Mathematics Curriculum Research Articles

The Empowering Innovative Mathematics Curriculum and Industry Collaboration in Gearing Malaysia for IR4.0 Era

This paper aims to illustrate the global megatrend of IR4.0 and points out their impacts and gaps faced by today's industries and mathematics applications. Meanwhile, in responding to the MoHE Education Framework 4.0 plan and direction, this paper adopts the qualitative approach to review and investigate the needs of transformation in mathematics curriculum, gears up to the change of industry requirements and adapts to the shift of market demands and operations landscape. Therefore, the outcome of study urges to form a closer tie or partnership between industries and mathematics collaboration in industrial research and problem-solving. With this, the role of industrial mathematics has to become part of the necessity for Malaysia's leading mission to achieve the status of a developed nation. In conclusion, based on the missing links between mathematics and industries, the paper recommends the realignment and rebranding of existing university mathematics curriculum and formation of the National Industries and Mathematics Community (NIMC). It expects industrial mathematics will be one of the key boosters besides engineering and technologies fields, to produce the industries talents and expertise, which will contribute to Malaysia's mission in IR4.0, the migration of industries into high-value services and technological intelligence-based productions era.

Square Root Expressions and Irrational Numbers in Middle School Mathematics Textbooks Throughout the History of the Republic

Irrational numbers, a fundamental set that extends rational numbers to real numbers, have been a subject of limited study in the context of textbook analyses. This study, therefore, examines how square root expressions and irrational numbers have been addressed in middle school mathematics textbooks throughout the history of the Republic of Türkiye. The research was conducted using a comprehensive approach, with qualitative research methods and content analysis was applied to 37 mathematics textbooks (seven 5th grade, twelve 6th grade, nine 7th grade, and nine 8th grade) from 1932 to 2022. Data were collected from mathematics textbooks available at the Ferit Ragıp Tuncor Archive and Documentation Library affiliated with the Ministry of National Education. The results of this study indicate that changes in mathematics curricula are reflected in textbooks, and this reflection is directly influenced by the learning theory adopted in the curriculum. The study also provides insights into how irrational numbers are introduced in textbooks based on the sequence of topics, and recommendations are made based on the findings.

Problem solving in mathematics education: tracing its foundations and current research-practice trends

In tracing recent research trends and directions in mathematical problem-solving, it is argued that advances in mathematics practices occur and take place around two intertwined activities, mathematics problem formulation and ways to approach and solve those problems. In this context, a problematizing principle emerges as central activity to organize mathematics curriculum proposals and ways to structure problem-solving learning environments. Subjects’ use of concrete, abstract, symbolic, or digital tools not only influences the ways to pose and pursue mathematical problems; but also shapes the type of representation, exploration, and reasoning they engage to work and solve problems. Problem-solving foundations that privilege learners’ development of habits of mathematical practices that involve an inquiry method to formulate conjectures, to look for different ways to represent and approach problems, and to support and communicate results shed light on directions of current research trends and the relevance of rethinking curriculum proposals and extending problem-solving environments in terms of teachers/students’ consistent use of digital tools and online developments.

Curriculum Reform of Higher Vocational Mathematics Under the Background of Digital Transformation

Under the background of digital transformation, the reform of the higher vocational mathematics curriculum faces urgent challenges and opportunities. This article explores the impact of digital transformation on the reform of higher vocational mathematics curriculum and emphasizes the importance of improving teaching methods centered on learners. The article proposes specific reform methods and discusses the practical application of digital technology in the reform process. By combining digital technology with specific reform methods, further conducting innovative practice research, and continuously exploring the path of reform, we can effectively improve the quality of higher vocational mathematics classroom teaching and provide strong support for the cultivation of comprehensive qualities and employment abilities.

외국 교육과정 자료 및 공학 도구 사례 분석을 통한 사분위수 지도 방안 탐색

Objectives This study examined elementary and secondary school level curriculum materials from major contries and technological tools and attempted to derive pedagogical implications for teaching the concept of quartile in mathematics education in Korea. Methods To this end, this study collected primary and secondary curriculum data from nine representative countries and examined how each country deals with quartiles from various aspects. In addition, 13 types of technologicla tools were selected for analysis and then it was confirmed which quartile calculation method each technology follows. Results As a result, most countries first introduced the concept of quartile in the 8th and 9th grades of middle school. In addition, it was confirmed that the concept of quartile was included in the ‘spread of data’ or ‘measure of dispersion’ section. Also, it was confirmed that the method of stating the definition of quartile in most countries' curriculum materials is common, and the method of calculating quartile is also the same as M2. Meanwhile, differences were identified in the way each technology defines the calculation of quartile, but when analyzed by dividing them into three categories according to the purpose of use, several common characteristics were discovered. Conclusions Based on the results of this study, suggestions for quartile instruction were presented in mathematics classes and the writting of middle school textbooks according to Korea's 2022 revised mathematics curriculum.

Examining The Problems Posed By Classroom Teacher Candidates According to Mathematical Process Skills

In mathematics teaching, problem posing is an expected outcome for students. It is important for future teachers to be able to pose problems effectively when implementing the mathematics curriculum. This study aimed to examine the problems posed by classroom teacher candidates based on their mathematical process skills. The Problem Posing Test, used as a data collection tool, was was developed based on four objectives within the domain of measurement learning. In this quasi-experimental study, both the experimental and control groups comprised 25 volunteer classroom teacher candidates each. Analysis of the problems posed by teacher candidates was carried out according to the conceptual framework created by the researchers. The analysis revealed that classroom teacher candidates struggled with mathematical communication, association, and reasoning skills. Specifically, it was observed that they often wrote mathematical units incorrectly or incompletely, overly relied on verbal representation, failed to make interdisciplinary connections, and frequently posed problems requiring analogy-based reasoning. After instruction in problem posing, teacher candidates in the experimental group demonstrated improved mathematical process skills. Future studies should examine the problems posed by teachers or teacher candidates across different grade levels to assess their mathematical process skills.

Students' Errors in Constructing Mathematical Proofs by Direct Method

In mathematics, there are several methods for proving mathematical statements, two of them are direct method and indirect method. Both the methods were included in the mathematics curriculum at senior high school level as a learning topic. It implied that the teachers or pre-service teachers must master these methods. In addition, learning advanced mathematics courses also needed the ability of mathematical proving. The direct method was often used in proving mathematical statements. This descriptive qualitative study was conducted to examine what errors were written by the students in constructing mathematical proofs by direct method. Two basic problems (mathematical statements) were administered to 13 college students. They were pre-service mathematics teachers in one of the public universities in Aceh, Indonesia, and were asked to prove the statements by direct method. The data were analyzed by using Miles and Huberman step. The results showed that there were three main errors, (1) errors in using definition correctly, (2) errors in algebraic process, and (3) proving by examples. It concluded that the students must be accustomed to mathematical proving activities to avoid errors in constructing mathematical proofs. Keywords: constructing mathematical proofs, direct method, students’ errors

Designing effective continued professional development for primary teachers during curriculum reform in mathematics

ABSTRACT Mathematics curriculums worldwide are being refined to prepare students for the twenty-first century by focusing on developing students’ higher-level thinking skills. As a result, teachers need to adjust their pedagogical approaches to enact new curriculums, which is frequently facilitated through continued professional development (CPD). During curriculum change, the challenges to fostering effective CPD are often exacerbated, signalling a necessity to understand better how CPD can be structured during reform. This research study aims to design a curriculum resource that acts as a form of CPD, seeking to enhance teachers’ use of higher-level thinking questions in mathematics lessons while also gaining a greater understanding of what constitutes effective CPD during curriculum reform. Six Irish primary school teachers in an urban school collaborated for one year with the primary researcher to develop a curriculum resource. Analysis of data collected from observations, focus groups, and researcher field notes guided the iterative design of the curriculum resource. Design characteristics of the curriculum resource and their impact on teachers’ practice are discussed. Finally, suggestions for designing and facilitating CPD during periods of change and implications for further research are proposed.

An Investigation of The Connection of Bloom’s Taxonomy to the Core Mathematics Curriculum for Senior High Schools in Ghana

This paper attempts to preview the connection of Bloom's taxonomy to Ghana's Senior High School mathematics curriculum. Mathematics is a vital tool for economic growth and national development as a STEM subject. Bloom's taxonomy, which presents a hierarchical model, helps educators teach school mathematics to enable students to acquire basic Knowledge known as order thinking (LOT) skills and develop higher-order thinking (HOT) skills. The analysis of the mathematics syllabus concerning Bloom's taxonomy revealed that the syllabus concentrates more on the three fundamental skills in Bloom's hierarchy of teaching and assessment. Remember 18.1%, Understand 33.3%, and Apply 29.8%, totalling 81.2%, leaving only 18.8% for the top three HOT skills. The study recommends that Ghana adopt a curriculum model that focuses on teaching transversal skills that can churn out informed citizens rather than putting students under the shackles of tests.

Core competency oriented problem-solving teaching ----Taking "Solving Application Problems with a System of Equations" as an Example

The teaching of Mathematical problem-solving is one of the three key teaching points in junior high school mathematics. Solving applied problems through equations (systems) is an important component of the first module of teaching content, "Numbers and Algebra", and holds a very important position. It is a key focus in junior high school mathematics problem-solving teaching. At present, under the premise of the implementation of the new curriculum reform in the field of mathematics in China, based on the recent publication of compulsory education curriculum standards,the teachers of mathematics should focus on cultivating excellent mathematical core literacy among junior high school students, and ensuring that they can independently cope with and solve problems in the math teaching of junior high school. Based on the above background, the author focuses on the newly published mathematics curriculum standards in 2022, and studies the teaching design of "solving application problems for systems of equations". In this paper, we explore the mathematical core literacy elements contained in the teaching of solving applied problems in equations, study the improvement path of mathematical problem-solving teaching, share the teaching design practice and thinking based on core literacy oriented problem-solving teaching, and the important role that this teaching design can play in cultivating students' core literacy .

An Innovative Model to Promote Secondary Students' Critical Thinking Skills in Algebra Learning

This research aims to explore a learning model based on 21st-century skills and the Australian curriculum to cultivate students’ critical thinking skills in junior secondary mathematics algebra learning. This study used a mixed method. Quantitative data was collected through a questionnaire that provided information about perceptions of the challenges in learning algebra. Qualitative data was collected through semi-interviews with secondary mathematics teachers, which provided an opportunity for teachers to evaluate their understanding of critical thinking skills for algebra, it further clarified teachers’ expectations of mastering the key algebraic contents. Based on the data from the questionnaire and semi-interview, a practical model for embedding critical thinking skills and strategies in learning algebra was designed. The mathematical curriculum in Victoria and Australia were explored as they provided the basis of the model.

The influence of using Learning Videos for High School Mathematics Curriculum Subjects with Flipped Classroom Models on Learning Achievement in the UIN Walisongo Semarang

During the current pandemic, students are having difficulty understanding mathematical material; normally, they are taught by lecturers face-to-face, but now online. The obstacle that students face is that they believe that learning is not optimal because the signal is often poor and inconsistent, and they are unable to meet with the lecturer. To alleviate this issue, it is required to create a video of learning material that will be supplied by a mathematics lecturer by the lecturer who teaches, the video is published on YouTube, and the youtube link is given to students to study beforehand for the forthcoming meeting. This is consistent with the flipped classroom concept, in which students are expected to first understand the lecturer's video before being discussed directly by the lecturer.It is expected that students are able to think creatively about video content created by their professors, and students are able to examine material flaws that they have not understood and then clarified by their lecturers at the next meeting. In research on the development of instructional video media for high school mathematics curricular with the ADDIE stage model. This model, as the name suggests, consists of five main phases or stages, namely (A) analysis, (D) design, (D) development, (I) implementation, and (E) evaluation. The Implementation and Evaluation stage was carried out in the second year, with expanded tests carried out at UIN Walisongo Semarang in a fun and enjoyable manner, with posttests and user response questionnaires given with the following results: Based on research at UIN Walisongo, posttest results were processed using tests t results obtained are 0% <5%, then H0 is rejected. This means that we accept H1, which means that the results of learning mathematics using video learning media for high school mathematics curriculars are better than conventional learning models. Looking at the average learning achievement in the mean column, Group Statistics table, the experimental class average is 86.00, while the average -the average control class is 64.74. These results show that the learning outcomes of the experimental class are better than the control class. R Square value of 0.804 = 80.4%. This value means that the influence of virtual lab media on learning achievement is 80.4%, while 19.6% of learning achievement is influenced by other variables outside of the independent variables in this research.

A Practical Study on Enhancing Students’ Mathematical Literacy by “Integration of Doing, Learning and Teaching”

In face of the mathematical foundation of students in higher vocational colleges, Tao Xingzhi’s educational thought is of great guiding significance. “Integration of doing, learning and teaching” is not only the theoretical basis of Tao Xingzhi’s educational thought, but also his methodology and action guideline. Tao Xingzhi emphasizes the unity of knowledge and action, among which action is greater than knowledge. This concept is isomorphic with the mathematical culture curriculum. Drawing on the idea of “integration of doing, learning and teaching”, we explore the math culture curriculum and expand the four forms of teaching and learning in math culture: theoretical training, practical exploration, research-based learning, and reflective learning. In the implementation of the school-based curriculum, local teaching resources should be fully exploited, constructing the mathematics teaching mode of “Integration of doing, learning and teaching”, effective teaching methods and classroom evaluation algorithms, ensuring the relevance of vocational education and improving mathematical literacy.

Connectivity and Application of the Principle of Multiple Intelligences in the Three Domains of Learning Mathematics

The study aimed to examine how Gardner's Multiple Intelligences applied to Ghana's Senior High School's core mathematics curriculum and instruction. The Core Mathematics curriculum was the primary document reviewed for the study. The action verbs used in the objective, section teacher-learner activities section, and the evaluation section of the core mathematics syllabus were identified and grouped with respect to the multiple intelligences. The analysis revealed that the mathematics curriculum was linked to several intelligences, although some intelligence was underserved. The Senior High School Mathematics Curriculum fails to consider diverse learning styles and preferences. It should provide a diverse range of topics using various instructional techniques. However, children with different intelligences should not experience mathematics as a hindrance. A re-evaluation is necessary to address these issues.

Tren penelitian kemampuan pemecahan masalah pada pendidikan matematika: Analisis bibliometrik

This research aims to look at research trends on the topic of problem solving abilities in mathematics education. This research used 204 documents searched in the Scopus database, with the analysis technique used, namely bibliometric analysis using RStudio and Vosviewer. From the results that have been analyzed, it can be concluded that this research started from 1976 to 2023, with an increase of 6.69% every year. The most productive affiliates are Katholieke Universiteit Leuven, Monash University, The Chinese University of Hong Kong, and Semarang State University. Journal of Mathematical Behavior and ZDM - International Journal on Mathematics Education were ranked highest h-index. Hegarty & Kozhevnikov (1999) discussing types of visual-spatial representation and their relationship to solving mathematical problems, with the highest total citations. STEM, Programming, Mathematics Curriculum, and Computational Thinking being the recommended keywords to use if you want to conduct research on the topic of problem solving abilities in mathematics education.

Developing teachers’ cultural competencies through co-design of robot-coding mathematics activities for Latinx and Black elementary school students

This year-long case study involved the professional development of teachers in New York City elementary schools, who co-designed with researchers culturally relevant robot-coding mathematics activities to advance teachers’ understanding of culturally responsive mathematics pedagogy. Study findings indicated that co-designing culturally relevant robot-coding mathematics activities led to the development of teachers’ cultural competencies, deeper understanding of culturally responsive mathematics pedagogy and their students’ cultures, stronger agency, and ability to integrate culturally responsive pedagogy into their mathematics curriculum. Teachers also began to perceive the robot as a mathematical tool rather than a motivational add-on, and started to develop their own cultural lens while focusing less on school structure constraints. The study emphasises the importance of engaging teachers as active co-designers of culturally relevant coding curriculum in professional development programmes.

Crafting Mathematical Minds by Engaging Braille-Tangible 3in1 3D Printed Geoboards Module for Visually Impaired Children

Worldwide, visual impairment and blindness stand as prevalent health challenges, exerting substantial effects on individuals and the communities they belong to. These conditions pose significant disabilities for visually impaired individuals and their immediate surroundings. Children with visual impairments encounter numerous challenges in their daily lives and learning, unlike their sighted counterparts. Nevertheless, despite these obstacles, they depend significantly on their tactile and auditory senses to glean information from their surroundings. Meanwhile, mathematics poses a unique challenge for students, as its abstract concepts can be difficult to visualize, potentially diminishing interest in the subject. Recognizing the potential of 3D printing technology to enhance visualization and interaction with three-dimensional models, this study aims to develop a module that combines mathematics in Braille with 3D printed models. The goal is to facilitate a more accessible and engaging learning experience for visually impaired children, fostering a deeper understanding of mathematical concepts. The module incorporates tactile games designed to improve focus and study habits, thereby addressing the specific needs of visually impaired learners. The module comprises 3 games as 3in1 Geoboard: Numerical Jumble, Pinpoint Placer and Geo Art. The game tools employed in this module underwent 3D design through computer-aided design (CAD) software, integrating Braille code within mathematical constructs tailored to the requirements of visually impaired children and their mathematics curriculum. Subsequently, the 3D model was transformed into a tangible object using a 3D printer. These printed objects served as educational tools within the development of an integrated module encompassing both 4IR elements and Braille components. Instructions for the game were seamlessly integrated to facilitate straightforward delivery of module content by educators. Therefore, adopting a game-based learning module approach not only proves effective for individuals who are blind but also provides visually impaired children with a practical avenue to learn Braille and enhance their understanding of mathematical concepts. This educational approach holds particular significance for visually impaired children in their daily lives while greatly revolutionize educator-coordinated learning of mathematics through engaging education for the framework of 10-10 MySTIE Socio-economic drivers.

Tapping into the art of teaching: Unveiling pedagogical content mastery through a riveting case study

This study aims to examine investigate variations in teachers’ perspectives regarding the pedagogical content knowledge acquired through the school experience in the pre-2018 curriculum for elementary mathematics teaching compared to its updated counterpart, now known as teaching practice in the current curriculum. In this direction, six teachers from the department of elementary mathematics teaching at the faculty of education of a university in Western part of Turkey were selected by criterion sampling method. A semi-structured interview form developed by the researchers was used as a data collection tool in the study in which holistic multiple case design, one of the qualitative research methods, was used. The data obtained were analyzed by content analysis. As a result of the research, it was found that the teachers who studied with the old program were inadequate compared to the teachers who studied with the updated program in terms of classroom management, communication with students teaching methods, skills to use techniques.

2022 개정 수학과 교육과정에 따른 공학 도구 활용 자료 개발 연구

This study aimed to develop teaching, learning, and assessment materials emphasizing the use of technological tools in the revised 2022 mathematics curriculum. To achieve the aim, this research reviewed previous studies to list technological tools applicable to the curriculum, analyzed achievement standards related to the use of technological tools, and developed 20 teaching, learning, and assessment materials based on these achievement standards. This process was conceptualized using the LED model, which consists of the List-up, Elaboration, and Development stages, allowing for systematic relations with technological tools, mathematics curriculum, and teaching, learning, and assessment. To ensure the quality of the developed materials, validity was secured through Delphi surveys, expert consultation, and field trials. The research findings are expected to provide assistance to teachers who aim to design and implement student-centered inquiry-based classes using technological tools, and to offer insights for developing relevant educational policies.

초등학교 수학과 교육과정 도형 영역의 교수학적 의도와 실행에 관한 분석

The purpose of this study is to analyze the pedagogical intentions contained in the shape area of the 2015 revised elementary mathematics curriculum and textbooks and to critically examine the contents that may be difficult in the pedagogical implementation process through teaching and learning. The 2015 revised curriculum and authorized textbooks that embody the pedagogical intentions of the curriculum were analyzed, and the knowledge of teachers in the evaluation items developed by teachers based on the curriculum and textbooks was examined. As a result of the study, there were cases where it was difficult to properly convey pedagogical intentions to students in the teaching and learning process due to the definition of terms used in the curriculum or the order in which concepts were presented, and there were teaching and learning contents presented in textbooks but not revealed in the curriculum. In addition, there were cases where there were differences in the presentation method for each textbook regarding the definition and properties covered in the shape area. In addition, there were cases where teachers inappropriately interpreted the pedagogical intent contained in the curriculum, and it was confirmed that in some of these cases, there was a possibility that the intent of the curriculum could be misinterpreted due to the contents presented in textbooks or teacher’s guide.