National Mathematics Curriculum Research Articles

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.

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.

A COMPARISON OF PUBLIC AND PRIVATE HIGH SCHOOLS LEARNERS’ PERFORMANCE IN MATHEMATICS IN DISTRACT LAYYAH PUNJAB, PAKISTAN

The key purpose of the current study was to inspect the mathematics teaching and education performs of high schools educators and to recognize the break between present mathematics teaching performs in distract Layyah Punjab Pakistan and the finest teaching performs advocated through literatures. In teaching to understand this purpose, the researcher chosen a samples of 100 high school learners and 100 teachers. The sample of study were taken in two phases. In 1st phase 25 high school males schools and 25 government females schools were designated. Likewise 25 private males’ institutes and 25 females’ private institutes were also designated. 10 learners from every of the sample institutes were designated by mean of methodical random sampling method. The study was quantitative data gathering and examination expired parallel and the results accompaniment every other. The quantitative facts were composed with the help of two surveys tool 1 for learners and the other for educators. The reliability coefficient resulting in a pilot study designated that surveys were dependable sufficient to be used in the full study for data gathering. The outcomes presented a thoughtful gap among present and professed coaching and knowledge performs. It was too originated that educators did not even know what class room performs were recommended in instruction policy documents and the National Mathematics Curriculum. In the survey, it was piercing out that the argument and protest method is extremely used by the educators, though the class room comment exposed that the educators frequently used the drill and practice method. Educators give learners a guide for remembering numerous ideas and then practice it. Though numerous educators have spoken intangible considerate of mathematics, it is missing in class rooms. Problem solving teaching technique is claimed to be the best and operative repetition with the standard stated in Nationwide Curriculum Mathematics (2006), data presented that this repetition is infrequently used in mathematics class rooms. It is decided that Pakistani high school mathematics educators do not usage numerous of the finest mathematics instruction performs recommended in the literature. The study likewise observed that certain of the finest mathematics instruction practices are used in private institutes, which is illustrated in the teacher survey. It was recommended that teachers orientate themselves on the usage of the best mathematics instruction performs in high school class rooms. With the purpose of emerging a profounder conceptual considerate amongst learners. Moreover, educators may be given the chance to progress their individual knowledge and considerate of the best performs for coaching mathematics as recommended in national education policy and curriculum pamphlets. Furthermore, it is recommended that upcoming study may be lead to inspect how pre-service and in-service preparation makes middle school mathematics educators to usage the best performs in coaching mathematics.

예비 중등 수학교사들의 함수 개념의 도입 방식 탐색

The purpose of this study is to analyze and present what aspects of the concept of function that prospective mathematics secondary teachers emphasize when designing a class that introduces the concept of function using curriculum and textbooks. For this purpose, virtual instruction and reflections on virtual instruction were analyzed. The results are as follows. The prospective mathematics secondary teachers thought of function as correspondences and processes. Their conception of function was consistently observed during virtual instruction and reflections on virtual instruction. The prospective mathematics secondary teachers’ conception of function was closely related to the form of expressing functions. These results are considered to be empirical evidence that suggests implications for the prospective mathematics secondary teachers’ education and research to introduce the concept of function based on the dependent relation between variables presented in the 2015 revision of the national mathematics curriculum.

데이터 기반 확률교육을 위한 수학과 교육과정 재구조화 방향 탐색

The aim of this study is to explore how to restructure the probability content standards in the national mathematics curriculum by pursuing the goals of developing probabilistic thinking competence and probabilistic problem solving. We named the perspective pursuing these goals as Data-Driven Probabilistic Education (DDPE) in that data sensitivity plays a significant role in probabilistic thinking and problem solving, and moreover relations between data and probability matter in statistics and machine learning fields. We further investigated into how to facilitate probabilistic thinking and probabilistic problem solving as well as what to adapt the meaning or grounding sense of the two major goals in the context of DDPE. Findings suggested some alterations to be made in the content standards and directions of teaching and learning in the curriculum document. First, to understand the probability concept based on data sensitivity, to understand randomness, and to solve probabilistic problems using modelling approach are suggested to be included in the contend standards. Second, we suggest to include contexts in which decisions about risk are made in the teaching and learning directions to enhance competence of dealing with volatility and uncertainty using probabilistic thinking competence. Third, rather than writing general statements on using technological tools, it is suggested to present specific ways or procedures of probability simulation using a computer in relation to understanding stages of probability concepts and solving probabilistic problems as guides to teaching and learning to realize DDPE.

한국, 싱가포르, 호주 수학 교과서의 행렬 단원 비교

The national mathematics curriculum revision process is underway in the background of the era where rapid technological development, uncertainty and volatility are expanded. In this process, consideration of matrix as a learning content emerged as one of the key issues, and conflicts among diverse educational participants are escalating. This study attempted to obtain implications for revising the presentation of matrix in textbooks by comparing the perspectives reflected in mathematics textbooks in Korea, Singapore, and Australia. First, the study compared and analyzed the learning contents, concept introduction and contents development methods in the textbooks from the three countries, and found that Korean textbooks cover more learning elements and tend to focus on calculation, while the other two textbooks from Singapore and Australia value the meaning of matrix as a useful means of expressing data. In addition, the results of comparing tasks based on the cognitive level framework developed by integrating the TIMSS cognitive domain and Jan de Lange’s framework showed that more than 80% of the tasks included in the Korean textbooks remained at the level of reproduction and connection, while Singapore and Australian textbooks provided various opportunities to learn such as making conjecture, justification and mathematical modeling through 70% and 45% of the tasks at the level of reflection, respectively. Drawing on the implications from the analysis, it is suggested to have fewer focus on content elements and more emphasis on conceptual understanding, mathematical reasoning, and mathematical modeling rather than calculation.

Estimation in the Mathematics Curricula of Denmark, Norway and Sweden: Inadequate Conceptualisations of an Essential Competence

ABSTRACT Acknowledging evidence that the ability to estimate has major consequences for both later mathematics learning and real-world functionality, this paper examines the national mathematics curriculum for compulsory school for each of Denmark, Norway and Sweden for the estimation-related opportunities it offers children. Framed against four conceptually and procedurally different forms of estimation (computational, measurement, quantity and number line), each of which is implicated differently in the later learning of mathematics, analyses indicated that none of the four forms of estimation were addressed explicitly in the Norwegian curriculum. Expectations of computational and measurement estimation were present in both the Danish and the Swedish curricula, although neither referred to either quantity or number line estimation. Even when estimation-related learning outcomes were articulated, there was no evidence of the processes by which they might be realised. Finally, there were no acknowledgements that estimation may contribute to the learning of other mathematical topics.

Research as a resource in a high-school calculus curriculum.

Documents specifying a national mathematics curriculum for grades K-12 have recently been written in Israel. We focus on the calculus component for the highest of three matriculation bound levels, and specifically on the influence of research on this component. In addition to issues of content, we identify three principles that have led the writing team, namely, the manner in which sample tasks in the curriculum document incorporate fundamental mathematical ideas and mathematical Reasoning, the Impact expected from connecting mathematics to its role in everyday life and science, and the Cultivation of fertile intellectual ground from which new concepts may emerge naturally. We demonstrate how these principles are implemented in the unit on integration. We show that mathematics education research, though not mentioned explicitly, has had a profound and pervasive influence on the content and principles of the curriculum document, from the design of entire units down to the formulation of sample tasks.

A Cross-National Comparison of Statistics Curricula

The purpose of this study is to compare Turkey to several other countries such as Singapore, Korea, the United States, and New Zealand according to the field of statistics learning in the curriculum. GAISE (Guidelines for Assessment and Instruction in Statistics Education) framework suggests using the components of statistical process (formulate question, collect data, analyze data, interpret results) and developmental levels of statistical process (Levels A, B, and C) in such comparisons. It is found that in both Korea and Turkey, the number of learning outcomes of statistics, as well as the weight of learning outcomes in the curriculum, have been having a weaker profile than in other countries. The field of statistics learning is mostly condensed around Level A in Turkey. On the other hand, other countries in the study included more Level B and C. Considering the importance of statistics instruction, Turkey's national mathematics curriculum needs improvements in its field of statistical learning. This study suggests designing and developing new standards for teaching statistics that deal with higher developmental levels of statistical process.

Goals of the national mathematics curriculum of Pakistan: educators’ perceptions and challenges toward achievement

PurposeThe national mathematics curriculum of Pakistan has emphasized on improving content knowledge, reasoning abilities and problem-solving skills of students about thinking, communicating and solving mathematics (national mathematics curriculum of Pakistan, 2006). Whereas, there is a need to understand the point of view of teachers about the challenges they face in achieving the goals of national mathematics curriculum. This will help leading teacher training institutions to revisit their math teacher continuous professional development (CPD) programs and facilitate school leadership in improving the quality of math education in rural schools of the province. However, the purpose of this research study is to figure out the challenges that teachers are facing while achieving the goals of the national curriculum by teaching mathematics at the primary level in educational institutes of Pakistan.Design/methodology/approachIn this research study qualitative research approaches have been utilized, in which focus group discussions (FGDs) were used as data collection techniques. Furthermore, thematic analysis of the data led toward the development of four overarching themes such as teachers' knowledge about mathematics curriculum, challenges relating to mathematics content and pedagogy, difficulties in developing conceptual understanding and designing lesson plans to address students' diversity.FindingsThe overall findings of this research study suggested that the majority of teachers are facing difficulties in mathematics content teaching such as decimal fraction, unitary method, measurement principles, practical geometry and data handling. Moreover, teachers are also facing challenges and difficulties in developing hands-on and minds-on activities in the teaching of mathematical concepts to the students of primary level in educational institutes of Pakistan.Practical implicationsThis research study will facilitate the teachers and stakeholders to address the problematic issues in the domain of content delivery of mathematics. Whereas, this study recommends educating teachers about national mathematics curriculum and to develop a CPD framework for mathematics teachers for the enhancement of their pedagogical content knowledge. The study also recommends orientating school heads about the different aspects of math curriculum so that they can mentor math teachers in achieving math curriculum goals.Originality/valueThis is the first research study of its nature, which targets and highlights the teacher's perceptions toward the achieving the goals of national mathematics curriculum of Pakistan and addressing the pedagogical challenges faced in mathematics teachers. There is a dearth of studies in mathematics education in Sindh province. The issue is of immense importance, the findings will help teachers to improve mathematics instructions at primary level.

Mathematics Teaching in Vietnam in the Context of Technological Advancement and the Need of Connecting to the Real World

In the context of fundamental and radical reform of education and training in Vietnam, the educational goals are changing towards students’ competencies instead of knowledge and skills for students as in the past. Vietnam’s mathematics curriculum is going to innovate after 2018. Mathematical education constructs the connection between mathematical ideas, between mathematics and other subjects, and between mathematics and real life. This article investigates two significant issues in mathematics teaching in Vietnam: the purpose of learning mathematics among Vietnamese pupils and mathematics teaching methods concerning reality. Based on the findings from these questions, the article proposes some recommendations for mathematics teaching regarding the methods and appropriate extent to which teachers should connect mathematics to the real world in the context of rapid science and technology development as well as the adjustments to the current mathematical content at schools. Also, this article presents some examples of exploring practical content problems and designing real-life contexts in mathematics teaching to develop students' competency in Vietnam. The researchers also suggest that Vietnam's national mathematics curriculum needs reforming to keep up with the pace of development in the field of information and communication in the country. https://doi.org/10.26803/ijlter.19.3.14

Changing Pedagogy to Improve Skills in Preschools: Experimental Evidence from Peru

Abstract Changing pedagogical practices is a promising, cost-effective avenue for improving education in developing countries, especially when done without changing current inputs such as teachers and instruction time. This article presents the results of a randomized evaluation of a program that aimed at changing the pedagogical approach used to teach the existing national mathematics curriculum. The program provides tools to regular preschool teachers to use an inquiry- and problem-based learning approach to tailor instruction to preschoolers in Peru. The results show an improvement of overall mathematics outcomes, which persist for some content areas even one year after the program ended. In contrast to results from previous research that suggest mathematics programs are biased along gender and socioeconomic lines, there is no evidence of differential effects by gender, language spoken at home, or proxies for socioeconomic status. Results also imply persistent stronger impacts on students whose teachers have university degrees.

학교 수학에서 디지털 리터러시 교육 양상 분석

The purpose of this study is to examine the current status of digital literacy education of the mathematics in accordance with the 2015 revised national curriculum and to draw up substantial improvements to foster digital literacy education in mathematics. This study intends to carry out a multi-layered inspection on how contents related to digital literacy has been adopted in the mathematics curriculum, how the math teacher perceive digital literacy education, and how they put this into practice in real classes. The study investigated how digital literacy has been adopted according to the changes of the mathematics curriculum and aggregate and considerate aspects how mathematics adopted digital literacy by characteristics in mathematics through analysis of standards in the 2015 revised national mathematics curriculum. In addition, this study analysis the current status of digital literacy education in mathematics education through surveying teaching cases, and exploring the improvements for digital literacy education in Mathematics education Through this study drew three suggestions so as to enhance digital literacy education of the mathematics: reinforcement of learning contents for strengthen digital literacy education of mathematics; activation of cooperative learning for digital literacy education of mathematics; and establishing a system to improve math teachers’ professionality.

Collaborative design of a reform-oriented mathematics curriculum: contradictions and boundaries across teaching, research, and policy

The reported study is situated within the process of developing a reform-oriented national mathematics curriculum for compulsory education in Greece by a design team that involved teachers, academic researchers, and policy-makers. From an activity theory perspective, we identify the activity systems of mathematics teaching, research in mathematics education, and educational policy interacting in the design process. We focus on the contradictions between the three activity systems and how these were dealt with. We based our analysis on email exchanges during the curriculum design, field notes from whole-team sessions, and interviews with key persons. Our results highlight that the emerging contradictions primarily concerned the teaching and research activity systems. Members of the team who acted as brokers between the different activity systems and facilitated their interaction played an important role in overcoming the contradictions.

Are Mathematics Curricula Harmonizing Globally Over Time? Evidence from TIMSS National Research Coordinator Data

Given the impact of international large-scale assessments (ILSAs) on policy-making in different educational systems around the world, this study aims to examine whether national mathematics curricula in different educational systems harmonize over time. Data from the Trends in International Mathematics and Science Study (TIMSS) is used to explore this issue. In addition to background questionnaires given to students, teachers and schools, a curriculum questionnaire was completed by each national research coordinator (NRC) in all participating countries in each TIMSS cycle. In the present study, data from 2003, 2007, 2011 and 2015 was used. The analyses focused on the information about the extent to which the national mathematics curriculum covered certain topics in the subdomains of mathematics tested in TIMSS Grade 8. Growth curve modeling and latent profile analyses were applied to uncover the development trend and countries’ unobserved profiles in mathematics content domains of Number, Algebra, Geometry, and Data. Three clusters of countries were identified. Most countries belonged to the same profile in the later cycles of TIMSS. The study found indications of a general harmonization with respect to number of topics covered in countries’ curricula over time, thus contributing to discussions of policy implications of a global curriculum.

Content analysis of the TEOG mathematics test items based on MONE attainments, TIMSS levels, and renewed Bloom Taxonomy<p>TEOG sınavlarındaki matematik test maddelerinin MEB kazanımlarına, TIMSS seviyelerine ve yenilenen Bloom Taksonomisine göre içerik analizi

The aim of the study is to classify and evaluate the mathematics test items in the Transition System of Secondary Education (TEOG) exam according to the attainment levels of the Secondary School National Mathematics Curriculum, TIMSS levels and Bloom’s renewed taxonomy. The study covers the TEOG math items between the years 2013 and 2016. In data analysis, content analysis, a qualitative research technique, was applied. For the classification of the materials, the acquisition list of the eighth grade mathematics course prepared by MONE, the scheme of TIMSS levels, and Bloom’s Renewed Taxonomy were used. Booklet A was taken as a base for the classification for each exam. According to findings, in the TEOG exams applied between 2013-2016, while the TEOG exam was consistently asking questions in certain examinations from certain acquisitions, it was seen that no questions were asked from some of the acquisitions. When the 260 mathematical items in the TEOG exams classified according to TIMSS levels, of the items 33.8% were at "Level 1", 45% were at "Level 2", 19.6% were at "Level 3" and 1.5% were at "Level 4 ". Parallel with these findings, when TEOG mathematics items classified according to Restructured Bloom Cognitive Domain Taxonomy, of the items17,69% were at "Remembering", 18,46% were at "Understanding", 54,23% were at "Implementation", 5,76% were at "Analysis" and 3.6% were at "Evaluation" levels. The results indicated that the majority of the math items in the TEOG exams were at the “Application level” and the number of items in the "Reasoning level" was limited. Such exams, as TEOG, directing students high school in consistent with their cognitive level, should measure higher order skills, as well. ÖzetÇalışmanın amacı, Temel Eğitimden Ortaöğretime Geçiş Sistemi (TEOG) sınavı matematik test maddelerinin, Milli Eğitim Bakanlığı Ortaokul Matematik Programı kazanımlarına, TIMSS düzeylerine ve Bloom’un Yenilenmiş Bilişsel Alan Taksonomisine göre sınıflandırılıp değerlendirilmesidir. 2013-2016 yılları arasında TEOG sınavı matematik soruları araştırma kapsamında incelenmiştir. Verilerin analizinde nitel araştırma tekniklerinden içerik analizi kullanılmıştır. Maddelerin sınıflandırılması için MEB tarafından hazırlanan sekizinci sınıf matematik dersine ait kazanım listesi, TIMSS sorularının düzeylerini gösteren TIMSS düzeyleri şeması ve Bloom’un Yenilenmiş Bilişsel Alan Taksonomisi kullanılmıştır. Sınıflamada her bir TEOG sınavının matematik temel alanına ait A kitapçıkları temel alınmıştır. Bulgulara göre 2013-2016 yılları arasında uygulanan TEOG sınavlarında belli kazanımlardan her sınavda soru sorulurken, bazı kazanımlardan hiç soru sorulmadığı görülmüştür. TEOG sınavlarında sorulan 260 matematik sorusu TIMSS düzeylerine göre sınıflandırıldığında %33,8'i “Düzey 1”, %45'i “Düzey 2”, %19,6'sı “Düzey 3” ve %1,5 'i “Düzey 4”de yer aldığı görülmüştür. TEOG matematik test maddelerinin; Yeniden Yapılandırılan Bloom Bilişsel Alan Taksonomisine göre dağılımına bakıldığında soruların %17,69’u “Hatırlama”, %18,46'sı “Anlama”, % 54,23'ü “Uygulama”, %5,76'sı “Analiz” ve %3,46'sı “Değerlendirme” bilişsel alan basamaklarında olduğu görülmüştür. Sonuçlara göre TEOG matematik test maddelerinin çoğunluğunun “Uygulama” basamağında olduğu, “Analiz” ve “Değerlendirme” basamaklarındaki madde sayısının sınırlı olduğu görülmüştür. TEOG gibi öğrencilerin bilişsel düzeylerine göre liselere yönlendirilmesinin hedeflendiği bir sınavdaki sorular bu amaca uygun olarak üst düzey bilişsel becerileri de ölçecek şekilde hazırlanmalıdır.

Enabling Pupils to Conceive Part-Whole Relations of Numbers and Develop Number Sense: Year One of Primary Schools in Malaysia

This review examines reasons for Malaysian pupils' underperformance in solving mathematics problems that demand numerical estimation and mental computation. Their underdeveloped number sense appears to be the major reason. According to the Ministry of Education, the national mathematics curriculum is unlikely to account for this underachievement. By contrast, this article argues that the curriculum largely focusing on written computation skills, is likely to account for the underperformance, given that the development of number sense has yet to become the focus of attention. This review further suggests teaching and learning activities that may enable the Malaysian pupils, in year one of primary schools, to conceive part-whole relations of numbers and thus develop number sense. The earlier they understand the part-whole relationship, the stronger they may develop number sense and thus the better can be their performance.

Mobile technologies in the service of students’ learning of mathematics: the example of game application A.L.E.X. in the context of a primary school in Cyprus

This article reports on the main experiences gained from a 2-year study which incorporated A.L.E.X., an educational puzzle game available on iPad or Android tablet devices, within the primary school mathematics curriculum. The study took place in a public primary school, located in a rural area of Cyprus. The majority of its students come from low socioeconomic status families. Among the school community, a group of 15 pupils (eight boys and seven girls), aged 10–11 years old, was randomly selected to comprise the sample. The same group of students was visited twice within a period of 2 years, and a teaching intervention was organized. In both interventions, the application A.L.E.X. accompanied by a student worksheet constituted the main means of instruction. The worksheets were designed to integrate a technology with core mathematical ideas embedded in the national mathematics curriculum. Findings gained from the teaching intervention suggest that game apps hold a lot of promise as a tool for reforming mathematics education. While working with A.L.E.X., the children identified and processed mathematical themes that emerged spontaneously. They experienced unique emotions of surprise and enthusiasm regarding the existence of games with mathematical content that led them to acknowledge the pedagogical role that tablet devices could play. This helped them to broaden their fundamentally narrow viewpoint of mathematics as being primarily computation and arithmetic.

The characteristics and issues of the 2015 revised National Mathematics Curriculum of Korea

The characteristics and issues of the 2015 revised National Mathematics Curriculum of Korea