Development Of Mathematical Thinking Research Articles

Designing a Hypothetical Learning Trajectory Using Prezi Presentation and GeoGebra Application on Flat-Shaped Triangle Geometry Materials

Technology plays a crucial role in enhancing the quality of math learning. In addition to adapting to the rapid advancement of ICT, technology serves as a visualization aid for abstract mathematical concepts, facilitating understanding. Prezi presentations and GeoGebra application are technological tools that can be used as a medium for learning math. Prezi Presentation is used as a presentation medium, while GeoGebra functions as a dynamic tool to enhance the understanding of geometry. They both positively impact the development of mathematical thinking, facilitate meaningful learning experiences, and can be used as alternatives in designing a hypothetical learning trajectory for concepts related to triangle types. This study aims to design a Hypothetical Learning Trajectory (HLT) using Prezi presentation and GeoGebra for the material related to triangle types. The HLT tailored to suit the characteristics of students, making it easier to construct independent understanding related to triangle types through the use of dynamic technology such as Prezi and GeoGebra. This study uses a design research approach consisting of three phases: introduction, design experiments, and retrospective analysis. This was carried out solely in the preliminary phase to develop the initial prototype of the HLT focusing on the concept of triangle types. The HLT will be further examined in subsequent research and retrospectively analyzed to develop the Learning Instructional Theory (LIT) as the final product. Keywords: flat-shaped triangle geometry materials, geogebra application, hypothetical learning trajectory, prezi presentation

Mathematical Thinking Among Pre-Service Teachers: A Critical Component of Teacher Preparation

This research examined pre-service mathematics teachers' mathematical thinking abilities, focusing on problem-solving, mathematical representation, reasoning, mathematical communication, and mathematical connection. Additionally, the study aimed to determine whether there were significant differences in mathematical thinking between pre-service students majoring and minoring in mathematics. The research employed a quantitative approach and involved 277 pre-service mathematics teachers enrolled in the Mathematics Teaching course at the Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris in Malaysia. The research design utilized a survey method, and data were collected through a mathematical thinking questionnaire. The collected data were analyzed using statistic descriptive including mean and standard deviation, while inferential statistics use t-test analyses. The study results revealed that the overall mean is 4.506, followed by standard deviation is 0.541, indicating that the pre-service teachers show a higher positive mathematical thinking. The result also shows a significant relationship between problem-solving, mathematical representation, reasoning, mathematical communication and mathematical connection. The findings also indicated significant differences in mathematical thinking between pre-service mathematics teachers based on gender. Lastly, the result shows that the study recommended the inclusion of mathematical thinking development in teacher education programs to enhance the mathematical thinking abilities of pre-service mathematics teachers. In conclusion, mathematical thinking is an essential aspect of teacher preparation, as it contributes to ensuring the quality of the next generation.

Didactic model for the development of mathematical thinking in naval engineering students in Colombia

The learning-teaching process in math is fundamental for navy engineering students, where specific subjects have a strong theoretical foundation in basic sciences, more concise in mathematics related areas. This research has the objective to construct a didactical model based in context problem solving, modeling and mathematical visualization for the learning-teaching process of contents from the Ship Stability subject for navy engineering students in the Colombian navy University “Escuela Naval de Cadetes Almirante Padilla (ENAP)”. The work lies in the research-action approach of the qualitative research. Results show the model structure composed of four parts; the first one contains the model principles: the epistemological and didactical foundations and the objectives and goals of the constructed model. The second one is a characterization of the model is described, and the necessity for students. The third one, named, resolutive, has three phases (exploration, resolution, and action), that are subdivided in inter-related components one to another. Finally, the fourth part is a proposal for the practical implementation of the model. The model obtained generates a robust construction of mathematical context for problems related to ship stability in the naval context.

Исследование парадоксов в развитии математического мышления: культурно-историческая перспектива

<p>Primary school teachers are the educators responsible for introducing children into the world of mathematics. In the process of learning mathematics, children may experience negative emotions and develop negative attitudes or mathematics anxiety. Some authors approach these issues by focusing on primary teachers’ mathematics anxiety or proficiency in mathematics. In this article, we explore whether and how certain social and educational practices shape or not the development of mathematical thinking in prospective primary teachers, from a cultural-historical perspective. The study’s sample consists of twelve prospective primary teachers in their last year of studies. The participants were interviewed about their experience with mathematics throughout their educational years. By examining and contrasting the different developmental trajectories of the participants, we identified their “imprisonment” in situational thinking and some of the paradoxes that characterise their development. Adopting a historical perspective in analysing participants’ trajectories was crucial in uncovering the paradoxical nature of the development of mathematical thinking. We conclude by highlighting the socially mediated nature of mathematics and the obstacles posed by the competitive and exam-driven nature of educational practices</p>

REALIZATION OF THE COMPETENCY POTENTIAL OF THE TECHNOLOGIGAL EDUCATION FIELD IN THE CONTENT OF EDUCATIONAL LITERATURE

The article discloses general algorithms for identifying the competence approach in the content of educational literature, during the organization of the educational process of learning technologies in the New Ukrainian School.A brief overview of the issues of competence training was carried out, the concept of key competence was outlined, taking into account theoretical research and taking into account the State Standard of Basic Secondary Education. The components of key competence and its difference from the leading technological educational field are determined.Learning outcomes, which are grouped in the field of technology education, into four groups of skills, written in terms of key competencies. Here one should distinguish between leading and key competence. Leading for technological education will be a part of the “competency in natural sciences and technologies” shared with the natural branch, which can be conventionally called “competencies in technology”.The leading technology competence (or competences) is formed and developed by the teacher in the technology lessons of the same name, while other key competences are only developed. This will determine the content of the tasks in the educational literature on technologies, when the tasks, for example, on the development of mathematical competence will not contain new knowledge in mathematics, but only on the use of mathematics in practice, which will only involve the development of mathematical thinking during solving practical tasks.General approaches for identifying competence content in the technological education textbook are proposed.
 Keywords: New Ukrainian school; competence approach; technologies; technological educational sector; State standards of basic secondary education; learning results; key competence; leading competence; study guide; educational literature.

APPLICATION OF INFORMATION AND COMMUNICATION TECHNOLOGIES IN THE ACTIVITIES OF A MATHEMATICS TEACHER

The article discusses the use of information and communication technologies in the activities of a mathematics teacher. We all know that information and communication technologies are of great importance for the effective organization of the learning process, the development of mathematical thinking of students, that is, the learning process cannot be imagined without information and communication technologies. In our article, it is precisely because of these advantages that information and communication technologies are used to develop students’ mathematical literacy in mathematics lessons.; in the organization of independent work of students; in the implementation of an individual, personality-oriented approach.

Preparing Students for Studying in a Non-Native Language in Math and Science

This study aims to study how language teaching affects the development of mathematical thinking in children learning a language other than their mother tongue through a mixed methodology based on interviews with teachers of math and science in Asia and the Middle East. Our primary goal is to see if the language of instruction in second-language immersion programs impacts the development of mathematical thinking. Therefore, we determine that the language of instruction only influences the development of the first abilities in the pupils’ overall performance or specific areas. When mathematical thinking is established while teaching formal concepts in a non-native language, the analysis of variance and multiple regression results indicates how explicit the language of instruction is. The second language impacts the resolution of everyday difficulties, with pupils in first grade that have a language of instruction that matches their mother tongue being competent.

Подготовка учителя начальных классов к профессиональной деятельности по развитию математического мышления младших школьников

<p>The article discusses one of the aspects of the training of a teacher of primary general education – the ability to analyze the causes of students' mistakes made by them when mastering mathematical concepts. The special importance in the competence of the primary school teacher of understanding the value of the initial, initial representations of the child as a result of his own mental activity is noted. An overview of the concept of mathematical thinking in the psychological and pedagogical literature is given. The understanding of mathematical thinking as theoretical, carried out on mathematical material, is highlighted. The levels of development of mathematical thinking and its main components – analysis, planning and reflection – are recorded. The modules of the educational program for the training of primary school teachers are described, aimed at developing students' competencies that allow them to adequately assess the manifestations of mathematical thinking in younger schoolchildren on mathematical material traditionally studied in primary school. The sequence of actions aimed at identifying the error pattern is presented. Examples of tasks for students are given, showing ways of developing the educational action of control; determining patterns of mathematical errors.</p>

Validation of a Scale to Assess the Reversibility of Thought in Verbal Arithmetic Problems

Background : Reversibility is a key concept for the understanding and development of mathematical thinking. There is an agreement regarding problem-solving as a fundamental part of mathematical competence, and some authors regard reversible thinking as a requirement for it. Objectives : We want to validate an instrument that assesses the reversibility of thought when solving verbal arithmetic problems (word problems) involving various operations, semantic-mathematical structures and proximity of situational information. Design : A qualitative study was carried out from the data obtained by experts, and a quantitative study was carried out to determine the validity and reliability of the instrument. Setting and Participants : 318 students from different Spanish schools attending primary education (6 to 12 years) participated. Data collection and analysis: Participants performed 180 mathematical tasks distributed over three theoretical scales, two operations, and four semantic configurations. Results: To determine the consistency of the data, a reliability analysis was performed globally and on each of the scales, all values being greater than 0.90. Exploratory factor analysis resulted in three factors that explained more than 70%. To analyse the validity of the instrument, confirmatory factor analysis was performed, and its indices showed an adjustment of the models. Conclusions : We consider that the designed instrument is sufficiently robust to assess the reversibility of the basic addition and subtraction operations and, in addition, to analyse the discrimination of word problems according to the semantic-mathematical structure and their situational context.

PHÁT TRIỂN TƯ DUY TOÁN HỌC CHO TRẺ TỰ KỈ QUA CÁC TRÒ CHƠI LEGO THEO CÁCH TIẾP CẬN STEAM

Research on STEAM education has been and is being researched and applied by many educators, is an advanced educational trend applied in many countries around the world, including Vietnam. In Vietnam, STEAM education has been implemented since 2010 and has been widely implemented in schools, and preschools, as well as in educational applied research. The article analyzes the value of Lego games and suggests some games with Lego according to the STEAM approach to stimulate the development of mathematical thinking for preschool children with autism.

A Meta-analytic Review of the Relationship between Mathematics Anxiety and the Mathematical Thinking of Africa Students

The development of mathematical thinking is a crucial component of Mathematics education. Mathematics is needed for students to have the ability to manage, acquire, and make use of information to survive in competitive, uncertain, and ever-changing circumstances. Mathematical thinking is the primary goal of learning Mathematics. Despite the relative importance of Mathematics, it is highly disheartening to see that, due to Mathematics anxiety, students’ mathematical thinking has remained persistently subpar in Africa. Mathematics anxiety, which is the feeling of worry, stress, and trepidation when people engage with mathematics, has long been a topic of concern in education. This study investigated the relationship between Mathematics anxiety and the mathematical thinking of students in Africa. A meta-analysis method was used to statistically analyze the results of studies yielding 1789 samples that examined the relationship between Mathematics anxiety and the mathematical thinking of students. These studies were conducted from 2005 to 2021. The findings showed a strong negative correlation between Mathematics anxiety and the mathematical thinking of students in Africa. This study's statistical findings demonstrate how the problem-solving ability of students and the reasoning of students are affected by Mathematics anxiety. These results can help education stakeholders to create environments that will enhance students' mathematical reasoning abilities. This study recommends that curriculum developers should come up with strategies for incorporating fresh perspectives into the Mathematics curriculum that will make it engaging for African students and boost their thinking to become better not just in their academics but also in their day-to-day living.

An Assessment Of High School Leavers’ Development of Mathematical Thinking

This descriptive design study evaluated the mathematical thinking attainment level of 649 High School leavers, ages 18 to 19 years, in the context of their preparation for facing the challenges of the tertiary level math curriculum. The findings depict students' low level of mathematical thinking attainment regarding their paucity in critical thinking and a lack of heuristics repertoire as a guide to employing their contextual knowledge in solving fundamental non-routine problems. These findings are a matter of concern as there seems to be a mutual exclusivity between the content learned in school and the ability of students to think mathematically. Keywords: Mathematical Thinking; Non-Routine; Problem-Solving; Heuristics eISSN: 2398-4287 © 2022. The Authors. Published for AMER ABRA cE-Bs by e-International Publishing House, Ltd., UK. This is an open-access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer–review under the responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians) and cE-Bs (Centre for Environment-Behaviour Studies), Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, Malaysia. DOI: https://doi.org/10.21834/ebpj.v7iSI8.3907

Towards Data-Driven Teaching Strategies to Develop Mathematical Thinking

Mathematics learning is not only about learning knowledge but also about cultivating mathematical thinking and learning how to think about and solve mathematical problems. Unfortunately, the way teachers evaluate students is still based on the student’s academic achievement. Many students learn by rote, which is unsuitable for developing their thinking ability at different levels. With the advent of the era of big data, teaching has become more accurate and convenient. In this paper, we analyze the student’s academic performance at different levels from the point of view of mathematical thinking. We collected the learning achievement of two classes in a middle school in Beijing. We then analyzed the overall thinking of the two classes, and the mathematical thinking level of students at different levels. Based on the analysis results, we put forward some teaching suggestions on improving mathematical thinking to help improve teaching methods and quality and promote students’ mathematical thinking development.

A Brief Analysis of the Training Countermeasures of Mathematical Number Sense in Primary School

The development of mathematical thinking has steadily become the attention of primary school mathematics teachers as the basic literacy of primary school mathematics. To promote teaching development and further deepen teaching reform, primary school mathematics teachers must change their educational concept, pay attention to the cultivation of students’ mathematical thinking in the teaching process, and create an effective teaching classroom with the help of new teaching methods and rich teaching contents. This research examines how primary school mathematics teachers cultivate kids’ understanding of numbers and proposes appropriate remedies, with the goal of serving as a model for teachers’ teaching improvement.

Use of electronic textbooks in teaching mathematics: Problems and solutions

In this article, the development of mathematical thinking and the imagination of students in the teaching of mathematics reveal the role of electronic textbooks, the requirements for them, and their types. The creation of an ET in mathematics should address the humanities and universal values as much as possible paying attention to distance learning the student cannot interact directly with the teacher. The didactic and methodological aspects of the general laws of teaching, which are determined by the teaching mathematics are interrelated and are related to the issues of the program for the implementation of ET in practice.

THE DEVELOPMENT OF MATHEMATICAL THINKING THROUGH ADAPTIVE EDUCATION: THE CASE OF A LINEAR ALGEBRA COURSE

The one-size-fits-all model is widely used in teaching and learning processes around the world. This model does not recognize students’ learning conditions and preferences. As an alternative, the adaptive education model has been developing in recent years. In mathematics, the current state of this adaptive education model is oriented to the learning of objects and algorithms and not to the development of mathematical thinking. To overcome this shortcoming, the design-based research approach was used to create and implement an adaptive learning management system framed in a module of a linear algebra course, in which adaptation was done based on modes of thinking (SIERPINSKA, 2000). The results of this implementation show that people manifest diverse modes of thinking when conceiving mathematical objects and that these modes affect the way they learn. These results also highlight some existing limitations for adaptive educational processes such as these to generate greater impacts.

Desenvolvimento do pensamento numérico através de uma seqüência didática na segunda série novo modelo educacional escolar para a segunda série

Introduction: The article aims to demonstrate the use of a didactic sequence in the Escuela Nueva model, which due to its integrating characteristics must be present at various times in the process of developing numerical thinking. Objective: To analyze the effects evidenced by the implementation of the didactic sequence in the Escuela Nueva model, in the development of numerical thinking in second grade students. Methodology: Mixed research, in the line of research: development of mathematical thinking. It was carried out with students from the second grade of primary school, between 7 and 9 years old, from the Guavio de Fusagasugá Municipal Educational Institution. Results: To achieve this goal, a pedagogical proposal was designed and applied, which consisted of a didactic sequence that contains three sessions, where cooperative work is used, the game as a motivating agent, the use of didactic material that in turn is conducive to the students activities such as counting, numbering, relating, comparing, performing mental calculations as well as the use of addition and subtraction operations, which offered opportunities to enhance students' numerical thinking. Conclusions: Continuous and effective commitmentwas demonstrated, which allows to initiate a process of methodological and didactic change in the teaching and learning process in the area of mathematics, taking advantage of and adapting all the resources of the institution and the community, such as: physical spaces, didactic material and development of a playful pedagogy that allowed the interaction of students and teachers for the development of numerical thinking, demonstrating that through a didactic sequence, students build knowledge, make numerical relationships and learn significantly.

USE OF COMPUTER TOOLS TO DEVELOP MOTIVATION OF STUDENTS TO STUDY MATHEMATICS: CRITERIA OF EFFICIENCY

The article considers the problem of development of cognitive activity of students in mathematics lessons. The peculiarities of the use of the formative system of assessment in the process of teaching mathematics with the use of computer tools in the context of the tasks of personality-oriented learning. The main risk factors for increasing the mathematical anxiety of students are identified. The pedagogical factors of motivation development and increase of interest in learning, development of mathematical thinking and reduction of mathematical anxiety due to the development of methods to increase the clarity of learning and cognitive activity of students related to the use of computer tools are substantiated. The criteria are substantiated and the indicators of assessment of the development of cognitive activity of students of 7‒9 grades of gymnasiums in the process of teaching mathematics with the use of computer tools are distinguished: motives of students learning at school; interest in studying the study of mathematics (algebra and geometry); success in the study of mathematics (algebra and geometry); motivation to study mathematical disciplines; mathematical anxiety. A method of assessing the impact of the use of computer tools to study certain topics and sections of mathematics in grades 7‒9 in general secondary education, which will increase the motivation of students to study the subject and reduce the level of mathematical anxiety of students. The results are presented and the dynamics of the indicators of the experimental influence of the use of computer interactive tools on the motivation of students to study mathematics is analyzed.
 Keywords: personality-oriented learning; mathematical disciplines; mathematical anxiety; pedagogical conditions; mathematics teaching aids; motivation to study mathematics; interactive computer learning tools; success in the study of mathematics.

Origins and development of the Maria Montessori’s mathematical proposal

The introduction of complex mathematical concepts through perceptual and sensorial hands-on experiences is one of the most relevant aspects of the Montessori method proposal. This article aims to investigate the origins of the Montessori’s profound interest for mathematics, studying the history of the education of mathematics, after the unification of Italy, in which her school education took place. Her key concepts and beliefs about the learning of mathematics and, furthermore, the evolution of her proposal will be illustrated through the analysis of her main publications, both the generalist and the specialized ones in the field of mathematics (Psicoaritmetica and Psicogeometria), and handwritten notes about the lessons of XVI° international course, held in Rome in 1931, which the Opera Nazionale Montessori acquired from her students’ archives. Finally, an overview of the actualization of the Montessori method in the contemporary research will be explained, particularly focusing on the neuroscientific discoveries which have proved the effectiveness of the Montessori proposal to empower the cognitive processes involved in the development of mathematical thinking.

The effectiveness of an educational program based on the Brunner model in developing problem solving and mathematical thinking in mathematics for tenth grade female students in the Karak District Education Directorate: فاعلية برنامج تعليمي قائم على نموذج برونر في تنمية حل المشكلات والتفكير الرياضي في مادة الرياضيات لدى طالبات الصف العاشر الأساسي في مديرية تربية منطقة الكرك

The study aimed to uncover the effectiveness of an educational program based on the Bruner model in developing problem-solving, mathematical thinking and motivation in mathematics among tenth grade students in the Karak Education Directorate, and to achieve the objectives of the study the quasi-experimental approach was used by dividing the study sample into two groups, experimental and control groups, and the study sample consisted of (150) students who were randomly selected, and a set of tests were developed include solve problems test, mathematical thinking test, and motivation questionnaire. The study reached results, the most important of which are: There are statistically significant differences at the level of significance (α≤0.05) in the development of problem solving in mathematics among the tenth grade students in the Directorate of Education of the Karak due to the teaching method, and in favor of the students of the experimental group, and there are statistically significant differences at the level of significance (α≤0.05) in the development of mathematical thinking in mathematics among the tenth grade students in the Directorate of Education of the Karak due to the teaching method, and in favor of the students of the experimental group. In the light of the results, the study recommended that officials in the Ministry of Education should be interested in developing the teaching strategies used in teaching mathematics with a focus on the Brunner model due to its great and positive effect in improving students ’understanding and comprehension of mathematical content.