Mathematical Competence Research Articles

The Psychological Basis of Shaping the Mathematical Competences of Students (9th Grade) in Education Ukrainian Language

The article examines the psychological foundations of Ukrainian language learning. The psychological components that ensure students master a dynamic combination of mathematical and communicative skills, ways of thinking and a number of characteristics (memory, attention, perception, imagination, self-improvement, decision-making) for comprehensive personal development are outlined. The main skills (analysis, argumentation, comparison, generalization, abstraction, specification, etc.) that influence the success of basic education students in learning the Ukrainian language are highlighted.

The Trends and Highlights of Mathematics Textbook Research in Korea via Topic Modelling

The purpose of this study was to analyze the overall trends of mathematics textbook research in Korea. For this purpose, we collected 455 research articles on mathematics textbooks from all the articles published in seven domestic professional journals of mathematics education. We used topic modelling based on latent Dirichlet allocation algorithms to extract topics that reflected not only overall trends but also the trends by each curriculum revision period, including the top 10 words and three representative papers that best indicated each topic. The most frequent topic that appeared across almost all curriculum periods was concept and term, which focused on specific concepts and their definitions, examples, and representations used in textbooks. Another topic, comparing textbooks, was also popular, recently including more foreign textbooks. Topics such as storytelling and mathematical competency were emergent in a specific curriculum period, indicating the close relationship between textbook research and curriculum revisions. Based on these findings, this paper concludes by sharing several implications for future mathematics textbook research in Korea, discussing which topics continue to be studied and in what directions, as well as which topics need to expanded and why.

수학 심화학습이 한 유망한 초등학생의 수학 교과역량에 미치는 영향

수학 심화학습이 한 유망한 초등학생의 수학 교과역량에 미치는 영향

Key Factors that Predict Students’ Mathematics Competence in a College of Education in Hohoe, Volta region of Ghana

This study investigates the demographic factors, including gender, age, program of study, and financial background, that predict students' mathematics competence in a College of Education in Hohoe, Ghana. A quantitative research predictive design was employed to examine the relationship between these demographic factors and mathematics competence. The study population consisted of 80 Science and Mathematics major students enrolled in a College of Education during the 2023 academic year. A simple random sampling technique was used to obtain 69 participants who successfully filled their questionnaire. The collected data were analyzed using several predictive models. Evaluation metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Coefficient of Determination (R²) were utilized to compare the performance of these models. Among the models compared, Boosting Regression demonstrated the best overall predictive performance. Random Forest Regression ranked as the second-best model, while RLR, KNNR, and NNR had poorer performance. The findings indicate that gender and program of study are consistently important factors in predicting students' mathematics competence. Additionally, age showed a weak positive association with mathematics competence, while financial status was inversely associated with performance. The results provide valuable insights for educators and policymakers, facilitating the development of targeted interventions to enhance students' mathematics competence.

Gifted youths’ mathematical modelling-based project production: Structure, triggers and contributing factors

This study aims to determine gifted youths’ mathematical modelling project production competencies and structure, to examine the impact of a modelling-based project production and management program on these competencies and project production, and to identify the triggers and contributing factors of project production. Mixed method study was employed. The first study group consisted of 300 randomly selected gifted youths who were registered in the Project Production and Management Program (PPMP) in Science and Art Centers (SACs) throughout Türkiye. The second study group comprised 60 participants who were purposively selected from amongst the 300 participants that took part in the first study group. The data sources used in the study include scale, interview, log, modelling form, peer suggestion and expert suggestion forms. Structural equation modelling, ANCOVA, content analysis was conducted. It has been concluded that the mathematical modelling-based project production has a five-factor structure. It has been obtained that the modelling-based PPMP positively affected the mathematical modelling competencies and project productions and that this improvement was maintained. It has been found that identification of global, real-life and popular science problems in the field gifted youths are interested in is most important trigger. It was indicated there are 15 factors contributing to projects production.

Analysis of implementing Realistic Mathematics Education principles to enhance mathematics competence of slow learner students

One of the Education for Sustainable Development Goals is to provide equitable and inclusive access to quality education for all. However, some children with special needs, particularly slow learners, have yet to be able to enjoy inclusive and high-quality learning services. This research aims to enhance slow learners' competence by implementing the Realistic Mathematics Education Approach. It is descriptive qualitative research, with data collection techniques including focus group discussion, interview, and learning observation. The analysis involved comparing the principles of Realistic Mathematics Education in theory with those applied by teachers, as well as the learning approach used by teachers with those required by slow learners. The findings indicate that while some teachers have implemented learning based on the principles of Realistic Mathematics Education for all students, there needs to be more focus on interventions specifically tailored to the needs of slow learners. Furthermore, teachers still need to fully understand the services required by slow learners based on their unique characteristics. The implementation of Realistic Mathematics Education to meet the learning needs of slow learners in mathematics has primarily focused on activity and interactivity principles without emphasis on the understanding of concepts to enhance their competence.

Satisfaction of Postgraduate Students With Hybrid Flipped Learning to Develop Their Mathematical Competencies

The objective of the research is to assess the effectiveness of flipped learning in the development of mathematical competencies of postgraduate students to determine the level of satisfaction achieved during academic training in hybrid modality. The methodological approach was a quantitative a descriptive scope. The questionnaire was the instrument used with a cross-sectional design. The sample was 32 postgraduate students. The results are that hybrid flipped learning promotes the usefulness of the contents; integrates through discussions, practical cases or problems what has been learned for work performance. The mathematical competencies with the highest level of development are the use of mathematical terminology; use digital tools for the presentation of the strategy. The relevance of the research is to contribute about the effectiveness and use of flipped learning with the support of digital tools to promote quality mathematical training.

Мониторинг предметных образовательных результатов в интересах устойчивого развития

The article examines the problem of improving the quality of subject educational results at an economic university in the interests of sustainable development. The authors noted that the modern unstable world requires a professional in any field to be able to solve new problems in changing circumstances. This makes it necessary to develop a strategy for preparing a competent, mobile and creative worker in the field of education. In this regard, the emphasis in the organization of the educational process naturally shifts from the procedural component to the productive component. At the same time, the significance of the student’s subjective position increases: the integration of his motivational attitudes, social and market demand as a future professional. Based on the analysis of the most important international documents, the principles of education for sustainable development are identified, which are grouped according to their functional orientation. The first group determines the development of the individual (continuity of education, professional culture of interaction, the effectiveness of education, transformative intelligence). The second group provides conditions for personal development (fundamentalization, openness of education, advanced learning, active learning, informatization, monitoring of learning outcomes, etc.). The requirements for the results of subject mathematical training at the University of Economics are determined in the context of the principles of education for sustainable development. Based on the results of the study, a pedagogical experiment was conducted, during which the monitoring of educational results within the disciplines of the subject area “Mathematics” was carried out. The influence of experimental learning (use of case-tasks, project-type tasks) in the course of mathematical training on the level of formation of the components of mathematical competence in the context of ESD principles was studied. The results of pedagogical measurements showed a positive dynamics of the components of mathematical competence, in particular, the motivational and value qualities of future bachelors and masters.

Ortaokul matematik öğretmen adaylarının model oluşturma etkinliği tasarlama yeterlikleri, problem çözmeye yönelik inançları, problem kurmaya yönelik öz-yeterlik inançları ve aralarındaki ilişki

This study aimed to determine the change and the relationship between elementary school mathematics teacher candidates' competence to design model-eliciting activities, their beliefs towards problem-solving, and their self-efficacy beliefs towards problem posing according to gender and overall academic grade point average (GPA). Modeling activities designed by 64 elementary school mathematics teacher candidates in Turkey were evaluated by means of a grading key created in the context of "compliance with MEA design principles". In addition, a scale consisting of 24 items was applied to determine the beliefs of the teacher candidates towards problem-solving, and a 26-imoetem scale was applied to determine their self-efficacy beliefs towards problem-posing, and the responses were analyzed by quantitative methods (one-way multiple variance analysis, correlation analysis, multiple regression test). The findings reveal that elementary school mathematics teacher candidates' proficiency in designing model-eliciting activities is generally at a high level, while their belief in problem-solving and self-efficacy beliefs in problem posing is generally at a moderate level. Based on the studies that concluded that modeling competencies develop as they work on modeling problems and that the experience of mathematical modeling affects their mathematical modeling competencies, it was concluded that modeling problems were used to solve mathematical problems and teach these solutions in the mathematical modeling course they took. It was determined that the linear combinations of teacher candidates' proficiency in designing model-eliciting activities, beliefs in problem-solving, and self-efficacy beliefs in problem-posing did not show a significant difference. The fact that pre-service teachers' beliefs about problem solving and posing are not related to their MEA design competencies is thought to be due to their previous routine mathematical problem solving experiences being more dominant. On the other hand, since the mathematical modeling process is basically considered as a problem-solving process, it was expected that these beliefs of pre-service teachers would be related to MEA design proficiency. It is important to conduct qualitative research with teacher candidates in order to examine this situation in more detail and to reveal the underlying causes.

ИГРИТЕ С LEGO И МАТЕМАТИЧЕСКИТЕ КОМПЕТЕНТНОСТИ НА ПЕТ ГОДИШНИТЕ ДЕЦА

The present report describes an innovative pedagogical practice related to the formation of mathematical competences in five-year-old children through the use of Lego games. The interdisciplinary approach teaches adolescents to apply their skills in the creation of a product /model/, which shows the inextricable connection between knowledge and a game situation related to real-world events. For this purpose, we took advantage of the educational sets „STEAM Park“, „Coding Express“ and the materials of LEGO Education. Applying the approaches „learning through playing“, „learning by doing“ and „learning from experience“ have a significant contribution to improve children’s skills in planning activities and working in small groups. During the process, children ask questions, propose solutions, try out ideas, gain experience. Lego games give them the opportunity to explore materials, make discoveries, test theories. Using the STEM approach in kindergarten ensures the development of critical thinking, communicative, creative and cooperative individuals prepared for the innovative professions of the future.

Comparing the Learning Environments Related to Mathematical Modelling Through Distance Education

This study aims to compare two different learning environments designed online in terms of their contributions to the development of mathematical modelling competencies. In the research, which was designed with the triangulation method, among the mixed research methods in which the qualitative and quantitative research methods are used together. The participants, determined with the purposeful sampling technique, consisted of 53 fourth class students who were studying at the mathematical teaching department of a faculty of education. In the research, while the quantitative data were analyzed with the paired samples t-test and Wilcoxon test, the qualitative data were analyzed with the content analysis. As a result of the analyses, while a significant difference was found in favour of the post-test between the modelling test questions of the pre-service teachers who attended the distance education in groups, the modelling test results of the pre-service teachers who attended individually did not differ. In addition, while it was observed that the participants who attended individually had difficulty in expressing themselves more throughout the process, it was determined that those who worked with groups tried to verify the results they reached more during the modelling process compared with those who participated individually.

Development and Validation of Self-Learning Packets in Linear Equation and Inequalities in Mathematics 8

The shift of modality brought on by the COVID-19 pandemic, the Department of Education in the Philippines implemented the Distance Learning Modality, which averted the New Normal. Self-Learning Packets (SLPs), satisfy the challenge of distance learning. This descriptive-developmental study aimed to develop and validate SLPs that is aligned with the Most Essential Learning Competency in Mathematics 8. This study underwent five phases guided by the ADDIE Model (Analysis, Design, Development, Implementation, and Evaluation). The developed SLPs was very acceptable as validated by five expert validators invited from Saint Columban College and the Division of Zamboanga Sibugay. Selected Grade 8 students were also asked to evaluate the pretest and posttest. Results shows that the developed SLPs in grade 8 Mathematics were generally valid and acceptable as validated by the experts. The SLPs obtained 96.92% compliance in Content and 95.93% in Layout and Design. Paired t-test was conducted to check if there were significant changes of the student’s performance from pretest and posttest. Based on the results there was a significant difference in the scores in pretest and posttest. The mean of pretest and posttest of SLP 1 were 5.10 and 7.30 with mean difference of 2.2 and the mean of pretest and posttest of SLP 2 were 4.60 and 7.20 with mean difference of 2.6, and p-value is lower than 0.05 for both SLPs. The expert validators strongly agreed that the SLPs possesses adequacy, coherence, usefulness, and reliability in equipping and enhancing student skills in linear Equations and Linear Inequalities.

Are active school transport and leisure-time physical activity associated with performance and wellbeing at secondary school? A population-based study.

Physically active pupils may be better and more resilient learners. However, it is unclear whether walking or cycling to school yields similar educational and school-related mental health benefits as leisure-time physical activity. We examined the associations of active school transport and leisure-time moderate-to-vigorous physical activity with perceived academic performance, competency in academic skills, school burnout and school enjoyment. We included 34 103 Finnish adolescents (mean age 15.4 years; 53% girls) from the 2015 School Health Promotion study cohort. For the analyses, we used logistic regression, adjusting for major sociodemographic, environmental, lifestyle and physical activity covariates. Active school transport was positively associated with educational outcomes and school enjoyment, but not with school burnout. For example, compared with non-active transport, 10-30 min of daily active school transport was linked to 30% [odds ratio (OR) 1.30, 95% confidence interval (CI) 1.21-1.40] and 17% (OR 1.17, 95% CI 1.08-1.27) higher odds of high perceived academic performance and high reading competency, respectively. Leisure-time physical activity was robustly associated with all outcomes. For example, compared with the inactive, the most physically active adolescents had 86% higher odds of high perceived academic performance (OR 1.86, 95% CI 1.66-2.08), 57% higher odds of high competency in mathematics (OR 1.57, 95% CI 1.39-1.77) and 40% lower odds of school burnout (OR 0.60, 95% CI 0.52-0.69). Compared with active school transport, leisure-time physical activity was more strongly associated with educational and school-related mental health outcomes. Nevertheless, walking or cycling to school might lead to improvements in classroom performance and school enjoyment.

Inquiry-based mathematics education and attitudes towards mathematics: tracking profiles for teaching

Research on the relationships between the main constructs underlying inquiry-based learning is rarely reported in mathematics education research. Considering this as a complex problem which is worth to be investigated, the present study aims to provide some empirical evidences that might serve as an insight to support further investigations on the relationships between attitudes towards mathematics and inquiry-based learning approaches. Thus, this study adopts a descriptive research design where no variables are manipulated but observed and measured in order to identify changes depicted in data collection. An instructional design focusing on the nature of mathematical inquiry is carried out with the participation of 304 secondary and high school students, and a clustering approach is used to look at how participants are grouped around certain attitudinal profiles before and after such mathematical practice. The results show how the heterogeneity of attitudinal profiles present in the classroom evolves positively in terms of perceived usefulness of mathematics and mathematical self-concept as perception of competence in mathematics. This fact provides some basis that might be used for further research on the idea that certain forms of development in inquiry-based mathematics education (IBME) based on greater immersion in the nature and culture of mathematics can help students to improve their attitudes towards mathematics.

Evaluating the Results of PISA Assessment: Are There Gaps Between the Teaching of Mathematical Literacy at Schools and in PISA Assessment?

<p style="text-align:justify">The problems in education in the countries of the Organization for Economic Cooperation and Development (OECD) vary from country to country. The differences between "upper class" and "lower class" countries in PISA assessment results have led to a research gap. The purpose of this study was to (a) test students' mathematical literacy skills on the Program for International Student Assessment (PISA) test and compare the results using the sum of means across OECD countries; (b) examine the relationship between students' mathematical competence, precision, and self-perception of mathematical literacy skills in the PISA test; and (c) analyze the gaps that exist between the implementation of mathematics instruction in school and the mathematical literacy as measured on the PISA test. This study was designed as a mixed method with an explanatory sequential design. The data collection methods included test procedures, questionnaires, and interviews. The result of this study showed that the overall mean score obtained was below the OECD average. In general, the respondents achieved only level 2 mathematics proficiency. A significant relationship was found between mathematical competence, precision, and self-perception in mathematical skills. On the other hand, there was a gap, namely the difference at the implementation level, where mathematical literacy measured by PISA differed from the measurement of mathematical learning achievement by teachers in school. The results showed that teaching that emphasizes only problem-solving procedures affects low mathematical competence and is not useful enough for students to deal with the PISA mathematics test.</p>

Construction and Validation of Symbolic Retention Ability Test

Education is a method or process of transmitting or learning universal mental processes, developing the abilities of thought and assessment, and, in general, intellectually modifying oneself or others for mature life. The ability to compare number and symbols, such as digits, efficiently is linked to mathematical competence across the life span. The teacher's use of symbolic representations becomes second nature, as they are deeply integrated with conceptual understanding and subject knowledge. Such representations, however, may place significant additional demands on learners who are already challenged by the abstract nature of concepts as well as the variety of unfamiliar substances to which these concepts are applied in the curriculum. Taking a broadly constructivist approach to learning, While the majority of students are conceptual thinkers who communicate verbally, some students have a different learning style, that the students are more interested to solve the mathematical problems by using formula and symbols. Thus, the Symbolic Retention Ability help the student to understand the mathematical problems in a meaningful way and solving them in a systematic way. This paper is an attempt to construct and validate a tool for assessing the symbolic retention ability among higher secondary students. For this purpose, a collection of 60 mathematical statements with related symbols from the content of XI standard mathematics text-book covering six dimensions viz. geometry, statistics, probability, number theory, calculus and set theory. These gathered 60 statements were undergone pilot study with 100 higher secondary students in Puducherry region and on the basis of index of difficulty and index of discrimination values 37 statements have been selected. The reliability and validness have also been found for this test. Hence, a complete and full-fledged Symbolic Retention Ability Test has been constructed and validated through this study and it will be an enough tool to measure the Symbolic Retention Ability of the higher secondary students.

An investigation of eighth-graders’ mathematical communication competency and mathematical literacy performance

This study aimed to investigate eighth-grade students’ mathematical communication competency and mathematical literacy performance in a classroom experiment designed based on the mathematical modeling approach. Accordingly, a teaching experiment methodology was applied. Data were collected from three eighth-grade students through the Mathematical Communication Competency Measurement Tools, video recordings of the teaching episodes, student products, and clinical interviews before and after the teaching experiment. PISA mathematics proficiency level and communication competency level assessment schemes were used in the data analysis process. A deductive analysis was performed on the data collected through the clinical interviews, whereas a retrospective analysis was conducted to examine the data collected through teaching episodes. The results showed that the modeling-based teaching experiment helped develop the mathematical communication competency of all participating students. The results also showed that improving students’ mathematical communication competencies increased their mathematical literacy performances.

Croatian Elementary School Teachers’ Maths Teaching Efficacy Beliefs: Knowledge Domains and Cross-Curricular Maths in the Post-Digital Era

This correlational study addressed two issues pertinent to developing mathematical competences for the 21st Century. Firstly, in a post-digital society, technology is recognized in teachers’ pedagogic and subject-specific knowledge domains. Secondly, cross-curricular teaching must be introduced to respond to societal requirements for maths knowledge application in diverse areas of life and work. Croatian educational reform recognized the importance of informatics and the integration of ICT across curricula supporting cross-curricular teaching. When reforming teaching, teaching efficacy beliefs inform change, and the study examined how technology pedagogy content knowledge (TPACK) contributes to teaching efficacy beliefs. Six hundred and six Croatian elementary school classroom teachers were surveyed for maths teaching efficacy beliefs (MTEBI) and self-assessment of their technology pedagogy content knowledge (TPACK). The study confirmed that the integration of technology knowledge in teachers’ pedagogical knowledge is, in addition to content knowledge, essential and predicts, with a large effect size ( f2 = 0.64), the MTEBI subscale math teaching efficacy (MTE), while isolated technology knowledge does not. In addition, there is a positive correlation between years of service and pedagogy content knowledge and a negative correlation between years of service and technology pedagogy knowledge and technology knowledge, however, with a small effect size.

Mathematics Identity of Prospective Mathematics Teachers: Content Analysis of Open-Ended Survey Questions

Many problems faced by mathematics learners both at the school and college levels have occurred so far. Mathematics education students involved in mathematics daily also face various problems, be it problems related to cognitive and affective abilities. Problems such as the emergence of mathematical anxiety, negative self-perception of mathematics, lack of mathematical competence, and many other problems have become the recent focus in mathematics education research. So, how do mathematics education students, especially prospective mathematics teachers, view themselves as related to mathematics? What is their mathematical identity? This study aims to determine the mathematics identity possessed by prospective mathematics teachers. To find out the mathematics identity of prospective mathematics teachers, a descriptive design utilizing a survey with five open-ended questions was asked. Demographic data were analyzed using descriptive frequencies, while the five open-ended questions were analyzed using summative content analysis to analyze free-text responses from 225 prospective mathematics teachers. Free-text responses contain answers to five questions in each component of the mathematical identity obtained from disseminating questions through google forms. We obtained the results that prospective mathematics teachers generally have a positive mathematical identity, but some components need improvement. However, it was also found that the results were quite surprising concerning the mathematical identity of the prospective mathematics teacher. A complete explanation will be discussed in this article.

Formation of Mathematical and Algorithmic Competence within the Framework of the Discipline “Information Theory” According to “Information Security” Enlarged Groups of Specialties and Direction

The article considers the formation of mathematical and algorithmic competence within the discipline “Information Theory”, as well as overcoming the interdisciplinary gap of fundamental areas of knowledge. The author provides justification of the choice of this discipline, clarification of its role both in the educational process and as necessary for further qualitative mastering of disciplines of the professional cycle, in particular, for solving professional problems. When conducting this study, the author proceeded from the features of this discipline and its role in the educational process in the directions of the Enlarged Groups of Specialities and Directions “Information Security”. Within the framework of the study below, the systematic approach to the structure in general and interdisciplinary interaction in particular in the discipline “Information Theory” prevails. The examples of this interdisciplinary interaction of fundamental disciplines within the framework of “Information Theory” considered in the article represent the justification for the designation of the formed competence (mathematical-algorithmic), as well as the uniqueness and necessity of its formation in the process of teaching students in the directions of EGSD “Information Security”. The results of the study are of practical interest for teachers, students, as well as for potential employers of graduates of the directions of EGSD “Information Security”, because the effectiveness of further training and solving practice-oriented problems depends on the quality of mastering this discipline.