School Mathematics Research Articles

‘기둥’과 ‘뿔’에 대한 초등 예비교사의 교과 내용 지식 분석

The purpose of this study was to examine elementary preservice teachers’ subject matter knowledge (SMK) of prisms, pyramids, cylinders, and cones. The analysis of the preservice teachers’ SMK regarding the extension of each solid figure revealed that they had more difficulties with cylinders and cones compared to prisms and pyramids. Some of them classified cylinders and cones as solids of revolution based on the instructional sequence of the curriculum. This study also analyzed their SMK by dividing it into three categories: (a) mathematical definitions, (b) school mathematics, and (c) instructional sequence. The mathematical definitions group demonstrated a high overall level of specialized content knowledge (SCK). The school mathematics group, on the other hand, had mostly common content knowledge (CCK). The instructional sequence group often showed SCK only for cylinders and pyramids. Based on these analysis results, we proposed specific measures for preservice teacher education to develop their SMK and knowledge at the mathematical horizon (KMH).

Impact of Alternative Learning Activity Program on Student Leadership Development in a Science, Technology, Engineering, and Mathematics School

This study explored the impact of the alternative learning activity (ALA) program offered in the Philippine Science High School-Ilocos Region Campus toward students’ leadership abilities. A mixed-methods approach was used to conduct the study through a survey of 132 student leaders affiliated with ALA clubs in the years 2022 to 2024. The results indicated that the participants exhibited strong expertise in communication, critical thinking, character development, citizenship, diversity appreciation, global understanding, and skill development in the measured indicators, suggesting that the ALA program is effective in producing well-rounded leaders. The findings also showed that almost all dimensions of leadership qualities exhibited the strong positive relationships between indicators, indicating their significant relationship and hinting that effective leadership is multidimensional. In ALA clubs, it was found that excellent leadership practices include providing diverse learning opportunities (kataguyod), offering targeted skill training (katuwang), offering mentorship and peer support (kaagapay), provision of leadership support (kalakbay), and inclusivity enhancement (kabahagi). These are beneficial practices, not only instill skills among the members but they also promote personal development. These findings show the importance of specialized leadership training in preparation for varied leadership roles.

Effects of Teachers’ Motivation on Students’ Academic Performance in Mathematics in Public Lower Day Secondary Schools in Rwanda: A Case of Kirehe District

Effects of Teachers’ Motivation on Students’ Academic Performance in Mathematics in Public Lower Day Secondary Schools in Rwanda: A Case of Kirehe District

Influence of Project-Based Learning on Adolescent Motivation in Mathematics in Day Secondary Schools in Rwanda: A Case of Nyamasheke District

Influence of Project-Based Learning on Adolescent Motivation in Mathematics in Day Secondary Schools in Rwanda: A Case of Nyamasheke District

Effects of Geogebra use on the Academic Performance of Students in Mathematics in Public Secondary Schools in Rwanda

This study examines the impact of GeoGebra, a dynamic mathematics software, on the academic performance of students in mathematics at a public secondary school in Nyaruguru District, Rwanda. Specifically, it explores GeoGebra’s use in mathematics, its effects on student performance, and the correlation between its usage and academic outcomes. A sample of 7,916 participants was surveyed, including 69 math teachers, 309 students, and three headteachers. Data were collected through questionnaires, interviews, and observations, using purposive, stratified, and simple random sampling. The study revealed that 87.4% of participants agreed that GeoGebra enhanced students’ mathematical problem-solving abilities, while 94.1% agreed that it improved class participation. Additionally, 89.9% noted improvement in mathematics exam and test performance, with 91.3% observing better homework completion rates. GeoGebra use correlated with higher test scores and increased engagement in mathematical analysis, including trigonometry, transformations, and equation-solving. Although correlations with some outcomes were statistically minor (p > 0.05), the tool consistently supported mathematical independence and exploration. GeoGebra’s interactive features, including graphs, charts, and 3D models, facilitate students’ understanding of complex concepts, fostering improved memory and problem-solving skills. It enables collaborative learning, which promotes critical thinking, and highlights real-world applications of mathematics, increasing engagement. Personalized feedback features allow students to progress at their own pace, suggesting GeoGebra as an effective tool for enhancing mathematical comprehension and performance in secondary education.

Effects of Teachers Qualification and Experience on Students’ Competences in Mathematics Subject in Public Secondary Schools in Rwanda

This research investigates the impact of teachers' qualifications and experience on students' competencies in mathematics in Rwandan public secondary schools. The study aimed to assess how teachers' mathematical qualifications influence students' learning outcomes and to analyze the relationship between teacher experience and student competence. A descriptive research design utilizing a mixed-methods approach was employed, with a sample of 185 respondents selected from a population of 343, including mathematics teachers, head teachers, and students. Data was collected through questionnaires, interviews, and document analysis, using SPSS Version 23 for evaluation. The results were presented in tables and shared with stakeholders to promote teacher development and improve student performance in mathematics. Findings revealed that teacher qualifications significantly affect student competence. Specifically, 37.5% of respondents strongly agreed that teaching experience enhances students' understanding, while 50% agreed. The mean score was 4.21 (SD = 1.6). Additionally, 62.5% affirmed that teaching resources and diverse methods positively impact their learning, with a mean of 4.11 (SD = 1.12). The study also highlighted that specialized training in mathematics motivates students, as indicated by 46.5% who strongly agreed and 48.6% who agreed, with a mean of 4.42 (SD = 0.84). The research recommends that the Rwanda Education Board (REB) and schools support teachers through ongoing training and monitoring to enhance teaching quality. It is essential for teachers to ensure students are comfortable with their teaching methods, provide ample exercises, and foster an appreciation for mathematics as a vital subject in everyday life.

중등수학교사의 수학적 신념에 따른 수업목표 이해 및 과제 선별

The purpose of this study is to determine how secondary school mathematics teachers interpret the geometry unit lesson objectives in relation to the characteristics of teachers' mathematical beliefs and what main tasks they present during specific classes with the interpreted lesson objectives. For this purpose, a survey was conducted targeting secondary mathematics teachers regarding mathematical beliefs, teaching goals, and task selection. As a result of the study, no evidence was obtained that there was a difference in mathematical beliefs depending on the teaching goals understood by teachers. In general, teachers were found to select class goals that correspond to knowledge and understanding, and only in some units did specific mathematical beliefs appear to influence teachers' interpretation of class goals. Second, there was no significant difference in the level of cognitive demand of tasks teachers wanted to present in class depending on the class goals. However, in certain units, it was found that there was a difference in the ratio of cognitive demand levels. The findings provide important implications for better understanding of teachers' behaviors focusing on cognitive demands of tasks and mathematical beliefs.

고등학교 수학교사의 디지털·AI 교육과정 실천 사례: 생태학적 교사 행위주체성에 기반한 탐색

With the advent of the era of digital transformation, digital·AI-related policies are being actively promoted in the curriculum. This study aims to explore high school mathematics teachers’ practice of digital·AI curriculum based on ecological approach to teacher agency. For this, interviews were conducted with four high school mathematics teachers, focused on the following research questions: 1) How do high school mathematics teachers practice the digital·AI curriculum? 2) What are the factors that influence high school mathematics teachers’ practice of the digital·AI curriculum? The results of the study showed that high school mathematics teachers practiced the digital·AI curriculum, showing various teacher agency, ranging from neutral·critical acceptance, passive practice, and proactive implementation. In addition, these various practices are influenced by personal factors (prior experience or knowledge, beliefs to mathematics classes, recognition to future competencies) and contextual factors (school environment, attitudes of mathematics teachers at the same school, teacher learning community). This study discusses the usefulness and value of ecological approach to teacher agency in interpreting mathematics teachers’ curriculum practice, and suggests the need for structural, environmental, cultural support to enable teachers' autonomous and independent practice of the digital·AI curriculum.

의미론적 정합성 관점에서 분수의 연산 단원 분석: 의미 관계와 수량 유형을 중심으로

Mathematical concepts are derived from real-world situations, and their construction and application can be facilitated when real-world meanings and mathematical meanings are aligned. According to educational psychology research, the depth of interpretation and use of operations depend on whether the semantic relations between the objects presented in the problem situation and the potential mathematical relations are consistent. This study analyzed the semantic relations between objects in problem situations and the semantic alignment between the quantity types of objects and visual models in the fraction operation units of elementary school mathematics textbooks. The analysis revealed that, in problem situations, symmetric relationships were predominantly presented in fraction addition, subset-set relationships in fraction subtraction, and asymmetric relationships in fraction multiplication and division. Regarding quantity types, continuous quantities were presented more often than discrete ones, and in most cases, the quantity type of the object matched that of the visual model, though a few did not. Based on these findings, implications were drawn for selecting problem situations and instructional models that align with mathematical meanings and support student understanding from the perspective of mathematics learning psychology.

Motivation and Behavioral Engagement: The Mediating Role of Mathematics Self-Efficacy in Primary Education

The primary objective of this study is to explore the interrelation between motivation, self-efficacy, and behavioral engagement in primary school mathematics learning. This study also examines the mediating role of self-efficacy in the relationship between motivation and behavioral engagement. The research involved 660 fifth and sixth grade students in four schools in Surabaya, Indonesia. The data collected was analyzed using structural equation modeling. The study revealed that motivation is key to enhancing students’ self-efficacy and behavioral engagement during mathematics learning. Additionally, self-efficacy was found to be linked with students’ behavioral engagement. Furthermore, self-efficacy was identified as a mediator in the relationship between motivation toward mathematics and behavioral engagement during mathematics learning. The study provides valuable insights into these variables in the Indonesian context, particularly in elementary schools for mathematics learning. The research also discusses the implications of the study for teaching practices.

Understanding Barriers to STEM: Teachers' Insights on African American Underrepresentation

This study focuses on the development of a measurement instrument to identify Middle and High School mathematics and science teachers’ beliefs about the main factors of underrepresentation of African American students in STEM (Science, Technology, Engineering, and Mathematics) fields. The research method using the stages of instrument development were (1) test design which involved construction of initial item pool by conducting extensive review of literature and coding of participating teachers personal statements (2) determination of validity which involved expert review process to confirm construct and face validity of items, (3) pilot testing which involved collecting data from a second set of participants, (4) determination of reliability which involves conducting a reliability analysis based on data collected from pilot testing and (5) determination of factorial structure which involved Exploratory Factor Analysis (EFA) to identify underlying factors in participating teachers’ belief structures. First, to obtain trustworthy information, voluntary middle and high school mathematics and science teachers were asked to write personal statements where they explain their main reasons for choosing teaching as a career. Secondly, qualitative data obtained from participating teachers’ personal statements were coded. Coding was applied to identify and to group the phrases or sentences that convey the same or similar reasons. Then results from an extensive literature review on this topic were blended in teachers’ common expressions which were determined because of coding procedure. Then 8 content experts assessed content validity and face validity. Finally, the survey was piloted to African American middle and high school mathematics and science teachers. Fifty-three (53) surveys were completed and received back from teachers. Then, exploratory factor analysis was conducted to identify any underlying factors in the scale. Reliability analyses were also conducted for both the entire survey and for each of the factors. Results of the study suggested four underlying components: (1) Access and Resources, (2) Role Models and Representation, (3) Bias and Discrimination, (4) Curriculum and Pedagogy.

OPTIMIZING MATHEMATICS LEARNING IN FIFTH GRADES: THE CRITICAL ROLE OF EVALUATION IN IMPROVING STUDENT ACHIEVEMENT AND CHARACTER

The aim of this research is to describe the role of learning evaluation in fifth grade elementary school mathematics subjects. This research was conducted on Fifth-Grades students of UPT SD Negeri 060809 Medan Kota. The research method used in this research is descriptive qualitative. The subjects in this research are Fifth-Grades students and Fifth-Grades teachers and the objects in this research are the results of interviews and observations. Data collection techniques in this research are interviews with students and teachers, conducting classroom observations, analyzing supporting documents and literature studies. The data analysis technique used in this research is content analysis. The research results show that evaluation of mathematics learning in Fifth Grades of SD Negeri 060809 Medan Kota has an important role in measuring learning achievement, providing feedback, identifying weaknesses and strengths, and directing learning improvements. The evaluation instruments used include oral tests, assignments and portfolios. Apart from that, evaluation also aims to measure academic achievement and character, foster multicultural awareness, and encourage the application of values in real contexts. Furthermore, evaluation also plays a role in developing student learning competencies by measuring student progress, identifying their learning needs, and planning appropriate interventions. It also involves providing constructive feedback, developing metacognitive skills, and encouraging reflection and continuous improvement for students.

Investigation of Secondary School Mathematics Teacher Candidates' Technological Pedagogical Content Knowledge and Information Technology Use through Online Photovoice Method

Investigation of Secondary School Mathematics Teacher Candidates' Technological Pedagogical Content Knowledge and Information Technology Use through Online Photovoice Method

AI 디지털교과서 도입과 활용에 관한 중등수학교사의 인식 조사 연구: 학습자 맞춤 교육 실현을 위한 과제

This study explores mathematics teachers' perceptions of the adoption and utilization of AI digital mathematics textbooks and provides implications for both the development of AI digital textbooks and teacher education. A survey was conducted in November 2023 with 130 secondary school mathematics teachers to analyze their perceptions regarding (1) understanding and necessity of AI digital textbooks, (2) key features, (3) application in mathematics instruction, and (4) teacher professional development. The results reveal that while secondary mathematics teachers recognize the necessity of adopting AI digital textbooks, there is a significant gap in their understanding and experience with the core functionalities. There is a strong demand for features such as learning diagnostics and dashboard to support adaptive learning, along with expectations for student-centered adaptive learning and emotional support. However, concerns were also raised about decreased interactivity and challenges in lesson preparation due to changes in the educational environment. Based on these findings, the study suggests the need for enhanced teacher professional development to deepen teachers’ understanding and support practical implementation, as well as functional improvements to AI digital textbooks to ensure their effective and practical adoption in educational settings.

중학교 수학 교과의 협력적 문제해결을 위한 수업 모형 개발

The purpose of this study is to develop a teaching model of a school mathematics that utilizes meta-affect to help middle school students develop collaborative problem solving skills in mathematics. To this end, a collaborative mathematics learning program based on student-student interaction in mathematics, including a teaching and learning model, a mathematics diary for self-reporting on meta-affect and metacognition, and a letter: writing form for students to write to themselves and their teachers. As a developmental study, this study developed a mathematics teaching model so that mata-affect could be added to the metacognition that had been used for reflective thinking activities in existing research and conducted a case study of applying the CPS-M lesson program to 10 first-year middle school students in cities D and G to confirm its applicability in the field. Based on the analysis of class videos, students' math diaries, and teachers' observation evaluation etc., during the collaborative problem solving process, students used mata-affect to become aware of and control their emotions in the process of understanding and sharing the meaning of the problem and sharing problem solving strategies. In particular, as a result of the pre-post test on meta-affect, students' grades increased in awareness of affect and emotional control among the detailed factors of meta-affect.

The use of multimedia technologies in the illustrative teaching of the school mathematics course

The article emphasizes the importance of combining traditional teaching methods in the school mathematics course with modern illustrative methods. Traditional methods such as lectures and textbooks play a crucial role in the transfer of basic knowledge and concepts. However, the use of illustrative techniques such as visualization, games, and interactive applications can significantly improve students' understanding and assimilation of mathematical concepts. The combination of these methods allows for a more efficient and modern educational environment, encouraging active student participation and encouraging their creative thinking. In the course of the work, it is proposed to talk about the illustrative method and the traditional method, about the advantages and disadvantages of their application, compare the illustrative method and the traditional method, the results of research and their application. Based on data analysis and pedagogical methods, he proposes strategies for integrating multimedia resources to improve the visual and conceptual understanding of mathematical concepts in the school classroom. Analyzing the results of experiments and teaching methods, the authors discuss the practical use of multimedia resources to increase interest and understanding of mathematical concepts among students. In the course of the work, approaches to learning were considered, the advantages and disadvantages of the illustrative method and the traditional method were identified, analogs were analyzed and recommendations were given.

Pictorial Riddle Learning Model to Improve Critical Thinking Skills of Fifth-Grade Elementary School Students in Mathematics Learning

The research aims to see the improvement of Critical Thinking Skills through pictorial riddle learning. The research method used was classroom action research on mathematics and building cubes and blocks for 21 elementary school students in Pangandaran Regency. The instruments used are observation, tests, interviews, and documentation. This study adopted a quantitative data analysis method, including test sheets measuring students' critical thinking skills and teacher and student observation sheets. Based on the research results, it was found that There was an increase in students' Critical Thinking Skills by using the pictorial riddle learning model, as evidenced by the increase in students' motivation in the learning process, the courage to move forward, students' attention when the teacher explained, the courage to answer questions and student participation in the learning process. This can also be seen from cycle I, with an average score of 74.2 or as many as 10 students who completed out of 21 students with a percentage of (57.1%), then experienced an increase in cycle II with an average of 91.4 or as many as 18 of 21 students completed the percentage (85.7%). The N-Gain criterion value was 0.87>0.7 with high criteria. Thus, the Pictorial Riddle Learning Model can improve students' critical thinking skills in mathematics in elementary schools very well.

Understanding the Influence of 21st Century Diverse Mathematics Educators on Secondary School Student Outcomes in Mathematics in Mezam Division, Cameroon

This study explores the influence of 21st-century diverse mathematics educators on student outcomes in secondary school mathematics within Mezam Division, Cameroon. Employing an ex-post facto research design, the study assesses how gender, cultural diversity, and pedagogical diversity among mathematics teachers affect students' academic outcomes. The sample consisted of 518 students from 16 public and private high schools, who had completed their General Certificate of Education (GCE) Ordinary Level exams and were transitioning to Lower Sixth. Data were collected via a self-designed questionnaire, which evaluated perceptions of the impacts of teacher gender diversity, cultural diversity, and pedagogical diversity. Statistical analyses, including one-sample t-tests, revealed that male mathematics teachers had a significant positive impact on student outcomes compared to female teachers. Furthermore, cultural diversity among teachers significantly enhanced students' mathematics outcomes, and pedagogical diversity had a substantial positive effect as well. The findings underscore the importance of balancing gender representation, fostering cultural diversity, and embracing various pedagogical approaches to improve educational outcomes in mathematics. Recommendations include implementing policies for gender-balanced recruitment, supporting cultural inclusivity, and promoting diverse teaching methods to optimize student performance in mathematics.

Making Mathematics Accessible to Visually Impaired High School Learners in South Africa: Teachers’ Instructional Approaches, Assistive Devices and Challenges

ABSTRACT This case study explored the instructional approaches and assistive devices employed by high school mathematics teachers in teaching visually impaired (VI) learners and the challenges encountered by the teachers in facilitating the learners’ construction of mathematical knowledge. The participants were two high school mathematics teachers from a special school for the visually impaired in South Africa. Data was collected via semi-structured interviews and lesson observation. Inadequate skills in using Braille codes, time constraints, lack of learners’ home support structure, and technology failure are some of the challenges encountered by the teachers in teaching the VI learners. The approaches used by the teachers to teach mathematics to the VI learners in this study are direct instruction, contextual linking, scaffolding, peer tutoring, and problem-solving. The technologies the teachers used included text enlargers, text translators, text embossers, structure embossers, and scientific talking calculators. The study recommends in-service training for teachers teaching mathematics to

The development of pre-service teachers’ competence to teach mental calculation strategies

Background: There is a concern in South Africa that pre-service teachers do not have the required knowledge to teach mathematics in primary school and to develop learners’ number sense. In this study, pre-service teachers taught the mental strategy of bridging through ten through a structured teaching sequence from the Mental Starters Assessment Project (MSAP) materials as a work-integrated learning opportunity.Aim: We ask the question: How do the MSAP materials support pre-service teachers in competently teaching mental mathematics?Setting: Thirty-eight Bachelor of Education (Foundation Phase) third-year preservice teachers from an Eastern Cape university participated in this study.Methods: Participants taught the strategy during their Teaching Practice, quantitatively analysed the results of their classes and reflected on the experience in a questionnaire and focus group interviews.Results: Results indicate that the teachers were relatively successful in their teaching of the strategy; however, all indicated that they taught the sequence for a more extended period than recommended. Qualitative responses provide evidence of the teachers’ development in their knowledge of learners and their characteristics, general pedagogical knowledge, pedagogical content knowledge and knowledge of educational contexts.Conclusion: This study offers evidence of the professional learning of pre-service teachers that resulted from taking an integrated approach to facilitating a mathematics teaching methodology course through requiring a work-integrated learning component.Contribution: We argue that such an approach is necessary for pre-service teachers to be adequately prepared for the challenges of teaching mathematics in the South African classroom.