Review of Mathematical Thinking and Problem Solving.

1996 ◽  
Vol 41 (1) ◽  
pp. 80-80
Author(s):  
Daniel Stalder ◽  
Shubhangi Stalder
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking

The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment

2021 ◽  
pp. 073563312097993
Author(s):  
Zhihao Cui ◽  
Oi-Lam Ng
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Computational Thinking ◽  
Programming Environment ◽  
Primary School Students ◽  
School Students ◽  
Mathematical Concepts ◽  
Block Based

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12–14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation.

EXAMINATION OF SECONDARY SCHOOL 7TH GRADE STUDENTS' MATHEMATICAL THINKING AND PROBLEM SOLVING SKILLS ON RATIONAL NUMBERS

2021 ◽  
Vol 6 (15) ◽  
pp. 552-562
Author(s):  
Fatma Berna BENLİ ◽  
Kübra GÜRTAŞ
Keyword(s):  
Problem Solving ◽  
Secondary School ◽  
Reading Time ◽  
Mathematical Thinking ◽  
Rational Numbers ◽  
Female Students ◽  
School Education ◽  
Problem Solving Skills ◽  
Significant Difference ◽  
New Knowledge

In our new education curriculum, it has been seen that it is no longer sufficient for students to learn only the achievements, unlike these gains, solution strategies that the student visualizes in his mind and designed by himself are also needed. Mathematical thinking, which is the process of obtaining new information completely different from the student's old knowledge and new knowledge, using it in the solution of the problem, and transforming that knowledge into new knowledge, has become extremely important. MEB asks students for deep mathematical thinking and problem solving skills in all questions they ask in the skill-based tests and student selection exam LGS. In this study, mathematical thinking and problem solving skills of middle school 7th grade students while solving problems will be examined. The research was applied to 241 students in 7 different secondary schools in the province of Bingöl in the Eastern Anatolia Region in the 2020-2021 academic year. In the study, it was investigated by quantitative and qualitative methods whether the mathematical thinking and problem solving skills of the students on rational numbers are related to gender, whether they had pre-school education and daily reading time. In the research, the SPSS 25 package program was used in the analysis of quantitative data, and in the analysis of qualitative data by examining the process steps in the answers from the students. As a result of the research, a statistically significant difference was found between male and female students, and this difference is in favor of female students. According to the findings obtained from the research, no statistically significant difference was found between the students who had and did not have pre-school education. Secondary school 7th grade students’ mathematical thinking and problem solving skills are related to their daily reading time. According to the results, students who read for an hour a day are more successful than students who read for fifteen minutes a day.

scholarly journals TYPICAL CLASS METHODS FOR SOLVING EQUATIONS AND INEQUALITIES WITH DIFFERENT STRUCTURES

2021 ◽  
Vol 58 (3) ◽  
pp. 53-62
Author(s):  
A.K. Alpysov ◽  
◽  
A.K. Seytkhanova ◽  
I.Sh. Abishova ◽  
◽  
...  
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematical Concept ◽  
Thinking Skills ◽  
Practical Application ◽  
Mathematical Concepts ◽  
Theoretical Substantiation ◽  
New Methods ◽  
General Article ◽  
Solving Equations

The article discusses the ways of developing skills and abilities to effectively solve problems when describing methods for solving equations and inequalities, clarifying theoretical knowledge, the basics of forming skills for practical application. The formation of mathematical concepts through solving problems in teaching mathematics opens the way to the development of mathematical thinking, the application of knowledge in practice, and the development of search skills. To master a mathematical concept, along with its definition, it is necessary to know its features and properties. This can be achieved primarily through problem solving and exercise. Problem solving is based on the development of new methods, the creation of algorithms, ways of developing practical skills in the methods and techniques mastered with the help of tasks.In addition, transforming equations and inequalities through the development of thinking skills helps to identify common or special properties in order to draw correct conclusions. Solving various problems, it shows what operations should be used to determine the situation in which a solution was found, and what features of the solution allow choosing the most effective methods. Thanks to the theoretical substantiation of the general article, it is possible to master convenient methods for solving equations and inequalities of various structures.

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.

scholarly journals Piloting a problem solving module for undergraduate mathematics students

2019 ◽  
Vol 17 (2) ◽  
pp. 46
Author(s):  
David McConnell
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Thinking Skills ◽  
Mathematical Work ◽  
Assessment Practices ◽  
Traditional Teaching ◽  
Mathematics Students ◽  
Undergraduate Mathematics ◽  
Students First ◽  
Academic Year

We report on a new problem solving module for second-year undergraduate mathematics students first piloted during the 2016-17 academic year at Cardiff University.  This module was introduced in response to the concern that for many students, traditional teaching and assessment practices do not offer sufficient opportunities for developing problem-solving and mathematical thinking skills, and more generally, to address the recognised need to incorporate transferrable skills into our undergraduate programmes.  We discuss the pedagogic and practical considerations involved in the design and delivery of this module, and in particular, the question of how to construct open-ended problems and assessment activities that promote mathematical thinking, and reward genuinely original and independent mathematical work.  

Collaborative Solution Discovery: A Problem Solving Process

2019 ◽  
pp. 100-103
Author(s):  
Katharine Clemmer
Keyword(s):  
Problem Solving ◽  
Learning Environment ◽  
Real Time ◽  
School System ◽  
Mathematical Thinking ◽  
Self Regulation ◽  
Math Learning ◽  
New Approach ◽  
Problem Solving Process ◽  
The Way

Loyola Marymount University (LMU) has developed a new approach to problem solving, Collaborative Solution Discovery (CSD), to help practitioners in a school system leverage their individual passions in a way that grows students’ positive math identity through mathematical thinking, problem solving, and self-regulation. By focusing on how students and teachers interact with each other in real-time in an ideal classroom, practitioners take ownership of a process to guide their students in growing their positive math identity and thus taking ownership of their own math learning. Practitioners measure progress along the way through metrics that are created, defined, used, and continually refined by themselves to attain their ideal math learning environment. The entire CSD process results in a system that owns ist improvement efforts—improvement efforts that are flexible, adaptable, and sustainable.

scholarly journals Design of problem-solving questions for measuring student’s mathematical thinking type representation

2019 ◽  
Vol 1318 ◽  
pp. 012102 ◽  
Author(s):  
I Irenika ◽  
E Susanti ◽  
C Hiltrimartin ◽  
H Hapizah ◽  
M Meryansumayeka
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Type Representation
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