scholarly journals Exploring the Educational Value of Mathematical Beauty and Effective Ways of Discovering Mathematical Beauty

2021 ◽  
Vol 5 (10) ◽  
pp. 82-87
Author(s):  
Cunrong Wang
Keyword(s):  
Problem Solving ◽  
Mathematics Teaching ◽  
Mathematical Reasoning ◽  
Knowledge Systems ◽  
Mathematical Language ◽  
Mathematical Culture ◽  
Educational Value ◽  
Formalization Of Mathematics ◽  
Mathematical Beauty ◽  
Opening Up

The precision of mathematical reasoning, the abstractness of mathematical language, the profundity of mathematical thought and method, as well as the excessive formalization of mathematics teaching have formed an impassable gap, hindering students in approaching mathematics. This has concealed the beauty of mathematics and the light of mathematical culture. However, if students are able to cross this gap, they would find that mathematics is a vast world full of vitality, imagination, wisdom, poetry, and beauty. The pursuit of mathematical beauty is one of the motivations for scientists to research this field. Experiencing mathematical beauty is of great significance to students’ learning and growth. In teaching, the value of mathematical beauty is explored, such as stimulating emotions, opening up to the truth, and cultivating goodness. Several effective ways are suggested in this article to guide students to discover the mathematical beauty in life while finding it in problem-solving methods and exploring it in knowledge systems.

scholarly journals Examining Problem-Solving and Problem-Posing Skills of Pre-Service Mathematics Teachers: A Qualitative Study

2021 ◽  
Author(s):  
Furkan Özdemir ◽  
Halil Coşkun Çelik
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Mathematics Teaching ◽  
Alternative Assessment ◽  
Problem Posing ◽  
Research Approach ◽  
Mathematical Language ◽  
State University ◽  
Assessment Approach ◽  
Study Participants

The aim of this study is to examine the problem-solving processes and problem-posing skills of pre-service mathematics teachers, which consists of four stages (understanding the problem, preparing a plan for the solution, applying the plan, evaluating) defined by Polya (1997) with the progressive scoring scale based on the alternative assessment approach. Qualitative research approach has been adopted in the study. Participants of the study consist of 71 pre-service teachers studying at the department of primary education mathematics teaching at the education faculty of a state university in the Southeastern Anatolia region of Turkey. Since the problem solving and problem posing behaviors of the participants were examined separately in the study, the gradual scoring scale developed by Baki (2008) was used. As a result of the analysis, it was determined that the participants showed the highest performance in the category of understanding the problem, and the lowest performance in the category of evaluation and problem posing. It was determined that participants who failed in the problem posing phase either wrote the same problem or could not write a problem. Another result reached in the study is that the participants had difficulties in expressing the operations in mathematical language.

scholarly journals Examining Problem-Solving and Problem-Posing Skills of Pre-Service Mathematics Teachers: A Qualitative Study

2021 ◽  
Vol 4 (4) ◽  
Author(s):  
Furkan Özdemir ◽  
◽  
Halil Coşkun Çelik
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Mathematics Teaching ◽  
Alternative Assessment ◽  
Problem Posing ◽  
Research Approach ◽  
Mathematical Language ◽  
State University ◽  
Assessment Approach ◽  
Study Participants

The aim of this study is to examine the problem-solving processes and problem-posing skills of pre-service mathematics teachers, which consists of four stages (understanding the problem, preparing a plan for the solution, applying the plan, evaluating) defined by Polya (1997) with the progressive scoring scale based on the alternative assessment approach. Qualitative research approach has been adopted in the study. Participants of the study consist of 71 pre-service teachers studying at the department of primary education mathematics teaching at the education faculty of a state university in the Southeastern Anatolia region of Turkey. Since the problem solving and problem posing behaviors of the participants were examined separately in the study, the gradual scoring scale developed by Baki (2008) was used. As a result of the analysis, it was determined that the participants showed the highest performance in the category of understanding the problem, and the lowest performance in the category of evaluation and problem posing. It was determined that participants who failed in the problem posing phase either wrote the same problem or could not write a problem. Another result reached in the study is that the participants had difficulties in expressing the operations in mathematical language.

scholarly journals Pengembangan Bahan Ajar Matematika Berbasis Integrasi-Interkoneksi Untuk Memfasilitasi Penalaran Dan Pemecahan Masalah

2019 ◽  
Vol 4 (2) ◽  
pp. 31-42
Author(s):  
Mulin Nu'man
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Mathematics Teaching ◽  
Mathematical Reasoning ◽  
Research Result ◽  
Teaching Materials ◽  
School Students ◽  
Problem Solving Skills ◽  
Stage Of Development

This research aims to produce and see the effectiveness of interconnection-based mathematics-based teaching materials to facilitate the reasoning and problem-solving skills of high school students. The method used is research model development Borg & Gall with three phases: an introduction that includes literature review and analysis of student characteristics, stage of development which include determining the basic competencies and indicators, the analysis of the materials, writing materials, and instruments, and the stage of validation includes expert validation, revision I, small group trial, analysis of the trial results, revision II, and packaging the final product. The research result is drafting a set of mathematics teaching materials based integration-interconnection effective to facilitate reasoning, and problem-solving abilities of high school students worthy with the results of the assessment of Very Good is 157.5 of the maximum score 172 or percentage 91.2% and posttest result of average mathematical reasoning 77.21 and average problem-solving ability 76.01. Also of the test is found that teaching materials can be used well in learning with positive impact. Keywords: mathematics teaching materials, interconnect integration, reasoning, problem-solving

scholarly journals Students’ agency, creative reasoning, and collaboration in mathematical problem solving

2021 ◽  
Author(s):  
Ellen Kristine Solbrekke Hansen
Keyword(s):  
Problem Solving ◽  
Driving Forces ◽  
Mathematical Reasoning ◽  
Mathematical Problem ◽  
Linear Functions ◽  
Shared Understanding ◽  
Interaction Patterns ◽  
Collaborative Processes ◽  
Mathematical Properties ◽  
Shared Agency

AbstractThis paper aims to give detailed insights of interactional aspects of students’ agency, reasoning, and collaboration, in their attempt to solve a linear function problem together. Four student pairs from a Norwegian upper secondary school suggested and explained ideas, tested it out, and evaluated their solution methods. The student–student interactions were studied by characterizing students’ individual mathematical reasoning, collaborative processes, and exercised agency. In the analysis, two interaction patterns emerged from the roles in how a student engaged or refrained from engaging in the collaborative work. Students’ engagement reveals aspects of how collaborative processes and mathematical reasoning co-exist with their agencies, through two ways of interacting: bi-directional interaction and one-directional interaction. Four student pairs illuminate how different roles in their collaboration are connected to shared agency or individual agency for merging knowledge together in shared understanding. In one-directional interactions, students engaged with different agencies as a primary agent, leading the conversation, making suggestions and explanations sometimes anchored in mathematical properties, or, as a secondary agent, listening and attempting to understand ideas are expressed by a peer. A secondary agent rarely reasoned mathematically. Both students attempted to collaborate, but rarely or never disagreed. The interactional pattern in bi-directional interactions highlights a mutual attempt to collaborate where both students were the driving forces of the problem-solving process. Students acted with similar roles where both were exercising a shared agency, building the final argument together by suggesting, accepting, listening, and negotiating mathematical properties. A critical variable for such a successful interaction was the collaborative process of repairing their shared understanding and reasoning anchored in mathematical properties of linear functions.

scholarly journals Complex Problems in Entrepreneurship Education: Examining Complex Problem-Solving in the Application of Opportunity Identification

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Yvette Baggen ◽  
Jakob Mainert ◽  
André Kretzschmar ◽  
Thomas Lans ◽  
Harm J. A. Biemans ◽  
...  
Keyword(s):  
Problem Solving ◽  
Entrepreneurship Education ◽  
Complex Problem ◽  
Complex Problem Solving ◽  
Conceptual Level ◽  
Opportunity Identification ◽  
Domain Specific ◽  
Masters Students ◽  
Opening Up ◽  
General Skill

In opening up the black box of what entrepreneurship education (EE) should be about, this study focuses on the exploration of relationships between two constructs: opportunity identification (OI) and complex problem-solving (CPS). OI, as a domain-specific capability, is at the core of entrepreneurship research, whereas CPS is a more domain-general skill. On a conceptual level, there are reasons to believe that CPS skills can help individuals to identify potential opportunities in dynamic and nontransparent environments. Therefore, we empirically investigated whether CPS relates to OI among 113 masters students. Data is analyzed using multiple regressions. The results show that CPS predicts the number of concrete ideas that students generate, suggesting that having CPS skills supports the generation of detailed, potential business ideas of good quality. The results of the current study suggest that training CPS, as a more domain-general skill, could be a valuable part of what should be taught in EE.

scholarly journals ANALISIS KEMAMPUAN PEMECAHAN MASALAH PADA SOAL CERITA MATEMATIKA BERDASARKAN TEORI POLYA DITINJAU DARI ADVERSITY QUOTIENT

2020 ◽  
Vol 2 (1) ◽  
pp. 105-128
Author(s):  
Novita Nurul Aini ◽  
Mohammad Mukhlis
Keyword(s):  
Problem Solving ◽  
Data Collection ◽  
Mathematical Reasoning ◽  
Linear Equations ◽  
Learning Goals ◽  
Problem Solving Skills ◽  
Data Presentation ◽  
Validity Test ◽  
Descriptive Research ◽  
Qualitative Descriptive

One of the studen learning goals mathematics is mathematical reasoning for outcomes training student to solve the problems. One of the problems faced by students is word questions. There are several students responses in dealing with word question which is known as Adversity Quotient. This research aims to describe the students' problem solving skills in system of three-variable linear equations subject based on Polya's theory in terms of Adversity Quotient. This is a qualitative descriptive research with three subjects of students class X IPA 1 SMAN Arjasa Jember, there are one climber student, one camper student and one quitter student. These subjects took purposive sampling with consideration according to the results of questionnaire scores that meet each of the criteria of Adversity Quotient. Data collection techniques used were questionnaires, tests, interviews and observations. The validity test used is technical triangulation. Data analyzed through data condensation, data presentation and conclusion drawing. The results showed that student with the type of climber was able to meet all the indicators of problem solving in the problem of the word questions which included indicators of understanding the problem, planning the solution, carrying out the plan of solving and re-checking. Camper type student met all indicators of problem solving except at the re-checking stage. Quitter type student in completing word questions met the stage of understanding the problem and planning the solution, while the stage of carrying out the plan and re-checking is not fulfilled by the quitter student.

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 Resolución de problemas matemáticos en GeoGebra

2020 ◽  
Vol 9 (1) ◽  
pp. 26-42
Author(s):  
William Enrique Poveda Fernández
Keyword(s):  
Costa Rica ◽  
Problem Solving ◽  
Secondary School ◽  
Secondary School Teachers ◽  
Mathematical Reasoning ◽  
Mathematical Thinking ◽  
School Teachers ◽  
Mathematical Objects ◽  
Problem Solving Strategies ◽  
Problem Solving Process

RESUMENEn este artículo se analizan y discuten las ventajas y oportunidades que ofrece GeoGebra durante el proceso de resolución de problemas. En particular, se analizan y documentan las formas de razonamiento matemático exhibidas por ocho profesores de enseñanza secundaria de Costa Rica, relacionadas con la adquisición y el desarrollo de estrategias de resolución de problemas asociadas con el uso de GeoGebra. Para ello, se elaboró una propuesta de trabajo que comprende la construcción y la exploración de una representación del problema, y la formulación y la validación de conjeturas. Los resultados muestran que los profesores hicieron varias representaciones del problema, examinaron las propiedades y los atributos de los objetos matemáticos involucrados, realizaron conjeturas sobre las relaciones entre tales objetos, buscaron diferentes formas de comprobarlas basados en argumentos visuales y empíricos que proporciona GeoGebra. En general, los profesores usaron estrategias de medición de atributos de los objetos matemáticos y de examinación del rastro que deja un punto mientras se arrastra.Palabras claves: GeoGebra; Resolución de problemas; pensamiento matemático. RESUMOEste artigo analisa e discute as vantagens e oportunidades oferecidas pelo GeoGebra durante o processo de resolução de problemas. Em particular, as formas de raciocínio matemático exibidas por oito professores do ensino médio da Costa Rica, relacionadas à aquisição e desenvolvimento de estratégias de resolução de problemas associadas ao uso do GeoGebra, são analisadas e documentadas. Para isso, foi elaborada uma proposta de trabalho que inclui a construção e exploração de uma representação do problema, e a formulação e validação de conjecturas. Os resultados mostram que os professores fizeram várias representações do problema, examinaram as propriedades e atributos dos objetos matemáticos envolvidos, fizeram conjecturas sobre as relações entre esses objetos e procuraram diferentes formas de os verificar com base em argumentos visuais e empíricos fornecidos pelo GeoGebra. Em geral, os professores utilizaram estratégias para medir os atributos dos objetos matemáticos e para examinar o rasto que um ponto deixa enquanto é arrastado.Palavras-chave: GeoGebra; Resolução de problemas; pensamento matemático. ABSTRACTThis article analyzes and discusses the advantages and opportunities offered by GeoGebra during the problem-solving process. In particular, the mathematical reasoning forms exhibited by eight secondary school teachers in Costa Rica, related to the acquisition and development of problem solving strategies associated with the use of GeoGebra, are analyzed and documented. The proposal was developed that includes the elements: construction and exploration of a representation of the problem and formulation and validation of conjectures. The results show that teachers made several representations of the problem, examined the properties and attributes of the mathematical objects involved, made conjectures about the relationships between such objects, and sought different ways to check them based on visual and empirical arguments provided by GeoGebra. In general, the teachers used strategies to measure the attributes of the mathematical objects and to examine the trail that a point leaves while it is being dragged.Keywords: GeoGebra; Problem Solving; Mathematical Thinking.

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