mathematical problem solving ability of students to get a better problem posing approach compared to conventional, 2. there is no difference in the ability of mathematical communication between students who received conventional approach to problem posing, 3. there was no significant association between mathematical problem solving skills with communication skills in students who get a mathematical problem posing approach.

scholarly journals MENINGKATKAN KEMAMPUAN PEMECAHAN MASALAH MATEMATIK SISWA MTS DENGAN MENGGUNAKAN PROBLEM POSING

2018 ◽  
Vol 1 (6) ◽  
pp. 1055
Author(s):  
Elza Efriyani Nursyifaa ◽  
Eka Senjayawati
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Research Data ◽  
Problem Posing ◽  
Mathematical Problem Solving ◽  
Problem Solving Skills ◽  
Learning Procedure ◽  
Mathematical Problems ◽  
Planning Problems ◽  
Better Than

The purpose of this research is to assess whether the improvement of students' mathematical problem solving skills using Problem Posing approach is better than those using ordinary learning. The population in this research is MTs Nurul Falah Cimahi. This research instrument in the form of a test of mathematical problem solving skills of five items. This research data is processed using software SPSS Version 22. Data analysis used is test of normality and test of two difference of mean. The result of this research stated that the achievement and improvement of problem solving skills of MTs students using Problem Posing approach is better than the normal learning, and the implementation using Problem Posing approach has been run in accordance with the learning procedure found and the difficulties experienced by students in solving the problem of solving skills mathematical problems are present in indicators of understanding problems, planning problems, implementing problem-solving plans, and re-examination.

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 INVESTIGASI KEMAMPUAN PROBLEM SOLVING DAN PROBLEM POSING MATEMATIS MAHASISWA VIA PENDEKATAN REALISTIC

2018 ◽  
Vol 5 (3) ◽  
pp. 269-280 ◽  
Author(s):  
Ekasatya Aldila Afriansyah
Keyword(s):  
Problem Solving ◽  
Prospective Teachers ◽  
Diagnostic Tests ◽  
Quantitative Research ◽  
Mathematical Problem ◽  
Problem Posing ◽  
Mathematical Problem Solving ◽  
Mathematical Skills ◽  
Realistic Approach ◽  
Post Test

AbstrakKemampuan problem solving dan problem posing matematis merupakan kemampuan matematis yang perlu dimiliki oleh mahasiswa. Melalui kedua kemampuan ini, seorang mahasiswa dapat lebih kreatif dalam mengungkapkan ide serta gagasannya dengan cara menghubungkan pengetahuan yang dia peroleh sebelumnya dan mengaitkannya dengan pengetahuan yang dia diperoleh sekarang; serta mampu menuangkan gagasan/ide dalam menyelesaikan persoalan matematis yang dihadapinya. Namun pada kenyataannya, masih banyak mahasiswa yang belum memiliki kedua kemampuan ini, sehingga perlu diadakan perbaikan pembelajaran melalui pendekatan yang tepat. Pada penelitian ini, pendekatan pembelajaran yang dijadikan sebagai solusinya adalah pendekatan Realistic. Penelitian ini bertujuan untuk mengetahui peningkatan kemampuan problem solving dan problem posing matematik mahasiswa melalui pendekatan Realistic. Metode penelitian yang digunakan pada penelitian ini adalah metode kuantitatif. Instrumen yang digunakan pada penelitian ini berupa tes diagnostik berupa pre-test dan pos-test, dan angket. Hasil dari penelitian ini, kemampuan problem solving dan problem posing mahasiswa cenderung meningkat. Rekomendasi bagi peneliti lain adalah melakukan penelitian sejenis ini dengan subjek penelitian yang berbeda, seperti mahasiswa calon guru.AbstractMathematical problem solving and problem posing skill are the mathematical skills that need to be owned by students. By having this skill, students can be more creative in expressing ideas by connecting the knowledge that they held previously. But in reality, there are some students who are lack of problem solving skill; therefore it is really important to improve learning through appropriate approach. Realistic approach had been chosen as the learning theory to be applied in the class. This study has the objective to find out whether the use of realistic approach enhances students’ mathematical problem solving and problem posing skills. The research methodology used in this study is a quantitative research. The instrument used diagnostic tests (pre-test and post-test); and questioner. The results of this study, the mathematical problem solving and problem posing skills students tend to increase. Recommendations for other researchers are do the research of mathematical problem solving and problem posing skills in other populations, especially prospective teachers.

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