scholarly journals Teaching Mathematics: Heuristics Can and Ought to Lead the Way

2021 ◽  
Vol 11 (2) ◽  
pp. 392-404
Author(s):  
Marshall Gordon
Keyword(s):  
Problem Solving ◽  
Teaching Mathematics ◽  
Mathematics Textbooks ◽  
Mathematics Problems ◽  
Mental Actions ◽  
The Way

In contrast to problem-solving procedures that are the “bricks and mortar” of demonstrations in mathematics textbooks, heuristics, defined by Polya as “the study of means and methods of problem solving”, are those mental actions that enable the practitioner to make progress when it is not clear how to solve problems directly. Yet, as essential as heuristic tools are, they tend not to be included in presentations in mathematics textbooks. The overarching problem can be understood in terms of students’ not developing productive means for engaging problems. A few mathematics problems are included to argue for the validity, if not the priority, of the need for the incorporation of heuristics along with problem-solving procedures as standard content in mathematics textbooks.

Math by the Month: Passport to Travel

2008 ◽  
Vol 14 (9) ◽  
pp. 528-529
Author(s):  
Linda Chick ◽  
Andrea S. Holmes ◽  
Nicole McClymonds ◽  
Steve Musick ◽  
Patti Reynolds ◽  
...  
Keyword(s):  
Problem Solving ◽  
Small Groups ◽  
Number Sense ◽  
Logical Thinking ◽  
Mathematics Problems ◽  
Whole Class ◽  
Mathematical Justification ◽  
The Way

“Math by the Month” activities are designed to engage students to think as mathematicians do. Students may work on the activities individually or in small groups, or the whole class may use them as problems of the week. No solutions are suggested, so students look to themselves for mathematical justification and develop confidence to validate their work. Most children have done some type of traveling. Whether it is a trip around their neighborhood, to another city, or to a different state or country, traveling is an adventure. This month, students will use the context of travel to engage in mathematics problems that promote logical thinking, graphing, measurement, number sense, and problem solving. With summer on the way, it is time for a trip!

ANALYSIS OF NARRATIVE MATHEMATICAL QUESTIONS ON TEXTBOOKS BASED ON SOLO TAXONOMY AND MATHEMATICAL POWER

2017 ◽  
Vol 5 (3) ◽  
pp. 299
Author(s):  
Imam Kusmaryono
Keyword(s):  
Problem Solving ◽  
Grade Level ◽  
Mathematical Representation ◽  
Structural Level ◽  
Mathematics Textbooks ◽  
Solo Taxonomy ◽  
Research Procedure ◽  
Quantitative Descriptive ◽  
The Ideal

This study aimed to identify the proportion of diversity and suitability of narrative mathematical questions with SOLO taxonomy level and mathematical power ability. The research was conducted through quantitative descriptive. Sources of data in the forms of narrations contained in mathematics textbooks. The research procedure was conducted by making the classification and determining the percentage of the narrations based on the compatibility of SOLO taxonomy and the mathematical power ability. The results showed that, the narrative mathematical questions with uni-structural level are of 7.5%, multi-structural of 33.8%, relational of 46.6% and extended abstract of 12.1 %. In terms of compatibility of the narrative  questions were able to measure 23% reasoning aspect, 18% problem solving, 8.3% connection, 28% communication and 22.6% mathematical representation. In general, mathematics textbooks as the object of research should be revised, since they have not yet achieved the ideal alignment between SOLO taxonomy based on grade level and the objective of learning develop mathematical power

IDENTIFICATION OF PROBLEM SOLVING STRATEGIES IN MATHEATICS AMONG HIGH SCHOOL STUDENTS

2017 ◽  
Vol 4 (36) ◽  
Author(s):  
J. Navaneetha Krishnan ◽  
P. Paul Devanesan
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Sample Survey ◽  
Survey Method ◽  
Teaching Mathematics ◽  
School Students ◽  
Problem Solving Strategies ◽  
Achievement In Mathematics

The major aim of teaching Mathematics is to develop problem solving skill among the students. This article aims to find out the problem solving strategies and to test the students’ ability in using these strategies to solve problems. Using sample survey method, four hundred students were taken for this investigation. Students’ achievement in solving problems was tested for their Identification and Application of Problem Solving Strategies as a major finding, thirty one percent of the students’ achievement in mathematics is contributed by Identification and Application of Problem Solving Strategies.

scholarly journals Teaching Mathematics at Distance: A Challenge for Universities

2020 ◽  
Vol 11 (1) ◽  
pp. 1
Author(s):  
Rosalinda Cassibba ◽  
Daniela Ferrarello ◽  
Maria Flavia Mammana ◽  
Pasquale Musso ◽  
Mario Pennisi ◽  
...  
Keyword(s):  
Teaching Mathematics ◽  
State University ◽  
Distance Teaching ◽  
Face To Face ◽  
University Mathematics ◽  
Learning Platform ◽  
E Learning ◽  
University Level ◽  
Teaching Modality ◽  
The Way

The focus of this research is how Sicilian state university mathematics professors faced the challenge of teaching via distance education during the first wave of the COVID-19 pandemic. Since the pandemic entered our lives suddenly, the professors found themselves having to lecture using an e-learning platform that they had never used before, and for which they could not receive training due to the health emergency. In addition to the emotional aspects related to the particular situation of the pandemic, there are two aspects to consider when teaching mathematics at a distance. The first is related to the fact that at university level, lecturers generally teach mathematics in a formal way, using many symbols and formulas that they are used to writing. The second aspect is that the way mathematics is taught is also related to the students to whom the teaching is addressed. In fact, not only online, but also in face-to-face modality, the teaching of mathematics to students on the mathematics degree course involves a different approach to lessons (as well as to the choice of topics to explain) than teaching mathematics in another degree course. In order to investigate how the Sicilian State university mathematics professors taught mathematics at distance, a questionnaire was prepared and administered one month after the beginning of the lockdown in Italy. Both quantitative and qualitative analyses were made, which allowed us to observe the way that university professors have adapted to the new teaching modality: they started to appropriate new artifacts (writing tablets, mathematical software, e-learning platform) to replicate their face-to-face teaching modality, mostly maintaining their blackboard teacher status. Their answers also reveal their beliefs related to teaching mathematics at university level, noting what has been an advantageous or disadvantageous for them in distance teaching.

scholarly journals Proses Berpikir Kreatif Siswa dalam Memecahkan Masalah Matematika Berdasarkan Model Wallas

2017 ◽  
Vol 10 (1) ◽  
pp. 18 ◽  
Author(s):  
Agus Purnama Sari ◽  
M Ikhsan ◽  
Saminan Saminan
Keyword(s):  
Qualitative Research ◽  
Problem Solving ◽  
Creative Thinking ◽  
Model Problem ◽  
High Category ◽  
Mathematics Problems ◽  
Mathematics Ability ◽  
Solution Verification ◽  
The Given

[Bahasa]: Penelitian kualitatif ini bertujuan untuk mengetahui proses berpikir kreatif siswa dalam memecahkan masalah matematika berdasarkan model Wallas (1926). Subjek penelitian terdiri dari 6 siswa kelas VII, masing-masing dua siswa memiliki kemampuan matematika tinggi, sedang, dan rendah. Pengumpulan data dilakukan dengan menggunakan tes dan wawancara. Hasil penelitian menunjukkan bahwa proses berpikir kreatif siswa kategori tinggi yaitu siswa memahami permasalahan dan informasi yang diberikan dengan menuliskan apa yang diketahui maupun yang ditanyakan (persiapan), siswa tidak membutuhkan waktu yang lama untuk memikirkan solusi dari permasalahan yang dihadapi dengan mengingat soal yang sudah diajarkan (inkubasi), siswa mendapatkan ide untuk memecahkan masalah (Iluminasi), dan siswa menguji ide dan memeriksa kembali pemecahan masalah sebelum mengambil kesimpulan yang tepat (verifikasi). Proses berpikir kreatif siswa kategori sedang yaitu siswa mencoba untuk memahami permasalahan akan tetapi kurang memahami informasi atau petunjuk yang diberikan (persiapan), siswa diam megingat kembali rumus yang digunakan untuk memecahkan masalah (Inkubasi), siswa menghasilkan ide berdasarkan pemahamannya terhadap soal untuk memecahkan masalah (Iluminasi), dan siswa menguji ide dihasilkan dan tidak memeriksa kembali proses pemecahan masalah (verifikasi). Proses berpikir kreatif siswa kategori rendah yaitu siswa tidak memahami permasalahan dan informasi yang diberikan (persiapan), siswa membutuhkan waktu yang lama untuk memikirkan solusi dari permasalahan (Inkubasi), siswa gagal dalam menemukan ide untuk memecahkan permasalahan (Iluminasi), dan siswa menguji ide yang dihasilkan dan tidak memeriksa kembali jawaban yang telah diujikan (verifikasi). Kata kunci: Berpikir Kreatif; Model Wallas; Pemecahan Masalah; Kemampuan Siswa  [English]: This qualitative research aims at getting insight on students’ creative thinking in solving mathematics problems based on Wallas’ model (1926). The subjects are six students in 7th grade, each two students respectively have high, medium and low mathematics ability.  Data is collected through test and interview. This research shows that the students in high category can understand the problem and given information by writing what is known and asked (preparation), can easily think the solution of the problem by remembering the previous problem (incubation), get the ideas to solve the problem (illumination), and examine the ideas and re-check the solution before drawing the proper conclusion (verification). The students in medium category try to understand the problem but they are less in understanding the given information or hint (preparation), remember the formula to solve the problem (incubation), generate the ideas from their understanding to solve the problem (illumination), and examine the ideas and do not check the solution again (verification). For students in low category, they do not understand the problem and the given information (preparation), have a while to think the solution (incubation), fail to find any ideas to solve the problem (illumination), and examine the generated ideas and do not re-check the solution (verification).     Keywords: Creative Thinking; Walla’s Model; Problem Solving; Students’Ability

scholarly journals Inconsistency Among Beliefs, Knowledge, and Teaching Practice in Mathematical Problem Solving: A Case Study of a Primary Teacher

2017 ◽  
Vol 7 (2) ◽  
pp. 27-40
Author(s):  
Tatag Yuli Eko Siswono ◽  
Ahmad Wachidul Kohar ◽  
Ika Kurniasari ◽  
Sugi Hartono
Keyword(s):  
Problem Solving ◽  
Teaching Practice ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Primary Teacher ◽  
Mathematical Problem Solving ◽  
Mathematics Problems ◽  
And Mathematics ◽  
Teacher's Beliefs

This is a case study investigating a primary teacher’s beliefs, knowledge, and teaching practice in mathematical problem solving. Data was collected through interview of one primary teacher regarding his beliefs on the nature of mathematics, mathematics teaching, and mathematics learning as well as knowledge about content and pedagogy of problem solving. His teaching practice was also observed which focused on the way he helped his students solve several different mathematics problems in class based on Polya’s problemsolving process: understand the problem, devising a plan, carrying out the plan, and looking back. Findings of this study point out that while the teacher’s beliefs, which are closely related to his problem solving view, are consistent with his knowledge of problem solving, there is a gap between such beliefs and knowledge around his teaching practice. The gap appeared primarily around the directive teaching which corresponds to instrumental view he held in most of Polya’s process during his teaching practice, which is not consistent with beliefs and knowledge he professed during the interview. Some possible causes related to several associate factors such as immediate classroom situation and teaching practice experience are discussed to explain such inconsistency. The results of this study are encouraging, however, further studies still need to be conducted.

scholarly journals IMPROVEMENT OF MATHEMATICAL PROBLEM SOLVING ABILITIES USING MISSOURI MATHEMATICS PROJECT LEARNING MODEL

2019 ◽  
Vol 7 (1) ◽  
pp. 1539-1549
Author(s):  
Joy Frandero Yoni Astra Pasaribu ◽  
Louise M Saija
Keyword(s):  
Problem Solving ◽  
Small Group ◽  
Mathematical Problem ◽  
Learning Model ◽  
Mathematical Problem Solving ◽  
Mathematics Problems ◽  
Life Problems ◽  
Significant Difference ◽  
Questionnaire Result ◽  
Problem Solve

Introduction: Mathematical problem solving ability is very important in mathematic learning, because is can help students to solve daily life problems better. But the students mathematical problem solve ability is not high yet, one of the factor is because many students only know the standard procedures of solving mathematics problems, and when the given problem are different from the examples they tend to give up easily. This comparative design study aims to find out the improvement of students mathematical problem solving ability using Missouri Mathematics Project (MMP) learning model with individual assignments and small group assignments, and to find out whether there are differences between those two. Method: The sample in this study was VII grade students at SMP Advent Cimindi and SMP Advent II Bandung, Bandung. The instruments used in the study are mathematical problem solving test and questionnaire for response toward the Missouri Mathematics Project (MMP) learning model as the non-test instrument. Result: The results showed that the improvement of mathematical problem solving abilities of students who obtained the Missouri Mathematics Project (MMP) learning model with individual assignments and students who obtained the Missouri Mathematics Project (MMP) learning model by assigning small groups was categorized as high. Statistically, there is a significant difference in the students mathematical problem solving improvement after being taught using Missouri Mathematics Project (MMP) learning model, between students who get individual assignments and small group assignments. The response questionnaire result shows that students who acquire individual assignments like the Missouri Mathematics Project (MMP) learning model, more further the students who acquire group assignments really like the Missouri Mathematics Project (MMP) learning model.

scholarly journals Um cenário de estudos envolvendo o ensino de Matemática através da Resolução de Problemas em periódicosA study scenario involving the teaching of mathematics through problem solving in journals

2020 ◽  
Vol 22 (2) ◽  
pp. 252-280
Author(s):  
Kaique Nascimento Martins ◽  
Jamille Vilas Bôas
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
The State ◽  
University Education ◽  
Teaching Mathematics ◽  
Mathematics Teaching And Learning ◽  
Teaching Of Mathematics

ResumoO presente estudo é uma pesquisa bibliográfica inspirada no Estado do Conhecimento, tendo como objetivo compreender focos temáticos nas produções acadêmicas que utilizam/abordam o ensino de matemática através da resolução de problemas. Para tanto, realizou-se um mapeamento das produções acadêmicas publicadas nos periódicos: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista e Educação Matemática Pesquisa, entre janeiro de 2011 e junho de 2019. De um modo geral, percebemos uma variedade de estudos contendo diferentes perspectivas discutidas e abordadas tanto na educação básica quanto no ensino superior.  A partir deste trabalho, é possível ampliar o entendimento sobre a temática, fortalecendo a ideia de que esta pode potencializar o processo de ensino e aprendizagem de matemática.Palavras-chave: Resolução de problemas, Mapeamento, Educação matemática.AbstractThe present study is a bibliographic research inspired by the state of knowledge, aiming to understand thematic focuses on academic productions that use/approach teaching mathematics through problem-solving. For this purpose, we mapped the academic productions published in journals: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista, and Educação Matemática Pesquisa, published between January 2011 and June 2019. We noticed a variety of studies containing different perspectives discussed and addressed both in basic and university education. From this work, it is possible to broaden the understanding of the theme, strengthening the idea that it can enhance the mathematics teaching and learning process.Keywords: Problem solving, Mapping, Mathematics education. ResumenEl presente estudio es una investigación bibliográfica inspirada en el estado del conocimiento, con el objetivo de comprender enfoques temáticos sobre producciones académicas que utilizan/abordan la enseñanza de las matemáticas a través de la resolución de problemas. Para ello, mapeamos las producciones académicas publicadas en las revistas: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista y Educação Matemática Pesquisa, publicadas entre enero de 2011 y junio de 2019. Notamos una variedad de estudios que contienen diferentes perspectivas discutidas y abordadas tanto en educación básica como en educación universitaria. A partir de este trabajo, es posible ampliar la comprensión del tema, fortaleciendo la idea de que puede potenciar el proceso de enseñanza y aprendizaje de las matemáticas.Palabras clave: Resolución de problemas, Mapeo, Educación matemática.

scholarly journals Profil Berpikir Kritis Mahasiswa PGMI dalam Memecahkan Masalah Matematika Dasar

2018 ◽  
Vol 6 (1) ◽  
pp. 11 ◽  
Author(s):  
Sintha Sih Dewanti
Keyword(s):  
Critical Thinking ◽  
Problem Solving ◽  
Reciprocal Relationship ◽  
Applied Problem ◽  
Math Ability ◽  
Descriptive Research ◽  
Mathematics Problems ◽  
Thinking Process ◽  
High Level ◽  
Complex Translation

Abstrak Tujuan penelitian ini adalah untuk mendeskripsikan profil berpikir kritis mahasiswa PGMI UIN Sunan Kalijaga Yogyakarta dalam memecahkan masalah matematika dasar. Pemecahan masalah merupakan proses mental tingkat tinggi dan memerlukan proses berpikir yang lebih kompleks termasuk berpikir kritis. Pemecahan masalah juga mempunyai hubungan timbal balik dengan berpikir kritis. Berpikir kritis pada penelitian ini mengacu pada berpikir kritis dengan kriteria FRISCO. Jenis penelitian ini adalah penelitian deskriptif dengan pendekatan kualitatif. Pada penelitian ini diambil 9 subjek penelitian, yaitu 3 subjek pada kemampuan matematika dasar tinggi, sedang, dan rendah. Pengumpulan data dilakukan dengan pemberian soal pemecahan masalah dan wawancara. Ada 5 tipe masalah yang digunakan dalam soal pemecahan masalah yaitu: simple translation problem, complex translation problem, process problem, applied problem, dan puzzle problem. Profil berpikir kritis mahasiswa dalam memecahkan masalah matematika dasar menurut kriteria FRISCO pada setiap langkah pemecahan Polya sebagai berikut: a) Mahasiswa dengan KPM tinggi mengetahui fokus, alasan, situasi dan kejelasan dalam setiap tahap pemecahan masalah juga menjelaskan inferensinya pada setiap tahap pemecahan masalah Polya pada simple translation problem, complex translation problem, dan applied problem, tetapi belum dapat untuk 2 masalah lainnya; b) Mahasiswa dengan KPM sedang, mengetahui fokus, alasan, situasi dan kejelasan dalam setiap tahap pemecahan masalah juga menjelaskan inferensinya pada setiap tahap pemecahan masalah Polya pada simple translation problem dan applied problem tetapi belum dapat untuk 3 masalah lainnya; dan c) Mahasiswa dengan KPM rendah, mengetahui fokus, alasan, inferensi, situasi, klarifikasi dan memeriksa kembali pada setiap langkah pemecahan masalah Polya pada masalah simple translation problem, dan belum dapat pada puzzle problem, sedangkan untuk 3 masalah lainnya mengetahui fokus dan alasan hanya sampai pada langkah melaksanakan strategi, tetapi belum dapat mengetahui inferensinya. Kata kunci: berpikir kritis, pemecahan masalah, kemampuan matematika dasar Abstract The purpose of this research is to describe the critical thinking profile of PGMI UIN Sunan Kalijaga Yogyakarta students in solving basic mathematics problems. Problem solving is a high level mental process and requires a more complex thinking process including critical thinking. Problem solving also has a reciprocal relationship with critical thinking. Critical thinking in this study refers to critical thinking with the FRISCO criteria. The type of this research is descriptive research with qualitative approach. In this study, 9 subjects taken, that is 3 subject to the ability of high-basic mathematic, medium, and low. Data was collected by way of tests and interviews. There are 5 types of problems used in problem solving tests: simple translation problem, complex translation problem, problem process, applied problem, and puzzle problem. The profile of critical thinking of students in solving basic mathematics problems according to FRISCO criteria at each polya solving step as follows: a) Students with high problem solving abilitys know the focus, reason, situation and clarity in every problem solving step also explain the inferences at each stage of solving Polya problem on simple translation problem, complex translation problem, and applied problem, but not yet for 2 other problems; b) Students with medium problem solving abilitys know the focus, reason, situation and clarity in each stage of problem solving also explain the inferences at each stage of polya problem solving on simple translation problem and applied problem but not yet for the other 3 problems; and c) Students with low problem solving abilitys know the focus, reason, inference, situation, clarification and re-examine each step Polya problem solving on the problem of simple translation problem, and not yet in the puzzle problem, while for 3 other problems know the focus and reason only to the step of implementing the strategy, but not yet know the inferences. Keywords: critical thinking, problem solving, basic math ability

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