National Mathematics Research Articles

The sample is not the population

AbstractGiven sample data, how do you calculate the value of a parameter? While this question is impossible to answer, it is frequently encountered in statistics classes when students are introduced to the distinction between a sample and a population (or between a statistic and a parameter). It is not uncommon for teachers of statistics to also confuse these concepts. An excerpt of a national mathematics examination paper, where a sample is mistaken for the population, is used to illustrate this confusion as well as sample variation and its link to sample size. We discuss two techniques that can be used to explain the difference between a parameter and a statistic. The first is a visual technique in which the variability in calculated statistics is contrasted to the fixed value of the corresponding parameter. Thereafter, we discuss Monte Carlo simulation techniques and explain the contribution that these methods may have.

Utilization of Theoretical and Conceptual Frameworks: An Analysis of National Mathematics Education Theses Published in 2019-2023

This study aimed to examine the use of theoretical and conceptual frameworks in master's and doctoral theses published in the field of mathematics education in Turkiye between 2019 and 2023. For this purpose, a total of 237 master's and doctoral theses downloaded from the Council of Higher Education national thesis center were analyzed within the scope of the method and the framework used. Given that master's and doctoral theses in the field of mathematics education were reviewed, the document analysis method was utilized. The theses were analyzed based on characteristics: methodology (quantitative, qualitative, mixed research paradigm) and framework (theoretical, conceptual, theoretical and conceptual, other). In the analysis phase, the distribution of theses according to types and years was also examined. The findings indicated that the majority of thesis studies were conducted using a qualitative method within a theoretical framework. This was followed by quantitative studies using a theoretical framework and mixed-method studies within a theoretical framework. Additionally, there were qualitative studies classified under other and qualitative studies using a conceptual framework. The qualitative thesis studies using the theoretical framework were predominant and that these were mostly master's theses and published in 2023. The findings were discussed in the light of the relevant literature and suggestions were made for future research.

Why Britain needs a national mathematics discovery centre

On the 3rd of January 2023, the UK Prime Minister, Rishi Sunak, first advocated that Mathematics should be a compulsory subject for all students to the age of 18. He was supported in principle by the following statement from the President of the Royal Society, Professor Sir Adrian Smith, issued on the 4th of January 2023: “Maths, data, statistics and numeracy are essential skills for a modern world, whether for the workplace or for playing an active role in society. If we want our economy to thrive and young people to be prepared for well paid jobs, we need a radical overhaul of our education system that will include all young people doing some level of maths to 18 years of age. The PM understands this and today’s announcement is welcome.

Geometry-based multi-beam survey line layout problem

Abstract The multi-beam measurement system plays a crucial role in ocean mapping and underwater terrain detection. By simultaneously transmitting multiple beams, the system can accurately receive sound waves reflected from the seabed, providing more precise and comprehensive water depth information while effectively revealing the complexity and characteristics of underwater terrain. Under the background and application provided by Question B of the 2023 National Mathematical Contest in Modeling for College Students, this paper investigates the relationship between ocean floor width measurement and factors such as beam position, angle, and slope. Utilizing geometric relations, trigonometric similarity, and sine theorem, a mathematical model is established to determine adjacent strip coverage width and overlap ratio. Furthermore, an optimal strategy is determined by using a greedy algorithm, while binary search backtracking is employed to derive the interval of the next adjacent survey line with the required overlap ratio to obtain an optimal terrain detection strategy.

How teachers’ reading of competency-oriented national mathematics curriculum documents relates to their sense-making of reform messages

Although implementing a competency-oriented national mathematics curriculum is a global trend, limited studies have explored how teachers read their national mathematics curriculum documents and make sense of the competency-oriented reform messages present in these documents. This study investigated the patterns of teachers’ reading of the competency-oriented national mathematics curriculum documents and how the reading relates to the teachers’ sense-making of the reform messages in the documents. Participants included 18 in-service mathematics teachers who took part in a graduate course designed to support interpreting the recently revised competency-oriented national mathematics curriculum documents in Korea. Content analysis of the teachers’ writings regarding their interpretations of the documents revealed three types of reading: <i>identifying</i>, <i>clarifying</i>, and <i>extending</i> competency-oriented curriculum messages. Reading accompanied by ‘clarifying’ formed a <i>dialogic relationship</i> between the teachers and the curriculum, leading to <i>accommodation</i> of competency-oriented messages. Conversely, reading accompanied by ‘identifying’ but without ‘clarifying’ led to a <i>monologic relationship</i> between the teachers and the curriculum, resulting in the <i>assimilation</i> of competency-oriented messages. We conclude by suggesting that teachers’ nuanced interpretations of competency-oriented national mathematics curriculum documents may contribute to professionalism in handling the curriculum.

EFFECT OF SCHOOL FEEDING PROGRAMME PRACTICES ON STUDENTS ACADEMIC PERFORMANCE IN MATHEMATICS SUBJECT IN PUBLIC PRIMARY SCHOOLS IN RWANDA

The purpose of this study is to evaluate how school feeding programs impact academic performance in mathematics among students in public primary schools within Nyanza District. Its objectives were twofold: firstly, to assess the effectiveness of these feeding programs secondly, to determine the relationship between the feeding program and students academic achievements. The research employed a descriptive research design, utilizing both questionnaires and interviews to gather data. A sample size of 173 participants was determined using the Yamane formula, consisting of 155 teachers and 18 head teachers selected via simple random sampling and purposeful selection methods. Data collection involved administering teacher surveys and conducting interviews with head teachers. The gathered quantitative data were analyzed using IBM/SPSS, focusing on percentages and correlation coefficients. Key findings indicated mixed perceptions among respondents regarding the adequacy of food and cleanliness of water provided by the feeding programs. Approximately half of the respondents believed their students performed well in national mathematics exams and learned effectively after lunch, while a majority felt that learners were motivated during teaching activities. The study found a moderate positive correlation (coefficient of determination = 0.809) between aspects of the school feeding program and students academic performance in mathematics. Limitations of the study included potential biases in self-reported data and the narrow geographical focus on Nyanza District, limiting generalizability to other regions. Implications suggest that improving the quality and consistency of school feeding programs could positively influence academic outcomes in mathematics.

Implementation of Single National Curriculum Mathematics 2020 Intended and Enacted Determinants Perspective at Primary Level in Punjab

The current study was framed to determine the gap between intended and enacted single national mathematics curriculum implementation determinants instructional material, teaching methods, formative assessment, and teachers’ professional development. The nature of the study was quantitative descriptive based on the survey method. Single National Curriculum of Mathematics Implementation Questionnaire for Teachers (SNCMIQT) was developed for data collection from public primary school mathematics teachers. Content validity of SNCMIQT was ensured by five curriculum education experts and reliability was calculated employing Cronbach’s Alpha score; .918, and used to collect the data from the sample of 230 teachers selected through a simple random sampling technique. The collected data were analyzed by applying descriptive and inferential statistics. The study results revealed that 82% of mathematics curriculum determinants were implemented and an 18% gap existed regarding SNC mathematics. The results further, showed that 78% of instructional materials were in use and a 22% gap existed regarding instructional materials. The results declared that 78% of teaching methods were used according to the SNC and a 22% gap existed in teaching methods. The results declared that 87% of formative assessment techniques were in use, while a 13% gap existed regarding the usage of formative assessment. The results revealed that 87% of teachers were provided with teacher training, while 13% were not provided with teacher training, furthermore, results declared no significant difference between locale curriculum implementation determinants. Based on the results of the study, it was recommended that the government provide funds for mathematics instructional materials; learning labs, teaching kits, and learning gadgets for the mathematics curriculum. The education department and head teachers ensured the implementation of curriculum-based teaching methods and formative assessment strategies. Teachers training institutions may provide mathematics curriculum-based teachers training on the usage of instructional materials, teaching methods, and assessment. Head teachers may bind teachers in using instructional materials, teaching methods, and formative assessment techniques for effective SNC mathematics curriculum implementation.

Construction of line Layout Model Based on Geometric Deduction and Constrained Heuristic Search

Based on problem B of the National Mathematical Contest in Modeling for College Students in 2023, this paper establishes a model through geometric deductive deduction, and establishes and solves an optimal model of survey line layout through constrained heuristic algorithm. In problem 1, a mathematical model of coverage width and overlap rate is established based on triangle relation and triangle sine theorem by finding the mathematical relationship between target quantity and known quantity. In problem 2, the angle between the known direction of the survey line and the projection of the normal direction of the submarine slope on the horizontal plane is . We can imagine a surface perpendicular to the direction of the measurement line, and then find the slope of the imaginary surface according to the geometric relationship, and replace the slope Angle of problem 1 with the imaginary slope Angle to obtain the mathematical model of the coverage width. Based on this, the constraints of the Angle and overlap rate of the line are added, and the problem 3 is simplified into the optimization problem of multiple routes in problem 2. Finally, by changing the parameter setting of slope Angle in the model, the sensitivity analysis is carried out, and it is found that the model is stable and reliable.To sum up, the problems from one to four are gradually deepened and progressively advanced, and the development of Marine survey field is facilitated by establishing a model of depth survey line layout.

Recognizing professional development of mathematics and statistics learning support staff

Abstract Tutors play an important role in effective Mathematics Learning Support, and ensuring good initial training and development is key. Typically, in the UK and Ireland, tutors do not gain any formal recognition for the training they receive. This paper details a four competences model of training for tutors and presents the analysis of feedback from 11 tutors and two staff involved in piloting the model at two institutions. The model, which is informed by professional development guidelines, consultation across the mathematical sciences community, and enabled by a national Mathematics Learning Support Network, provides immediate recognition of the professional development undertaken and is amenable to formal accreditation. A structure of four digital badges is used to assign immediate value to the training and development of tutors. To add further value for tutors, a capstone tutor badge has been established for those completing all four competences. Thematic analysis of feedback from the piloting of the model identifies three overarching themes: the importance of community, developing as a professional, and motivating and enabling professional development. Although primarily of interest to those involved in Mathematics Learning Support, the innovative structure of the model and the insights gained from its piloting are such that it offers potential for genuine transferability across other subject disciplines.

An artificial intelligence application in mathematics education: Evaluating ChatGPT’s academic achievement in a mathematics exam

The aim of the research is to investigate the academic achievement of ChatGPT, an artificial intelligence based chatbot, in a national mathematics exam. For this purpose, 3.5 and 4 versions of ChatGPT were asked mathematics questions in a national exam. The method of the research is a case study. In the research, 3.5 and 4 versions of ChatGPT were used as data collection tools. The answers given by both versions of ChatGPT were analyzed separately by three researchers. As a result of the analysis of the data, it was found that ChatGPT-4 was more successful in the exam compared to ChatGPT-3,5 version, was better at understanding the questions asked, understood the instructions better and included more details in the question solution, and at the same time, both versions made common and different mistakes. According to the findings of the study, it was concluded that ChatGPT sometimes worked very well, sometimes only worked well and sometimes failed. In the light of the findings of the study, it can be suggested to use ChatGPT versions in mathematics education to obtain basic information and to get supervised help.

Some Selected Secondary School Students Perception of the Quality of PGDE Teachers Trained by National Teachers Institute

This study samples the Perception of Secondary School Students on the quality of PGDE Teachers produced through National Teachers Institute (NTI) of Nigeria program. The study was guided by four hypothesis and three research questions. Stratified random sampling technique was adopted in selecting a sample of 100 Secondary School Students from National Mathematical Centre International Model Science Academy and Government Secondary School Hajj camp. Questionaire containing sixteen items was used to elicit information. The data collected was analysed. The findings were PGDE Teachers produced through NTI program are competent in the general studies aspect of education, competent in their area of specialisation and in the professional aspect of teacher education. Some gray areas were identified in the general studies aspect of education and recommendations were made on how to improve NTI program generally.

Exploring impact of student attitude, parental involvement, and teacher competence on mathematics performance in selected schools in Northern Ghana

The purpose of this study was to see how students’ attitudes towards mathematics influenced their academic achievement in the Savelugu Municipality in the Northern Region of Ghana. The study employed the pragmatic paradigm and quantitative methodology. A 41-item semi-structured questionnaire rated using 5-points Likert scale, and document reviews were used to collect data. A combination of purposive and simple random sampling procedures was used to select 35 junior high school (JHS) in the Savulugu Municipality, questionnaires were administered to 350 JHS students, however, 315 questionnaires were returned. Data obtained from questionnaire were analyzed using Pearson product moment correlation coefficient, t-test, means, standard deviation, and percentages. The results revealed that educational institutions should develop programs to help parents become more active in their children’s education. To influence students’ attitudes towards mathematics study, policymakers and the Ghanaian Educational Service should promote programs such as National Mathematics Day to raise students’ awareness of the importance of mathematics in their daily lives. The Ministry of Education and non-governmental organizations should endeavor to offer enough instructional resources and financial incentives to instructors to help them make teaching relevant in the classroom.

교육과정 변천에 따른 고등학교 1학년 수학의 변천 분석

High school 1st year mathematics has been considered explicitly or implicitly as a common curriculum or a common subject in Korea. Which changes have occurred in high school 1st year mathematics according to changes of national mathematics curriculum? In this paper we investigate changes of high 1st year mathematics according to changes of curriculum focused on changes of contents of algebra. For this we first analyze literature including national mathematics curriculum from the 1st national mathematics curriculum to the 2022 revised national mathematics curriculum, research reports, mathematics textbooks and so on. As the result of our analysis, we identified that high school 1st year mathematics has always played a role as a basic and common subject in view of its subject name and its place in high school mathematics curriculum for each curriculum period. And we alos identified that there were some contents of algebra, that is, sequence, exponent and logarithm, etc. included in high school 1st year mathematics and 2nd or 3rd year mathematics alternately, and other contents of algebra disappeared in mathematics curriculum. Our analysis results seem to be basic data in discussing the range of contents of common mathematics curriculum for citizens in future.

Unlocking Potential: The Impact of Success Criteria as a Self-Assessment Strategy on Elevating Mathematics Achievement among AlKhair School Students in UAE.

This research aims to investigate the impact of success criteria as a self-assessment strategy on enhancing mathematics achievement among sixth-grade students in the United Arab Emirates (UAE), aligning with the "We the UAE 2031" vision for education. Employing a quasi-experimental quantitative design, the study involved 120 sixth-grade students from Al Khair public school in Al Ain, UAE, with two classes serving as the experimental group (60 students) and two other classes as the control group (60 students). Pre-test and post-test scores on national mathematics assessments, as well as international Measures of Academic Progress (M.A.P) scores, were analyzed. Teaching strategies included detailed steps using success criteria, remedial activities, and consistency checks across groups. Data analysis encompassed descriptive and inferential statistics, including independent t-tests in SPSS. The findings revealed a significant improvement in short-term mathematics achievement among students exposed to success criteria-based self-assessment compared to traditional assessment methods with as mean score difference of 10.572 (p < 0.05). Additionally, the analysis of M.A.P test scores showcased a substantial median score difference of 15.92 in favor of the success criteria-based self-assessment group, further reinforcing the effectiveness of this approach in promoting long-term academic growth and proficiency in mathematical concepts. Success criteria were found to enhance teacher clarity, student learning, and self-regulation abilities. Recommendations include integrating success criteria-based self-assessment into teaching practices and policy frameworks to enhance student engagement and academic performance. Future research directions involve exploring diverse populations, conducting longitudinal studies, and comparing different self-assessment strategies for effective implementation in education.

Problems and challenges of using randomized automatically evaluating geometric construction problems in Moodle LMS

<abstract><p>The objective of this paper was to examine the present state of geometric constructions in both international and national mathematics assessments. Additionally, it aimed to shed light on the noticeable lack of geometric construction items in these assessments and propose a solution to incorporate such items by utilizing a web-based mathematics assessment tool. After providing a brief summary of the unique benefits associated with geometric construction problems, the subsequent paper explored the development of a web-based mathematics assessment tool, the procedure for generating automatic evaluation GeoGebra applets for geometric construction problems, and their integration into Moodle learning management system (LMS). The purpose of this assessment tool was to enhance the evaluation of a substantially larger group of students within the realm of geometric constructions. The final section of the paper examined the difficulties encountered in the creation of the automatic evaluation applets and their incorporation into Moodle LMS. Through the development of such a web-based mathematics assessment tool, we enabled the evaluation of a significantly larger number of students, thus aiding not only national and international mathematics examinations but also assisting mathematics teachers in tracking students' scores and progress.</p></abstract>

Bimbingan Belajar Olimpiade Sains Nasional (OSN) Matematika Siswa di SMPN 3 Batusangkar

<p>The national mathematics science olympiads in junior high schools in the mathematics branch have an important role in the world of education by providing students with the ability to understand, apply and appreciate mathematical concepts in a scientific context. This includes developing a deeper understanding of mathematics, understanding of the scientific method, the ability to think logically, effective communication skills, and the ability to solve problems. This discussion details how the national science Olympiad helps students become individuals who are experts in mathematics and ready to play a role in science, technology and society.</p><p> </p>

A Bourdieusian Analysis of the Conversion Between Mathematical Achievement and Science Capital

Mathematics serves as a universal language and set of thinking tools for science. While prior research indicates associations between academic success in mathematics and science, there is a gap in the research that explores the possible relationship between mathematical achievement during early secondary school (ages 11-13) and subsequent participation in advanced science courses during senior secondary school (beyond age 16). This research is valuable because it could provide further insights into how early achievement in non-science subjects is related to senior participation in science. The analysis of national mathematics test data found that students who studied different science subjects in senior secondary school all had stronger foundational mathematical skills than those who did not. The results differed according to science subjects. The analysis indicated differences of over 7.2 months of equivalent learning at early secondary level in favour of those who studied physics, 6.1 months for those who studied chemistry and 2.5 months for biology. I apply a Bourdieusian lens as a way of explaining students’ conversion of mathematical achievement into participation as a form of science capital. These findings add empirical weight to previous research promoting mathematics as a crucial foundation for science learning. This research has implications for policies and practices that promote learning in mathematics and science pathways.

Revised national mathematics curriculum: improving competence in mathematical communication through teaching methods

The article delves into the topic of mathematical communication development, a key competence outlined in the updated National Mathematics Curriculum. It explores the integration of this competence within the context of the revised curriculum, examining relevant research on mathematical communication and teaching methodologies to foster its growth. Suggestions for pedagogical strategies aimed at enhancing mathematical communication are presented.

A Review of Statistics Education Reform Efforts in Korea

Statistics education reform in Korea has played a critical role in innovating school mathematics education, as it provides students with skills necessary for a data-driven world. Over the past two decades, numerous researchers, teachers, and governmental support have been devoted to enhancing statistics education. The impact of these reform efforts has led to significant changes in the goals, learning content, structure, instructional methods, and assessment approaches in the national mathematics curriculum, mathematics textbooks, and mathematics classrooms. This article outlines key contributions to improving statistics education since the end of 1990s. It reviews the trend of statistics education research and government initiatives in developing a research-based statistics education system and highlights major changes in the national mathematics curricula and the mathematics textbooks: namely, the enhancement of real-world connection, the integration of statistical problem solving approaches, and the incorporation of technology in statistics education at all school levels. The article also presents prospects and challenges for continuing the reform of statistics education in Korea, based on lessons learned during the review of the reform efforts.

Top Achievers in Mathematics in the End of Upper Secondary School

Important questions regarding mathematical giftedness are how and when it is possible to identify. To be identified as gifted, the student must have natural potential but also an appropriate mix of motivation, support, and challenges. This study is based on longitudinal data following students from 3rd grade in primary school to the end of upper secondary school between 2005 and 2015. We focus on top achievers (<2% of age cohort) of the national mathematics final exam at the end of upper secondary school. We investigate how accurately top achievers at the end of secondary school can be identified in 3rd, 6th, and 9th grades using national tests. We identify mathematical tasks that predict future top achievement and analyze how attitudes, gender, and parental background factors relate to high proficiency. Most top achievers had already been identified by 3rd grade and almost all of them by 9th grade. However, recognizing future top achievers was not very accurate, as they were indistinguishable from many students whose performance did not reach the same level over time. The best predictor for future top achievement was a student’s ability to solve non-routine and atypical tasks in early school years.