scholarly journals Visual Reasoning in Mathematics Education: A Conceptual Framework Proposal

2021 ◽  
Vol 14 (1) ◽  
pp. 115-126
Author(s):  
Mehmet Ertürk GEÇİCİ ◽  
Elif TÜRNÜKLÜ
Keyword(s):  
Mathematics Education ◽  
Conceptual Framework ◽  
Mathematics Teaching ◽  
Mathematical Thinking ◽  
Visual Representation ◽  
Clear Distinction ◽  
Abstract Reasoning ◽  
Basic Process ◽  
Process Skill ◽  
Research Areas

Abstract: Reasoning is handled as a basic process skill in mathematics teaching. When the literature was examined, it was seen that many types of reasoning related to mathematics education were mentioned. In the present study, it was focused on visual reasoning, which is one of the types of reasoning and also used in different research areas. The purpose of the study was to propose a conceptual framework for what visual reasoning is and what its components are. The conceptual framework constructed consists of three components as visual representation using, visualization, and transition to mathematical thinking. In this framework, a clear distinction was made between the concepts of visual reasoning and visualization, which are thought to be intertwined with each other in the literature. At the same time, we tried to explain where visualization will take place in visual reasoning. Additionally, how visual reasoning will relate to mathematical thinking also distinguishes the framework from other frameworks.

It Doesn't Add Up: African American Students' Mathematics Achievement

1997 ◽  
Vol 28 (6) ◽  
pp. 697-708 ◽  
Author(s):  
Gloria Ladson Billings
Keyword(s):  
Mathematics Education ◽  
Mathematics Achievement ◽  
School Reform ◽  
Mathematics Teaching ◽  
Mathematical Thinking ◽  
Leadership Role ◽  
Reform Effort ◽  
Grade Levels ◽  
American Students ◽  
The U.S

Mathematics education has been heralded for its leadership role in the U.S. school reform effort (Stein, Grover,&Henningsen, 1996; Grant, Peterson, & Shojgreen- Downer, 1996). Prominent in the reform of mathematics education is the call for students not merely to memorize formulas and rules and apply procedures but rather to engage in the processes of mathematical thinking, that is, to do what mathematicians and other professional users of mathematics do. The revamped mathematics education program is based on engaging students in problem posing and problem solving rather than on expecting rote memorization and convergent thinking. These changes in mathematics education suggest that mathematics teaching must build on students' learning and on their ability to pose and solve problems previously considered too difficult for their age-grade levels (Carpenter&Fennema, 1988; Fennema, Franke, Carpenter,&Carey, 1993).

scholarly journals Emphasizing the Teaching Exploration and Practice of Cultivating College Students’ Mathematical Thinking Ability

2019 ◽  
Vol 3 (2) ◽  
pp. 97
Author(s):  
Zhenzhen Liu
Keyword(s):  
College Students ◽  
Mathematics Education ◽  
Mathematics Teaching ◽  
Mathematical Thinking ◽  
New Methods ◽  
Educational Concept ◽  
Thinking Ability ◽  
Thinking Process

<p>Mathematics education in essence belongs to thinking education, which is the positioning of mathematics education in modern educational concept. In order to cultivate students' mathematical thinking ability, this paper analyzed the thinking process of mathematics teaching and made a sufficient study on the ways to cultivate students' ability to discover new things, reveal new laws, create new methods and solve new problems.</p>

scholarly journals CONTRIBUTIONS OF FIGURES NUMBERS IN THE DEVELOPMENT OF GEOMETRIC THOUGHT

2019 ◽  
Vol 7 (1) ◽  
pp. 16-30
Author(s):  
Maria José Costa dos Santos ◽  
Arnaldo Lopes Bezerra
Keyword(s):  
Mathematics Teaching ◽  
Teaching And Learning ◽  
Basic Education ◽  
Mathematical Thinking ◽  
Algebraic Thinking ◽  
Ethical Awareness ◽  
Pedagogical Tools ◽  
Geometric Thinking ◽  
Virtual Libraries ◽  
Abstract Content

This study was constituted with the purpose of promoting reflections on Mathematics of basic education, from a transdisciplinary view of teaching and learning processes. To do so, we aim to analyze the contributions of figures in the development of geometric thinking. We characterize this research in empirical-exploratory, because for Lakatos and Marconi (2017), this type of research distinguishes itself as a scientific process of investigation that allows the researcher to formulate questions, with three purposes: to raise hypotheses, to increase the familiarization of the researcher in order to research, modify or clarify concepts, based on a qualitative and quantitative approach, according to the depth of the discussion about the object in question. For this, we look for information in other researches, databases of universities and virtual libraries, periodicals.  We hope that the results contribute to the critical and ethical awareness from views of the importance of the development of mathematical thinking, but specifically of geometric thinking, aiming at non-rupture with arithmetic thinking, in order to interweave with algebraic thinking . We consider this research relevant because mathematics teaching is based on abstract content that often makes no sense to the student, and here we show a part of mathematics that is formal but can be fun when well crafted in the classroom. Finally, we present pedagogical tools of innovation, aimed at contributing to the emancipation of the knowledge of this science, without ruptures. Keywords: Geometric thinking. Figurative numbers. Mathematics Teaching.

scholarly journals HISTORY OF MATHEMATICS EDUCATION IN PRIMARY SCHOOL AND IN TEACHER TRAINING IN BRAZIL

2020 ◽  
Vol 24 ◽  
Author(s):  
Wagner Rodrigues Valente ◽  
Maria Célia Leme da Silva
Keyword(s):  
Mathematics Education ◽  
Teacher Training ◽  
Primary School ◽  
Mathematics Teaching ◽  
History Of Mathematics ◽  
Theoretical Hypothesis ◽  
Disciplinary Field ◽  
History Of ◽  
The 19Th Century ◽  
The Relationship

Abstract This article discusses results from research developed on the transformations in mathematics teaching in primary school and the mathematics in teacher training from the 19th century to the mid-20th century in Brazil. We have analyzed the understanding of the relationship between the mathematical disciplinary field and pedagogy in order to confirm the theoretical hypothesis that the interactions between the two fields produce mathematics of different natures, which are interconnected.

scholarly journals COMPLEMENTARY EDUCATION SPACES OF VENEZUELAN MATHEMATICS EDUCATORS. CASE: VENEZUELAN SCHOOL FOR THE TEACHING OF MATHEMATICS - EVEM

2020 ◽  
Vol 24 ◽  
Author(s):  
Cinthia del Carmen Humbría Burgos ◽  
Fredy Enrique González
Keyword(s):  
Mathematics Education ◽  
Qualitative Study ◽  
Social History ◽  
Mathematics Teaching ◽  
Scientific Field ◽  
Epistemology Of Science ◽  
Complementary Education ◽  
Mathematics Educators ◽  
Teaching Of Mathematics ◽  
Teaching Learning

ABSTRACT Qualitative study on mathematical educators complementary education spaces, considering the Venezuelan School for Mathematics Teaching. Referents: Social history (Bernal); Epistemology of Science (Toulmin); Scientific Field (Bourdieu); Systemic vision of Mathematics Education in Venezuela (Beyer). Finding: EFC-EMVs are dialogic, interdisciplinary, generate knowledge about teaching-learning of mathematics, for the Venezuelan educational reality.

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.

Integrated Experiences

2015 ◽  
pp. 278-295
Author(s):  
Carol Carruthers ◽  
Dragana Martinovic ◽  
Kyle Pearce
Keyword(s):  
Young Adults ◽  
Statistical Analysis ◽  
Mathematics Education ◽  
Conceptual Framework ◽  
Knowledge Bases ◽  
Successful Implementation ◽  
Community Of Learners ◽  
Mathematical Concepts ◽  
Education Environment ◽  
K 12

This chapter discusses the integrated experiences of a group of instructors who are using tablets to teach mathematics to adolescents and young adults. iPad technology offers learners in different educational streams and with different knowledge bases an environment that fosters the growth of a community of learners engaged in mathematical concepts and processes. The authors present an in-depth examination of the design of a tablet-based mathematics education environment and provide a statistical analysis to highlight the full richness of their classroom-based experiments. The results are presented using the five foundational aspects of a conceptual framework for the successful implementation of technology in a K-12 environment.

The development of concepts through thousands of years

2019 ◽  
pp. 105-112
Author(s):  
Katalin Fried
Keyword(s):  
Mathematics Education ◽  
Prime Number ◽  
Cognitive Processes ◽  
Visual Representation ◽  
Concept Development ◽  
Scientific Content ◽  
Number Concept ◽  
The Everyday ◽  
Development Goals ◽  
The Individual

There are several difficulties when teaching concepts; we have to consider its content, its abstract meaning, its visual representation, verbal and nonverbal aspects of it, etc. Also, the individual content of a concept changes with the knowledge of someone. However, the content of the concepts through the ages vary but education does not necessarily follow the changes. Not talking of the everyday meaning of a concept, this can get stuck at a certain level, while the scientific content changes. The concepts we teach in schools are not necessarily the actual ones. Thus, it is necessary to revise how we teach some of the concepts. One of the most important concepts of this kind is the prime number. Classification: D30, D39, C30, C39. Keywords: Prime number, concept development, goals of mathematics education, cognitive processes.

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