Mathematical Competence Research Articles

Investigating Students' Problem Solving Achievements, the Modeling Steps reached and Modeler Types in the Process of Mathematical Modeling Activities

The aim of this study is to identify the effect of mathematical modeling activities applied as action plans on the development of students' achievement in solving algebraic verbal problems, as well as to investigate the mathematical modeling competencies they use during these mathematical modeling activities and the modeling steps they reach. Moreover, the types of mathematical modelers that the students demonstrated during this application process were examined in the study. The study was conducted as an action research with a total of 15 7th grade students in rural areas. It was aimed to reveal the mathematical modeling competencies that students achieved during mathematical modeling activities through observations, researcher and student diaries, as well as interviews conducted with students. Content analysis was implemented to analyze the data. During the study, the mathematical modeling competencies demonstrated by the students in each mathematical modeling activity and the mathematical modeling steps they reached were identified. As a result of the study, it was confirmed that students' mathematical modeling competencies were related to competencies such as general mathematical knowledge or verbal comprehension, and it was also revealed that students' mathematical knowledge competence could be examined in more detail. It was also observed that students could achieve competencies through group work and it was found that students' success in solving the verbal algebraic problems generally improved based on their mathematical modeling competencies.

Establishing benchmarks for assessing early mathematical competence in children

Establishing benchmarks for assessing early mathematical competence in children

Extended Learning through After-School Programs: Supporting Disadvantaged Students and Promoting Social Sustainability

After-school programs in Romania are not mandatory, and most of the time, they are funded by parents. In Romania, over 41.5% of students come from disadvantaged families that cannot afford to finance after-school activities. In recent years, there have been only a few free after-school programs for disadvantaged students. Our study aimed to measure the impact of such an after-school program, which mostly uses alternative teaching methods, on several aspects of learning improvement at the level of disadvantaged students in primary and secondary education. The research results revealed a significant improvement in the education of children after they participated in after-school programs for a large range of learning results. Among the intervention actions, mathematical competencies, basic competencies in science and technology, and digital competencies were identified as the main predictors of high learning performance. The results also revealed that a longer length of such programs had a positive effect on educational performance and the socio-emotional development of disadvantaged students. It was also shown that the impact of intervention is more pronounced in the case of young students and adults who followed the “Second Chance” programs. The results support the effectiveness and importance of such projects in promoting holistic and sustainable education and in providing valuable information to decision-makers regarding the impact of after-school programs on the education of disadvantaged people to improve social sustainability.

Assessing Data Literacy Competencies in Mathematics Among Junior High School Students in Yogyakarta City

This research aims to assess students' data literacy skills, focusing on their ability to translate data from one format to another, comprehend data-related problems, analyze strategies for data-driven problem-solving, predict outcomes based on data, draw conclusions, and construct arguments grounded in data. The study employs a survey methodology with both quantitative and qualitative approaches. A total of 362 students from various educational levels in Yogyakarta's state junior high schools were surveyed and selected through stratified and proportionate random sampling techniques. Data were collected using a test instrument comprising six questions designed to measure different aspects of data literacy, alongside interview results. The students' data literacy was categorized into high, medium, and low levels. The findings indicate that a significant majority (95%) of students exhibited low data literacy, particularly struggling with drawing conclusions and constructing arguments based on data. Students with high data literacy skills successfully met all the indicators. Those with medium-level skills performed well on most indicators but faced difficulties in choosing strategies for data problem-solving and drawing conclusions, often due to insufficient time for deeper reflection. Conversely, students with low data literacy struggled to meet any of the indicators effectively.

Modelo pedagógico basado en el constructivismo para desarrollar la competencia resolución de problemas en estudiantes de Ingeniería

The purpose of this study is to propose a pedagogical model to improve mathematical problem-solving competence in mining engineering students. The approach used was qualitative and applied research, propositional modality. The research was carried out in two phases. The diagnosis was carried out with a sample of 40 second cycle students. The sampling was non-probabilistic. The data were taken from an auxiliary register. The model proposal took into account the foundations, characteristics, design, description of the components, methodological guidelines for application and evaluation of the model. The results show that the level of achievement of problem-solving skills is high. The use of the pedagogical model allowed the development of problem-solving skills. The development of declarative content allowed us to have the necessary theoretical foundation to propose solutions to the problem linked to procedural content, allowing self-learning to be promoted through active strategies: thus, the attitudinal content will also allow us to organize favorable learning environments to develop a positive attitude towards the math.

Implementation of the practice-oriented mathematics teaching methodology to future rescue engineers

Introduction. In modern conditions, the practice-oriented training of rescue engineers, whose professional activities are associated with high-risk situations, is being updated. The purpose of the study is to describe the implementation of the author's methodology of practical-oriented training in mathematics of future specialists in fire and technosphere safety and experimental verification of efficiency. Materials and methods. The experimental training was attended by 685 students of the Donetsk Institute of the State Fire Service (Russian Federation), studying in the specialty "Fire safety" and the areas of training "Technosphere safety" (321 students in experimental groups, 347 in control groups). Methods of mathematical statistics: Wilcoxon signed-rank test, Fisher's exact test, Chi square test, Student's t-test. Results. The methodology of practice-oriented teaching mathematics to future rescue engineers has been developed. Mathematical training of students based on a practice-oriented approach ensures the formation of students' practice-oriented skills and mathematical modeling skills in the field of civil protection, as well as the development of personal qualities of a rescuer. Practice-oriented learning technologies are used: integration of educational and future professional activities of students, educational and practice-oriented research activities. Practice-oriented teaching methods are used (imitation of the practical activities of rescue engineers, "rapid response" and practice-oriented visualization of mathematical objects). The implementation of the developed teaching methodology contributes to the effective formation of practice-oriented mathematical competence among students (T = 0.32, α = 0.05). Conclusions. The implementation of practical-oriented training in mathematics of future specialists methodology in fire and technosphere safety contributes to increasing the level of development of practical-oriented mathematical competence due to the formation of personal qualities of the rescue engineer and his value orientations, knowledge of mathematical and practical-oriented knowledge, skills and methods of activity in mathematical and computer modeling.

Mathematical Literacy as a Key Competency for Maritime Education: Systematic Review of Cadet Competencies

This study discusses the role of mathematical literacy as the main competency that cadets need to have in the field of maritime education. Through a systematic literature review (SLR), the mathematical literacy competencies needed by cadets in the maritime field are navigation, problem solving, use of modern technology, operational management, critical and logical thinking, and accurate data-based decision making. This systematic review provides an illustration of literacy mastery Mathematics not only supports cadets' understanding of basic maritime concepts, but also improves cadets' abilities in dealing with challenges or unexpected situations on board ships and while at anchor. Therefore, developing mathematical literacy must be a priority in cadet education and training programs to produce graduates who are competent and ready to face the complexity of the global maritime industry.

PHÁT TRIỂN NĂNG LỰC GIAO TIẾP TOÁN HỌC CHO HỌC SINH LỚP 10 TRONG DẠY HỌC CHỦ ĐỀ PHƯƠNG PHÁP TỌA ĐỘ TRONG MẶT PHẲNG

Mathematical communication is one of the core competencies that needs to be formed and developed for students in the teaching of Mathematics in high schools. In this research, we have identified the manifestations of mathematical communication competence in 10th-grade students in teaching the topic “Coordinate Methods in the Plane”, based on a survey of opinions from 68 high school mathematics teachers in the provinces of Nghe An and Ha Tinh. Additionally, the research was also conducted with 32 10th-grade students who were assigned several learning tasks related to the topic “Coordinate Methods in the Plane”, with the aim of understanding the manifestations of students’ mathematical communication competence and the mistakes they made related to these manifestations. From there, propose several teaching methods to contribute to the development of mathematical communication competence in students in teaching this topic. Keywords: Mathematical communication competencies; 10th-grade students; coordinate methods in the plane.

Effectiveness of Problem-Based Learning to Develop Mathematical Competencies at the Postgraduate Level

The objective of the article is to determine the effectiveness of PBL to develop the mathematical competencies of postgraduate students. The methodology used was quantitative with a correlational scope. The study participants were a total of 29 postgraduate students in administration. The instrument used was the questionnaire to obtain information on the effectiveness of PBL. The data were organized with the SPSS 25 statistical program that allowed us to calculate: descriptive statistics such as the mean (M) and standard deviation (SD), the Shapiro-Wilks test and Pearson correlations (r) with a level of significance (p) of 0.05. The main results are: The significant direct associations were greater satisfaction regarding the use of technology (r = 0.789, p = 0.00); with their academic performance (r = 0.854, p = 0.00); promote collaborative work (r = 0.811, p = 0.00); encourage mathematical learning (r= 0.791, p = 0.00); analyze and discuss the contents through problems (r = 0.825, p =0.00).

Systemic preparation of future mathematics teachers for training schoolchildren to solving Olympiad problems

The article actualizes the problem of developing the readiness of a future mathematics teacher to teach schoolchildren to solve Olympiad problems. Based on the analysis of scientific and methodological sources and the results of mathematics students’ self-assessment of their readiness for this type of activity, the need for a systematic approach to solving the identified problem is substantiated. The study outlines the author's view of the university training system aimed at developing future mathematics teachers with mathematical and methodological competencies that determine their readiness to teach schoolchildren to solve Olympiad problems, and outlines the problems that may arise during its implementation.

What pupil size can and cannot tell about math anxiety.

Math Anxiety (MA) consists of excessive fear and worry about math-related situations. It represents a major barrier to numerical competence and the pursuit of STEM careers. Yet, we currently do not dispose of many tools that can capture its multifaceted nature, e.g. moving beyond the exclusive reliance on self-reports and meta-cognition. Here we sought to probe Pupil Size (PS) as a viable tool in the study of MA by administering arithmetic problems to university students in the humanities (N = 70) with various levels of MA. We found that arithmetic competence and performance are indeed negatively associated with MA, and this is accurately tracked by PS. When performance is accounted for, MA does not further modulate PS (before, during, or after calculation). However, the latency of PS peak dilation can add a significant contribution to predicting MA scores, indicating that high MA may be accompanied by more prolonged cognitive effort. Results show that MA and mathematical competence may be too crystalized in young university students to be discernible. We therefore call for early educational interventions to tackle and mitigate this dysfunctional association early on.

A Relational Frame Theory-Based Intervention for Improving Reading and Mathematical Competencies Among School Children

A Relational Frame Theory-Based Intervention for Improving Reading and Mathematical Competencies Among School Children

Project-Based Learning Model: Its Implication in The Initial Training of Mathematics Teachers

Objective: The objective of the study was to analyze the benefits of a study curriculum under the competency-based approach and to analyze the implications of the implementation of the project-based learning model in the initial training of mathematics teachers in the context of university higher education. Theoretical Framework: The concepts related to the project-based learning model, its characteristics, its phases and educational competencies in the twenty-first century are systematically addressed. The relevance of the curriculum under the competency approach in university education is also analyzed from a critical perspective. Method: The research approach was mixed, non-experimental design, 30 teachers and 54 students in initial training for mathematics teachers participated in the study; the data were collected through a Likert questionnaire, the analysis and interpretation of the results was carried out with the Minitab software, complemented with the information from the semi-structured interview applied to the teachers. Results and Discussion: On average, more than 77% of teachers and more than 72% of students who attended the study have a favorable opinion about the implementation of project-based learning (PBL) in university education; therefore, it favors and strengthens the development of mathematical skills and competencies in the initial training of mathematics teachers based on the realization of mathematicsof tasks and problem solving through collaborative activities for efficient learning of mathematical concepts and procedures. Research Implications: This research highlights the importance of the project-based learning model from the theoretical and practical perspective of competency-based curricular implementation. Theoretically, the concepts of project-based learning are deepened and contextualized, while the practical implication translates into collaborative work between students and the teacher in problem solving. Originality/Value: The findings value the PBL model as a viable alternative for the efficient initial training of secondary school mathematics teachers, with a broad mastery of conceptual, procedural and digital technology knowledge in problem solving.

Correction: Longitudinal and reciprocal links between metacognition, mathematical modeling competencies, and mathematics achievement in grades 7–8: A cross-lagged panel analysis

Correction: Longitudinal and reciprocal links between metacognition, mathematical modeling competencies, and mathematics achievement in grades 7–8: A cross-lagged panel analysis

Mathematical competencies in the digital era

The paper begins with a discussion of the characteristics of digitization that influence school mathematics, its goals and practices: the digitization of everything, the invisibility of computation, the era of big data and information on everything, and changes in the social role of mathematics due to increased global competitiveness. This leads directly to Theme 1, where we discuss the diminished economic and personal value of the ability to carry out routine mathematical procedures from arithmetic to calculus. Two other themes are then discussed: the reorientation of school mathematics content to support students to solve real world problems, and the need for students to understand about how mathematics can provide insight into real world problems, even when they are not able to actually do this themselves. These themes are only three of the many aspects of mathematical competence in the digital era which might have been chosen for discussion.

PISA 2022. Predictores de la competencia matemática de los estudiantes españoles de Educación Secundaria

Mathematical competence is fundamental for active, participatory and engaged participation in the 21st century, and for facing the challenges of a globalised society. This study aims to analyse the simultaneous effect of a set of predictors on the mathematical competence of Spanish students who have participated in PISA 2022. The sample consists of 28,792 Spanish students (14,465 boys, 50.24%; 14,327 girls, 49.76%), from 935 schools. Two questionnaires are used to collect data: one for students and one for school principals. A hierarchical linear model is used according to the three levels presented by the data (Level 1=Students, Level 2=School and Level 3=Autonomous Community). At the first level, sex, socio-economic background, family cultural level, mathematics anxiety and self-efficacy is included; at the second level, the socio-economic background of the school; and at the third level, GDP per capita. The results show that girls experience more anxiety and less self-efficacy in mathematics than boys. The socio-economic background of the students, the cultural level of the family, mathematics anxiety and mathematics self-efficacy are significant predictors of mathematical competence. At school level, socio-economic background has an impact on achievement. These findings suggest the need to strengthen collaboration between school and family, as well as to provide specific training for teachers on how to address socio-affective feelings towards mathematics.

PISA 2022. Predictors of the mathematics achievement of Spanish students in Secondary Education

Mathematical competence is fundamental for active, participatory and engaged participation in the 21st century, and for facing the challenges of a globalised society. This study aims to analyse the simultaneous effect of a set of predictors on the mathematical competence of Spanish students who have participated in PISA 2022. The sample consists of 28,792 Spanish students (14,465 boys, 50.24%; 14,327 girls, 49.76%), from 935 schools. Two questionnaires are used to collect data: one for students and one for school principals. A hierarchical linear model is used according to the three levels presented by the data (Level 1 = Students, Level 2 = School and Level 3 = Autonomous Community). At the first level, sex, socio-economic background, family cultural level, mathematics anxiety and self-efficacy is included; at the second level, the socio-economic background of the school; and at the third level, GDP per capita. The results show that girls experience more anxiety and less self-efficacy in mathematics than boys. The socio-economic background of the students, the cultural level of the family, mathematics anxiety and mathematics self-efficacy are significant predictors of mathematical competence. At school level, socio-economic background has an impact on achievement. These findings suggest the need to strengthen collaboration between school and family, as well as to provide specific training for teachers on how to address socio-affective feelings towards mathematics.

A holistic framework to model student's cognitive process in mathematics education through fuzzy cognitive maps

This study introduces a pioneering framework for modeling students' cognitive processes in mathematics education through Fuzzy Cognitive Maps (FCMs). By integrating key educational theories—Duval's Semiotic Representation Theory, Niss's Mathematical Competencies, Marton's Variation Theory, and the broad Engagement, Motivation, and Participation framework— the model offers a comprehensive and holistic understanding of students' cognitive landscapes. This research underscores the necessity of a multidimensional approach to capturing the intricate interplay of cognitive, affective, and behavioral factors in students' mathematical learning experiences. The novelty lies in its methodological innovation, employing FCMs to transcend traditional qualitative analyzes and facilitate quantitative insights into students' cognitive processes. This approach is particularly relevant in the current era dominated by digital learning environments and artificial intelligence, where real-time, automated analysis of student interactions is increasingly vital. The proposed FCM has been developed over the years with a data-driven approach; the concepts and relationships in it have been derived from the literature and refined by the author's experience in the field. Illustrated through case studies, the framework's utility is demonstrated in diverse contexts, highlighting how the quantitative data obtained are confirmed by qualitative approach: analyzing the impact of remote learning during the Covid-19 pandemic on student engagement and exploring Augmented Reality's role in enhancing mathematical conceptualization. These applications show the framework's adaptability and its potential to integrate new technologies in educational practices. However, the transition from qualitative to quantitative methodologies poses a challenge, given the prevalent use of qualitative approaches in mathematics education research. Additionally, the technological implementation of the FCM model in educational software presents practical hurdles, necessitating further development to ensure ease of integration and use in real-time educational settings. Future work will focus on bridging these methodological gaps and overcoming technological challenges to broaden the FCM model's applicability and enhance its contribution to advancing mathematics education.

EFFECTS OF INSTRUCTIONAL MEDIA ON LEARNERS COMPETENCES IN MATHEMATICS IN PUBLIC SECONDARY SCHOOLS IN RWANDA A CASE OF RULINDO DISTRICT

This study explored the impact of instructional media on mathematics competencies in public secondary schools in Rulindo, Rwanda. Employing a descriptive and correlational design with a mixed approach, the study aimed to identify influential instructional media, assess mathematics competence levels, and determine their relationship. The target population included 616 teachers and 100 head teachers, totaling 716 individuals, with a sample size of 257 determined using the Yamane formula through purposive and random sampling. Data were collected via questionnaires, documentation research, and a pilot study, then analyzed using SPSS version 21.Key findings indicated strong agreement (85.5%-98.6%) on the effectiveness of computer-based tools, graphing calculators, mathematics textbooks, and dynamic geometry environments in teaching mathematics. Significant associations were found (p < 0.05) between competencies in numeracy, use of instructional media, and students comprehension of mathematical subjects. Recommendations included government scholarships to enhance teachers mathematics skills, optimized use of teaching resources, training by MINEDUC, and increased educational support for students. The study highlighted the need for further research to explore instructional materials broader impacts on secondary school students mathematics performance.

Exploring the relationship between students' attitudes and fraction sense proficiency across lower secondary grades

Understanding fractions is a critical mathematical skill necessary for more advanced mathematical concepts and applications. However, many students struggle with fraction sense, which is the foundational understanding and flexible use of fractions. This study aims to explore the relationship between students' attitudes toward learning fractions and their proficiency in fraction sense in lower secondary grades. Using a descriptive-correlational design, data were collected from 296 students aged 13 to 15 using the Fraction Sense Test (FST) and the Attitudes Towards Learning Fractions Questionnaire (ATLF). The study found that students consistently struggled with fractional concepts, achieving low scores across all grades. Nevertheless, a significant, though diminishing, relationship was observed between positive attitudes towards fractions and fraction sense proficiency from Secondary One to Secondary Three. These findings suggest the need to integrate meaningful fraction learning approaches to maintain students' positive attitudes, thereby improving their overall mathematical competence.