Mathematics Learning Research Articles

Deep Learning for Solving Partial Differential Equations: A Review of Literature

Partial Differential Equations (PDEs) are fundamental in modeling various phenomena in physics, engineering, and finance. Traditional numerical methods for solving PDEs, such as finite element and finite difference methods, often face limitations when applied to high-dimensional and complex systems. In recent years, deep learning has emerged as a promising alternative for approximating solutions to PDEs, offering potential improvements in both efficiency and scalability. This paper provides a comprehensive review of the literature on deep learning-based methods for solving PDEs, focusing on key approaches such as Physics-Informed Neural Networks (PINNs), deep Galerkin methods, and neural operators. These methods leverage the expressiveness of neural networks to capture underlying physics while avoiding the curse of dimensionality associated with classical techniques. We explore the theoretical foundations, advantages, and limitations of these deep learning models, along with their applications in diverse fields like fluid dynamics, quantum mechanics, and financial modeling. Additionally, this review examines recent advancements in hybrid models that combine traditional numerical methods with deep learning approaches to enhance accuracy and stability. Through this review, we highlight key trends and open challenges in the field, paving the way for future research at the intersection of deep learning and computational mathematics.

Think Pair Share Learning Assisted By Wordwall On Mathematics Learning Outcomes

Mathematics is a mandatory subject that plays an important role, therefore the lack of adjustment to learning models and supporting media in the learning process can be one of the factors causing low learning outcomes. The purpose of this study was to determine the effect of think pair share supported by wordwall on the mathematics learning outcomes of fifth-grade students at Elementary School. The research was conducted at SDN Batu Ampar 02 Pagi in the second semester of the academic year 2023/2024. The research method used was quantitative research with a quasi-experimental design. The sampling system used non-random sampling of 30 students in the experimental class and 30 students in the control class. The instrument used was an essay test that had been validated and tested for reliability. In data analysis, tests for analysis requirements were conducted through tests of normality (Kolmogorov-Smirnov) and homogeneity, while hypothesis testing used independent sample t-test with SPSS version 29.0.0.0. Based on the analysis, it was found that the average learning outcomes of the experimental class using think pair share supported by wordwall were 79.75, which was significantly better than the average learning outcomes of the control class students using conventional learning, which scored 70.25. The t-test result obtained a sig value (2-tailed) of 0.003 (0.003 < 0.005), hence Ha is accepted and H0 is rejected. Therefore, it can be concluded that in this study, there is an influence of the think pair share supported by wordwall learning model on the mathematics learning outcomes of fifth-grade elementary school students.

Teachers’ Perceptions towards Practical Instruction Approach in Teaching Mathematics: A case of Selected Teachers in Ugandan Secondary Schools

Globally, there is a need to address learners' academic achievement, which has historically been poor, particularly in underdeveloped countries. Practical instruction (PI) approach has been perceived by many teachers as a better teaching strategy. Students in Ugandan secondary schools have consistently performed poorly in their O'Level national mathematics examinations. This has been attributed to teachers' failure to teach these students with practical approach in some examinable topics, making the subject very abstract to candidates. This qualitative case study analyzed teachers' perceptions of the practical instruction approach to teaching mathematics and its impact on students' academic achievement in mathematics. Sixteen teachers from chosen secondary schools in Kigezi and Ankole regions were interviewed for the study in order to understand more about their opinions on the value and use of practical instruction in the teaching and learning of mathematics. The data gathered were analyzed using thematic analysis. The study showed that teachers regard PI as one of the best teaching methodologies since it incorporates components that help improve students' creativity and critical thinking. The study also indicated that teachers' perceptions of practical instruction approaches for teaching mathematics are diverse and influenced by a variety of circumstances. Creating supportive settings, offering professional development opportunities, and providing access to resources can assist teachers in effectively incorporating practical instruction methodologies into their teaching practice, resulting in improved student learning outcomes in mathematics. It is recommended that teachers should be well prepared before commencing the teaching and learning process, including all PI components.

Pursuing systemic improvement through heterarchical school systems: A case of educational resources

AbstractEngland's schooling landscape is being remodelled and the move from hierarchical to heterarchical modes of governance has implications for systemic change strategies. Balancing local and networked autonomy with centralising policies complexifies choices for schools, creating tensions that this article explores through the context of curriculum resourcing policies. In particular, we consider the contemporary case of mathematics textbook schemes in England's heterarchical school system, comparing them with an earlier resource‐driven systemic change programme—the National Numeracy Strategy—which was implemented in a more hierarchical governance system. Drawing on key ideas from implementation science and data from a Wellcome‐funded study of primary teacher professional learning in mathematics in England, we exemplify the challenges of implementing centralised improvement policies in a nominally schools‐led, self‐improving, heterarchical education system. Each of the 19 participating schools had evolved a bespoke curriculum, and these hybridised ‘mashups’ of different resources were enacted with varying degrees of fidelity by teachers. We discuss the implications of this comparative case for systemic improvement, both in the use of educational resources and for policy implementation more generally.

Exploring The Perceptions and Use of Information and Communication Technology Tools Among High School Mathematics Teachers in The Northern Region of Ghana

This study explored the extent to which senior high school mathematics teachers in the Northern Region of Ghana use Information and Communication Technologies (ICTs) in teaching and learning mathematics. A descriptive survey design was employed for the investigation. Using a stratified sampling technique, 20 public high schools in the northern region of Ghana were selected for the study. A simple random sampling was used to select 100 teachers (i.e., 50 teachers from urban and 50 teachers from rural schools) from the 20 schools for the study. Questionnaires were used to collect data for the study. The findings revealed that the mathematics teachers’ perceived knowledge of the benefits of ICT usage for instructional delivery, assessment, and professional learning networks in mathematics were low compared to their actual usage of the ICTs for the same purposes. The findings suggest that the participants utilize ICTs more for social networking than for instructional delivery, assessment, and professional development in mathematics. Further, the findings showed a positive relationship between the teachers’ perceived knowledge of the benefits of ICTs usage for instructional delivery and their actual use of ICTs for instructional delivery. Mathematics teachers from urban schools use ICTs for all instructional purposes more than their peers from rural schools. Implications for ICT policies, teacher training, and professional development are provided.

Enhancing mathematical function understanding in university students: a comparative study of design thinking vs. traditional teaching methods

Mathematical education requires innovative didactic strategies to enhance the understanding and application of mathematical concepts, as traditional teaching methods often lack relevance. This methodology aims to develop a problem-solving scientific approach called design thinking as a strategy for learning mathematics functions. The study was applied to a sample of 138 students of biochemical, biological, and industrial engineering careers attending the first academic cycle at the Faculty of Natural and Exact Sciences of the Particular Technical University of Loja-Ecuador. The methodology uses a quasi-experimental design with a convenience sampling method. All participants were divided into a control group (C, D, K) and an experimental group (P, Q, R). Knowledge, skills, perceptions, and engagement were measured through pretest, posttest, workshop, rubric, project, and survey instruments. The pretest results indicate that both groups had similar knowledge of mathematical functions (pretest mean experimental group: 1.42/2 and mean control group: 1.55/2). Moreover, after applying design thinking strategy to the experimental group, variables questionnaire, project, and workshop show statistical differences (p < 0.001) between groups related to the traditional learning strategy, increasing the experimental group’s score in the project (posttest mean experimental group: 1.62/2 points, and mean control group: 1.65/2). The survey opinion indicates that 53.5% of the experimental group highlighted the project’s development as positively impacting their academic training. In conclusion, problem-solving design thinking using scientific projects as a mathematical function learning strategy contributes to improving the comprehension of polynomial functions and developing mathematical competencies, abilities, and skills to generate tangible solutions for real problems.

Upaya Meningkatkan Hasil Belajar Matematika Materi Bangun Datar dengan Pendekatan Matmatika Realistik di Kelas V SDN 101766 Bandar Setia

The purpose of this research is to see the results of learning mathematics on flat shapes material after using a realistic mathematics approach in class V of SD Negeri 101766 Bandar Setia. The research method used is Classroom Action Research (CAR). The CAR model used consists of 4 stages, namely planning, action, review (observation), and reflection. The subjects in this study were 22 students of class V-B of SD Negeri 101766 Bandar Setia, consisting of 10 male students and 12 female students. The data collection technique used in this study was observation and test analysis. The results of the study from the implementation of two cycles showed that the percentage of student learning activities increased by 60% in cycle I to 88.5% in cycle II. The percentage of student learning outcomes also increased from 59% (good) in cycle I to 86% (very good) in cycle II. Based on the results of the data analysis obtained, it can be concluded that the realistic mathematics approach can improve student learning outcomes in the mathematics subject of flat shapes material in class V of SD Negeri 101766 Bandar Setia

The Perceived Value of Proving in Learning Engineering Mathematics and its Dependence on Motivation and Study Habits

This study reports on engineering students (N=369) from two Swedish universities and focuses on their perceived value of proving in learning engineering mathematics and some factors that may explain the observed variation in the perceived value. Our findings show that there is no significant difference in the perceived value between female and male students. In general, proving is not highly valued, and students are not confident in their skills in proving, except for proving by mathematical induction. However, students’ motivation in mathematics correlates with the perceived value and certain study habits are more regular among those students who appreciate proving as a suitable method for learning mathematics. Examples of such study habits include actively communicating with mathematics course teachers and reading the course textbook both before and after lectures.

Mobile-Based Realistic Mathematics Learning Design to Improve Students' Reasoning Ability and Problem-Solving Ability

<p> Mathematical reasoning and problem-solving skills have become a very necessary need at this time. Students who do not have mathematical reasoning and problem-solving skills will have difficulty adapting to current technological advances. The purpose of this study is to design mobile-based mathematics learning to improve students' mathematical reasoning and problem-solving skills. The subjects of this study were junior high school students. The research method developed was ADDIE (Analysis, Design, Development, Implementation, Evaluation). The results of the study showed that improving students' mathematical reasoning skills had a very positive impact on students' mathematical problem-solving skills. These results provide additional contributions and references for mathematics teachers who want to add knowledge related to improving the quality of mathematics learning in the classroom.</p>

LEARNING MATHEMATICS IN TELUKDALAM MARKET: CALCULATING PRICES AND MONEY IN LOCAL TRADE

This study aims to develop a contextual mathematics learning method using the market as a learning medium in Telukdalam. The main focus of the research is to enhance students' abilities in calculating prices and money within local trade. Through this approach, students not only learn basic mathematical concepts but also relate them to real-life situations they encounter in their daily lives. A literature review method is employed to examine relevant literature on contextual mathematics learning and the importance of social interaction in the learning process. The results indicate that learning experiences in the market can enhance students' motivation and understanding of mathematical material. Additionally, this learning approach enriches local social and cultural values, leading students to appreciate their environment and traditions more. It is hoped that the findings of this study will contribute to the development of a more relevant and contextual mathematics curriculum.

Dimensional versus categorical approach: A comparative study of mathematical cognition

BackgroundResearchers have employed two distinct methods to understand the cognitive underpinnings of mathematical ability: categorical and dimensional. These two methods have different underlying assumptions. However, to the best of our knowledge, research to date has not empirically tested which method can better predict variance in mathematical ability. Method104 children from Indian public schools in the 3rd and 4th grades completed a mathematical ability test. For the categorical approach, participants were categorized into two groups: mathematical learning difficulty and high math achieving. For the dimensional approach, the data of all participants were considered. The cognitive abilities measured included approximate number system, working memory, inhibitory control, and spatial ability. ResultsMixed factorial ANOVA and hierarchical regressions revealed that the dimensional approach demonstrated better predictive power for mathematical ability than the categorical approach. ConclusionsThe dimensional approach offers a more comprehensive insight into mathematical cognition, enabling greater control over the predictors.

Sustaining Teacher Education During COVID-19: Challenges with Remote Teaching and Learning Faced by Preservice Mathematics Teachers

Education institutions worldwide implemented remote teaching and learning to ensure the sustainability of their academic programmes and continuity of study. However, evidence from the literature revealed that remote teaching and learning posed challenges to teaching and learning. This study seeks to explore whether there is a relationship between remote teaching and learning and the challenges faced by preservice mathematics teachers when learning mathematics education during COVID-19. It focuses on remote teaching at four universities: two in South Africa, one in Ghana, and one in New Zealand. The study design followed a quantitative research approach, with 95 preservice mathematics teachers from the four universities randomly assigned to complete an online survey after signing informed consent forms. This study revealed two challenging factors facing preservice mathematics teachers during remote teaching and learning: data, and technological devices for learning. The findings revealed no significant difference (p < 0.000) between remote teaching and learning and the challenges faced by preservice mathematics teachers when learning during the COVID era. Therefore, the null hypothesis is rejected, since p < 0.05. This study concludes that a significant relationship exists between accessibility to technological devices for learning as a challenge to preservice teachers and remote teaching and learning during COVID-19. It is recommended that appropriate technological devices are provided to assist preservice teachers to study mathematics education, thus ensuring continuing access to quality education.

Parents' use of sustained shared thinking during joint mathematics activities with young children: Aninvestigation of its measurement, antecedents, and outcomes.

There is currently a dearth of tools to assess parents' use of effective interactive strategies for supporting early mathematics learning. One potential such strategy is sustained shared thinking. This study therefore constructed and validated a scale for measuring parents' use of sustained shared thinking during joint mathematics activities with young children, and examined its antecedents and outcomes. Four hundred and sixty-six parents completed a questionnaire about their conceptions of mathematics teaching and learning, home practices, as well as their kindergarten children's approach and avoidance motivation to learn mathematics. Additionally, the children were tested on numeration skills. Results showed that our new scale has three factors: exchanging ideas with children about mathematical problem-solving processes, creating a child-centred atmosphere for mathematics learning, and engaging children in mathematical thinking. Parents' uses of these three strategies were predicted by their constructivist conception of mathematics teaching and learning, and were differentially associated with the children's numeration skills, approach, and avoidance motivation to learn mathematics. Potential uses of our new scale in future home mathematics environment research are discussed.

Students' Creative Thinking Strategies As High-Level Thinking, Solving Hot Problems In Improving Mathematics Learning

Creative Thinking Strategy of Students as Higher-Order Thinking, Solving Hot Problems Under Mathematics Learning Improvement. In our observation during PLP at SMK 2 Pancasila Jember, all students in one flat improved their' creative thinking strategy To improve higher-order thinking in mathematics learning. Therefore, this condition results in an imbalance in learning practices. Thus, this study fills the imbalance gap by describing students' creative thinking strategies as higher-order thinking skills in improving mathematics learning. Results of the study: This can contribute knowledge for educators to manage teaching strategies that can improve mathematics learning, which refers to higher-order thinking skills for all levels of creative thinking. This study is a qualitative descriptive study. The course is SMK 2 Pancasila Jember data collection, a test, observation, and interview. Data analysis is done using the data reduction method, presenting data, and concluding. The results of this study are descriptions of students' creative thinking strategies as higher-order thinking skills in improving mathematics learning, namely students' problems in planning detailed problems; students take time breaks to make a plan, identify the core of the problem, provide original ideas, provide alternative plan solving problems, combine previous ideas with question problems; operate and implement their plans by creating various solution original.

MATHEMATICS LEARNING STRATEGIES THAT SUPPORT PANCASILA MORAL EDUCATION: PRACTICAL APPROACHES FOR TEACHERS

This study aims to identify and develop mathematics learning strategies that support moral education based on the values of Pancasila. Using a qualitative approach, the research involves mathematics teachers from several elementary and secondary schools to explore effective methods for integrating Pancasila values into mathematics instruction. The findings indicate that learning strategies, including contextual learning, collaborative projects, and reflective discussions, can enhance students' understanding of mathematical concepts while also strengthening their character. Additionally, the study identifies challenges in implementing these strategies, including time constraints and a lack of training for teachers. It is hoped that these findings can serve as a reference for developing more effective educational practices in integrating moral values into mathematics learning.

Engineering Academics and Students’ Views on the Phases of Teaching and Learning of Engineering Mathematics in an Antenna Design Course

An antenna design course, naturally, aims to teach students to produce an antenna device, which is a vital tool in technological development. Typically, this course is taught and designed in an abstract manner, which may be an inappropriate approach to teaching it. This approach could be due to engineering academics and students’ poor understanding of how to model mathematics concepts. As a result, antennae experts suggest that antenna technology is a difficult device when it comes to mathematical descriptions, which has resulted in a sudden loss of interest among students in a school of engineering. Thus, this paper reports on the four phases of teaching antenna design using mathematical modelling approaches, with the specific aim of resolving the difficulties encountered in teaching an antenna design course. In achieving this teaching, the study explains the approaches and impact of teaching Mathematical Modelling (MM) in antenna design among engineering academics. In this study, the sample population included one engineering academic and four engineering students. The data were collected using a qualitative research approach, utilising an interview guide and an open-ended questionnaire. Finally, the results of this study confirmed the four major phases of teaching antenna design using engineering mathematics.

Analysis of Mathematics Performance Trends in Certificate of Secondary Education Examination, Tanzania, from 2015–2022: A projection for eight years

Mathematics is essential to life as everyone uses mathematical concepts daily. Many countries have advanced in science and technology by investing in mathematics. This study aimed to determine the trend of students who sat for the Certificate of Secondary Education Examination (CSEE) in mathematics from 2015 to 2022; analyse performance trends in mathematics during this period, examine mathematics failure rate trends, and project pass rates in mathematics for the next eight years, from 2023 to 2030. This study employed a quantitative research approach and an ex-post facto research design. Participants were 4,459,009 students who sat for CSEE from 2015–2022. Analysis from the Statistical Package for Social Sciences version 26.0 revealed a consistent rise in student enrollment, with 136,481 more students by 2022. The pass rate was low, as the maximum was 20.12%, while failure rates consistently exceeded 78%. The findings indicated further that the pass rates would remain low from 2023 to 2030. The study recommends reviewing secondary school mathematics curriculum, increasing teaching and learning materials, providing regular in-service training in innovative pedagogical practices and assessment, and hiring more mathematics teachers in secondary schools.

Fostering Inclusivity: A Critical Emancipatory Approach to Dyscalculia in Primary School Mathematics

This research endeavoured to revolutionise primary school mathematics education by implementing an active learning approach tailored to addressing dyscalculia. The study used a critical emancipatory framework as the theoretical foundation, and participatory action research as the chosen methodology. The researcher employed purposive sampling to select two mathematics teachers, one school-based teacher, a district education psychologist, two learners displaying dyscalculia symptoms, and two parents. The research collaboratively engaged participants to identify challenges, crafting interventions, and reflecting on outcomes through the lens of the critical emancipatory framework and participatory action research,. The researcher assessed the effectiveness of the active learning strategy to enhance students’ mathematical abilities, self-efficacy, and attitudes toward mathematics. Critical discourse analysis shed light on the potential of active learning strategies to improve mathematical learning outcomes and create a supportive learning atmosphere. The results indicated that the implemented active learning strategy offers effective pedagogical practices for learners with dyscalculia by influencing positive changes in their attitude towards mathematics and the learning environment. The participating teachers gained insights into understanding the behaviour of learners with dyscalculia and the role of active learning in intervention strategies. The study’s findings can guide educators, policymakers, and researcher in developing inclusive mathematics instruction for diverse learners in primary school classrooms.

The construct of attitude in mathematics education research: current trends and new research challenges from a systematic literature review

AbstractThe crucial role of attitude towards mathematics in the processes of teaching and learning mathematics is now recognized by both school practitioners and researchers in the field. However, “attitude” is a construct borrowed by disciplines other than mathematics education, and it is still conceptualized in various ways within the broad body of research about the role of affect in the teaching and learning of mathematics. In this context, developing a systematic literature review is particularly significant to characterise the recent trends—through the critical description of studies, foci, and approaches—and to guide future research by highlighting new possible research challenges in light of the current state of the art. Adhering to the Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) guidelines, this paper describes the systematic literature analysis of 180 papers published between the beginning of 2016 and the end of 2023, sourced from the Web of Science and Elsevier’s Scopus databases. The review confirms the worldwide interest and production about attitude towards mathematics, highlighting new remarkable findings and interests, such as the critical discussion about the translation of validated scales, as well as the persistence of some typical critical issues related to the “quantitative domain” in methodologies and to the widespread absence of precise definitions for attitude or of appropriate theoretical frameworks.

Parental Gender Stereotypes and Student Well‐Being in China

ABSTRACTA prominent gender stereotype claims that “boys are better at learning mathematics than girls.” Confronted with such a parental attitude, how does this affect the well‐being of 11‐ to 18‐year‐old students in Chinese middle schools? Although well‐being has often been shown to be not much gender‐diverse, the intergenerational consequences of such stereotypes are not well studied. Expecting too much from boys and too little from girls might damage self‐esteem among school kids. Using large survey data covering districts all over China reveals that one‐quarter of the parents agree with the math stereotype. It is shown that this has strong detrimental consequences for the offspring's well‐being. Students are strongly more depressed, feeling blue, unhappy, not enjoying life, and sad with no male–female differences, whereas parental education does not matter for this transfer. Various robustness tests including other than math stereotypes and an IV analysis confirm the findings. Moderating such effects, which is in line with societal objectives in many countries, not only supports gender equality but also strengthens the mental health of children.