Theory Of Mathematics Education Research Articles

Development of an Exploring System: An Integrated Approach to Children’s Math Education in China

In terms of the leap-forward development for education experiment, both the Chinese and English educational experiment have been very successful, while the progress of the children’s mathematics education experiment in China has been relatively slow. It is believed that the main reason for this is the lack of an efficient cognitive tool or system that supports students’ study and exploration and correspondingly covers the whole curriculum of children’s math education. In recent years, basic mathematics education cognitive tools have undergone rapid development, whereas the lack of a common normalization method for continued in-depth inquiry of the relationships among Objects, Algebra, and Geometry (OAG) has led to the fragmentation of students’ mathematical knowledge. Thus, it is difficult for students to develop a systematic understanding of mathematics. Therefore this project attempts to construct a Children’s Mathematics Exploring System (CMES), which integrates with cognition theory, method, and contents of basic mathematics education to query the essence of the relationships among OAG. Specifically, the functions of CMES include the following: (1) providing cognitive tools with typical characteristics for the relationships among OAG; (2) offering a general normalized open system on which sustainable in-depth research can be conducted and a conversion tool through which the complete textbook unit of the basic mathematics education can be converted to reveal the relationships among OAG; and (3) presenting a set of cognitive theories, methods, and a system of basic mathematics education to further explore the relationships among OAG. This project will accelerate the development of cognitive technology in basic mathematics education, widen its practical applications, reduce the difficulty of mathematics cognition, and finally improve the quality and efficiency of basic mathematics education.

Estudiante de docencia en matemáticas y la construcción de la identidad disciplinar

In this research we offer empirical evidence that disciplinary identity is a factor in the training of students in mathematics teaching. We show, with the Socioepistemological Theory of Mathematics Education, how this factor intervenes in the resignifications of mathematical knowledge and in the definition of the mathematics teacher function. The source of analysis was found in the student’s school-academic setting accompanied by the development of the vision of teaching and mathematical knowledge that is building on the permanent habit of school activity designs. Using ethnographic methods and semi-structured interviews, immersions were conducted with communities of students who are being trained in teaching. As a result of the research it was found that in the permanent habit of designing school activities is the source of meaning that defines the disciplinary identity.

Finding meaning in quadratic equations through a physical context: falling objects motion

This paper presents the results of the implementation of a design focused on the resignification of the parameters of the quadratic equation (parabolas) through the context of a physical phenomenon. This design was based on an epistemology of practices framed in principles of cognitive and social constructivism, particularly the socioepistemological theory of mathematics education, based also on the model of guided discovery. Based on the students’ arguments, evidence of resignification is shown in the parameters of the quadratic equation in such a way that relationships between algebraic and graphical expressions were established. It was identified that the students’ experiences, as well as the context, were determining elements for success in the resolution of the design.

Realistic Mathematics & Vygotsky’s Theories in Mathematics Education

Mathematics education is not mathematics, it makes a basic use of highly specialized kinds of mathematical knowledge. The modern world feels a crisis of proper mathematics education in any nation. Realistic Mathematics Education is a domain-specific instruction theory for mathematics. This paper introduces realistic mathematics education (RME) and Vygotskian impacts on mathematics education for learning mathematics. This article describes the development of teaching-learning mathematics & learning theories from a socio-cultural perspective. The methodology of the study is based on qualitative type.

Reform and implementation of technical English course for brewing engineering undergraduates based on STEAM theory

Technical English is a compulsory course for brewing engineering undergraduates. To improve the quality and effectiveness of teaching, we introduced science, technology, engineering, arts and mathematics (abbreviated to STEAM) education theory in technical English teaching of brewing engineering students, and selected, designed, integrated and optimized the teaching contents. With the help of the Rain Classroom, Massive Open Online Courses of Tsinghua University (XuetangX), Open Language, Wine Folly, training courses of Wine and Spirit Education Trust (WSET) and other platform resources, teaching methods, assessment ways and multi-element teaching evaluation system have been innovatively reformed. By using advanced teaching methods such as mind mapping drawing, micro-video production, situational dialogues, topic speech, creative program design and design competition of wine label and bottle packaging, it could effectively improve students' learning interest and engagement, and enhance students' knowledge of professional English and comprehensive application ability.

The Nature of Mathematics Education; The Issue of Learning Theories and Classroom Practice

To achieve a successful mathematics education through the implementation of the school mathematics curriculum, the teacher’s beliefs emanating from their experiences (including learning theories) with their environment should be a considerable factor. This is to ensure that all learning situation in mathematics classroom generate understanding among the individuals involve for it to be meaningful. In this paper my goal is to highlight on some issues which are of great importance to mathematics education as a field of study. The issues in focus are; theory and practice, the role of theory in mathematics education research, some widely used learning theories in mathematics education, theories of models and modelling and their impact on mathematics research, teaching and learning, the aims of teaching and learning mathematics, and the status of mathematics education as knowledge field.

Contextual problem in mathematical problem solving: core ability in Realistic Mathematics Education

Problem solving is one of the ability existed in the component of Realistic Mathematics Education. This ability becomes more important for a student to understand, analyse and formulate the daily-life problem into formal mathematics, such as real-life problem, problem-based specific context, and the problem itself. Even though problem solving is an important component that must be mastered by the student in learning mathematics, not every student has a certain skill to understand and solve the problems occured in daily life. Many students do neither master the basic mathematics concepts nor know the specific criteria in problem solving ability. Regarding the fulfilment, this paper aims to investigate how to optimize problem solving ability using Realistic Mathematics Education as a part of student’s learning. The method used in this article is literature review in which the data collected through a study of several theories and the results of relevant scientific research such as mathematics learning, problem solving concept, Realistic Mathematics Education theory and the others. The result shows that the ability of problem solving and Realistic Mathematics Education interconnected each other, which is Realistic Mathematics Education has the important role in optimizing problem solving, especially in solving contextual problem. According to the result, this article contribute to improving teachers and students mathematics proficiency and deepening the learning theories especially the theories of mathematics problem solving to be more skilful and well-experienced in learning mathematics.

PHÂN TÍCH SÁCH GIÁO KHOA MÔN TOÁN DỰA TRÊN LÍ THUYẾT GIÁO DỤC TOÁN THỰC (REALISTIC MATHEMATICS EDUCATION) VÀ MỘT SỐ KHUYẾN NGHỊ

Writing and evaluating textbooks under the Vietnam new general education curriculum (2018) is a topic of interest to society as well as researchers. This study aims to evaluate the practical elements in current Mathematics textbooks (according to the previous Mathematics Education Curriculum). In order to conduct research, the author offers two frameworks for analyzing textbooks, basically built on the approach to Realistic Mathematics Education theory (RME). This study found that real contexts, real tasks, historical-cultural images, integrated or interdisciplinary elements are presented quite a lot in current Math textbooks. However, it is also necessary to innovate, update, supply real tasks, and pay attention on the structure and level of real tasks, cultural, historical and integrated elements in the mathematics textbooks in order to implement and develop the new math Mathematics Education Curriculum in Vietnam new general education curriculum. The new textbook analytical framework mentioned in this research can also be used to evaluate the “practicality” of the new mathematics textbooks.

Dealing with opposing theoretical perspectives: knowledge in structures or knowledge in pieces?

A great deal of progress has been made in dealing with the multiplicity and diversity of theories in mathematics education. However, relatively little attention has been paid to the opportunities offered by conflicts, tensions, and paradoxes among accepted yet opposing theoretical perspectives for theory building and theory advancement. In this paper, four modes of dealing with opposing perspectives are outlined: (1) taking contrasting theoretical perspectives as incommensurable; (2) holding opposites not as conflicting but as complementary; (3) dissolving or surpassing oppositions by blending perspectives; and (4) preserving paradoxes by recognizing the interdependence of constitutive oppositions. These four modes are illustrated by application to the long-standing debate of knowledge-in-structures versus knowledge-in-pieces and further exemplified by turning to the research literature on students’ understanding of limit.

Land subdivision: How students determine equal area

This study aims to support student’s understanding of the properties of a bisector related to the area of the triangle. A context and a set of activities is design based on Realistic Mathematics Education (RME) theory to develop students’ understanding and to engage them in meaningful activities. Design research is chosen as the research approach with two cycles of experiment. A context of land subdivision problem was selected to activate students’ prior knowledge and to bring them into the activities. At First, the activities is presented in small group of mathematics students and in the regional mathematics competition as one of the final question for the finalists. Then, the second cycle is conducted in the classroom with students from mathematics education program in Universitas Ahmad Dahlan. The result showed that none of the students and finalists in the competition were able to solve the question because they do not have idea how to do land subdivision. They cannot use their prior knowledge of bisector to solve the problem. After revising the activities, in the classroom, all groups in the class were able to solve the problem. These activities are land subdivision with three different levels of difficulties and purposes.

An alternative to broaden the school-promoted meanings of mathematics in electrical sciences from socioepistemology

This paper is the result of a research done from the Socioepistemological Theory of Mathematics Education, perspective in which we enquire about the reasons to study trigonometric Fourier series in electrical engineering, and what historical and epistemological conditions can be considered to develop more profound meanings when this topic is addressed in class. The findings in this research are four notions for the social construction of mathematics knowledge found in a qualitative historical-epistemological analysis of the original works of nineteenth century scientists. These notions consider transversal aspects from the scientists’ works: the use of analogies from heat to electricity give mathematical support to their findings; the shift from a static to a dynamic paradigm about electricity; the concern of a steady state as the situational context in which the knowledge was built; and the presence/confrontation of an epistemological obstacle. We propose that these conditions can be used to broaden the meanings overshadowed by mathematics courses in schools that primarily promote the operational aspect of mathematics.

Introducing the slope concept

ABSTRACT Many students do not have a deep understanding of slope. This paper defines what a deep understanding of slope is in terms of mathematics-education theory. The various factors which help explain why such a deep understanding is difficult to acquire are then discussed. These factors include the following: the different representations for slope; graphical understanding; ratio and rate; and proportional reasoning. In light of this discussion, the design of a mathematical resource to help give students a deep understanding of slope is described. The resource was used at one university, amongst Chinese first-year undergraduate science and engineering students. Evidence would suggest that those students who did not evidence a correct understanding of all the aspects of slope (deep understanding) before completing the resource improved their understanding of these aspects upon completion of the resource.

The power of place: spatializing critical mathematics education

ABSTRACT Place-based education has traditionally had a limited focus on mathematics, and critical mathematics education often lacks explicit attention to place and space. We explore integrating theories of place, spatial justice, and critical mathematics education. To begin, we consider various frameworks of place—including Indigenous, urban, and critical perspectives—to situate a discussion on how place acts as a shaping force on social relations like race, gender, and sexuality, and, conversely, how social relations shape place. We include mathematics as a category of social relations in that guiding framework. We next summarize and build on various notions of place and spatial justice, toward their integration with critical mathematics education. In so doing, we present teaching mathematics for spatial justice, or using mathematics 1) to identify power relations in and through place and 2) to transform the world by re-imagining and remaking place. We sidestep a false urban-rural divide and instead, illustrate the potential of teaching mathematics for spatial justice using rich examples organized around four thematic categories: geographies of opportunity, mapping, human mobility, and land relations and obligations.

Un posible enfoque de complementariedad entre espacios de trabajo matemático y modelización

This article presents a study on a possible complementarity between Mathematical Working Spaces (MWS) and Blomhoj's modeling approach. From a theoretical perspective that provides foundations to connect theories in mathematics education, it intends to extend the discussion on the scope of complementarity and illustrates it by a well-known example proposed by Blomhoj. The main result shows that both theoretical frameworks would complement each other even in the epistemological dimension, characteristic that would distinguish the Blomhoj cycle from others that mainly emphasize the cognitive dimension of modeling. This aspect would enrich the analysis of this type of tasks, expanding the articulation between both theoretical frameworks, a question that, as far as it knows, has not been done so far.

On note-taking

Note-taking, or copying quickly and accurately the material that the professor puts on the blackboard, is the predominate – and preferred – student activity in college-level mathematics classrooms. This activity is herein investigated in relation to the following eleven topics in the constructivist theory of mathematics education: student-centered environment, the professor as an authority figure, dialogue and participant activities, personal autonomy, self-reliance, real math, interconnected cognitive spaces, metacognition, assessment, interpersonal relations and social values. In each case, it is found that the activity of taking notes is not compatible with the constructivist position on these topics. A few remarks are also made regarding note-taking in more general, non-constructivist settings.

Experts’ Construction of Mathematical Meaning for Derivatives and Integrals of Complex-Valued Functions

We engaged five mathematicians who conduct research in the domain of complex analysis or use significant tools from complex analysis in their research in interviews about basic concepts of differentiation and integration of complex functions. We placed a variety of constructivist, social-constructivist, and embodied theories in mathematics education in conversation with one another to explore the development of the expert participants’ construction of mathematical meanings while moving between varying levels of abstraction from embodied concepts and real-world contexts to symbolic manipulation and formal theories. The mathematicians relied heavily on direct application of concepts and analogies from differentiation of real-valued functions and employed rotation and dilation as a local linear description of the action of a complex differentiable function with attendant repeated mental imagery and physical gestures. They also employed reasoning about real-valued line integrals to interpret contour integrals but acknowledged significant struggle to conceptually interpret what was analogously accumulated in the complex case. Instead, they all developed more personal meanings through a process of reconciling various aspects across their concrete to formal domains of reasoning. Much of the observed construction of meaning was manifested through contextualizing well-understood aspects of formal mathematical theory. We consequently explore implications for characterizing mathematical conceptual development as an interplay between concrete and formal reasoning rather than a development from one to another.

Design and research for developing local instruction theories

Innovation in mathematics education needs the involvement of teachers, textbook authors, policy makers and researchers. This paper sketches the role and importance of instructional design aiming at new local instruction theories in mathematics education. The approach is shown with a study that investigated how students can be supported in the development of the basic principles of the mathematics of change. The study combines design and research in three successive phases. In the first phase a hypothetical learning trajectory and instructional activities are designed, in the teaching experiment phase the trajectory is acted out, and in the phase of the retrospective analysis the articulated hypotheses are reflected upon. In this way, a cyclic process of (re)design and development of innovative teaching is structured. The resulting local instruction theory is expected to create opportunities for teachers, textbook authors and researchers to consider contextual factors and to adapt results for their research or teaching.

Learning Situation for the Trigonometric Fourier Series from a Socio-epistemological Stand Point

This article aims at showing a didactic proposal that favours the signification of the Trigonometric Fourier Series through a learning situation, based on the Socio-epistemological Theory of Mathematics Education, on research where this knowledge has been problematized. The Fourier Trigonometric Series is a complex topic for learning at a higher level, where the process is usually mechanised without fully understanding its operation and characteristics. We want to verify that with activities that support the relationship between algebra and geometry, making use of GeoGebra —dynamic geometry software— as a control variable, the series and its convergence can be signified using a physical-geometric context.

O que mais se pode dizer sobre teoria e prática? Ou: como ainda se pode dizer? Ou: pode-se ainda dizer? Um ensaio sobre teoria e prática em educação matemática

Esse ensaio, em forma de narrativa, conta a história de um professor de matemática ao lidar com a faina do fazer pesquisa em educação matemática, deparando-se com suas próprias tensões identitárias, dialogando consigo mesmo e também com uma Professora, sujeito de sua ulterior pesquisa de mestrado. A narrativa expõe uma crítica ao papel da pesquisa, especialmente aquela cujo objeto é a prática e o saber do professor, estabelecendo uma relação entre o papel da teoria em educação matemática e o trabalho dos professores de matemática, em sala de aula. Assim, tratando a crítica também como uma questão referente à sua própria constituição como professor e pesquisador, a narrativa mescla ficção e realidade para mostrar um modo de lidar, de estar e de ser, quando pensamos nessa falsa dicotomia entre teoria e prática, em educação matemática.

Teorias de Educação Matemática: contribuições na formação do futuro pesquisador

Este artigo tem como objetivo apresentar um estudo sobre elementos teóricos de diferentes autores que influenciam e atuam diretamente nas discussões sobre problemas no ensino e aprendizagem da matemática, durante aulas de teorias de educação matemática em um programa de doutorado, realizado em uma universidade brasileira. O principal objetivo aqui foi identificar quais contribuições este estudo construiu para a formação de um potencial pesquisador em educação matemática. É organizado em categorias, de acordo com teorias e trabalhos correlatos estudados, tomando como perspectiva os aspectos históricos, filosóficos, epistemológicos e cognitivos da educação matemática. Após uma cuidadosa análise sobre os temas estudados, as construções escritas e uma produção de seminários dos alunos, foi possível deduzir que o trabalho realizado durante essas aulas poderia auxiliar na aquisição de conhecimentos sobre uma área em constituição, seus conflitos e alguns de seus conceitos teóricos