Mathematical Skills Research Articles

Mother tongue-based education in a diverse society and the acquisition of foundational skills: Evidence from the Philippines

The Philippines is an ethnolinguistically diverse country with 180 languages spoken. In 2012, the government massively expanded the language of instruction (LoI) options, a shift from a bilingual Filipino-English education to mother tongue-based education using 19 languages targeting students in kindergarten to grade 3. The policy intended to create a closer link between the school instructional language and students’ mother tongue in the early stage of formal schooling, which would improve foundational skills and increase the students’ ability to acquire proficiency in additional languages. We use nationally representative data to evaluate the policy's impact on foundational reading and mathematics skills, exploiting a variation between student cohorts and the variation in the instructional languages before and after the policy. We find that the policy reduced the mean linguistic distance between children's mother tongue and school LoI by between 43 % to 76 %. However, we find a statistically significant and negative effect on foundational reading skills when tested in Filipino or English. The magnitude is not negligible given the Philippines’ flat learning profiles. We find the policy also negatively impacted the foundational mathematics skills of the first cohort fully exposed to the policy. Our findings imply that governments need to reconsider the mother tongue-based education policy as a tool to improve foundational skills in a diverse society.

Професійна спрямованість математичної підготовки студентів технічних спеціальностей у контексті фундаменталізації освітнього процесу

The article examines the peculiarities of mathematical training of future technical specialists in the context of fundamentalization of the educational process. The study of the definitions of fundamentalization, mathematical preparation was carried out, the main characteristic features of mathematical preparation, proposed by the researchers of the problem of mathematical preparation, were singled out. An analysis of the work of scientists dedicated to the selected research problem was carried out. It has been established that the mathematical training of future technical specialists is a dialectical combination of formed mathematical skills and abilities for their applied application and the direct process of forming these skills. The fundamentalization of mathematical training is considered to be the concept of improving mathematical training, in which basic mathematical invariants are selected for their further application in professional activities. To implement the approach of professional orientation of mathematical training of students of technical specialties, it is recommended to take into account the peculiarities of the construction of the course of higher mathematics and courses of special disciplines in order to enable the integration of educational material, as well as the organization of the educational process in higher education institutions. Based on the analysis of educational programs for students of various specialties of the Vinnytsia National Technical University, a conclusion was made about the difference in program results in mathematics for students of the same lecture stream. On the basis of which it is proposed to unify tasks of professional content. Examples of professional tasks from the "Theory of Probability" section are given.

Formation of students’ subject skills in mathematics in the process of digital didactic game

The work is devoted to the study of the problem of gamification of mathematics teaching in primary school using methods of studying pedagogical experience, comparing and generalizing the results of observations, analyzing scientific articles and the content and structure of didactic games in mathematics. The urgency of the problem is due to the digital transformation of education currently taking place. Digitalization of education in the context of teaching mathematics in primary school entails the need to develop new learning tools. Such teaching tools should contribute to the development of students’ mathematical skills, while meeting the needs of students of the digital generation for the form of information presentation. Digital didactic games can be used as an effective means of teaching mathematics at school. The potential of such games in the formation of students’ mathematical and logical skills, cognitive motivation is indicated. In the mathematical content of the game, it is proposed to provide for a change of types of educational activities. This will expand the range of skills formed through digital play, make it more dynamic and interesting for students, which will contribute to their involuntary learning. To develop the skills to perform various graphical constructions using the tools of modern graphical calculators, it is proposed to include tasks at certain stages of the game, for which digital tools can be used (online calculators, electronic programs, mobile applications, etc.). The conclusion is made about the expediency of using digital didactic games in the process of teaching mathematics to schoolchildren.

Systematic Literature Review: Mathematical Literacy Skills in Terms of Mathematics Learning Motivation

Mathematical literacy and motivation to learn mathematics are two important aspects of education. Mathematical literacy enables students to understand and apply mathematical concepts in everyday life, as well as think logically and solve problems. Mathematics learning motivation influences students' effort and perseverance in learning the material, improving academic interest and performance. The combination of the two is essential for educational success and the development of critical thinking skills required in the modern world. The objectives of research generally cover the following aspects Measuring Mathematics Literacy Level, Assessing Mathematics Learning Motivation, Identifying the Relationship between Mathematics Literacy and Learning Motivation, Recognizing Barriers and Challenges, Developing Effective Learning Strategies. This research uses the SLR (Systematic Literature Review) method by reviewing 16 articles. Data collection in this study was carried out by reviewing all articles related to Mathematical Literacy Ability, Learning Motivation, Mathematical Literacy Ability in terms of Learning Motivation published from 2019 to 2023. Based on the results of the study, it was found that motivation to learn mathematics plays an important role in students' mathematical literacy skills. Students with low motivation tend to learn by force, so their mathematical literacy skills are low because they tend to do problems procedurally without in-depth analysis. The implication is the need for motivational strategies, curriculum design, teacher training, literacy programs, and parental involvement.

Interdisciplinary STEM education foundational concepts: Implementation for knowledge creation

Interdisciplinary thinking is essential to understanding and solving real-life problems and requires multiple disciplinary viewpoints. Research into STEM education highlights that it promotes an interdisciplinary learning process integrating science, mathematics, engineering, and mathematics knowledge and skills. However, STEM definitions are varied, and implementation recommendations are scant, resulting in diversity in the development and implementation of the learning process. This study critically analyses the literature to determine the fundamental concepts of STEM education and STEM discipline integration. Our analysis discovers six key components of STEM education, encompassing the integration of discipline, utilization of multiple representations, engagement with realistic and relevant problems, application of the engineering design process, encouragement of active collaboration, and emphasis on student-centered learning approaches. Then, we transform these key components to a practical learning process. The STEM-DTaM (STEM with Design Thinking and Makerspace) learning model consists of seven steps. We then unfold how this proposed learning could facilitate interdisciplinary thinking construction.

An analysis of calculus application questions in grade 12 mathematics exams in South Africa

This study employed a quantitative survey methodology to analyze the 2021-2023 grade 12 calculus application exam questions in the context of South Africa. A total of 11 grade 12 teachers and 220 grade 12 students participated in the study. Analysis of the survey data and students’ test results points to the view that examiners sometimes misjudge the level of difficulty of the exam questions and include questions that are very difficult, which fail to discriminate between strong and weak candidates. It was noticed that calculus applications questions that most students could not correctly answer included multiple mathematical skills that were compacted in a short statement. This paper recommends that mathematics examiners should continuously reflect on their own work and find ways to improve their skills in setting future exam papers. The inclusion of item difficulty and item discrimination indices in post-exam analysis of results could be part of the examiners’ reflective practice. Feedback from the grade 12 mathematics teachers on the standard of each exam question is just as important to the examiners as the examiners’ reports are to the teachers.

Analysis of High School Students' Mathematical Literacy Skills in Solving Contextual Problems on SPtDV Material

Mathematical literacy is one of the abilities that must be possessed in today's 21st-century education. This study aims to describe the mathematical literacy skills of grade X students at one of the Yogyakarta high schools in Bantul Regency in solving contextual problems on SPtDV (System of Inequality of Two Variables) material. The method used was descriptive qualitative. Data were collected through multiple-choice tests, descriptions, and questionnaires using SPtDV material. Data analysis was done by reducing and presenting data, and drawing conclusions based on indicators of students' mathematical literacy (mathematical process). Sampling of the population was carried out using a non-purposive sampling technique. To determine the number of samples to be taken, researchers used a saturated sampling technique. The research subjects were students of class X of Yogyakarta Private Senior High School in Bantul Regency in the first semester of the 2023/2024 academic year, with a total of 20 students. The results showed that students with high ability were able to fulfill all three aspects of the indicators in mathematical literacy skills, namely formulating, using, and interpreting. While students with moderate ability were able to fulfill two aspects of the indicator, namely formulating and using. And students with low ability were only able to fulfill one aspect of the indicator, namely formulating. The percentage of results obtained is based on the Mathematical Literacy Profile Criteria, namely: 10% proficient, 60% proficient, 15% basic, and 15% need special intervention. This study implies that it is important for other researchers to explore the factors that influence the mathematical literacy skills of low-ability students, especially in high school students or equivalent.

Kemampuan Literasi Matematis Ditinjau dari Motivasi Belajar pada Siswa Kelas XI SMA Negeri 2 Padang Panjang

This research is motivated by the fact that the number of students who have low mathematical literacy skills is caused by various factors. One of the factors that affects mathematical literacy ability is learning motivation. This study aims to determine the ability of mathematical literacy when viewed from the learning motivation of students. This type of research is quantitative descriptive. The sample in this study is grade XI students of SMA Negeri 2 Padang Panjang. The sample selection technique in this study uses the Stratified random sampling technique where the sample is selected based on strata. The instrument used in this study is test questions in the form of essays to see students' mathematical literacy skills. Data analysis was carried out descriptively on all research data. The results showed that the average mathematical literacy ability was 50 which was classified as low. If viewed from high learning motivation is classified as medium with an average score of 69, when viewed from medium learning motivation has low mathematical literacy skills with an average score of 56 and mathematical literacy ability reviewed from low learning motivation is classified as low in the low category with an average score of 25

PYTHON IN ORDINARY DIFFERENTIAL EQUATIONS LEARNING

Using software in mathematics learning can improve students' soft and hard mathematics skills at the high school and college levels. Therefore, using software in the learning process is important, including in learning Differential Equations. This research examines the use of the Python programming language with Jupyter Lab software and the SymPy library in solving ordinary differential equation problems symbolically in the Differential Equations course. The use of the Python programming language in Differential Equations learning includes solving linear ordinary differential equations of first-order, second-order, higher-order, and the Laplace transform. This research also examines the effect of using Python on the learning outcomes of differential equations of Mathematics Education Study Program students, Study Program Outside the Main Campus, Pattimura University. The population in this quantitative research is all students who programmed differential equations courses in the even semester of the 2023-2024 academic year as many as 19 students. The Python programming language can be used to solve differential equation problems symbolically easily, quickly, and accurately. In addition, using Jupyter Lab makes the process of solving differential equation problems easier and more interactive. Furthermore, t-test results show that the use of Python in learning differential equations can improve students' learning activities and learning outcomes. Using the Python programming language with Jupyter Lab software and the SymPy library can be developed to create teaching materials, textbooks, and reference books for Differential Equations courses.

Mathematical skills classification through primary education

By the end of primary school, children are expected to acquire a range of mathematical skills that progressively develop. This study aimed to gain insight into how a large number of numerical and geometrical measures are grouped and whether the structures shift or remain invariant along child’s development based on the data obtained from a sample of 1346 s to sixth grade children. On the basis of correlation analyses and exploratory factor analyses, we came up with an invariant four-factor structure for each grade. The four factors obtained were the following: (a) early and retrieval skills (subitizing, enumeration, number facts) (b) transcoding and ordinality skills, (c) numerical advanced skills and (d) visual-spatial advanced skills. Confirmatory factor analyses showed that the four-factor model fits well to the data (RMSEA < 0.06, CFI > 0.95, GFI > 0.93, SRMR < 0.05) at all grades. The associations between the mathematical measures were captured in each factor and the revealed invariant structure is discussed and compared with previous classification models of mathematical skills. Given that the difficulties in learning mathematics is currently being viewed as a continuum of academic abilities instead of a distinct problem, the underlying invariant four-factor structure can facilitate experts and educators to better understand how a broad area of mathematical skills are related across the primary education, in order to carry our comprehensive assessment of both the mathematical strengths and weaknesses of their students and to apply the appropriate customized teaching strategies.

The Effect of Habits of Mindo n Junior High School Students’ Mathematics Communication Ability

This research aims to determine the effect of habits of mind on junior high school students' mathematical communication skills on triangles and quadrilaterals. Habits of Mind is defined as a habit of thinking that is carried out as an intelligent behavior pattern when faced with a problem whose solution isn’t easily known so that productive action occurs. The problem in this research is motivated by its importance habits of mind in learning mathematics and improving students' mathematical abilities. The method used in this research is method ex post facto. The population in this study were all class VIII students in one of Junior High Schools in Karawang Regency. The sample in this study was 42 students using the technique purposive sampling. The instrument used in this research is a test, namely mathematical communication skills which consists of 5 (five) description questions. Apart from that, it also uses non-test instruments in the form of questionnaires habits of mind which consists of 30 statements. Data analysis was carried out using simple linear regression techniques. The research results obtained a linear regression equation Y = -25.065 + 1.345X. The magnitude of the correlation coefficient r2 = 0.848 and coefficient of determination = 84.8%. This shows that there is habits of mind had an influence on students' mathematical communication skills of 84.8%, while 15.6% was influenced by other factors not measured in this research.

Analyzing Junior High School Students’ Mathematical Communication Ability and Self Esteem using Discovery Learning Model

Mathematical reasoning, mathematical communication, mathematical problem solving, conceptual understanding, mathematical understanding, creative thinking and critical thinking are part of the mathematical abilities that students must have. One of the goals of learning mathematics according to NCTM is learning to communicate (mathematical communication). Mathematical communication skills in mathematics learning really need to be developed. This type of research design uses a quasi-experimental research design, namely pretest and post-test with non-equivalent control group design . The research used research subjects into two groups, namely the experimental group and the control group. The subjects of this research were students of class VII I MTs As-Sa'adah Padahanten Majalengka, numbering 64 people. Subjects were selected based on experimental class VIII A, 32 people and control class VIIIB, 32 people. Walkthroughs, questionnaires, and tests are techniques used in data collection. Data processing analysis was carried out qualitatively and quantitatively. The results of this research are that there is a difference in the effectiveness of the Discovery Learning model learning approach with the ordinary (conventional) learning model in terms of the aspects of mathematical communication skills and self-esteem of MTs in statistics material. The implications of the Discovery Learning learning model in this research are that it makes it easy for students to remember the lessons learned, integrate self concept according to their initial abilities, focus, be creative in exploratory projects, and the effect of knowledge transfer on learning outcomes can last a long time.

The Development of Discovery Learning Model Teaching Materials to Improve Students’ Mathematical Problem Solving Ability on Junior High School

In order to enhance students' mathematical problem-solving skills, this study looks at how teaching materials are developed using the Discovery Learning model. Since every student nowadays needs to be able to think critically, the study specifically looks at the process and outcomes. development, viability testing, feedback from students, and improving mathematical problem-solving skills. This kind of research makes use of the Research and Development (R&amp;D) or Research-based Development research method, which is a way to create a specific product and use a model to test the product's viability. Students in class VII at MTs Al Bidayah West Bandung Regency served as the research sample for S. Thiagarajan's 4D (Define, Design, Develop, and Disseminate) study. The process and outcomes of creating educational materials lead to the conclusion that the materials, when viewed from the various stages, follow the procedures or methods outlined in 4D. Based on students' responses, which were 68.4% and 70.2% in the good category, the viability of teaching materials made possible by the Photoshop program can be concluded, along with the students' improved problem-solving skills. If this teaching material is used in a classroom setting, it is imperative that the necessary facilities be set up ahead of time because learning with it requires sufficient facilities. There are tasks and content in this teaching resource that need to be altered. so that students' learning experiences are not dull and monotonous.

Learner perceptions of a national CLIL innovation in foreign languages in the Republic of Ireland (5474)

This paper describes a Content and Language Integrated Learning (CLIL) curriculum innovation to improve motivation in language learning undertaken in the Republic of Ireland through a national pilot in transition year (TY) in 2021–2023 for learners aged 15–16. Here we extract data from part of an empirical evaluation study focussing on the research question, what are learner perceptions of learning through CLIL approaches in a national pilot module? A CLIL module on the theme of Fair Trade based on geographical and mathematical skills and content was taught through either French, German, Italian or Spanish. Models varied between schools—most undertook the module by teaching two to three lessons per week within a six-eight week period. A minority taught through this approach throughout the year. Results are presented from learner focus groups in three diverse school contexts and an online learner questionnaire drawn from all participating learners in these schools. Group discussions were recorded and transcribed. Thematic analysis was undertaken based on the Process Motivation Model for investigating CLIL in the classroom (PMM). Analysis and discussion include the positive impact on a large majority of learners and practical implications around the nature of learning a linear school subject in TY. Lessons learned include the need to extend this innovation to the wider curriculum, and the need for further professional learning for teachers. Constraints due to the nature of TY year and the module are acknowledged.

Analyzing Student’s Mathematical Critical Thinking Ability of Concept Newman’s Error Analysis Review from Habits of Mind

This study aims to analyze and describe the mistakes made by students in completing mathematical critical thinking skills in terms of habits of mind (HOM) with three categories, namely limited, developing, and proficient. The review was also analyzed from the factors that led to the occurrence of errors based on error analysis according to Newman. This research uses qualitative research methods. The data collection techniques used are questionnaires, tests, and interviews. The instruments used are HOM questionnaires and mathematical critical thinking ability tests. The selection of the study subject was carried out purposively with the consideration that the subject had a HOM category. A total of 25 students who filled out the HOM scale and mathematical critical thinking ability test, 3 students were selected to be interviewed based on the HOM category classification. The data analysis techniques used in this study are data reduction, data presentation, and drawing conclusions. Based on the results of the study, students with limited HOM were only able to solve questions up to indicator 1 because they made mistakes in reading and process skills. Students with HOM develop, only able to solve problems up to indicator 2 due to Comprehension and transpormation errors. Students with proficient HOM, are able to solve questions up to indicator 3 because they make mistakes in the skill and encoding process.

Exploring the Effect of Mathematics Skills on Student Performance in Physics Problem-Solving: A Structural Equation Modeling Analysis

AbstractStudents’ success in physics problem-solving extends beyond conceptual knowledge of physics, relying significantly on their mathematics skills. Understanding the specific contributions of different mathematics skills to physics problem-solving can offer valuable insights for enhancing physics education. Yet such studies are rare, particularly at the high school level. This study addresses the underexplored area of this topic in secondary education by investigating the associations between physics problem-solving performance using a robust methodological framework. We applied exploratory factor analysis (EFA) to identify latent sub-mathmetics skills relevant to physics problem-solving and employed structural equation modeling (SEM) to examine the causal impact of these skills on students’ performance in physics. The study analyzed data from a municipal-wide assessment involving 1,878 grade 12 students in Southern China. The results demonstrate that mathematics skills impacting high school students’ physics problem-solving performance can be categorized into two sub skills, algebraic skills and geometric skills. It also indicates that algebraic skills have a stronger direct effect on physics problem-solving performance compared to geometric skills in high school setting. These findings suggest that integrating focused algebraic training within physics education can significantly improve student outcomes in STEM fields. We recommend that educators design curricula and instructional strategies that emphasize the development of algebraic skills necessary for solving complex physics problems. Additionally, these findings have important implications for policymakers, who should consider integrating targeted mathematics training within physics curricula to foster interdisciplinary learning and better prepare students for challenges in STEM education.

Systematic Review on the Essentials of Creative Mathematical Thinking

Creative thinking skills can prepare students to be tangent, creative, and competent problem solvers in an ever-evolving world, so educators are required to understand patterns and factors that positively influence the development of creative thinking skills. The aim of this research is to identify patterns and factors that influence creative thinking skills in learning. The method used in this research is the exploration and conceptualization of mathematical creative thinking skills. The research explored 15 articles through Scopus databases, Google Scholar, Publish or Perish, and Google. Data analysis is conducted through CAQDAS ATLAS.ti, with coding objectives, methodology, and research conclusion. This research found that most of the articles highlighted task orientation, epistemological approaches, problem submission tasks, Multidimensional Creativity Assessment (MCA), tutor beliefs, problem solving, SCAMPER methods, valid instruments, social skills, confidence, belief and anxiety, and Practical Mathematical Talent Models. Overall, the contributions from this research have shown the importance of building creative thinking skills in mathematics and science education, along with various approaches and factors that contribute to the development of such skills.

Breaking Math Anxiety: A Success Story From an Indian Government School

Mathematics anxiety and fear among children pose significant educational challenges worldwide. This study examines the efficacy of a hybrid learning approach that combines digital game-based learning with hands-on activities to enhance mathematics engagement, reduce anxiety, and improve numeracy skills while fostering algebraic and mathematical thinking. The research was conducted at Government School, Ramagondanahalli, Bengaluru (RGHL), involving over 400 children aged 6-10 years from grades 1-5. Participants were primarily first-generation learners from economically disadvantaged backgrounds with limited access to educational resources. The intervention comprised weekly 70-minute sessions over six months, featuring the digital game "Magic Math Spell Caster" alongside modified traditional board games such as Snakes &amp; Ladders, Bingo with Place Value Cards, and a custom Memory Card Game. The curriculum also incorporated activity worksheets with math manipulatives and practice sheets. The didactical approach underpinning the intervention was based on six key principles: Treating mathematics as a language to be spoken, promoting algebraic thinking; Structuring games into levels with well-defined learning objectives to scaffold mathematical thinking; Connecting concrete and abstract concepts to deepen understanding; Employing a hands-on approach to reinforce learning; Providing resources to every child to ensure equal access; Integrating assessments as digital interactive worksheets within gameplay. This approach allowed children to explore, make connections, and construct knowledge independently, fostering both algebraic and broader mathematical thinking skills. The program encouraged peer-to-peer learning by grouping children with different math proficiencies. Students progressed through game levels at their own pace, often exceeding curriculum expectations. This study contributes to the growing body of evidence supporting hybrid learning approaches in mathematics education for all children, emphasizing the development of robust mathematical and algebraic thinking skills.

Improving Mathematical Problem-Solving Skills through the Development of Interactive Digital Modules

Modul digital merupakan bahan pembelajaran dengan visualisasi konten berformat digital yang dapat diakses menggunakan perangkat elektronik. Penelitian ini bertujuan untuk mengembangkan media pembelajaran berupa modul digital interaktif serta efektivitasnya dalam pembelajaran. Modul digital interaktif dikembangkan mengadopsi tahapan model Alessi dan Trollip yaitu planning, design, dan development. Teknik pengumpulan data dengan kuesioner dan test hasil belajar terkiat kemampuan pemecahan matematis. Berdasarkan hasil uji alpha modul digital interaktif, penilaian ahli desain 83.3%, penilaian ahli materi 82%, dan penilaian ahli media 84.34%. Penilaian peserta didik terhadap modul digital interaktif 82.4% (sangat praktis). Penerapan modul digital interaktif dalam pembelajaran matematika dapat meningkatkan kemampuan pemecahan matematis dengan peningkatan 0.4 (sedang). Digital modules are learning materials with visualisation of digital format content that can be accessed using electronic devices. This research aims to develop learning media in the form of interactive digital modules and their effectiveness in learning. The interactive digital module was developed adopting the stages of the Alessi and Trollip model, namely planning, design, and development. Data collection techniques with questionnaires and learning outcomes tests related to mathematical solving ability. Based on the results of the interactive digital module alpha test, the design expert assessment 83.3%, material expert assessment 82%, and media expert assessment 84.34%. Learners' assessment of interactive digital modules 82.4% (very practical). The application of interactive digital modules in learning mathematics can improve mathematical solution skills with an increase of 0.4 (medium).

Enhancing mathematical problem-solving ability through project-based learning: A study of vocational high school student

This study aims to improve the mathematical problem-solving ability of students at Vocational High School (VHS) through implementing Project Based Learning (PjBL). The research method used was a quasi-experiment with a matching-only pretest-posttest control group design, with a sample of 64 students divided into two classes, namely experimental and control classes, each consisting of 32 students. The sampling technique used was purposive sampling, where the sample was selected based on specific criteria relevant to the research objectives. Data were collected using tests of mathematical problem-solving ability administered before (pre-test) and after (post-test) the treatment. Data were analyzed using an independent sample t-test and a two-way ANOVA test with univariate general linear model (GLM) analysis. The results showed a difference between the experimental and control groups before the treatment. However, after the treatment, the experimental group had higher mathematical problem-solving ability than the control group, including the improvement and interaction between PjBL implementation and the Early Mathematics Skills (EMS) category.