Problems In Mathematics Education Research Articles

Eye movements in conceptual and non-conceptual thinking

AbstractHow to influence and assess whether students engage in conceptual thinking are longstanding methodological problems in mathematics education. Recently, eye-tracking technology has fueled a discussion on whether eye movement analysis can support valid inferences about mathematical thinking. This study investigates whether eye movement analysis can distinguish between conceptual and non-conceptual thinking in a geometric classification task where both modes of thinking lead to identical responses. Participants were asked to classify geometric shapes while we tracked their eye movements and to report their thinking verbally. Our findings indicate that self-reported conceptual thinking is characterised by fewer eye movements between task shapes and response shapes, and that self-reported non-conceptual thinking involves comparing the shapes’ similarity directly. A logistic regression model correctly classified the self-reported ways of thinking in 80.3% of the cases. We conclude that eye-tracking can contribute to making inferences about mathematical thought processes and facilitate research on how to engage students in conceptual thinking and development.

GAME EDUKASI AUGMENTED REALITY BERBASIS RME (REALISTIC MATHEMATICS EDUCATION) UNTUK MENINGKATKAN COMPUTATIONAL THINKING SISWA

This research addresses the common problem in mathematics education in Indonesia, which is the students' difficulties, as reflected in Indonesia's declining ranking in the Program for International Student Assessment (PISA). The research aims to create an innovative Augmented Reality (AR) Educational Game based on the Realistic Mathematics Education (RME) approach to improve students' understanding of the spatial geometry mathematics subject at the elementary school level. AR technology allows students to interact with mathematical objects in real-world contexts using Android devices. This game is designed to make mathematics more engaging and relevant to elementary school students. The research was conducted at Purwantoro 1 Public Elementary School in Malang City over four months, following the Game Development Lifecycle (GDLC). The test results showed an n-gain improvement of 0.71, indicating a positive impact of the game's development on students' learning outcomes.

Lower average estimate for the minimum modulus on circles foran entire function of genus zero

The article was written based on the materials of the joint report of the authors, made by them at the Sixth International Conference “Functional spaces. Differential operators. Problems of mathematical education,” dedicated to the centenary of the birth of Corresponding Member of the Russian Academy of Sciences, Academician of the European Academy of Sciences L.D.Kudryavtsev. For an entire function represented by a canonical product of genus zero with positive roots, the following result is proved. For any \(\delta\in(0,1/3]\), the minimum modulus of such a function exceeds on average the maximum of its modulus raised to the power \(-1-\delta,\) on any segment whose end ratio is equal to \(\exp(
 2/\delta).\) The main theorem is illustrated by two examples. The first of them shows that instead of the exponent \(-1-\delta\) it is impossible to take \(-1.\) The second example demonstrates the impossibility of replacing the value \(\exp(2/\delta)\) by the value\(28/(15\delta)\) in the theorem for small \(\delta.\)

An Analyzing critical thinking skills using the context of the learning package for students of Madrasah Tsanawiyah Negeri 2 Jambi

Indonesia is a country that is also a participant in PISA, the fact is that even though it has known PISA for a long time, it still experiences a slump, especially the upper level PISA caused by many factors. Among them can be seen in the findings of PISA in 2018 where Indonesiais in the Low Perfomence quadrant with High Equity, then also Gender Gap Performance and also learning conditions in schools that are still in the zone of very simple math problems. This concludes that students in schools have not fully explored cognitive abilities in solving mathematical problems that are analytical, especially. The problem of low mathematical ability of students in solving a contextual problem in mathematics learning is the biggest problem in mathematics education in Indonesia. This study aims to analyze the critical thinking ability of students using the context of learning packages. This research is a quantitative descriptive type with the population of this study is students of class VIII Madrasah Tsanawiyah Negeri 2 Jambi City. The data collected is Student test results.

THE USE OF STEM TECHNOLOGIES IN MATHEMATICS LESSONS WITH VISUALLY IMPAIRED HIGH SCHOOL STUDENTS

The article highlights the problem of teaching mathematics classes for high school students with low vision, a study of factors limiting the participation of visually impaired schoolchildren in the field of mathematics, an analysis of thematic literature, the results of modern scientists in the field of using STEM technologies in mathematics lessons (Mbulaheni Maguvhe, M S Oyebanji & Ubong Sam Idiong) are summarized. Since the teacher is still one of the most important and influential factors in the formation of a child’s personality, it is important to investigate the problems of teaching mathematics to visually impaired students. Scientists have found that while technology is being incorporated into the teaching of mathematics, responsibility for its use is also evolving. Visually impaired students may experience problems in mathematics education due to the lack of accessible materials designed to support a conceptual understanding of mathematics. The purpose of our study is to summarize modern evidence-based knowledge about electronic and digital technologies for teaching mathematics among children with low vision. In addition, with the advent of digital technology student rewards have also changed. Many students today are offered computers equipped with increasingly sophisticated software, dynamic geometry and web applications that offer virtual teaching. The new educational landscape has great potential to empower students to improve learning. And in our case – to meet the needs of schoolchildren with a reduced level of vision. Assistive technology has become a tool for the exploration and study of mathematics in various areas of the curriculum. Some programs may cover many areas of mathematics, while others are designed to in-depth study of only one area. The programs are filled with content that can be customized for a wide range of learning modes, guiding the student step by step towards more open exploration. The advent of technologies of wider mathematical expressiveness has managed to influence the range of curriculum topics. Digital tools “empty of content” such as spreadsheets, graphing software, computer algebra systems (CAS) are technologies that are loosely associated with specific learning contexts, but are suitable for mathematical calculations, material creation and intelligence. These tools are more commonly used by middle and high school students. This article reflects examples of possible options for STEM technologies in teaching mathematics to high school students with a reduced level of vision.

Teaching school mathematics to prospective teachers

What kind of mathematics should be taught to prospective mathematics teachers has been a longstanding open problem in mathematics education. We contend that we should teach them exactly what they need for their work: school mathematics

Investigation Of Students’ Metacognitive Awareness Failures About Solving Absolute Value Problems in Mathematics Education

Investigation Of Students’ Metacognitive Awareness Failures About Solving Absolute Value Problems in Mathematics Education

METHODOLOGICAL ASPECTS OF TEACHING MATHEMATICS BASED ON THE RESULTS OF MONITORING RESEARCH

The article reviews the actual problems of mathematics education. The difficulties encountered by a modern schoolchild when solving tasks of monitoring research in mathematics are indicated. Methodological recommendations are given that should increase the productivity of interaction between a modern teacher and a modern schoolchild, and, accordingly, the quality result of training, through the improvement of pedagogical techniques, an increase in the level of professionalism of teachers, their motivation, initiatives, the creative and emotional component of the educational process, professional competence of the teacher.

Characterizing the Role of Technology in Mathematics Teachers’ Practices When Teaching About the Derivative

A current research problem in mathematics education is the characterization of the role of teachers in the processes of technology integration in mathematics classrooms. This article shows how two secondary mathematics teachers taught the concept of derivative of a function at a point and the concept of derivative function, one of them using digital technology and the other one without using it. Their teaching was characterized by describing their hypothetical learning trajectories (learning goals, learning activities and the hypothetical learning processes). APOS theory (which stands for Action, Process, Object and Schema) was used to describe the hypothetical learning processes. The results showed that the use of digital technology in class may promote reflection among students without excessive computations, thus helping them to construct the concept of derivative.

Categories to Assess the Understanding of University Students about a Mathematical Concept

Background: One of the problems in mathematics education is students’ little understanding of mathematics both at the basic and higher educational levels, which is why we consider essential the design of adequate instruments and methods that can measure understanding about specific concepts. Objective: To assess the understanding of university students of the concept of a real function. Design: The research is qualitative as the attributes of a cognitive construct were analysed and interpreted. Setting and participants: There were 36 students of a degree in mathematics (18-20 years old) whose productions were analysed. All the students had taken the Calculus I course. Data collection and analysis: A test of six items related to tasks that involved the concept of function was applied, the data analysis was carried out from the evaluation categories proposed by Albert and Kim, who consider three categories to assess understanding, those being: the ability to justify, to understand why a particular mathematical statement is true, and to understand where a mathematical rule comes from. Results: The evaluation of the understanding of the concept of function has shown that, in order to achieve a high understanding, not only skills must be developed for the recognition of aspects of the function such as its definition, its discrimination or its application, but the ability to be able to justify such aspects must be considered too. Conclusion: The categories of understanding considered help to strengthen conceptual and procedural understanding, indicating comprehensive understanding.

Why teach mathematics? – A study with preservice teachers on myths around the justification problem in mathematics education

In this article we report on a study focused on revealing and categorizing the arguments that preservice mathematics teachers put forward when they are asked about why mathematics is taught, which is a question closely related to the justification problem in mathematics education. Another focus of the study is the identification of myths within such arguments. The study is based on semi-structured interviews with 19 preservice mathematics teachers from Mexico. The results show that the arguments of the future teachers to justify the teaching of mathematics can be divided into three categories: (1) mathematics is related to the development of mental or thinking skills, (2) mathematics is useful for daily life, and (3) mathematics fosters positive attitudes and emotions. On the other hand, a presence of myths was identified in the arguments of the prospective teachers, namely: (1) the myth of reference, (2) the myth of participation, (3) the myth of importance, and (4) the myth of cognitive development. The report concludes by discussing the results and pointing out some future research routes.

PROFIL BERPIKIR RELASIONAL DALAM PEMECAHAN MASALAH MATEMATIKA SISWA SMA DITINJAU DARI GAYA KOGNITIF REFLEKTIF DAN IMPULSIF

Relational thinking is one of the interesting problems in mathematics education, this is motivated by the students low relational thinking ability. The characteristic of relational thinking is that students can think by building relationships from various objects/contexts that are related to each other. This type of research is qualitative descriptive research. The analysis of data in this study was done by reducing MFFT test data, troubleshooting tests and interviews, data presentation, and withdrawal conclusions. The subject of this research is two students grade XI of SMA Negeri 15 Surabaya in 2020/2021 year with trigonometric ratio material. In this research, the way students thinking with relationally can be seen from how students build the relationship of information in identifying problems as a whole because there is a possibility of students writing information in full or not also the different concepts they used. Subjects with a reflective cognitive style redrawed the problem to make it easier to solve the problem, while subjects with an impulsive cognitive style only wrote briefly what was known on the problem. The relational way of thinking of reflective cognitive style subjects is more visible than the impulsive cognitive style subjects. One subject mistakenly used the settlement plan. Both of them checking back on the completion of each answer sheet, but the focus of checking is different.
 Keywords: Cognitive style, Impulsive, Problem solving, Reflective, Relational thinking

Проблемы математического образования и их решение

Проблемы математического образования и их решение

Geometry learning in vocational high school: Investigating the students’ difficulties and levels of thinking

Student’s difficulties and low-level thinking in geometry topic is not a new problem in mathematics education. It is portrayed on student’s low achievement both on national and international tests. Van Hiele’s model has been used as a useful framework to justify student’s difficulties as well as their level of thinking in geometry. Therefore, the aim of this study to investigate student’s difficulties and level of thinking using Van Hiele’s theory. Participants in this study were 12th grades vocational high school students. This study is descriptive qualitative research with a phenomenology approach. Data has been collected through a test and interviews. Further, the obtained data were analyzed by looking for a specific theme, then, the researcher found the inter-theme relationship in order to gain a proper understanding of student’s difficulties in geometry and level of student’s geometrical thinking. Based on data analysis, there are some difficulties faced by the student such as, unable to properly identify the geometry shapes based on their formal definition, lack of visualization ability, failed to understand specific terms or symbols of geometry, insufficiency in providing proper reasoning related relationship within geometric shapes. Moreover, it can be concluded that most of the students are on Level 1 of geometry thinking.

The Concept of Theoretical-Empirical Dualism in Teaching Math

Among the problems of mathematical education, the article highlights: (1) insufficient attention paid to the fundamental, structure-forming role of mathematics; (2) speculative learning, its isolation from practice. The concept of theoretical-empirical dualism in teaching is formulated as the unity of the abstract-theoretical and experimental-empirical cognitive activity of students. According to the author, a priori and a posteriori mathematical knowledge should be distinguished. A priori knowledge either seems to an individual to be completely obvious, indisputable, or he assimilates it uncritically, “on faith”. A posteriori mathematical knowledge subjectively arises in the process of student’s intense theoretical and practical activity, and is being actively and comprehensively verified experimentally – either using mathematical applications, or through mathematical experiments. The empirical component of teaching mathematics implies a variety of forms and methods of active (including computer) and professionally oriented learning, giving experience in independent formulation of problems, joint search for ways to solve them, interaction and teamwork. Particular attention is paid to the use of mathematical experiments in those frequent cases when it is necessary to replace or supplement complex evidence, illustrate new knowledge, and give research skills. Monte Carlo mathematical experiments are demonstrated, which serve, in particular, as a bright, figurative, and convincing form of reinforcing theoretical knowledge in the field of stochastic branches of mathematics. The research work of students is considered as the highest stage of the students’ theoretical-empirical activity. The article proposes subjects of research activities of students in the process or upon completion of the study of probabilistic and statistical disciplines.

LESSONS IN GRADE 10 MATHEMATICS FOR USE IN A FLIPPED CLASSROOM

Low-performance, insufficient instruction time and difficulty in providing instructional needs for diverse learners are some of the prevalent problems in mathematics education. Flipped Classroom is a rising pedagogical model that exhibits promising features in battling these dilemmas. This study aimed to develop lessons that integrates flipped classroom, uses student collaboration and incorporates contexts from students' culture and experiences. Mainly, this study provided ways on how teachers from rural areas with less technological accessibility, can implement this instructional model through the use of materials and platforms available in their community. The mixed method of research was used. Qualitative approach was utilized in the analysis of students’ responses in their interviews and journals and the quantitative approach was done through pre-experimental design. Interviews to teachers and analysis of available data in the chosen school were done to know which topics are to be included in the study. The identified topics were examined to develop lessons that are best suited for the use of the model to Grade 10 Geometry. Ten lessons were made and implemented to a Grade 10 class to determine its effect on their task performance, conceptual understanding and problem-solving skills.  Effects on study habits and interest were determined using interviews, journals and inventory. Results show that there is a significant difference on the performance of the students, within the considered constructs, before and after being exposed to flipped classroom. Moreover, positive change on responding to tasks, greater initiative to take part and higher interest levels were also revealed. The implementation of flipped classroom has deepen their understanding, positively affected the way they perceive and react to tasks, boost their interest and taught learners the accountability of their own learning. Additionally, availability of learning resources at home and support from knowledgeable others are important factors that help improve students’ performance.

Word problems in mathematics education: a survey

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and debates that have dominated the field. After a short introduction, we begin with research that has conceived word problems primarily as problems of comprehension, and we describe the various ways in which this complex comprehension process has been conceived theoretically as well as the empirical evidence supporting different theoretical models. Next we review research that has focused on strategies for actually solving the word problem. Strengths and weaknesses of informal and formal solution strategies—at various levels of learners’ mathematical development (i.e., arithmetic, algebra)—are discussed. Fourth, we address research that thinks of word problems as exercises in complex problem solving, requiring the use of cognitive strategies (heuristics) as well as metacognitive (or self-regulatory) strategies. The fifth section concerns the role of graphical representations in word problem solving. The complex and sometimes surprising results of research on representations—both self-made and externally provided ones—are summarized and discussed. As in many other domains of mathematics learning, word problem solving performance has been shown to be significantly associated with a number of general cognitive resources such as working memory capacity and inhibitory skills. Research focusing on the role of these general cognitive resources is reviewed afterwards. The seventh section discusses research that analyzes the complex relationship between (traditional) word problems and (genuine) mathematical modeling tasks. Generally, this research points to the gap between the artificial word problems learners encounter in their mathematics lessons, on the one hand, and the authentic mathematical modeling situations with which they are confronted in real life, on the other hand. Finally, we review research on the impact of three important elements of the teaching/learning environment on the development of learners’ word problem solving competence: textbooks, software, and teachers. It is shown how each of these three environmental elements may support or hinder the development of learners’ word problem solving competence. With this general overview of international research on the various perspectives on this complex and fascinating kind of mathematical problem, we set the scene for the empirical contributions on word problems that appear in this special issue.

Students' Relational Thinking in Solving Word Problem Based Cognitive Style

This study is motivated by students' low relational thinking ability. Relational thinking is one of the interesting problems in mathematics education. In this study will be examined the ability of relational thinking field-dependent and independent students in solving the arithmetic word problem. The method used in this study is qualitative descriptive. This research was conducted on 7th-grade of junior school students of Surabaya. The subjects of this study were 1 student who had a field-independent cognitive style and 1 student who had a field-dependent cognitive style. The data of the students' relational thinking process is obtained through the results of solving arithmetic word problem and interviews. Subject selection is done using instrument group embedded figures test. The results of the research showed that students with cognitive field-dependent experiences had difficulties in thinking and have not been able to establish the relationship between information elements and previous knowledge to solve problems. Whereas students with independent field cognitive styles were capable of relational thinking, namely by building interrelationships between elements of information and prior knowledge and knowledge of the properties of structure to solve problems.

Pre-service mathematics teachers’ knowledge, beliefs, and attitude toward using PISA-based problem in mathematics education

Attitude and belief have been considered as particularly important aspects in building students’ academic achievement. The current study aimed to examine Pre-Service Mathematics Teachers’ (PSMTs) general knowledge of PISA and their attitudes and beliefs towards using PISA-based problem in mathematics education based on their year level in teacher education programs. The sample included a total of 146 PSMTs in mathematics teacher education program from nine Universities in Indonesia. Data were collected through the knowledge of PISA test and Attitudes and Beliefs Questionnaires. From this study we revealed the poor score results of PSMTs knowledge of PISA. However, generally the female scores improve along with the increasing of year level education. On contrary, we found the opposite result showed by male subject. This indicate that the teacher education program needs to improve the PSMTs PISA skills and knowledge. PSMTs have a positive belief and attitude towards the use of PISA-based problems in learning. However, the positive belief and attitude is at the lowest indicator. This is most likely because of poor knowledge of Pre-service teacher on PISA itself. This is appearing from most of them that are rare or even never read PISA result development. Additionally, it was inferred that females scores better than males in both, knowledge also belief and attitude. In conclusion, the Pre-service teachers’ positive attitude and belief towards using PISA-based Problem emphasize that the importance of teacher education program for preparing the pre-services teachers implementing this alternative learning strategy.

MATHEMATICS CURRICULUM: AN OVERVIEW OF EDUCATIONAL CURRICULUM IN SIERRA LEONE

In Sierra Leone, Mathematics is core subject in all stages of schooling. This paper highlights the significant of Mathematics in education. Besides, it gives an overview of education, with a flash on the historical background of mathematics under consideration. The paper went on to show Mathematics Teaching Curriculum, the aim and objectives of teaching mathematics nationally. Moreover, there is flash on the scope of mathematics syllabus for secondary school, approaches to teaching and learning of mathematics in Sierra Leone. In a clearer picture, the paper measures Mathematics Teachers Training Colleges, the problems of mathematics education, and the remedy to mathematics education in Sierra Leone. In conclusion, recommendations for the improvement and developments of mathematics education in Sierra Leone were made. Article visualizations: