School Mathematics Research Articles

Ретроспективний огляд дисертацій українських дослідників з теорії і методики навчання математики

In this article, we conduct a retrospective review of dissertation research by Ukrainian mathematics educators in the field of 13.00.02 Theory and Methodology of Mathematics Education, covering the historical period from the mid-20th century to 2024. We consider this review useful for substantiating the need for knowledge about the development of methodological science (mathematics) in the process of forming the methodological competence of future mathematics teachers. Referring to the creative scholarly contributions of prominent Ukrainian mathematics educators and highlighting their methodological views in the context of historical epochs serves as an effective tool for researching and reconstructing facts about methodological science. Specifically, we provide a concise analysis of dissertations (Hlushkov P.M. (1952), Hichiy O.F. (1960), Danyliuk P.F. (1971), L.V. Kuzmych (1998)), which explore specific historical aspects of the development of Ukrainian methodological science. The information we collected about the number of dissertation studies conducted in Ukraine in various research areas during the historical period from the mid-20th century to 2024 is reflected in a table. We analyzed the topics of nearly 300 dissertations. In our study, the analysis of dissertation topics performs several functions: to identify the achievements of Ukrainian methodology in mathematics education as a science, to clarify the main trends in research on the didactics of mathematics over different time periods, and to determine the relevance and level of research on the history of the development of Ukrainian methodological science. Reform processes in the field of school mathematics education since the second half of the 20th century are interconnected with the results of dissertation research in the specialty 13.00.02 Theory and Methodology of Mathematics Education conducted in Ukraine during this period. The quantitative analysis of dissertation research conducted in Ukraine in various research areas allowed us to clarify the relevance of dissertation topics over different time periods and, accordingly, the trends in the development of the theory and methodology of mathematics education in Ukraine. Turning to the national methodological heritage and understanding contemporary national achievements in methodological science has significant scientific and practical importance, as it is a vital component in forming the national-patriotic consciousness of teachers and should contribute to the development of the methodological culture of creative mathematics educators.

METHODOLOGY FOR SOLVING EQUATIONS WITH MULTIPLICATIONS OF INTEGER AND FRACTIONAL PARTS IN SCHOOL MATHEMATICS LESSONS

This article describes the ways in which equations involving integers and fractions are given in school mathematics classes and their solution methods.

Study on Secondary School Mathematics Teaching Based on Blended Teaching Model in China

Blended teaching is of great significance for improving the quality of secondary school mathematics teaching and students' interest in learning mathematics. In recent years, some scholars have done research on the blended teaching model of secondary school mathematics, but there has not been any literature to sort out and summarize them. In order to determine the aspects included in the current research on secondary school mathematics teaching based on blended teaching, and to identify the deficiencies in the current research. This paper adopts the method of literature analysis to analyze the previous studies. That's 14 articles in all and draws the following conclusions: (1) Previous research mainly focuses on five aspects, the analysis of the current situation, the connotation of blended teaching, the advantages and significance of blended teaching, the implementation strategy of blended teaching in secondary school mathematics, and specific cases. (2) The research methods are relatively single, mainly qualitative research and less quantitative research. (3) The researchers are mostly teachers in secondary schools, and there are fewer studies by university professors and educational experts. (4) The research content are similar, most scholars have divided the blended teaching into three phases: before, during and after class, respectively, starting from how to do it online and offline, and the combination of online resources and offline teaching is shallow. (5) There are still some blank spots to be researched. For example, the challenges and deficiencies of blended teaching in secondary schools in China and how to deal with them; how blended teaching should be carried out in rural and remote areas; how to evaluate under blended teaching of mathematics in secondary schools. Therefore, it is necessary for future research to conduct deeper research on secondary school mathematics teaching under blended teaching with diversified research methods.

Interactive animation media and students' learning interest in learning mathematics in elementary schools

Interactive animation media and students' learning interest in learning mathematics in elementary schools

Teachers’ Reflections on Teaching Mathematics in English: A Consideration for Developing ESP Course

This research aimed to identify the Reflections done by mathematics teachers when delivering material when teaching mathematics in international schools. The study was conducted at Permata Bangsa Elementary School, which follows the Cambridge Curriculum and involved mathematics teachers from this school. This study used a Qualitative Method. Data were collected through interviews to obtain in-depth insights, and an interactive analysis method was used. The research found that they use the Team teaching method to improve their English fluency by studying from reference books and other print and online sources and working with their fellow teachers. Mathematics teachers actively aim to increase their knowledge related to mathematics through continuous learning, using special applications, book references, and YouTube online materials, attending webinars, exploring educational websites, collaborating with colleagues, and leveraging technology and online resources. The study's findings provide valuable insights for designing ESP courses for mathematics teachers and help teachers better prepare their English competence.

Змістова лінія «Функції» шкільного курсу математики та особливості її вивчення в середній школі

The article reveals the important circumstances and peculiarities of the study of the content line "Functions" in the school mathematics course. Among the circumstances is a different interpretation of the concept of function: in the basic school, the function is considered (classical approach) as a dependence between variables, and in the senior profile as a correspondence (modern, modern definition) between the elements of two sets. This leads to different schemes for studying the properties of a function and constructing its graph. It is noted that the content line "Functions" is the leading line of the school course of algebra, algebra and the beginnings of analysis. It is the basis for studying equations, inequalities, identical transformations of algebraic expressions, the beginnings of probability theory, geometric quantities (area of a figure, volume of a body, surface area of a body, etc.). It starts in grade 7 and is taught in three stages: Stage 1 - grades 7-9. The main purpose of studying functions is to justify the study of linear, quadratic, fractional rational equations and inequalities, identical transformations of single terms, polynomials and fractional expressions, to teach how to use them as mathematical models in the study of physics, solving practical and applied problems; Stage 2 - grades 10-11, when basic elementary functions and their important properties (increasing, decreasing, periodicity, continuity) are studied. The main goal of the course is to teach students to solve irrational, trigonometric, and exponential equations and inequalities, transform corresponding algebraic expressions, and create graphs of the glass

MATEMÁTICA ACADÊMICA E MATEMÁTICA ESCOLAR NO ÂMBITO DO CURSO DE GRADUAÇÃO EM LICENCIATURA EM MATEMÁTICA

This article analyzes the relationship between academic mathematics and school mathematics in the context of undergraduate mathematics courses. Definitions of both are provided, based on authors who argue on the subject. The importance of these conceptions in the training of mathematics teachers and mathematicians is also highlighted. The authors researched and their writings form the entire theoretical basis of the work, which consists of a bibliographical survey, so that it is possible to observe that, although there is a fundamental relationship between them, there is also a perceptible difference. In the mathematics degree course, it is possible to verify the existence of subjects that contemplate each of the two perspectives mentioned. In view of this, the aim of this paper is to establish an analysis of the contributions that Academic Mathematics and School Mathematics make to teacher training and performance, which facilitate student learning, with more descriptive definitions and the use of methodologies aimed at communicating mathematical knowledge in an objective and practical way.

비와 비율 개념 지도에 대한 초등수학 교과서 분석: 2015 개정 초등수학 교과서를 중심으로

Objectives The purpose of this study is to analyze how prior knowledge is utilized in introducing the concept of ratio and how context is utilized in introducing the concept of rate in 11 elementary school mathematics textbooks according to the revised 2015 curriculum, and to derive implications for teaching ratio and rate based on this. Methods From prior research, we derived the prior knowledge(subtraction comparison, division comparison, orrespondence relationship, multiple-batches perspective) that can be utilized in the introduction of the concept of ratio and the form of context utilization(whole-part rate, part-part rate, rate of two equal quantities) in the introduction of the concept of rate, and based on this, we analyzed the ratio and rate sections of 11 textbooks. Results In the introduction of the concept of ratio, 7 out of 11 textbooks were classified into passive use of subtraction comparison-division comparison, 2 textbooks were classified into active use of subtraction comparison-division comparison, 1 textbook was classified into subtraction comparison-division comparison and utilization of correspondence relationship, and 1 textbook was classified into utilization of multiple-batches perspective and correspondence relationship. In the introduction of the concept of rate, 8 out of 11 textbooks utilized the whole-part rate, 2 textbooks utilized the part-part rate, and 1 textbook utilized the context of the rate of two equal quantities. Conclusions This study confirmed that the 2015 revised elementary school mathematics textbooks attempted various approaches in introducing the concepts of ratio and rate, and the results of this analysis provide implications that can contribute to increasing the effectiveness of learning ratio and rate in elementary school mathematics education.

School Mathematics in Colonial India

This article analyzes a popular arithmetic textbook, Arithmetic: For the Use of Schools and Colleges, authored by Jadav Chandra Chakravarti, to examine the contents and pedagogies in the text for how mathematics was taught and learned from the end of the nineteenth century through the first half of the twentieth century in colonial India. The study findings provide us with a glimpse of the teaching and learning of mathematics in colonial India and help us to better understand current school mathematics and its curriculum evolution and development in the subcontinent. Even though Chakravarti’s textbook is mainly based on rule-method pedagogy, it has simple descriptions of rules and procedures, and a gradual progression from simple to complex in exercises and topics, which was unique at the time. The textbook maintains coherence in its style and presentation of the contents, and engages students and teachers by reflecting social life and cultural traditions in colonial India, which perhaps contributes to a long period of popularity of this book in the Indian subcontinent. The textbook has its legacy in modern education in the Indian subcontinent. Still, in the subcontinent, textbooks are one of the main sources of mathematics teaching and learning, as well as test preparation for high-stakes exams.

WORKING ON ARITHMETIC OPERATIONS IN PRIMARY SCHOOL LESSONS

This article highlights the topic of working with arithmetic operations in primary school mathematics lessons. It discusses how to teach students the arithmetic operations of addition, subtraction, multiplication, and division, focusing on when and in what order these operations should be performed.

WORKING WITH ALGORITHMIC TASKS IN PRIMARY SCHOOL MATHEMATICS LESSONS

This article explores methods for working with algorithmic tasks in primary school mathematics lessons, the sequence of algorithmic tasks, and the skills required to correctly structure these tasks. The significance of algorithms in enhancing mathematical literacy among primary school students is explained.

WORKING WITH VARIABLE EXPRESSIONS IN PRIMARY SCHOOL MATHEMATICS LESSONS

This article discusses the issue of working with variable expressions in primary school mathematics lessons.

Students’ Self-Efficacy in Senior Secondary School Mathematics: Academic Engagement as a Predictor Variable

Students’ Self-Efficacy in Senior Secondary School Mathematics: Academic Engagement as a Predictor Variable

The Correlation between Students' Problem-Solving Abilities and Their Mathematical Thinking in High School Mathematics Education

Purpose of the study: The aim of this study is to explore the relationship between students' problem-solving abilities and mathematical thinking, and to identify how these two abilities can support each other in the development of holistic mathematical skills in secondary education. Methodology: This study uses quantitative methods with correlational and survey designs. The instrument used is a written test, consisting of story questions and multiple choices. Data collection is done through structured observation and documentation. The software used for data analysis is SPSS, with descriptive and inferential statistical analysis techniques, including the Pearson correlation test and simple linear regression test. Main Findings: The results of the study showed that there was a strong and significant relationship between problem-solving ability and mathematical thinking of students in grades 11.F1 (r = 0.74, p = 0.001) and 11.F3 (r = 0.68, p = 0.003). Problem-solving ability was also shown to predict mathematical thinking with a significant effect (R² = 0.55, p = 0.001). The problem-solving factor can explain 55% of the variance in students' mathematical thinking. Novelty/Originality of this study: This study shows a strong correlation between secondary school pupils' mathematical thinking and problem-solving skills, particularly when it comes to number-related content. The study's originality is the finding that students' problem-solving skills can anticipate how their mathematical thinking will evolve, offering fresh perspectives for creating learning models that would simultaneously improve both abilities.

Improving Secondary School Mathematics Teachers’ Effective Lesson Implementation through Lesson Study

The main purpose of this study was to explore how engaging in lesson study improves secondary mathematics teachers’ effective lesson implementation to support students’ learning better. The research was conducted in Jimma City, Ethiopia, and employed design-based research with qualitative data collected from two secondary schools and 12 mathematics teachers. A purposive sampling technique was used to select participants. Interviews, observations, and document analysis were the main sources of data. The data were analyzed thematically supported by Atlas-ti qualitative data analysis software. Findings indicated that engaging in lesson study improved mathematics teachers’ effective lesson implementation. LS improved participants’ practice of lesson presentation, use of diverse student-centered teaching methods, assessment, behavior management, instructional aids, time management, and feedback strategies. School leaders’ positive attitudes and teachers’ commitment were found to be supportive, while shortage of time and teachers’ high teaching load were constraints. It would be vital to integrate lesson study into teachers’ school-based professional development programs to improve mathematics teachers’ effective lesson implementation in the study setting. The study suggests further investigation in more secondary schools by incorporating quantitative evidence with larger a sample size.

The development of mathematics revision resources and economics student demand for these resources

Abstract The article describes revision mathematics resources that were developed for students to work through prior to starting their university economics degrees. This was believed to be important as school mathematics syllabi differ. The development of the resources was timely, as when the resources were created, there was also concern that students’ pre university studies may have been disrupted during the pandemic. The resources included short films, sets of notes and multiple quizzing opportunities. The revision resources were made available via the university virtual learning environment. Take up of the resources was very good and the key resources are now also publicly available via The Economics Network website. We tracked students’ use of the revision resources prior to the start of their undergraduate economics degrees in 2023 and during the first term of their studies. The usage data demonstrates the demand for revision mathematics resources, with over 70% of new students engaging with the resources. Data from The Economics Network website support this conclusion. We suggest that usage data provide an important indicator of students’ revealed preference for the resources developed.

Effectiveness of Using Ludo Game-Based Learning Media to Improve Understanding of Spatial Building Concepts in Elementary School Students: Literature Review

Understanding the concept of spatial structures is a significant challenge in elementary school mathematics education due to its abstract nature. This study aims to evaluate the effectiveness of Ludo game-based learning media in enhancing students' understanding of spatial concepts. This research uses a literature review method to analyze various previous studies using game-based media to teach spatial concepts. The findings indicate that Ludo games significantly improve students’ cognitive understanding by visualizing abstract concepts more concretely, fostering active and interactive learning, and reinforcing concepts through repetition. Additionally, this medium enhances students' learning motivation and spatial skills. However, its implementation faces challenges, such as diverse student abilities, limited classroom time, and the need for teacher training to integrate the games into the curriculum. These findings highlight the substantial potential of Ludo games in addressing difficulties in mathematics education, particularly in understanding spatial concepts. This study recommends integrating game-based media into teaching strategies to create a more engaging and effective learning environment.

The methodology of teaching functions in the school mathematics curriculum using information and communication technologies

The article examines modern approaches to teaching the topic "Functions" in the school mathematics course using information and communication technologies (ICT). The relevance of the integration of digital tools, such as graphic calculators, interactive platforms, online boards and visualization tools, to increase the effectiveness of the educational process and better creation of material by students is revealed. Thus, the article describes the advantages of visualizing abstract mathematical concepts and creating a dynamic learning environment for a deeper understanding of functional interaction. The results of the study show that the combination of traditional methods with ICT promotes the development of critical thinking, ensures students' independence and facilitates the understanding of complex mathematical concepts.

Impact of a professional development program in formative assessment for mathematics teachers

ABSTRACT This study investigates the impact of a professional development programme in formative assessment (FA) for high school mathematics teachers. Through a collaborative approach between researchers and in-service teachers, a 16-week online course was designed focusing on feedback strategies, peer co-assessment, and student engagement. A mirrored scale was used where teachers and students reported frequency of FA practices. Pre-post tests were used to measure FA knowledge and practices in teachers (n = 110), as well as their self-efficacy. In students (n = 1029), mathematics learning and FA practices implemented by their teachers were evaluated. The results highlight a significant moderate effect on teachers’ self-efficacy, and large effects in FA knowledge, and implementation of FA practices, with noticeable changes perceived by both teachers and their students. Students perceived larger improvements in collaborative practices and peer assessment and weaker changes in practices that involved them in self assessment. Additionally, a transfer of these changes to students’ mathematics learning was observed, indicating that students’ reports of FA practices significantly impact their mathematics performance. This study underscores the importance of involving students in the FA process to improve mathematics learning.

Unpacking the gender equality paradox: narratives about mathematics and gender among teachers

ABSTRACT In school mathematics in Israel, there are contrasting trends in Hebrew-language and Arabic-language schools. In Arabic-language schools, girls consistently outperform boys in mathematics and are more represented in advanced coursework. This study explores the possibility that dominant narratives associating mathematics with boys and men might be less prevalent in Palestinian/Arab Israeli (P/AI) society. We surveyed 809 elementary, middle, and secondary teachers, including 457 teachers from Arabic-language schools and 352 from Hebrew-language schools, to assess their agreement with the Innate Ability in Mathematics myth (IAM) and the Boys’ Superiority Myth (BSM). On average, teachers from Arabic-language schools indicated moderate disagreement with BSM, but their responses to IAM items were symmetric, with an overall slight leaning towards agreement. Responses to IAM and BSM were positively correlated. Teachers from Hebrew-language schools disagreed more strongly with both narratives. These findings suggest that gender-related trends in school mathematics among P/AIs are shaped by factors other than societal rejection of or alternatives to narratives that associate mathematics with boys and men. The circulation of the IAM and BSM narratives likely influence trends for P/AI women in higher education and professional settings.