Mathematical Competence Research Articles

Changes in mathematical skills among freshman engineering students

This study investigates the critical transition from secondary to tertiary mathematics education, focusing on students’ challenges and the impact of curriculum reforms in Sweden. Through an analysis of diagnostic test scores and admission data from Umeå University over the period 2006–2021, we examine the evolving mathematical competencies of incoming engineering students and the broader implications of these shifts for educational policy and student preparedness for higher education. Our findings indicate a significant improvement in students’ mathematical readiness in the latter years of the study, correlating with the implementation of curriculum changes and variations in admission statistics. This research documents the positive outcomes of these educational reforms on student preparedness. It places these findings within a global context, highlighting the universal challenges and responses in mathematics education transitions. The study underscores the complex dynamics of the secondary-tertiary transition and provides valuable insights into the specific mathematical areas where students have shown varying degrees of improvement.

Structural and functional model of formation of STEM-competencies of students of professional higher education institutions in mathematics teaching

Abstract This study focuses on the vocational preparation of learners in professional pre-higher educational establishments. The primary objective is to provide a theoretical foundation for, construct, and empirically evaluate the efficacy of a structural-functional paradigm for cultivating STEM proficiencies among students in these institutions through mathematics instruction. The pedagogical experiment corroborated the research postulate that attaining advanced STEM competencies in mathematics among professional pre-higher education students can be facilitated through a learning model that incorporates specific pedagogical conditions: motivating and stimulating students to engage in educational, cognitive and research activities in mathematics through engagement in cooperation and the use of individual and group coaching; implementation of STEM projects in mathematics teaching; usage of ICT to ensure visibility and research orientation of mathematics teaching. The experimental outcomes and accompanying educational resources have enabled a comprehensive analysis of the challenges associated with implementing STEM methodologies in mathematics instruction. This article aims to elucidate the key attributes of the devised structural-functional model and evaluate its implementation efficacy, with particular emphasis on the application of the authors’ developed pedagogical support materials.

Vietnamese sixth graders' mathematical communication competency developed by teaching fraction topics using the 5E model

The 5E, an exploratory instructional model with growing popularity in current learner-centered educational practices, aims to develop learners' competencies. The study aims to evaluate the effectiveness of teaching fractions using the 5E instructional model to develop students' mathematical communication competency (MCC). The researchers used mixed methods with data triangulation in a 38-student experiment group (EG) who learned with the 5E model and a 41-student control group (CG) using traditional learning approaches to clarify the impact of the 5E model on the development of MCC, academic performance and learning attitude among learners. The research instruments include a pre-test, post-test, classroom observation, and a student survey. Subsequently, the data collected were analyzed qualitatively and quantitatively using IBM SPSS Statistics (Version 26) predictive analytics software. The independent t-test on the post-test scores of the two groups revealed that the academic performance of EG after the intervention was significantly better than that of CG with the significance level α = 0.05 and degree of freedom df = 77, yielding the p-value (Sig. 2-tailed) = 0.001. Meanwhile, given the significance level α = 0.05, the p-value (Sig. 2-tailed) = 0.001 and the Pearson correlation coefficient (r = 0.943), the result of the paired sample t-test implies that the mean post-test score of students in EG was significantly higher than that of their pre-test. Furthermore, with an effect size of approximately 0.88, these figures suggest that applying the 5E model in the experimental process positively affected the academic performance of the students in EG and the development of MCC. A qualitative analysis using classroom observations and student surveys revealed that the 5E model helped students in the EG develop their MCC and an increasingly positive attitude toward learning. In addition to these findings, it also reveals some limitations of the study and proposes recommendations for future research.

Examining motivation profile differences across students’ mathematics identity, performance, and parents’ attitudes

Declining development in Finnish students’ mathematics performance has highlighted the importance of mathematics competence and motivation research. We used the person-centred approach to investigate Finnish third-, fourth-, and fifth-grade students’ mathematics motivation profiles. In addition, we explored differences between the motivation profiles regarding students’ mathematics identity, performance, and their parents’ mathematics-related attitudes. A latent profile analysis (LPA) based on 304 third-, fourth-, and fifth-grade students’ answers revealed three math-related motivation profiles: high motivation, high cost and moderate. Further investigation of the profiles showed that students’ higher mathematics identity is represented strongly in the high motivation group, as are students’ mathematics performance scores. Parents perceived low mathematics competence as highly expressed in those students belonging to the high cost profile. Results concerning students’ broader learning environment and previous results relevant to the Finnish educational system are discussed.

Effects of Teachers Qualification and Experience on Students’ Competences in Mathematics Subject in Public Secondary Schools in Rwanda

This research investigates the impact of teachers' qualifications and experience on students' competencies in mathematics in Rwandan public secondary schools. The study aimed to assess how teachers' mathematical qualifications influence students' learning outcomes and to analyze the relationship between teacher experience and student competence. A descriptive research design utilizing a mixed-methods approach was employed, with a sample of 185 respondents selected from a population of 343, including mathematics teachers, head teachers, and students. Data was collected through questionnaires, interviews, and document analysis, using SPSS Version 23 for evaluation. The results were presented in tables and shared with stakeholders to promote teacher development and improve student performance in mathematics. Findings revealed that teacher qualifications significantly affect student competence. Specifically, 37.5% of respondents strongly agreed that teaching experience enhances students' understanding, while 50% agreed. The mean score was 4.21 (SD = 1.6). Additionally, 62.5% affirmed that teaching resources and diverse methods positively impact their learning, with a mean of 4.11 (SD = 1.12). The study also highlighted that specialized training in mathematics motivates students, as indicated by 46.5% who strongly agreed and 48.6% who agreed, with a mean of 4.42 (SD = 0.84). The research recommends that the Rwanda Education Board (REB) and schools support teachers through ongoing training and monitoring to enhance teaching quality. It is essential for teachers to ensure students are comfortable with their teaching methods, provide ample exercises, and foster an appreciation for mathematics as a vital subject in everyday life.

Lessons learned from designing an open-source automated feedback system for STEM education

AbstractAs distance learning becomes increasingly important and artificial intelligence tools continue to advance, automated systems for individual learning have attracted significant attention. However, the scarcity of open-source online tools that are capable of providing personalized feedback has restricted the widespread implementation of research-based feedback systems. In this work, we present RATsApp, an open-source automated feedback system (AFS) that incorporates research-based features such as formative feedback. The system focuses on core STEM competencies such as mathematical competence, representational competence, and data literacy. It also allows lecturers to monitor students’ progress. RATsApp can be used at different levels of STEM education or research, as it allows the creation and customization of the educational content. We present a specific case of its implementation in higher education, where we report the results of a usability survey (N=64), using the technology acceptance model 2 (TAM2), to evaluate the user experience of undergraduate students. Our findings confirm the applicability of the TAM2 framework, revealing that factors such as the relevance to the course of study, output quality, and ease of use significantly influence the perceived usefulness. We also found a linear relation between the perceived usefulness and the intention to use, which in turn is a significant predictor of the frequency of use. Moreover, the formative feedback feature of RATsApp received positive feedback, indicating its potential as an educational tool. Furthermore, as an open-source platform, RATsApp encourages public contributions to its ongoing development, fostering a collaborative approach to improve educational tools.

Formation of logical and mathematical competence of preschool children using modern game technologies

Formation of logical and mathematical competence of preschool children using modern game technologies

Self-Regulation Profiles of Pre-Service Mathematics Teachers for Primary Education in Mathematical Problem-Solving Contexts

Self-regulation in mathematical problem solving is of particular importance in the initial training of Primary Education teachers as it can contribute to improving their own competence in mathematics and at the same time enable them to teach effectively and in a personalized way. With this idea in mind, this study identifies self-regulation profiles present in university students in mathematical problem-solving contexts based on data from the application of a validated scale on a sample of 402 pre-service teachers of primary education at University of the Basque Country. The cluster analysis carried out made it possible to identify and characterize three profiles, labelled according to the level of self-regulation represented by each of them (low, medium, high). In view of the results obtained, we perceive a need to design didactic proposals that allow these profiles to evolve from the lowest to the highest levels.

OPEN SOURCE TEXTBOOK AS A RESOURCE FOR THE TEACHING-LEARNING PROCESS OF ALGEBRA IN INITIAL TRAINING OF MATHEMATICS TEACHERS

Objective: To determine the implications of the use of open source text in the teaching-learning process of algebraic structures in the initial teacher training of the mathematics specialty in a state university in Peru. Theoretical Framework: The conceptual and epistemic bases of open learning are systematically addressed through interactive texts, as well as the aspects related to the teaching-learning process in university higher education. Method: The study has a mixed approach, pre-experimental design and correlational level, the target population was mathematics education students and a sample of 46 randomly chosen students, data collection is carried out through a diagnostic questionnaire, another multiple alternative and an interview, in the study sample classes are held through the open source book; then the learning achieved at the conceptual level is evaluated. procedural of algebraic structures. Results and Discussion: In this research it is evident that students did not know the open source online text for the study of mathematics, but they have skills in the use of digital technology; but with the use of the digital book they assimilate the concepts, perform demonstrations and solve problems efficiently, raising their level of motivation towards learning. Thus, the relevant use of open source books significantly improves learning and the development of mathematical competence in students. Research Implications: Strengthening of interactive and personalized activities for a comprehensive training of mathematics content mediated by digital technology, reinforcing in a sustained way the culture and mathematical competence of teachers in initial training. Originality/Value: Implementation of an innovative approach in pedagogical practice, through the use of open resources for the assimilation of mathematical concepts and procedures in a dynamic, efficient and effective way. The value of research is evidenced in the praxis of didactic strategies in the context of the digital age, oriented to the knowledge of algebraic structures by mathematics teachers.

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.