Mathematical Competence Research Articles

Mobile computer-supported collaborative learning for mathematics: A scoping review.

This study conducted a scoping review of publications in mobile Computer-Supported Collaborative Learning for mathematics. Papers published between 2007 and 2021 inclusive were retrieved from research databases to achieve this goal. Twenty-eight papers met the inclusion–exclusion criteria of the study. It was shown that two papers were published on average over the last 15 years. The majority of the papers were published in peer-reviewed journals. Intending to improve mathematics pedagogy, the two most popular math mCSCL contents were general elementary mathematics and geometry. The review also revealed that math mCSCL benefited elementary students the most. The majority of math mCSCL software was custom-built and designed for synchronous sharing. The research designs were consistent with the existing reviews. The effects on social and attitude skills, as well as mathematics competency, were the most frequently mentioned benefits of math mCSCL. Usability issues, device unfamiliarity, inability to track students' activities, synchronization, and coordination concerns were among the problems highlighted during the implementation of math mCSCL. The implications for future research are discussed.

Modelling Improper Integrals, a Case Study

Background: University students show little clarity in applying content related to improper integrals due to a lack of meaning that does not allow them to connect them with the environment and everyday life problems. Objective: To recognise improper integrals as a mathematical tool with multiple applications inside and outside mathematics. Design: Qualitative action research. Setting and participants: University engineering students. Data collection and analysis: A proposal was designed and applied to articulate mathematical modelling by using software, where a sequence of ten selected situations involving this type of integrals was experimented and solved. Results: The importance of modelling as a didactic-dynamic resource is highlighted because it helps students to reach and understand real situations involving improper integrals in different contexts. Conclusions: Despite the numerous errors detected in the students, this strategy made it possible to demonstrate that they developed mathematical competencies, which was manifested in the progress of advanced mathematical thinking skills.

Localized Game-Based Learning Activity Sheets in Mathematics 7

To become a critical thinker and problem solver, learners need the mastery of the basic competencies. To ensure that meaningful learning occurs in a mathematics classroom, learning resources reflecting their context must be readily available. Unfortunately, there has been a dearth of localized materials for the Ilocano learners. Hence, this study developed Localized Game-Based Learning Activities (LGBLAs) in Mathematics 7 based on the teachers’ perceived level of mastery of the learners along with the Most Essential Learning Competencies (MELCs) in Number and Number Sense, Algebra, Geometry, and Statistics and Probability. Following the research and development (R and D) framework, data were gathered using a survey rating scale from the 66 Mathematics 7 teachers in the Schools Division of Ilocos Norte. Means with their equivalent descriptive interpretations were utilized to analyze and interpret the data. The results showed that learners exhibited nearly mastery in some of the learning competencies in Mathematics 7. This could mean that they have not sufficiently acquired the fundamental skills required to move to more advanced mathematical learning tasks. However, the key concepts and skills could be enriched by supplementing instruction with appropriate, contextualized, and relevant curriculum support materials. Hence, LGBLAs in Mathematics 7 was developed. The LGBLAs was found to be very highly valid and very highly acceptable as a curriculum support material for mathematics instruction as evaluated by the content experts and the key teachers in Mathematics 7. It is then recommended that LGBLAs be adopted for classroom use to improve the mastery level of learners in the different learning competencies along with Number and Number Sense, Algebra, Geometry, and Statistics and Probability.

The Effects of Social Desirability on Students’ Self-Reports in Two Social Contexts: Lectures vs. Lectures and Lab Classes

Attempts to detect socially desirable responding bias have mainly focused on studies that explore sensitive topics. However, researchers concur that the sensitive character of the survey could be affected by the social context within which the research is conducted. Little research has been reported worldwide investigating the potential effects of social desirability on students’ self-reports, considering the social context within which the survey is conducted. In this paper, we investigate the potential effects of social desirability on students’ self-reports in two social contexts within which the survey was conducted. More specifically, with a sample of 111 Greek students, we explored the effects of social desirability on students’ attitudes towards statistics in two cases: when the questionnaire was administered to participating students after attending (a) lectures and (b) both lectures and laboratory classes. Only in the second case were the items’ attitudes toward statistics associated with a score of socially desirable responding; moreover, social desirability accounted for the relationship between attitudes toward statistics and perceived competence in mathematics. Implications and limitations are also discussed.

Identification and characterization of high-achieving student subgroups using two methodological approaches: The role of different achievement indicators and motivational-affective characteristics

How high-achieving student subgroups are identified is widely discussed. Studies use different domain-general and domain-specific achievement indicators and methodological approaches. Traditional research included cut-off scores, which have been criticized as arbitrary. Recently, latent profile analyses have been used more often. The present study compared these approaches regarding their overlap to investigate their interchangeability. Afterwards, high-achieving student subgroups were characterized by their motivational-affective characteristics. Data from N = 1563 high-achieving students were investigated. We used three achievement indicators (two mathematical competences and figural reasoning) for identification and four motivational-affective characteristics for characterization. The four largest high-achieving student subgroups were found through both approaches. However, the two methodological approaches could not be used interchangeably. Large heterogeneity in achievement indicators and motivational-affective characteristics existed across the subgroups. Top Performers have been identified as the target state for education, as they showed high scores on all achievement indicators and the most positive motivational-affective characteristics.

Tools for solving systems of non-linear equations

When teaching numerical techniques in courses of numerical analysis of engineering careers at the Facultad Regional San Nicolás, little emphasis is placed on the mechanical procedures of the methods. Some math programmes offer the ability to design custom graphical interfaces. Taking advantage of this possibility, the Engineering & Education Group has been developing a collection of personalised graphical interfaces related to the different topics of numerical analysis. The use of these apps in the classroom allows for generating situations where students can appreciate the importance of applying different numerical methods and discussing different involved concepts. This paper presents the apps that have been designed and a sequence of activities that will be assigned, using the apps, to learn how to obtain approximate solutions to systems of non-linear equations. Rubrics designed to analyse the degree of development of mathematical competencies that the students are expected to acquire after the proposed activities will also be shown. Keywords: Engineering, mathematics, numerical analysis, non-linear equations, systems;

YouTube Video Playlist as Mathematics Supplementary Learning Material for Blended Learning

Blended learning in the new normal is a mix of distance learning modalities that aims to promote better instruction delivery since face-to-face modality is not yet permitted due to the continuous spread of mutated COVID-19. Online distance learning combines modular or TV and radio-based instruction in the Philippines. However, one-hour per subject for the synchronous session is not enough to cover the one-week lessons and develop the target competencies in mathematics. Students struggled to understand the mathematics lesson discussed by the teacher during synchronous. They need many explanations and illustrative examples to understand the underlying concepts, principles, and procedures for solving mathematical problems. Hence, video lessons are the best solution to help students cope with challenges. This study aims to determine the effectiveness of YouTube video playlists as mathematics supplementary learning materials for blended learning. The participants are grade 7 students in public school under the third grading period. The instruments are test materials, a survey questionnaire, and an interview guide validated by three experts in mathematics education. Findings showed that the YouTube video playlist helped the students to understand and develop students’ mathematics competencies. Watching the said intervention boosted the students’ confidence in answering the learning activities and performing tasks. However, they suggested uploading more videos with closed captions, illustrative examples, and explanations. Hence, similar studies must be conducted to verify the findings in different schools since the study was limited to one school.

Assessment of Learning Competencies in Mathematics: Basis for Contextualized Instructional Material Development

Assessment of Learning Competencies in Mathematics: Basis for Contextualized Instructional Material Development

Measuring mathematical self-concept in four- to six-year-olds: A comparison of picture and puppet supported procedures

In three mixed designed experiments with four- to six-year-olds we explored the comparability of different measurement tools for mathematical self concept (SC). All participants were asked to perform a picture scale (PIS) and a puppet interview (PUI) in the first experiment (N = 25), a PIS and a puppet scale (PUS) in the second experiment (N = 25) and a PUI and a PUS in the third experiment (N = 26). In all experiments, the order of presenting the scales was manipulated between participants. Mathematical competencies, German grammar comprehension and intelligence were measured. The experiments showed that all of the scales were reliable. In addition, no differences were revealed between the individual procedures for the assessment of mathematical SC. Due to the rather small sample sizes, data was merged across experiments to allow a one-way subject-to-subject comparison of the procedures, resulting in increased statistical power. Again, no differences between the SC scales were observed. Findings of moderate correlations between the PIS with mathematical skills and the PUI with mathematical skills indicated construct validity, but this was not observed for the PUS. When the sample is divided according to median split, a difference emerges in the older age group between PUS and PUI. In general, our findings showed that puppets and pictures are useful supporting materials in the SC measurement of four- to six-year-olds.

Effectiveness of Multi-Media approach Instructional Package on the development of selected competencies in mathematics among slum students -An Experimental study

Effectiveness of Multi-Media approach Instructional Package on the development of selected competencies in mathematics among slum students -An Experimental study

Формирование креативности студентов средствами электронной среды Moodle

The authors investigate the problem of the formation of creativity of students of economic university. The importance of solving this problem in the context of improvement of the quality of training of graduates of higher education from the standpoint of professional orientation of training is emphasized. The article highlights the role of e-learning environment Moodle (modular object-oriented dynamic learning environment) as a means of formation of the creativity of future bachelors of economics. The possibilities of electronic environment Moodle are demonstrated for creating of training courses, filling them in the form of electronic resources (lectures, practical tasks, questionnaires, tests, forums, etc.), providing interactive interaction of subjects of the educational process. In the course of the study, a table of indicators of the level of formation of the creative-activity component of students’ mathematical competence was built to identify creativity. Based on the results of the pedagogical experiment, the assessment of the formation of the creative-activity component of mathematical competence of future bachelors was carried out. The article presents the results of generalized indicators of the dynamics of the formation of the creative activity component at the subject, interdisciplinary and professional stages of multilevel mathematical training in economic university.

Taking a Closer Look: The Relationship between Pre-School Domain General Cognition and School Mathematics Achievement When Controlling for Intelligence

Intelligence, as well as working memory and attention, affect the acquisition of mathematical competencies. This paper aimed to examine the influence of working memory and attention when taking different mathematical skills into account as a function of children’s intellectual ability. Overall, intelligence, working memory, attention and numerical skills were assessed twice in 1868 German pre-school children (t1, t2) and again at 2nd grade (t3). We defined three intellectual ability groups based on the results of intellectual assessment at t1 and t2. Group comparisons revealed significant differences between the three intellectual ability groups. Over time, children with low intellectual ability showed the lowest achievement in domain-general and numerical and mathematical skills compared to children of average intellectual ability. The highest achievement on the aforementioned variables was found for children of high intellectual ability. Additionally, path modelling revealed that, depending on the intellectual ability, different models of varying complexity could be generated. These models differed with regard to the relevance of the predictors (t2) and the future mathematical skills (t3). Causes and conclusions of these findings are discussed.

Effects of mathematical modelling based project production and management program on gifted students’ mathematical modelling and reflective thinking for real-life problem solving

This study aimed to examine the relationship between mathematical modelling and reflective thinking and to examine the effects of employing mathematical modelling processes on perception of mathematical modelling competencies and reflective thinking skills for real-life problem solving of gifted students participating in Project Production and Management Program at Turkish Science and Art Centers. Correlational path analysis of 300 students data revealed that Mathematical modelling is a significant predictor of reflective thinking skills, and the constructed model was found to be of a good fit with excellent path coefficients. Experimental design with pre-post-maintenance-tests with comparison group was employed with 60 students purposefully selected chosen from the above regression study. Reflective thinking and mathematical modelling levels of experimental group students who employed mathematical modelling processes for Project Production and Management increased significantly more from pre- to post-tests, and the significant difference was found to be maintained.

What does ICT help and does not help?

Year by year, ICT tools and related teaching methods are evolving a lot. Since 2016, the author of the present lines has been looking for a connection between them that supports the development of mathematical competencies and could be integrated into Transcarpathian minority Hungarian language education too. As a doctoral student at the University of Debrecen, I experienced, for example, how the interactive whiteboard revolutionized illustration in Hungarian mathematics teaching, and how it facilitated students' involvement. During my research of teaching in this regard, in some cases, the digital solution had advantageous effects versus concrete-manipulative representation ofBruner's too.At the same time, ICT "canned" learning materials (videos, presentations, ...) allow for a shift towards repetitive learning instead of simultaneous active participation, which can be compensated for by the "retrieval-enhanced" learning method.I have conducted and intend to conduct several research projects in a Transcarpathian Hungarian primary school. In the research so far, I examined whether, in addition to the financial and infrastructural features of the Transcarpathian Hungarian school, the increased "ICT-supported" and the "retrieval-enhanced" learning method could be integrated into institutional mathematics education. I examined the use of two types of ICT devices: one was the interactive whiteboard, and the other was providing one computer per student.In this article, I describe my experiences, gained during one semester, in the class taught with the interactive whiteboard on the one hand, and in the class taught according to the "retrieval-enhanced" learning method on the other hand.I compare the effectiveness of the classes to their previous achievements, to each other, and to a class in Hungary.
 Subject Classification: 97U70

Investigating the Level of Mathematical Concepts Development in Pre-Primary Schools in Oredo Local Government Area

Mathematics is the building blocks on which other subjects (mostly the sciences) are laid on. But many pupils find it very difficult to comprehend. More so, a good mastery of the concept of mathematics at the pre-primary level will form a solid background for the pupils when they proceed to the primary and secondary level. This has been the reason why mathematics is given prominence in the school curriculum and timetable. For some time now, there has been a growing concern over the poor teaching and learning of mathematics with the resultant - poor and falling standard in secondary school student performance in mathematics. These failures may be caused by the little or no development of early childhood mathematics in schools. This study, therefore, investigates the level of mathematics concepts development of pre-primary school pupils in Oredo local government area of Edo state. The descriptive survey method was adopted, and the population comprises all public and private pre-primary school pupils and teachers in Benin Metropolis. Three hundred pupils and sixty teachers from thirty public and thirty private pre-primary schools in Oredo local government area were randomly sampled. The mathematics competency test was the instrument for data collection. The instrument was validated and the Kuder-Richardson reliability was estimated and it gave a value of 0.76. The data were analyzed using mean. The hypotheses were tested using the independent sample t -test. All the hypotheses were tested at 0.05 level of significance. Findings revealed that the development of mathematical concepts by pre-primary school pupils was moderate; and that a significant difference existed between male and female pupils, between public and private school pupils, and between pupils in rural and urban pre-primary schools. Considering the results of the study, provision of physical, instructional, learning, and human resources that will enhance pupils’ development of mathematical concepts was recommended.

Multiple solutions in dyads or alone – Fostering the acquisition of modeling competencies in mathematics

Generating multiple solutions is a promising approach in order to foster deep insight and understanding in mathematical contexts. However, in complex domains, students often struggle to generate just one solution, let alone more than one. This study investigates whether collaboration supports learners to generate multiple solutions, and to what extent collaboration and generating multiple solutions foster the acquisition of modeling competencies. In an experiment, students either learned alone or in dyads which were homogeneous or heterogeneous with respect to the level of prior knowledge, and they were prompted to generate one or multiple solutions in the learning phase (N = 193 seventh and eighth graders). Learning in homogeneous dyads fostered the acquisition of modeling competencies. Being prompted to generate a second solution was beneficial only for learners with high prior knowledge; overall, actually generating a second solution had positive impact.

Contributions of the psychology of mathematical cognition in early childhood education using apps.

Educational interventions are necessary to develop mathematical competence at early ages and prevent widespread mathematics learning failure in the education system as indicated by the results of European reports. Numerous studies agree that domain-specific predictors related to mathematics are symbolic and non-symbolic magnitude comparison, as well as, number line estimation. The goal of this study was to design 4 digital learning app games to train specific cognitive bases of mathematical learning in order to create resources and promote the use of these technologies in the educational community and to promote effective scientific transfer and increase the research visibility. This study involved 193 preschoolers aged 57–79 months. A quasi-experimental design was carried out with 3 groups created after scores were obtained in a standardised mathematical competence assessment test, i.e., low-performance group (N = 49), high-performance group (N = 21), and control group (N = 123). The results show that training with the 4 digital learning app games focusing on magnitude, subitizing, number facts, and estimation tasks improved the numerical skills of the experimental groups, compared to the control group. The implications of the study were, on the one hand, provided verified technological tools for teaching early mathematical competence. On the other hand, this study supports other studies on the importance of cognitive precursors in mathematics performance.

A Gender-Related Analysis of a Robots' Math Class

Using robot programming activities for learning in the classroom is one way to drive interest and engagement in the STEM field among students, especially girls. And this is a field that is particularly characterized by an underrepresentation of women. Accordingly, many countries are increasingly integrating activities related to computer science concepts into their education systems. The EU also sets the goal of considering the connections between STEM disciplines in schools and having students gain experience with robots as well. The use of robots for teaching purposes creates opportunities for motivating and meaningful mathematics lessons that are linked to the fundamental concepts of computer science. Mathematics teaching in such a context offers possibilities for an experimental and problem-oriented approach to the content and a deep insight into mathematical concepts. Research in this area shows that the use of robots can promote understanding of mathematical concepts, change attitudes and motivation, and develop metacognitive and problem-solving skills. However, as for gender differences in this context, little is known to date. Addressing this gap, for this work, we investigated learners' performance, mathematical and computational ideas and experiences, problem-solving strategies, and help used in an ER (Educational Robotics) activity. In addition, the learners’ mathematical competence and computational thinking skills as well as possible correlations of these measures with the learners’ performance on an ER activity were examined. For these purposes, an ER activity on the topic of plane geometric figures was designed, which was carried out in a 6th grade (11-12 years) class (n=24) of an Austrian middle school in the city of Salzburg using the TI-Innovator Rover. The comparison of six female and six male student groups, each consisting of two students, made it possible to address the above research questions. For this purpose, a mixed-methods approach was chosen. Qualitative data, consisting of the audio recordings of the student groups' conversations during the ER activity, the constructions made on the posters, the student notes, and the saved programs, form the basis for thematic analysis. The quantitative data include the number of tasks solved during the ER activity by the student groups, the mathematics grade of the last school year by the students, and the results of a test on the students' computational thinking skills with the related self-assessments. Appropriate quantitative methods for analysis include the Wilcoxon rank-sum test (Mann-Whitney test), the Welch Two Sample t-test, and Kendall's tau and Pearson's correlation coefficient to test for differences and correlations. The main results indicate that groups with female students perform better while showing high engagement in the activity, exhibit a more systematic approach to problem-solving and at the same time use less intensive help from the teachers than their male counterparts in this class. The paper concludes by giving future directions for research and the limits of the present work.

Values-Based Mathematics Teaching: Promoting Mathematical Performance, Competencies and Wellbeing

Innovative practices in mathematics pedagogy at all levels of schooling are needed to better prepare our students to thrive amidst the demands of living in the 21st century, given that in many jurisdictions mathematics performance has been flat and students’ attitude toward mathematics has dipped. Beyond cognitive knowledge and skills, and beyond affective factors, the motivational aspect (and values in particular) is just as important too. Drawing on some recent relevant research findings, this paper presents what values associated with effective mathematics learning and with positive mathematical wellbeing look like. The need for teachers to be more aware and more confident of their values espousal is emphasized. Research on the JEDI approach to values learning is presented. Recent research on teacher strategies at orchestrating values alignment in their mathematics classroom is also reported.

COGNITIVE AND METACOGNITIVE ACTIVITIES IN THE PROCESS OF DEVELOPING MATHEMATICAL COMPETENCE FOR SECONDARY SCHOOL STUDENTS

In an effort to innovate teaching and learning methods to prepare a new generation for the demands of a new era, many educators have discovered the value of metacognition. In this paper, the author presents these main issues: (i) cognitive activities and metacognitive activities; (ii) manifestations of cognition and metacognition in the 5 core components of mathematical competence for secondary school students; (iii) the influence and role of metacognition in learning Mathematics and developing mathematical competence for students.