Mathematics Curriculum Research Articles

Teachers' beliefs about the relevance of the mathematic curriculum given emerging societal crises and knowledge demands

In an era inundated with statistical and mathematical information through various media channels, members of the public must grasp these concepts if they are to understand global developments like public health crises and climate change. In this study, we explored teachers' beliefs about the relevance of the curriculum in the context of the COVID pandemic and sought to identify, from their perspectives, the changes needed to improve its relevance. We had 56 teachers participate in an online survey, eight of whom were also interviewed later. Our findings revealed that participants believed the curriculum helped prepare learners to understand certain aspects of the pandemic-related information. However, they noted that the information was more complex than mere mathematical calculations might be, so required a careful coordination of appropriate mathematical and contextual relationships. Many teachers suggested changes focused on providing more opportunities for learners to engage with real-life applications of mathematics. There were variations in teachers' perspectives on curriculum content, with some emphasizing the importance of broader cognitive processes while others focused on specific topics. These differences were influenced by factors such as teaching experience, educational background, and teaching phase.

Policy-based evidence: the schools inspectorate in England, research and school mathematics policy

ABSTRACT Increasingly, debates about school mathematics curriculum and pedagogy refer to evidence. The Office for Standards in Education (Ofsted), the inspection service in England, published a series of research reviews, including one on mathematics. Using features of education review quality, we analyse Ofsted’s departure from scholarly norms, identifying a lack of transparency, weakness of research design and search strategy, and lack of rigour in the selection of evidence. Further, cited research is frequently misinterpreted and unwarranted causal claims made due to overgeneralisation and oversimplification. A specific example of this is the misappropriation of research on problem solving leading to recommendations conflicting with both the National Curriculum in England and the findings of other, more rigorous, research reviews. From this analysis, we argue that the mathematics review is an example of “policy-based evidence” and point to alternative ways that inspection evidence can complement mathematics education research to support evidence-informed policy and practice.

Comprehending geometry proofs: A study on prospective mathematics teachers' perceptions and preferences of proof formats

The explicative aim of this research is to investigate the optics of proof format preferences held by prospective mathematics teachers (PMTs), in an effort to assess the effect that such preferences may have on their understanding of geometric proofs. The researchers employed a qualitative case study approach, in which six PMTs participated in Focus Group Discussions (FGDs) on the three styles of proof: paragraph proof, two-column proof and flow-chart proof. The methodology employed also focused on the formatting models by exploring the participants’ suggestions regarding each format in order to determine their cognitive responses as well as their preferences. The study exposes different preferences among PMTs which are a result of their personal cognitive style and experience with proofs. Some of the PMTs preferred the two-column format due to its systematic and logical nature, other PMTs preferred the storytelling nature of the paragraph proof format sponsored also flow-chart representation. These preferences bring out the requirement for the development of pedagogical strategies that employ different proof formats in order to meet the needs of different types of learners for effective understanding. In summary, this research demonstrates the need for customizing proof instruction to different students’ needs which can hopefully enhance PMTs’ responses and interactions with the concept of mathematical proofs. The practical outcomes show that teachers should not be afraid to think in more flexible witnessing forms of proof in order to aid students learning while minimizing the cognitive load in line with the principles of constructivist learning. It would be worthwhile however to extend this research and examine what these preferences would mean for the future and how those would fit within the context of online education with the overall aim of creating a better mathematics curriculum that is more effective and has a wider reach.

Learning Opportunities for Solving Context-Based Calculus Tasks in Nepal’s High School Mathematics Textbooks

ABSTRACT A vital skill for students to acquire in school mathematics involves solving problems embedded within real-world contexts. The extent to which students achieve intended learning outcomes largely depends on whether textbooks offer opportunity-to-learn (OTL) the assessed concepts and skills. The National Assessment of Students’ Achievements (NASA) reveals a significant deficiency in the performance of Nepali students in solving context-related problems. We conducted a content analysis of the most commonly adopted Nepali mathematics textbooks for grades XI and XII to assess the OTL they afford for tackling context-related problems in calculus. Results show that almost all mathematical concepts were introduced without providing related contexts, and around 95% of worked examples and exercise problems did not have any context and offered little or no opportunities for modeling and mathematization. Although most of the contexts presented in the problems were categorized as real and essential, the cognitive demands of many tasks were lower. The investigated textbooks were not necessarily aligned with Nepal’s updated National Mathematics Curriculum (2018), which underscores the integration of mathematics with real-world applications. Results of this study indicate that the limited access to quality mathematics textbooks might be a significant barrier hindering students’ ability to solve context-related problems.

Decolonising mathematics education: Teachers’ initial experiences of using ethnomathematical games in the intermediate phase

The African Agenda 2063 strives to attain the goals of peace and prosperity, and to do so, there must be a process of political liberation and decolonisation. In the South African context, decolonisation involves transforming the mathematics curriculum to one that is African by employing cultural approaches such as ethnomathematics. However, South African mathematics teachers still rely on Eurocentric methods for teaching mathematics. To decolonise mathematics in the Intermediate Phase, a project was initiated that utilised indigenous games for teaching mathematics. This paper aims to identify whether such efforts to decolonise mathematics education will be accepted or rejected by the mathematics teachers involved in this study. The paper is framed by the Critical Mathematics Pedagogy Theory. A qualitative case study approach was employed to collect data through a focus group interview with ten mathematics teachers who teach in rural and semi-rural areas of KwaZulu-Natal, South Africa. The findings demonstrate that ethnomathematical games encourage mathematics learning, that teachers’ initial apprehensions gave way to enthusiasm, that learners were excited to play and learn, and that teachers found it effortless to integrate mathematical concepts such as addition, subtraction, multiplication, factorisation, and quadrilaterals with the indigenous games of Morabaraba, Tshetershere, Diketo, and Kgati. Recommendations include that mathematics educational policies incorporate ethnomathematics as a policy directive and that teachers receive training in alternative cultural pedagogical practices for teaching mathematics, such as the use of ethnomathematics. Future research endeavours should focus on finding avenues to sustain ethnomathematics in the classroom.

Effect of Implementing a Competence-Based Curriculum on Students’ Academic Performance in Mathematics: A Case of Selected Lower Secondary Public Day Schools in Rwamagana District, Rwanda

This study is designed to determine the effect of implementing competence-based curriculum on students’ academic performance in mathematics in selected lower secondary public day schools in Rwamagana District, Rwanda. This study is beneficial to Rwandan secondary schools, to the researcher himself, teachers, and other researchers providing advice on how they can develop the students’ competences in mathematics subjects. Guided by constructivism and social constructivism learning theories, the study’s participants were 8 head teachers and Deans of studies (5 respondents), 7 teachers of mathematics (5 respondents) and 275 students (158 respondents). These made a sample size of 168 respondents from four secondary day schools in Rwamagana district were involved in this research. The target population of this study was 290 participants. Purposive sampling by choosing the Dean of studies and Head teachers and simple random sampling was used to choose teachers and students as well as stratified random sampling. Instruments used to collect data are questionnaires and interviews. The quantitative data was analyzed by using IBM SPSS 20 while analysis of qualitative data was done using inductive thematic analysis. Results on the implementation of competence-based curriculum structure indicated that 81.7% strongly agree that discussing math concepts with classmates helps them to learn better. 86.7% agree that the school leaders support the implementation of Competence-Based Curriculum (CBC) in mathematics. 89.9% of the asked students agree that their mathematics teachers seemed well prepared to teach the CBC. The study found that the CBC program is being implemented effectively in Rwamagana District. Students are more engaged, better at problem-solving, and have a better understanding of math. The study shows that the program should continue and be improved to help students succeed in school and their careers. It was proposed that Rwanda Education Board is advised to support and train schools in implementing the CBC in mathematics. It should regularly evaluate and adjust the curriculum to improve outcomes. Teachers should participate in professional development and adopt a student-centered approach. Schools should ensure adequate resources and foster a collaborative culture. Families should encourage active student participation, maintain open communication, and provide a supportive home environment.

LEARNING MATHEMATICS IN TELUKDALAM MARKET: CALCULATING PRICES AND MONEY IN LOCAL TRADE

This study aims to develop a contextual mathematics learning method using the market as a learning medium in Telukdalam. The main focus of the research is to enhance students' abilities in calculating prices and money within local trade. Through this approach, students not only learn basic mathematical concepts but also relate them to real-life situations they encounter in their daily lives. A literature review method is employed to examine relevant literature on contextual mathematics learning and the importance of social interaction in the learning process. The results indicate that learning experiences in the market can enhance students' motivation and understanding of mathematical material. Additionally, this learning approach enriches local social and cultural values, leading students to appreciate their environment and traditions more. It is hoped that the findings of this study will contribute to the development of a more relevant and contextual mathematics curriculum.

Analysis of Mathematics Performance Trends in Certificate of Secondary Education Examination, Tanzania, from 2015–2022: A projection for eight years

Mathematics is essential to life as everyone uses mathematical concepts daily. Many countries have advanced in science and technology by investing in mathematics. This study aimed to determine the trend of students who sat for the Certificate of Secondary Education Examination (CSEE) in mathematics from 2015 to 2022; analyse performance trends in mathematics during this period, examine mathematics failure rate trends, and project pass rates in mathematics for the next eight years, from 2023 to 2030. This study employed a quantitative research approach and an ex-post facto research design. Participants were 4,459,009 students who sat for CSEE from 2015–2022. Analysis from the Statistical Package for Social Sciences version 26.0 revealed a consistent rise in student enrollment, with 136,481 more students by 2022. The pass rate was low, as the maximum was 20.12%, while failure rates consistently exceeded 78%. The findings indicated further that the pass rates would remain low from 2023 to 2030. The study recommends reviewing secondary school mathematics curriculum, increasing teaching and learning materials, providing regular in-service training in innovative pedagogical practices and assessment, and hiring more mathematics teachers in secondary schools.

Research on the Practice of Ideological and Political Education in Mathematics Courses in Vocational Universities Based on Classroom-Training-Competition Mode

The purpose of this study is to explore how to effectively integrate ideological and political education into the mathematics curriculum by proposing a "combination of classroom teaching, practical training projects, and competition activities". By organically combining classroom teaching, practical training projects, and competition activities, it promotes students' learning of mathematical knowledge while enhancing their sense of social responsibility and professional ethics. Research results show that this model has significantly improved students' mathematics performance, especially in terms of basic knowledge and modelling ability. At the same time, by participating in mathematical modelling competitions and practical training, students have demonstrated strong teamwork spirit and innovation ability, and their professional ethics have been significantly improved. Through questionnaires and interviews, the feedback results show that students attach great importance to the practical value of the curriculum and ideological and political education. Finally, the research suggests that the integration of ideological and political elements into more mathematics courses should be explored in the future, in order to improve the quality of education and cultivate high-quality talents with a sense of social responsibility and professional ethics.

Developing the Competence of Using Tools and Materials in Learning Mathematics for 4th-Grade Students in Geometry and Measurement Content

In Vietnam's general education program, Mathematics is a significant tool for many other subjects. Mathematics originates from practicality and serves as the "key" in most human activities, as well as in learning other subjects. In teaching Mathematics, teachers not only guide students to acquire knowledge but also form and develop students' abilities and intellectual qualities, training their critical thinking and creativity. The ability to use tools and learning materials for Mathematics is one of the five components of mathematical competence in the 2018 Mathematics curriculum for general education. This article focuses on proposing some basic measures to develop and nurture the ability of using tools and materials in learning Mathematics for fourth-grade students through teaching Geometry and Measurement content.

VẬN DỤNG PHƯƠNG PHÁP DẠY HỌC KHÁM PHÁ TRONG DẠY HỌC PHƯƠNG TRÌNH LƯỢNG GIÁC Ở NƯỚC CỘNG HÒA DÂN CHỦ NHÂN DÂN LÀO

According to educational researchers, effective learning is not only just sitting in classes spectating other activities, and memorizing available imparted knowledge, but learners also should participate in the discovery process of new knowledge guided by instructors. It is necessary to apply the discovery learning method to teaching the subjects in general and teaching Mathematics in particular in the direction of developing the competencies and qualities for students. This paper focuses on researching the concept of the discovery learning method and its characteristics. Based on researching the Mathematics curriculum and practical teaching in The Lao People's Democratic Republic, this paper proposes applying the discovery learning method to teaching trigonometric equations at high schools in the Lao People's Democratic Republic.

Developing Computational Thinking through Mathematics Learning in Indonesia: Scientific Mapping and Bibliometric Analysis

This research aims to explore and map the teaching methods used in developing Computational Thinking (CT) through mathematics learning in Indonesia, using a bibliometric analysis approach. Based on a literature review from Scopus and Sprott-indexed databases, this research analyzes trends, contributions and challenges in the implementation of CT at various levels of education. Teaching methods such as Scratch, Problem-Based Learning (PBL), Augmented Reality (AR), and robotics were identified as the most effective strategies in improving students' computational thinking skills. The findings show that the majority of publications published in educational and CT-related sources about teaching mathematics are mostly about teaching computational skills and teaching computer programming using practice and algorithmic thinking, although these methods have had a significant impact, some limitations, such as lack of instrumentation, limited technological resources, and curriculum adaptation are still challenges. This analysis also highlights opportunities for further research in developing more comprehensive evaluation instruments and improving technology access in computational education. It is hoped that the results of this research can provide guidance for educators, policymakers and researchers to increase the integration of CT in the mathematics curriculum, as well as expand the scope of computational research in the Indonesian educational context. This research opens new insights to overcome barriers and optimize the potential of CT in the future.

2022 개정 특수교육 기본 교육과정 수학과 성취기준 분석: Bloom의 신교육목표분류학에 기초하여

Objectives This study aims to provide implications for the achievement standards of the basic curriculum for mathematics in the 2022 Revised Special Education Basic Curriculum by analyzing them based on Bloom's revised taxonomy of educational objectives. Methods To this end, a total of 182 mathematics achievement standards of the revised 2022 special education basic curriculum were analyzed for five grade groups and five mathematics areas based on Bloom's new taxonomy of educational objectives. Results First, the achievement standards for each grade were analyzed. As a result, among Bloom's knowledge dimensions in all grade groups, ‘factual knowledge’ was the highest with 104 (57.1%), and among the cognitive process dimensions, ‘Understanding’ was the highest with 89 (48.9%). A binary classification analysis of knowledge and cognitive process levels, the achievement standards for remembering factual knowledge were found in 55 achievement standards(30.2%). There were no achievement standards for ‘Meta-cognitive knowledge’, ‘Evaluation’, and ‘Create’. Second, as a result of analyzing the achievement standards by mathematics area, ‘Factual knowledge’ was the highest in the knowledge dimension with 45 achievement standards (48.9%) for numbers and operations, 28 (87.5%) for shapes, and 24 (92.2%) for measurement. ‘Conceptual knowledge’ was the highest with 12 (70.5%) in the regularity area and 9 (60%) in the data and probability area. In the cognitive process, ‘Remember’ was the highest with 29 (31.5%) in the number and calculation areas and 18 (56.3%) in the measurement areas was the highest with 17 achievement standards (65.3%), the regularity area with 7 achievement standards (41.1%), and the data and probability area with 9 achievement standards(60.0%). There were no achievement standards for ‘Meta-cognitive knowledge’, ‘Evaluation’, and ‘Create’. Conclusions Based on the results of this study, implications for the development of mathematics achievement standards of the basic curriculum for special education and suggestions for future research were made.

Indigenous Knowledge Content & Mathematics Curriculum

Cultural practices present opportunities for Mathematics Education to be more relevant, and effective, especially in post-colonial contexts. Despite national policies emphasising integration of Indigenous Knowledge (IK) into school curricula, there has been limited success in incorporating ethnomathematics into Mathematics teaching. We exploredgeometrical concepts inherent in traditional baskets produced by Aawambo women, an ethnic group in northern Namibia. We identified specific geometrical concepts that can be linked to the junior secondary school Mathematics syllabus. We employed ethnographic observations, interviews with local basket makers and focus group discussions with Mathematics junior secondary school teachers for triangulation. Furthermore, we adopted an interpretive paradigmusing a multi-modal method to source empirical data that demonstrated relevance to the curriculum. We explored socio-cultural perspectives of women and artefacts (baskets) to compare the subject matter from literature. The findings revealed common concepts as well as the ethnomathematical content not yet incorporated in the junior secondary school Mathematics curriculum comprising of symmetry (axial symmetry) and geometrical transformation (shear and translation). The study has implications for decolonizing western Mathematical practices through adoption ethnomathematics approaches across Africa.

Developing modelling competencies in pre-service mathematics teachers through reflective thinking skills

Background: Ghana’s commitment to quality education has been reflected in its goal of providing equal access to high-quality education, leading to the reforms of the New Common Core Mathematics Curriculum for Basic Schools. The study explored the integration of mathematical modelling using reflective thinking skills, which are not currently core competencies in Ghanaian basic school curriculum.Aim: The study examined the modelling proficiency of pre-service mathematics teachers by assessing their reflective thinking abilities in a modelling laboratory context.Setting: The study focussed on pre-service mathematics teachers from two education colleges in Ghana.Methods: Using purposive sampling to select participants, a quasi-experimental design with pre- and post-test interventions was employed. Data were analysed through content and inferential analysis, supplemented by interviews.Findings: The findings indicated that the comparison group lacked prior knowledge of modelling problems and struggled with comprehension tasks. In contrast, the experimental group successfully translated real-world problems into mathematical models.Conclusion: Providing pre-service mathematics teachers access to a modelling laboratory and modelling-eliciting activities was essential for developing future modellers. This approach would enhance their effectiveness in teaching foundational mathematics in Ghanaian education.Contribution: This study advocated for re-orienting the mathematics curriculum at both Basic schools and Colleges of Education in Ghana to include mathematical modelling and reflective thinking skills as core components.

Examining the Efficacy of a Physical Board Game for Geometric Transformations

A group of Hong Kong secondary school mathematics teachers collaborated on the creation of a physical board game, “War of Transformation”, specifically designed to aid Hong Kong Secondary 1 students in applying transformation (i.e. translation, reflection, and rotation) of 2D figures, a topic in the local mathematics curriculum. The objective of the study was to delve into the game design and player experience from the viewpoint of the students as indicators of the effectiveness of the board game, comparing these elements across different abilities. A mixed-method design was adopted, from which data was gathered utilizing questionnaires and a focus group. The study involved a total of 102 junior form students secondary school students from three districts in Hong Kong, with a selected group of five students and three school teachers participating in interviews. The questions for the questionnaire and interviews were derived from the Model for the Evaluation of Educational Games. Quantitative data were used to provide an overview of student experiences, while qualitative data from the interviews provided further insights of the results. The findings revealed that students valued the game’s design and had a positive gaming experience, comparing these elements across different abilities The design of the board and the use of online teaching aids were found to significantly enhance gameplay and learning. This study highlights the potential of thoughtfully designed game-based learning in fostering effective and engaging learning experiences.

Exploring geometry and measurement in the Perjuangan Subkoss Garuda Sriwijaya Museum: An ethnomathematics study

The Museum of Perjuangan Subkoss Garuda Sriwijaya is a museum that preserves the history of South Sumatra’s struglle against the Dutch and Japanese colonialists. This research aims to obtain the results of an ethnomathematics study from the Museum of Perjuangan Subkoss Garuda Sriwijaya regarding historical, philosophical, and mathematical aspects and implement it in the Merdeka Curriculum in mathematics for elementary schools. This research employs an ethnographic approach with a qualitative descriptive approach, utilizing observation, interviews, documentation, field notes, and data triangulation. The analysis techniques include data reduction, data presentation, verification, and conclusions drawings. The study involved three informants who had direct interaction with the Museum of Perjuangan Subkoss Garuda Sriwijaya. The results of this research shows that ethnomathematics studies offer several insights: the historical aspect introduces local history and culture through artifacts that supported the struggle during the physical revolution; the philosophical aspectteaches the values ​​of caring, cooperation, creativity, and diversity within society; and the mathematical concepts reveals the concept of geometry, including area, perimeter, volume of both two-dimensional figures and three-dimensional figures, and length measurement.

Collaborative Design Capacity for Enactment Framework: An Analytic Tool for Conceptualizing Pedagogical Design Capacity Within Social Context

ABSTRACTThis study examines an urban middle school teacher design team's capacity for creating integrated science, technology, engineering, and mathematics curricula. Using Brown's pedagogical design capacity (PDC) theory, which highlights interactions between personal and curricular resources, this paper introduces an extended framework that includes social interactions as key influences on teachers' design abilities. Findings show that individual teachers' spontaneous curriculum modifications were adopted by the team, becoming collective resources for ongoing redesign and improving their design capacity. Teachers effectively used each other as resources to address unexpected challenges in integrating science, engineering, and mathematics concepts. Three types of social interactions were identified as collaborative resources: (i) Storytelling: sharing experiences to make abstract concepts actionable for curriculum development; (ii) Protocols: structured methods to address curricular problems related to integration; and (iii) Assessment “for” curriculum redesign: using assessment tools to inform and improve the curriculum. The Collective Design Capacity for Enactment framework is introduced to describe PDC within a social context, highlighting the importance of social interactions in bridging curriculum use and development, thus extending the literature on PDC.

Navigating the seas of the curriculum: A mathematics teacher’s interactions with curriculum materials

Curriculum materials are not a fixed object; they are an active partner in a teacher’s practice. Teachers and curriculum materials interact in a participatory relationship where both the characteristics of the teacher and the characteristics of the curriculum material affect the instruction. Teachers interpret and tailor these materials to create particular instructional strategies, therefore, teachers can be considered as lesson designers. The study presented in this paper uses longitudinal case study design to investigate the relationship between a mathematics teacher and curriculum materials over a period of nine years. Using the lens of curricular noticing, the study examined what the teacher attends to, interprets and responds to while planning a lesson. Data collection occurred at four distinct time points, encompassing both teacher observations during lesson planning and interviews after lesson planning, as well as the teacher’s lesson plans for the same topic at each time point. The obtained longitudinal data provided comprehensive insights into how the teacher’s curricular noticing changed over time and how it affected the teacher’s practice. The findings show that the teacher attended the national curriculum and textbook at all four time points, indicating the stability of these particular resources; however, the interpretation of the textbook elements and response to this interpretation changed significantly. The teacher’s practice became more student-centered and inquiry-oriented. The implications of the study are also discussed.

Educational robotics and primary school mathematics teaching: An analysis of pre-service teachers didactic-mathematical knowledge

The scarcity of studies dedicated to the integration of educational robotics (ER) in teaching mathematical content, and the discomfort of teachers when integrating ER in their teaching practices make it pertinent to understand the development of the didactic knowledge of mathematics necessary to integrate ER in mathematics teaching practices during initial teacher training. This qualitative and interpretive study identifies the knowledge of the didactic dimension from the didactic-mathematical knowledge conceptual framework that is mobilized by pre-service teachers (PST) during the implementation of mathematical tasks that integrate ER during the practicum. Through content analysis of the data collected on the PST’s performance, we mapped the occurrence and co-occurrence based on the components of the didactic suitability criteria. From the results, we highlight: (i) the existence of a relationship between the mathematical knowledge needed to teach, knowledge of the mathematics curriculum, and knowledge of ER and how its integration in the teaching process can influence the learning process and (ii) the positive contribution of the implementation in the practicum of mathematical tasks that promote robot manipulation/programming at the same time as the exploration of the mathematical content for the development of the participants’ didactic knowledge of mathematics. A practical implication of our results is that these features should be part of future work dedicated to integrating ER in mathematics teaching practices of PST, aiming to assess their value in initial teacher training programs.