Mathematical Competence Research Articles

The Role of Continuous Assessment Learning Activities (CALA) in Enhancing Mathematics Competency and Proficiency in Secondary School Learners

This paper examines the significance and contribution of CALA to the mathematics knowledge of students. It focuses on the instruments and methods used in CALA to teach mathematics effectively in Zimbabwe. Learners’ failure to implement what they learn in mathematics has been worrisome to the Ministry of Education whose focus is to promote industrialisation through effective teaching and learning of STEM subjects. It is believed that most learners memorise mathematics with little understanding in order to pass an examination. Inappropriate and ill-suited assessment methods of mathematics are regarded as the principal causes of this rote learning approach by learners. The educational policy makers came up with the concept of CALA, which was effected in 2021, to all levels of education in Zimbabwe. According to the curriculum framework, learners are expected to demonstrate their knowledge of mathematics through CALA. However, whilst the intended goal of CALA is prudent, the concern is whether teachers are knowledgeable about how this model of assessment can be implemented effectively. Ten secondary school mathematics teachers were interviewed to examine their views and practices in the classroom implementation of the CALA component. In this study, the findings established that the incorporation of the component in the teaching and learning of mathematics has come with limited benefits that were marred by teachers’ knowledge deficiency to operationalise CALA. This study recommends thorough support and developmental programmes which can equip teachers with the appropriate skills to implement CALA.

수학과 교육과정에서의 빅 아이디어 접근의 이해와 실행 모델 탐색

To successfully implement the Big Ideas approach in the 2022 revised mathematics curriculum, it is necessary to thoroughly understand how the above approach has been discussed in mathematics education research and to prepare the foundations for its implementation. This study analyzed the meaning of Big Ideas in mathematics education research overseas and their implementation cases; moreover, we explored the goals and content of mathematics education that can be pursued through a Big Ideas approach and investigated how the said approach can be implemented. As a result, we found that the educational objects of the Big Ideas approach in the mathematics curriculum involve cultivating mathematical competency by setting implicit knowledge of Big Ideas as the content of mathematics education. Implicit knowledge of Big ideas has the potential to enable students to gain a deeper understanding of mathematical concepts and procedures, as well as to recognize the value of mathematics.
 To implement the Big Ideas approach in the mathematics curriculum, designing learning trajectories through understanding, interpretation, supplementation or substitution, as well as the creation of Big Ideas is crucial. “Topdown or bottom-up models can be considered.”

TEACHING HIGHER MATHEMATICS BASED ON COMPETENCE-BASED AND THESAURUS APPROACHES

Formulation of the problem. The requirement to increase the level of mathematical training of future engineers and reduce the number of hours devoted to teaching higher mathematics gives rise to the task of developing and improving the methodology for teaching higher mathematics. The purpose of this article is to describe the methodology for teaching higher mathematics based on the thesaurus approach. Materials and methods. The research materials are pedagogical and methodical literature, and experiences of foreign and domestic scientists. In the course of the study, general scientific methods (analysis, synthesis, concretization, systematization, and generalization) were used. Results. The thesaurus approach to learning helps to clarify the mathematical competence of a particular topic, the basis of educational information is the educational thesaurus, the student's lexicon necessary for the optimal distribution of educational information by type of training session and the development of didactic materials, the choice of methods and forms of education. Conclusions. Determining the content of the educational thesaurus of a specific topic of higher mathematics helps to clearly describe the mathematical competencies of the relevant topic, the stages of its formation, analyze and clarify the necessary educational information, distribute it by type of lesson (lecture, practical lesson, self-study). Determining the student's vocabulary necessary for mastering a new topic helps to determine the methodology and means of teaching, in particular, to develop auxiliary tasks and questions for updating the student's vocabulary, to establish successive links between the educational thesaurus and the student's vocabulary, to implement a differentiated approach to learning. The proposed methodology has the properties of flexibility, additions, and modifications depending on the learning objectives and specific academic group. Further research is needed on the effective use of the thesaurus approach in the process of teaching higher mathematics.

The use of Kahoot in preschool mathematics education

During the preschool period children acquire basic mathematics skills during preschool, the foundation for their later formal mathematics education. One tool that could enhance students' mathematical skills at this age and which utilizes the elements of games in non-game settings. This study aimed to implement an intervention program to examine whether gamification affects the mathematical competencies of preschool-aged students. Thirty-one students aged 4 to 6 participated, of which 15 shaped the experimental group and 16 shaped the control group. During the intervention program, students in the experimental group were tutored through tablets and games designed in Kahoot! application and involved basic math exercises such as addition and subtraction, while the control group did the same exercises without tablets. The results of the student's performance in the experimental group showed that their performance in mathematics before and after the intervention differed significantly. Therefore, students' mathematical skills were improved through Kahoot-based learning games. It can be concluded that the application of Kahoot! Learning games can improve the mathematical learning outcomes of preschool students. Pedagogical and psychological research should be used more to improve the mathematical skills of preschoolers.

Influence de la comparaison symbolique versus non symbolique sur le risque de difficultés d’apprentissage en mathématiques en éducation de la petite enfance

The main goal of this study was to clarify if students at risk of Mathematics Learning Disabilities had deficits in symbolic, non-symbolic processing, or both. Other purpose was to know if the Open Algorithm Based on Numbers (OBN) teaching method offers advantages over Closed Algorithms Based on Ciphers (CBC) method. A total of 307 Early Childhood Education students participated in this study. Based on student’ scores obtained in Test of Early Mathematics Ability (TEMA-3), that assesses formal and informal thinking, three analysis groups were designed: low-performance group, average-performance group, and high-performance group. There were significant differences in symbolic comparison and, consequently, the post hoc analysis showed significant differences between all groups in symbolic comparison except between the High and Average groups calculation. However, there were no differences in non-symbolic comparison between any of the groups. The teaching method and the mathematical competence showed a significant effect only on the symbolic comparison, resulting in a small size of effect for both the method and the Early Math Competence rate. These data support the dual representation hypothesis, in which the non-symbolic magnitudes would activate the Numerical Approximation System (ANS) and the symbolic quantities an exact representation of the numbers. This being a significant source of mathematical learning that could contribute to the improvement of the ANS.

Sex Differences in Developmental Pathways to Mathematical Competence.

The study tested the hypothesis that there are sex differences in the pathways to mathematical development. Three hundred forty-two adolescents (169 boys) were assessed in various mathematics areas from arithmetic fluency to algebra across 6th to 9th grade, inclusive, and completed a battery of working memory, spatial, and intelligence measures in middle school. Their middle school and 9th grade teachers reported on their in-class attentive behavior. There were no sex differences in overall mathematics performance, but boys had advantages on all spatial measures (ds = .29 to .58) and girls were more attentive in classroom settings (ds = -.28 to -.37). A series of structural equation models indicated that 6th- to 9th-grade mathematical competence was influenced by a combination of general cognitive ability, spatial abilities, and in-class attention. General cognitive ability was important for both sexes but the spatial pathway to mathematical competence was relatively more important for boys and the in-class attention pathway for girls.

Application of the Team Assisted Individualization (TAI) Learning Model in Improving Understanding of Mathematical Concepts

Purpose of the study: Research This done with objective For analyze understanding draft mathematics competence number with using the Learning Model Team Assisted Individualization (TAI) for students class IV Madrasah Ibtidaiyah Al-Hidayah Kebon IX Muaro Jambi.
 Methodology: Deep data study This in the form of quantitative and qualitative data which is analyzed in a manner descriptive and data obtained through stages observation as much as 2 cycles with sample as many as 18 students.
 Main Findings: After done 2 cycles obtained happen enhancement understanding draft improved mathematic using learning models Team Assisted Individualization (TAI). enhancement results from understanding draft mathematics competence number student by 26.73%.
 Novelty/Originality of this study: Updating from study This is related research with enhancement understanding draft mathematics competence number with using the Learning Model The previous Team Assisted Individualization (TAI).

The Development of Mathematical Model Consciousness in Junior Secondary Students: A Lesson Study of the Instruction of Congruent Triangles

The Compulsory Education Course Standards for Mathematics 2022 have highlighted the educational objectives of junior secondary mathematics by emphasizing the development of mathematical competence and practical learning. Model consciousness, as one of the fundamental mathematical competencies to be developed at the junior secondary level, can facilitate students’ comprehension of the universal application of mathematics. Teachers of mathematics in junior high school should construct effective classroom activities based on the cognitive qualities of their students in order to enhance their mathematical model consciousness and comprehension of the substance of mathematics knowledge. This paper is a lesson study of the education of Congruent Triangles, and its purpose is to investigate strategies for fostering mathematical model consciousness among junior high school pupils.

Modelleme Uygulamalarının Matematik Okuryazarlığı Üzerindeki Rolünün İncelenmesi

The mathematical literacy or competence notion in PISA deals with the capacity of students to analyze, reason and communicate efficiently as they pose, formulate, solve and interpret mathematical problems in a variety of situations. The best way to improve mathematics literacy is that students have the necessary mathematical knowledge and different problem solving strategies, know when and how to use these strategies, and work with activities that involve different contexts of interest. When considered in this respect, teachers have an important role in the development of students' mathematical literacy. The aim of this study was to investigate the mathematics literacy status of Mathematics Teacher Candidates through PISA questions. The mathematical literacy status of pre-service teachers was examined within the scope of conceptual, operational and contextual questions and in terms of gender, academic grade point average and mathematical modeling. At the same time, semi-structured interviews have examined the difficulties that pre-service teachers experienced. Fully mixed concurrent equal status design was used. The participants were 113 pre-service mathematics teachers. Independent samples t-test and covariance analysis was used for the comparisons. Qualitative data analysis was conducted with content analysis. The research results, together with the suggestions, reveal important points for future studies.

PROFILE OF MATHEMATICS LEARNING MEASUREMENT MATERIAL FOR SCAVENGER CHILDREN AT "SEKOLAH KAMI" BEKASI

<p class="Els-keywords">This study aims to describe the mathematics learning profile of scavenger children in the "Our School" study group, to determine the scavenger children's learning interest and motivation in our school. Researchers used qualitative research with the snowball sampling method, there were 5 informants. This research is supported by a descriptive approach. Data collection in this study was obtained from observation, interviews, and documentation. The research results obtained are generally related to learning mathematics for students of the 4th grade equivalent of elementary school at "Sekolah Kami" who are very enthusiastic about learning mathematics, although they still need explanations slowly and repeatedly so that students can follow the lesson well. The mathematics competence mastered by the 4th grade students of SD Sekolah Kami in measurement material is quite masterful, even though when it is reviewed, it still has to be reminded occasionally with a clue. For the interest and motivation to study during the research the students were quite high but to do their homework they often did not do it at home because they also received less guidance from their parents, so that the opportunity to study and do assignments at home was not used.</p>

Age group differences in SFON tendency and arithmetical skills of four to seven year olds in four countries with different school starting ages

This study investigated age group differences in Spontaneous Focusing on Numerosity (SFON) tendency and arithmetical skills across age groups with differing starting ages of formal mathematics instruction. Children (N = 685) aged 4–7 years participated from four countries, i.e., Northern Ireland, England, Belgium and Finland, where children start formal school at 4, 5, 6, and 7 years respectively. Children completed measures of SFON tendency, Arabic number naming, verbal arithmetic and written arithmetic. Results revealed strong age group effects for all measures and some developmental differences between SFON tendency and arithmetical skills. Whether children were, or were not, in school had a strong effect on SFON tendency but not on arithmetical skills. In the 5 and 6 years old age group, children already in school had significantly lower SFON tendency compared to those not yet in school. Within each country, when comparing consecutive age groups situated near school starting age, SFON tendency scores were similar in three out of the four countries. Results suggest both informal and formal mathematical skills need to be considered when assessing young children’s mathematical competence.

What About Early Childhood Mathematics Education in Early Childhood Teacher Education?

From existing research, it is known that early childhood teacher education provides few opportunities to learn mathematical content or mathematics pedagogical content knowledge. Furthermore, little is known about the extent to which teacher educators are qualified to teach early childhood mathematics within teacher education programs. This study investigates the frequency of opportunities to learn mathematical content knowledge and mathematics pedagogical content knowledge. Additionally, we investigate some characteristics of teacher educators, namely the sources they use for professional development with respect to early mathematics education. We report descriptive results as well as correlations. The results indicate that opportunities to learn mathematical content knowledge and mathematics pedagogical content knowledge have increased over time. Moreover, the results indicate that teacher educator professional development formats that encourage professional exchange among teacher educators, experts in early mathematics education and in-service teachers may increase teacher educators’ competence in early childhood mathematics and thereby the frequency with which this topic is addressed in teacher education.

What About Early Childhood Mathematics Education in Early Childhood Teacher Education?

From existing research, it is known that early childhood teacher education pro-vides few opportunities to learn mathematical content or mathematics pedagogical con-tent knowledge. Furthermore, little is known about the extent to which teacher educators are qualified to teach early childhood mathematics within teacher education programs. This study investigates the frequency of opportunities to learn mathematical content knowledge and mathematics pedagogical content knowledge. Additionally, we investigate some characteristics of teacher educators, namely the sources they use for professional development with respect to early mathematics education. We report descriptive results as well as correlations. The results indicate that opportunities to learn mathematical con-tent knowledge and mathematics pedagogical content knowledge have increased over time. Moreover, the results indicate that teacher educator professional development for-mats that encourage professional exchange among teacher educators, experts in early mathematics education and in-service teachers may increase teacher educators’ compe-tence in early childhood mathematics and thereby the frequency with which this topic is addressed in teacher education.

Profil Kompetensi Guru dalam Pembelajaran Daring Matematika pada Masa Pandemi Covid-19 di Kelas Tinggi

<em>Research has been carried out that aims to describe the pedagogical competence of teachers in planning, implementing, and conducting online learning assessments of mathematics in the high class of SDI Unggulan Al Azhar Klaten. This research uses a qualitative approach with a case study method. The sample used in this research is purposive sampling taken is high class teachers and school principals. Collecting data in this study is by observation, interviews, and documentation, as well as using the validity test of triangulation techniques and sources. Data analysis in this study used the interactive model of Miles, Huberman and Saldana. The results of this study, the pedagogic competence of high-grade mathematics teachers in planning, implementing, conducting assessments still tend to be lacking and not in accordance with Permendikbud number 14 of 2019 concerning the simplification of lesson plans from 13 components into 3 core components consisting of objectives, learning activities, and assessments. as well as other complementary components. The conclusion of this study, the pedagogic competence of high-grade mathematics teachers tend to have not met all the indicators of success in learning planning, learning implementation, learning assessment. The pedagogical competence skills of high-grade mathematics teachers in planning, implementing, and conducting assessments tend to be less appropriate and need to be further improved by conducting one of them continuous guidance on the development and preparation of learning and with training.</em>

The two-network framework of number processing: a step towards a better understanding of the neural origins of developmental dyscalculia

Developmental dyscalculia is a specific learning disorder that persists over lifetime and can have an enormous impact on personal, health-related, and professional aspects of life. Despite its central importance, the origin both at the cognitive and neural level is not yet well understood. Several classification schemas of dyscalculia have been proposed, sometimes together with an associated deficit at the neural level. However, these explanations are (a) not providing an exhaustive framework that is at levels with the observed complexity of developmental dyscalculia at the behavioral level and (b) are largely mono-causal approaches focusing on gray matter deficits. We suggest that number processing is instead the result of context-dependent interaction of two anatomically largely separate, distributed but overlapping networks that function/cooperate in a closely integrated fashion. The proposed two-network framework (TNF) is the result of a series of studies in adults on the neural correlates underlying magnitude processing and arithmetic fact retrieval, which comprised neurofunctional imaging of various numerical tasks, the application of probabilistic fiber tracking to obtain well-defined connections, and the validation and modification of these results using disconnectome mapping in acute stroke patients. Emerged from data in adults, it represents the endpoint of the acquisition and use of mathematical competencies in adults. Yet, we argue that its main characteristics should already emerge earlier during development. Based on this TNF, we develop a classification schema of phenomenological subtypes and their underlying neural origin that we evaluate against existing propositions and the available empirical data.

Investigating mathematical modeling competencies of primary school students: Reflections from a model eliciting activity

Investigating mathematical modeling competencies of primary school students: Reflections from a model eliciting activity

The impact of COVID-19 on mathematical entry competencies: 1 year on

Abstract The COVID-19 pandemic has affected the way we learn, teach and support students in many different ways. In particular, the impact of the pandemic on the mathematical capabilities of students arriving at university is now starting to be seen and reported. Students arriving at UK universities in 2021, and having completed their A levels in 2021, had received disruption to almost all of their A level learning and it seemed likely that this might cause them to find the transition into higher education more difficult. Despite the disruption, the number of students achieving the top A level grade has more than doubled since 2019. In this paper, the data from a diagnostic test that has remained the same for the past 30 years are considered to measure the mathematical preparedness of students starting their courses at one UK university in September 2021, updating the work of Hodds (2021). Furthermore, an ordinal logistic regression model predicting A level grade based on test performance and other factors is developed to help determine if grades were perhaps inflated as suggested. The results show that students entering in 2021 are significantly less prepared for the mathematics on their courses than their colleagues who entered in 2020 and pre-pandemic. The regression model predicts a higher probability of being awarded an A*/A for students with A levels awarded in the pandemic, despite far lower scores on the diagnostic test, and in particular in 2021 when A levels were awarded through teacher assessment of the topics covered and not necessarily the whole A level syllabus.

The Effectiveness of Teaching Derivatives in Vietnamese High Schools Using APOS Theory and ACE Learning Cycle

<p style="text-align: justify;">The actions, processes, objects, and schemas (APOS) theory is a constructivist learning theory created by Dubinsky based on Piaget's epistemology and used to teach math worldwide. Especially the application of APOS theory to the curriculum of a mathematics class helps students better understand the concepts being taught, which in turn contributes to the formation and development of mathematical competencies. With the aid of the APOS theory and the activity, classroom discussion, and exercise (ACE) learning cycle, this study sought to ascertain the effect of teaching derivatives in Vietnamese high schools. In this quasi-experimental study at a high school in Vietnam, there were 78 grade 11 students (40 in the experimental and 38 in the control classes). As opposed to the control class, which received traditional instruction, the experimental class's students were taught using the ACE learning cycle based on the APOS theory. The data was collected based on the pre-test, the post-test results and a survey of students' opinions. Also, the data that was gathered, both qualitatively and quantitatively, was examined using IBM SPSS Statistics (Version 26) predictive analytics software. The results showed that students in the experimental class who participated in learning activities based on the APOS theory improved their academic performance and attitudes. Additionally, it promoted the students' abilities to find solutions to problems about derivatives.</p>

How does mathematical modeling competency affect the creativity of middle school students? The roles of curiosity and guided inquiry teaching.

Mathematical modeling has become a crucial competence in mathematics education in many countries and regions due to the increasingly complex real-world problems that students face in the 21st century. Previous research has shown that mathematical modeling contributes to the development of students' creativity, particularly with respect to stimulating and protecting the curiosity of children. However, previous studies have not explored or examined the relationships among middle school students' mathematical modeling competency, curiosity, and creativity based on data drawn from large-scale assessments and have not investigated the influence of teachers' teaching methods in this context. This study used convenience sampling to select 4,531 seventh-grade students from eastern and western, urban and rural areas in China. Online tests and questionnaires were used to measure their mathematical modeling competency, curiosity, creativity and guided inquiry teaching, and a moderated mediation model was used to analyze the effect of mathematical modeling competency on creativity. The results showed the following. (1) There are statistically significant differences between boys and girls in terms of their mathematical modeling competency, curiosity, and creativity. Specifically, boys score significantly higher than girls on these variables. (2) Creativity exhibits a statistically significant positive correlation with mathematical modeling competency, curiosity, and guided inquiry teaching. (3) Curiosity mediates the relationship between mathematical modeling competency and creativity, and guided inquiry teaching moderates the influence of curiosity. In high-level guided inquiry teaching classes, curiosity has a stronger influence on creativity, and it mediates the relationship between mathematical modeling competency and creativity more strongly. This study empirically verified the influence of mathematical modeling competency on creativity and provided a possible way to cultivate children's creativity. Future research should use longitudinal analysis to verify the causal relationship between mathematical modeling competency and creativity and to systematically explore the possible path by which mathematical modeling competency affects creativity.

Parental Competences and Academic Competences in School Children: The Mediator Role of Executive Functions

The role of parenting in the development of children’s learning constitutes, at present, part of the discussion in the psychoeducational field. Although parental competences (pc) and executive functions (ef) have been investigated by psychology and neuropsychology, their relationship with academic competences remains to be fully studied. The aim of this investigation was to analyze the effect of pc perceived by parents on behavioral ef and performance-based measures of reading and mathematical competences in children. We worked with 131 school children of both sexes, between 9 and 11 years old, and their respective parents. Multivariate Analysis of Variance (manova) and structural equation model (sem) were used. The results indicate that parental skills from the parents’ perspective have a significant effect on ef, reading, and mathematical skills. However, the best fit model indicates that efs mediate the relationship between parenting skills and reading and math skills.