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In this case study, the researcher examines how three elementary teachers, all certified by their school district in culturally responsive teaching (CRT) through professional development (PD) opportunities, implement CRT in mathematics. The study was designed to understand 1) the CRT certification process and structures that were intended to support teachers in the focal district, and 2) how the teachers were enacting CRT in mathematics based on these experiences. Data were collected via interviews, questionnaires, observations, teacher journals, and other reportable data. The teachers were enacting CRT practices that aligned with Hammond's (2015) Ready for Rigor framework, which includes awareness, learning partnerships, community of learners, and information processing. Yet, at times, the teachers engaged in CRT practices that were more thoroughly captured in other literature, including that in mathematics education. Thus, the researcher created an adapted model to display these findings about practice across four quadrants. From these findings, researchers in mathematics education may gain a more informed understanding of how elementary teachers may enact CRT in mathematics based on their backgrounds and experiences with a district-developed and applied certification model, rather than a researcher-designed PD with selected participants of practicing teachers.

Blind students exclusively use braille materials for teaching math. Teaching tools that assist blind students' motor and hearing nerves are essential for learning. This study was to describe learning mathematics outcomes for blind students after using teaching material for Android devices based on Newman's theory. This research was a case study of blind students. Blind junior high school students from special schools for visual impairment-- extraordinary schools in Bandar Lampung, extraordinary schools in Cimahi, and Madrasah Tsanawiyah with special education in Yogyakarta-- contributed to the study's subjects. The study employed questionnaires and test questions as research instruments for both teachers and students. The results of this study demonstrate that learning mathematics outcame blind students' after using teaching material with Android apps based on Newman's theory, specifically: i) reading errors: students can understand the information in the questions; ii) comprehension errors: students do not write down things that are known and asked; and iii) transformation errors: students write down the mathematical model (formula) used; iv) skill errors: students can do calculations correctly; and v) coding errors: students do not write conclusions. The average score of the blind students' results using braille was higher than that of the Android application.

Mathematics education is looking for innovative methods to foster problem-solving skills in students. This research develops a problem-solving assessment using GeoGebra Classroom, a versatile interactive mathematics software, to revolutionize mathematics formative assessment and improve students' problem-solving skills. This study adopted the analysis, design, development, implementation, and evaluation (ADDIE) instructional design model stages. The design stage created a comprehensive assessment blueprint, incorporating GeoGebra Classroom functions to create interactive problem-solving tasks. Data analysis used both quantitative and qualitative approaches. Qualitative data consisted of feedback and suggestions from assessment experts, mathematicians, and GeoGebra specialists. Meanwhile, quantitative data included expert scores and cognitive tests that measured students' problem-solving abilities. A cognitive post-test was conducted to measure the progress of students' understanding while using the assessment product. The results of the content validity analysis, assessed using Aiken's V, ranged from 0.85 to 0.92, indicating a high level of validity for the problem-solving skills assessment in terms of content and construction. Some revisions were made to the design of the developed media to make it more interactive for students. These findings suggest that we can further use problem-solving questions integrated with GeoGebra Classroom to uncover the problem-solving skills of junior high school students.

The capacity for mathematical reasoning, pivotal in grasping core math concepts, directly shapes a student's success in their mathematical studies. This study aimed to detail and analyzed how the search, solve, create, and share (SSCS) instructional framework impacts mathematical reasoning skills within the context of linear equations. We adopted a quasi-experimental research approach using a non-matching control group design. To gather data on mathematical reasoning proficiency, a validated and reliable essay-type test was employed. Data collection on mathematical reasoning abilities used an essay test instrument that has been valid and is reliable. This research involved 102 eighth grade students whereby they were selected by using a purposive sampling. To measure and describe the effect size, we utilized a specific method, yielding a result of 0.97. The t-test was employed to assess the influence of the SSCS learning model, and the significance value obtained was less than 0.05. The effect size, as determined, stands at 0.97, suggesting a substantial impact. The t-test results underscore a significant relationship between the SSCS learning model and the enhancement of mathematical reasoning abilities. This research delineates a framework for employing the SSCS model to enhance students' mathematical reasoning capabilities. It is evident that such reasoning abilities play a pivotal.

The aim of the study is to examine how lesson study activities affect primary school preservice teachers' noticing of students' misconceptions. A qualitative research approach was adopted and action research method was used. The study was conducted with 9 primary school preservice teachers. The data were obtained from the observation form, video recordings, reflection reports and field notes in order to reveal how the lesson study model affected the noticing development of preservice teachers. In addition to these, the "video exam" at the end of the Teaching Practicum-II course also constituted one of the data collection tools. Descriptive analysis was used in the study. The data obtained were analyzed by adapting the theoretical framework of "Levels of Noticing of Students' Mathematical Thinking" developed by van Es (2011) as "Levels of Noticing of Students' Misconceptions" in order to reveal preservice teachers' noticing of students' mathematical thinking. As a result of the research, it was concluded that noticing skills of the lesson study group preservice teachers were mostly at the level of reasoning and justifying their reasons (level 3) and offering alternative pedagogical solution suggestions based on comments (level 4). It was concluded that the noticing skills of the comparison group preservice teachers were mostly descriptive (level 1) and at the level of identifying important events but being insufficient to expand their interpretations (level 2).

Purpose: Mathematical literacy and mathematical problem-solving are crucial abilities that link mathematics content to real life applications, facilitating both mathematics understanding and mathematical processes. The present study aimed to investigate the effectiveness of the STEMEN (STEM and educational neuroscience) teaching model in enhancing mathematical literacy and problem-solving skills. Methodology: This study adopted a pre-test and post-test control group design. Among 156 Grade 9 students from a secondary school in Phayao, Thailand, 70 were randomly selected. The STEMEN teaching model was implemented in the experimental group, while the 5E teaching model, typically used in a normal classroom was employed in the control group. Two types of tests, namely the mathematical literacy test and the mathematical problem-solving test, were used as research instruments. Pre and post-data were collected from both the experimental and control groups. Repeated measures ANOVA with Wilks' lambda was employed to analyze the mean comparison for mathematical literacy and mathematical problem-solving. Findings: The findings revealed that the mean scores for mathematical literacy and mathematical problem-solving were relatively higher in the STEMEN teaching model group compared to the 5E teaching model group. These results provide insights into the effectiveness of the STEMEN teaching model in enhancing learning outcomes, particularly mathematical literacy and problem-solving in mathematics. Significance: The results of this study showed that the STEMEN teaching model was effective in increasing learning outcomes, including mathematical literacy and problem-solving. These outcomes should enable teachers to design effective and efficient instructional strategies for enhancing mathematical literacy and problem-solving in classrooms.

Simon Fraser University in Vancouver, Canada offers two introductory calculus courses designed for students enrolled in science and engineering programs. Students identified as needing additional support based on their admission grades take the version of the course where students meet weekly for four hours instead of three. A new approach for the fourth hour was introduced in Fall 2019 splitting the class into smaller sections of 20-40 students to work in small groups on vertical whiteboards under the supervision of the instructor, complemented by peer tutors. This format introduces an active learning element that improves student performance and attitude. The project was first implemented in Fall 2019, although interrupted due to COVID-19. After returning to the in-person classroom, the whiteboard seminar program was reinstated. In Fall 2022 and Spring 2023, survey feedback was collected from both students and peer tutors for a more holistic perspective on the program. In this study, the results of these surveys are analyzed, focussing on four areas of measurement: students' satisfaction, learning calculus concepts and problem-solving techniques, the contribution of the instructor, and the contribution of the peer tutors. Exploratory factor analysis revealed three latent variables underlying student survey responses. The survey results suggest that interactions with the instructor, peer tutors, and active learning activities all contributed to students' enjoyment of the course and their perceptions of their own learning. We compared students' final course grades from Fall 2018, where the fourth hour was devoted to lecture before the program was implemented, to Fall 2019 and 2022. The data shows a decrease in the percentage of students failing the course and an increase in those earning A's and B's since the program's implementation. Additionally, survey results show that replacing a typical lecture-style hour with a whiteboard seminar improved students' attitudes and perceptions of the course.

The limitations of traditional education models and the advancement of technology have revealed the need to transform the learning experience. The "Flipped Learning" approach, born out of this need, is a model where students study learning materials in advance and participate in more interactive and hands-on activities in the classroom. This research discusses how the Flipped Learning model can be combined with ChatGPT. ChatGPT is a language model developed by OpenAI, and it can interact with students thanks to its natural language processing capability. In this way, combined with the Flipped Learning model, it can provide students with a more individualized and interactive learning experience. From this viewpoint, in this research, a model called "ChatGPT Aided Flipped Learning Model (CAFLM)" has been developed, which enables ChatGPT to be used in the "Flipped Learning" learning environment. CAFLM has three main phases: 1) Preparation, 2) Outside classroom teaching, and 3) inside classroom teaching. At these phases, the tasks of the student and the teacher are explained in detail. Sample activities and use cases are provided on how ChatGPT can be integrated into the Flipped Learning model and help students. To experience the model, activities developed for mathematics and science lessons were carried out using ChatGPT. The experiences have shown that the Flipped Learning model can be combined with Chatbots such as ChatGPT to provide students with a more effective and personalized learning experience. CAFLM can enable students to be more active in the learning process and contribute to innovative approaches in education.

Culture shapes pupils' mathematical learning, their performances and life trajectories of participation (César, 2013a, 2013b). It also contributes to the senses they attribute to mathematical learning (Bakhtin, 1929/1981). Using collaborative work and interempowerment mechanisms facilitates knowledge appropriation (César, 2009). This is particularly important for pupils participating in minority cultures, socially undervalued and whose L1 is not the instruction language. Bi-univocal culture mediation (César, 2017b) is important regarding empowerment. We used an instrument to evaluate pupils' abilities and competencies (IACC), conceived by the "Interaction and Knowlwdge" (IK) team (Machado, 2014), and other mathematical tasks. The goal we address is to trace the differences between their approaches to problems, mathematical reasoning and solving strategies used by pupils whose L1 is ideographic (Creole, Cape Verde) or phonetic (Portuguese). We developed an intrinsic case study (Stake, 1995). The main participants are the pupils from almost 600 classes (all over Portugal and Cape Verde) who participated in the IK. The analysis of some examples illustrates that L1 shapes pupils' approaches to problems, mathematical reasoning and solving strategies. This evidence plays an important role in their access to school achievement and in teachers' understanding about how they can promote pupils' mathematical learning.

Professional teacher collaboration, a fundamental characteristic of lesson study, has been pointed out as a principle of teacher personal and professional growth. This article aims to describe and analyze the development of professional collaboration in a lesson study, highlighting the main stages of this process. The investigation involved six elementary school teachers of Brazilian public schools, in planning, observing, and reflecting on a lesson on the curriculum topic of length measure at grade 4. The participants worked collaboratively planning a lesson about this topic. The methodology is qualitative, with data collected by records and field notes of sessions, conversations, and interviews. The analyses pointed out three remarkable stages of the development of professional collaboration, which constituted the categories of analysis: recognition of collaboration, development of collaboration, and valuing collaboration. The results show that the professional collaboration that developed during the lesson study was facilitated by the dynamics of the different steps of this process and, especially, by the relationship between participants and teacher educators. Collaboration emerged from the activities of planning, teaching, observing, and reflecting on the lesson, and was valued given the encouragement and strengthening of the group insofar as teachers felt confident, encouraged, and welcomed in the group.

Eye-tracking (ET) method provides a promising channel for educational researchers to connect learning outcomes to cognitive processes. The main principle of ET is that our gaze and our focus of attention are connected. Due to the advent of digital technologies, eye tracking studies are increasingly growing in different fields and in mathematics education. We assume that the provided task is one of the ways to analyse deeply cognitive processes, and we wonder how ET studies are dealing with the integration of digital technology in task-design in geometry. Starting from Strohmaier et al. (2020) we found three studies, one focused on geometric proofs and two based on construction of geometric objects. We highlight the contributions of integrating digital technology in learning and instruction, and in research in geometry.

The contents of calculus, known for their complexity, present significant challenges for students, particularly in mastering multiple integrals and effectively visualizing related concepts. The transition to distance learning prompted by the COVID-19 pandemic has further complicated the learning process in multiple integrals. In line with this and considering the potential of computer-supported collaborative learning (CSCL), in this research we explore the impact of teaching in a CSCL environment on student achievements, focusing on students from the computer science study program. Through data analysis using ANOVA and Bonferroni post-hoc tests, it was found that students exposed to collaborative learning in GeoGebra environment demonstrated higher levels of theoretical and practical knowledge compared to peers who acquired knowledge without using GeoGebra. Additionally, this group of students achieved results comparable to those of students who attended traditional in-person teaching, showing noticeable improvements in solving complex tasks. Our findings show the effectiveness of CSCL approach in context of distance learning and highlight potential of collaborative environments enhanced with technology in facilitating student understanding and achievements in calculus education.

Although student covariation reasoning has been explored in depth to improve understanding of the correspondence between variables, research has focused on studying existing reasoning about variables in Cartesian representations. The working method had a qualitative approach, with a descriptive exploratory scope, the spontaneous representations that the participants evidenced under the level of covariational reasoning of the variables present in three contextualized situations were explored, posed to a population of third-grade middle school students. The students argued with concrete and abstract drawings the general behavior of the variables. At low levels of reasoning they used pictorial representations, at higher levels they used graphical diagrams and tables. The exploratory study shows a relationship between the type of spontaneous representations and the student's level of covariational reasoning, as well as the rigor of the description of the problem.

Mathematical reasoning has been a critical concern in Turkey especially since the structure of the student selection examination for high schools changed six years ago. The ability to solve the questions in the new exam requires high level reasoning and argumentation skills. Schools, whether they are public or private, prepare 8th graders for this exam with intense educational programs. They frequently use skill-based questions--similar questions to the ones in the new exam, which require high level mathematical reasoning. This study indicates that students gain better mathematical reasoning skills in learning environments promoting collective discussion and argumentation. Hence, these questions need to be solved in these kinds of environments. In this study, two cases are analyzed to understand the argumentation process in classrooms in depth. Audiotapes of two 8 th grade classrooms, one from a public school, another from a private school, are analyzed. The same teaching material--a worksheet including skill-based questions--is used in the classrooms. During analyzing, qualified argumentation pattern--a pattern including students' claims and justifications/evaluations for those claims--is defined. Analysis of classroom audiotapes revealed that that there are significant differences between two classrooms' argumentation structure and type of dialogues emerged in the classroom. In one classroom there is a more qualified argumentation process than in the other classroom. In addition, analysis of the type of the dialogues indicates that two classrooms have different types of dialogues. Overall, the study reveals that despite the differences, both classrooms mostly included teacher-individual interactions and they have little collective discussion.

This article discusses multimodal practices in the context of teaching and learning and how this idea might inform and facilitate mathematical learning, especially for Latinx students. We discuss qualitative data drawn from a study of an elementary bilingual classroom (age 10 and age 11) in a Midwestern city (USA) that is exceptional because the students successfully do high-level mathematics. We describe one class episode and one student's use of multiple resources to create meaning. Through this we highlight the nature and relevance of multimodal practices for learning mathematics. This case highlights the necessity of creating environments, where students, especially those who have been historically excluded, use resources to make meaning and gain greater access to mathematics.

The tradition of studies involving the combinatorial approach to recurring numerical sequences has accumulated a few decades of tradition, and several problems continue to attract the interest of mathematicians in several countries. This work specifically discusses the Fibonacci, Pell, and Jacobsthal sequences, focusing on Mersenne sequences. The often-used definition of board involves considering how to fill a specific regular surface--the board--with a limited quantity of regularly shaped tiles. On the other hand, an analogous problem can be generalized and exemplifies current research developments. Finally, the examples covered constitute unexpected ways of exploring visualization and other skills in mathematics teachers' learning, consequently inspiring them for their teaching context.

Mathematical beliefs and metacognitive knowledge play significant roles in solving mathematical problems; thus, this study aims to investigate the influence of middle school students' beliefs on their metacognitive knowledge when solving geometry problems. This study utilizes both quantitative and qualitative research methods. A linear regression test was used to determine the effect of middle school students' beliefs on their metacognitive knowledge. The results of the quantitative research analysis were followed up with a qualitative research approach to describe the metacognitive knowledge of students who have high and low confidence in solving geometric problems. This research involved 352 middle school students in the Tarakan area. Based on the results of linear regression, it is known that the beliefs of middle school students have a positive effect on their metacognitive knowledge when solving geometric problems. In addition, it was found that students with different beliefs could solve a given geometry problem, but the approach to solving it varied among subjects. Middle school students have diverse beliefs, but these variations do not affect their capacity to apply their metacognitive knowledge at every stage of solving mathematical problems.

With the research discussed here I aimed to examine the effect of the COVID-19 pandemic on primary school mathematics teaching processes and specifically the teaching process of 1st-grade geometric shapes. A holistic multiple case study design was used in this qualitative research. The participants were primary school teachers who have taught both processes and geometric shapes in 1st grade primary school and were selected using purposive sampling. Semi-structured interviews based on an interview form developed by me was used as data collection instrument. In this form, questions about the 4 skills in the programme related to geometry were included. Lesson content, materials, and content related to the method of expression related to each skill were examined comparatively during and before the COVID-19 pandemic. Semi-structured interviews during which the questions on the form were asked, were conducted with participating teachers. The content analysis technique was used to analyse the obtained data. The results of the analysis show that the transition to online education during the COVID-19 pandemic had serious consequences. Positive and negative effects were found in both primary school mathematics teaching process and the teaching process of geometric shapes in the 1st grade.

This study aims to reveal the profile of open-start problem-solving with ethnomathematics regarding student learning styles. This research is a qualitative research study on 3 out of 31 students of Junior High School of 3 Magetan taken by purposive sampling. The three students carried out four stages: understanding the problem, planning problem-solving strategies, implementing problem-solving strategies, and reviewing again. The results of the research show that students with a visual learning style solve problems by understanding problems through writing known and being asked and drawing illustrations, planning problem-solving strategies by making examples, carrying out solving strategies by working on the calculation process; students with an auditory learning style solve problems by understanding problems through writing known and being asked, planning strategies by making problems and formulating formulas used, implementing solutions by doing calculations and reviewing; students with a kinesthetic learning style solve problems by understanding issues through writing known and being asked, making examples and writing the formulas used, carrying out solving strategies by applying the calculation process and reviewing the results obtained. However, of the three styles, the results of the accepted work were not correct because they did not write down the conclusions and were not thorough enough.

The study reported on here was conducted to explore four Grade 7 mathematics teachers' understanding of the relationship between the objectives indicated in the CAPS for teaching different topics/concepts and instructional time stipulated for doing so. Seven lessons were studied in 4 primary schools in the Vhembe district of the Limpopo province, South Africa. A constructivist philosophical approach was used. The data collection methods included interviews and classroom observations. The main finding indicates teachers' understanding of instructional time as either a regulatory or a teaching tool. The ability to translate instructional time into social time depends on the level of teachers' curriculum literacy. Consideration of how CAPS objectives could be fulfilled based on the topic/concept to be taught and the stipulated instructional time, influenced the learners' conceptual understanding, procedural fluency, and competency in mathematics. The conclusion underscores the importance of instructional time as both an essential authoritative regulatory tool and signal of a pedagogic device and communication required to advance the instructional objectives.

The COVID-19 pandemic compelled higher education institutions to adopt an alternative approach to learning. For mathematics education, supporting students through blended learning has become increasingly important as it will ensure students' learning is sustained in such a situation. This practical change has illuminated how cloud technology can be employed in mathematics education to improve the instruction process. Using a cloud classroom blended learning-instructional framework for integrating educational cloud tools into mathematics teaching, this study analysed students' metacognitive ability in mathematical problem-solving. A pre-experimental research using a one group pre-test-post-test design was conducted. The sample comprised sixty undergraduate mathematics students enrolled on a Numerical Analysis course. Sample selection was carried out using a simple random sampling technique. Data were analysed using a descriptive analysis, parametric tests, and n-gain. The results revealed that, firstly, the majority of students (90%) achieved a post-test score of metacognitive ability in mathematical problem-solving -- this exceeded the 60% threshold. Secondly, students' post-test score of metacognitive ability in mathematical problem-solving (mean score of 82.14, S.D. = 8.29) increased significantly compared to the pre-test score (mean score of 73.54, S.D. = 8.38). Further, the effect size was large. Thirdly, there was an enhancement of metacognitive ability in the mathematical problem-solving of students with a mean n-gain of 0.34, which is in the moderate category. Thus, cloud classroom blended learning significantly improved metacognitive ability in mathematical problem-solving among undergraduate students. Educators can apply the results to assess mathematics learning in order to improve the quality of metacognitive ability in mathematical problem-solving.

The ability to think creatively is the ability to generate new ideas, innovative solutions, and unconventional thoughts in response to a situation or problem. Creative thinking involves many aspects, including imagination, association of ideas, mental flexibility, and views that are different from the usual. Creative thinking needs to be grown in students because creative thinking is very important in learning which will greatly assist students in solving problems with various solutions. The use of appropriate learning model equipment can support the development of students' critical thinking skills. One effort that can be done is to use innovative teaching materials that combine various activities to develop students' creative thinking abilities. The purpose of this study is to describe the process of developing STEM-based teaching materials with a problem-based learning model on three-dimensional material, namely distance. This study uses the development method or the Research and Development method, namely 4D (define, design, develop, disseminate) but is limited to the develop stage. The data analysis technique of this research uses descriptive analysis techniques both qualitatively and quantitatively. Data collection uses a feasibility validation sheet, readability and student response questionnaires. The results showed that the average score of the eligibility of teaching materials was 81.66% in the appropriate category, the average score of readability of teaching materials was 90% in the easyto-understand category, and the average student response score to teaching materials was 99% with very good criteria. Thus, from this assessment it can be concluded that the teaching materials developed are feasible to use, easy to understand, and have a good response from students. The suggestions put forward are that other teachers/researchers are expected to be able to carry out the same research but develop teaching materials with different materials or abilities.

This study employed a qualitative research design to investigate the utilization of soft pedagogical documents among twelve mathematics teachers in five purposively sampled public secondary schools. Data was collected through interviews and analyzed thematically. The study, rooted in social constructivism theory, discovered a mixed pattern in the implementation of soft pedagogical documents. Scheme of works and notes summary were widely acknowledged as a guide for structuring the academic year, but only a minority of teachers consistently applied it. Lesson plans, crucial for effective teaching, faced challenges in adherence due to time constraints and heavy workloads. Tools like class diary and attendance register were considered essential, yet compliance varied. Marks records and evaluation records, vital for assessing student progress, proved challenging for half of the teachers. Unit assessment records and homework records suffered from inconsistent implementation. While exercises records and formative records were recognized for tracking student learning, their effective use remained infrequent. Despite disparities, the soft pedagogical documents played a crucial role in shaping the educational setting. The study highlighted the need for targeted interventions and support mechanisms to enhance consistent implementation across all documents.

Today math teachers can best reach their students and show them how math surrounds us by using manipulatives, children's literature, and GeoGebra while teaching mathematics. These are some of the best pedagogical practices for teaching mathematics today. In our high-tech world, students need to be proficient in science, technology, engineering, and mathematics (STEM) fields. As endorsed by National Council of Teachers of Mathematics (2000) and stressed in common core state standards in mathematics, it is important that we teach with technology, address dispositions and math anxiety, and make the math that young people are learning pertinent and meaningful. Frequently, it may be best to start teaching young people geometry first as opposed to numbers, which are considered more abstract and difficult to learn. Geometry is one of the most tangible divisions of math and concentrating on this first can help students' whole view of mathematics and their insolences towards learning the subject. Nowadays teachers also need to be cognizant and checking for attitudes and dispositions toward learning mathematics, as math anxiety is an issue in today's classrooms. This paper will revisit the best pedagogical practices for teaching math, the review of the use of math manipulatives, children's books, and GeoGebra to help teachers create mathematically confident young people.

In this article, we explore demands and tensions involved when schools implement ambitious mathematics teaching (AMT). Following a description of a framework that distinguishes between internal and external demands, we characterize the tension between these in terms of alignment, balance, and buffering, which collectively speak to coherence. We then describe AMT and how it represents a departure from traditional mathematics instruction found in most countries. We applied the framework to an illustrative case and found that while the school devoted considerable resources to reforming mathematics teaching and learning, challenges persisted. These challenges include ongoing language and participatory demands for students and, for teachers, balancing the demands of implementing AMT with a range of other initiatives. The framework provides a means of exploring the full range of demands associated with ambitious instructional reforms, how these demands are mitigated or exacerbated, and the kinds of resources necessary to sustain AMT.

This research aims to produce a mathematics module on circle material based on the small group discussion model to improve learning outcomes. The fact is that there are 48% of students who get low mathematics learning outcomes. Another fact is that at the high school level, 62% of students in circle material scored below the minimum completeness criteria. Urgent development research was carried out to produce circular module products. The method in this research is research and development (R&D). The subjects and objects of the research were high schools and there were 32 students. Data collection techniques, material expert instruments, teachers, and student data were also obtained from the results of student pre-tests and post-tests. The data was analyzed by adding up all the assessment scores on the instruments adding up the test results and averaging the individual and classical scores. The results, and assessment of all module components by material experts, mathematics teachers, small group trials, and large group trials were 88.29%, 90.45%, 93.50%, and 92.10% in the very good category. The average score of students' post-test results is 87.50. Conclusion, this circle module can improve student learning outcomes significantly.

In the study reported on here we used a qualitative case study design to examine the self-control and self-monitoring behaviour of gifted learners in problem-solving processes. We selected 3 gifted secondary learners using the purposeful sampling method. For the study, each learner completed 10 individual problem-solving sessions. A think-aloud protocol as well as observations and interviews were used in each problem-solving session. The gifted learners displayed various and intertwined self-control and self-monitoring behaviour to read, understand, and solve the problems, and to find and verify the answer. They also displayed this behaviour much more frequently in problems that required using visual drawings and/or had long texts. The gifted learners left or adapted self-control behaviour when the behaviour did not work for solving mathematical problems. They made decisions regarding self-control behaviour by means of the self-monitoring process. The participants presented insistent, quick, flexible, and fluent actions for both self-control and self-monitoring processes. Based on our findings, we propose a portrait of gifted learners' self-regulative behaviour in the mathematical problem-solving process.

The success of a school centers on teachers' ability to create well-aligned educational tools. The Merdeka Belajar curriculum requires adapting assessments, including Higher-Order Thinking Skills (HOTS) questions for real-world problem-solving scenarios. This study explored contexts proposed by teachers in Papua for developing Mathematics HOTS questions. A phenomenological approach within a qualitative framework was employed involving 24 mathematics teachers from public and private schools in focus group discussions. Participants included twenty teachers from Papua, two from Central Indonesia and two from Western Indonesia. Additionally, five teachers from Papua participated in in-depth interviews. Data was analyzed using Creswell's model with Atlas.ti software. Teachers developed HOTS assessment instruments based on daily life, scientific and social contexts. However, no cultural contexts were incorporated into these instruments by the interviewed teachers. This study highlights the importance of teacher preparedness in aligning contextual learning with the Merdeka Belajar curriculum and reveals a significant gap in using cultural contexts for HOTS assessments among teachers in Papua. These insights contribute to the discourse on math education in Indonesia advocating for the integration of cultural elements into the freedom to learn initiative.

Background: South African teachers' mathematical knowledge for teaching and number sense are markedly low, evidenced in national and international research. There is a call for supporting teachers in developing their knowledge and confidence in teaching mathematics. Aim: The aim of this article is to share how pre-service teachers (PSTs) used the empty number line (ENL) to demonstrate the jump strategy (JS) for efficient mental computation, related to the national Mental Starters Assessment Project (MSAP). Setting: This study was conducted at a tertiary institution in the Eastern Cape province of South Africa, with 40 first-year intermediate phase PSTs, during their mathematics didactics course. Methods: The data comprised 40 micro-teaching videos, analysed thematically, following an analytical model for video-recorded data. Videos were categorised according to the way they faithfully followed or departed from the MSAP teacher resources. Results: Findings suggest that more than 70% of the PSTs faithfully followed the teacher resources to teach the JS on the ENL, with regards to use of at least three of the four key elements, namely: ENL, jumps, gesturing, and key phrases and terminology. Conclusion: We suggest PSTs receive explicit instruction on the above-mentioned key elements for teaching mental calculation strategies with the ENL and opportunities to practise teaching these to their peers. Contribution: Most PSTs successfully used the ENL to demonstrate the JS for efficient mental computation, enabled by the opportunity to engage in developing (and reflecting on their) micro-teaching videos.

Background: This article critically examines the nature of isiXhosa translations in mathematics learning materials, specifically focusing on the doubling and halving unit within the 'South African Grade 3 Mental Starters Assessment Project (MSAP): Teacher Guide'. Teaching in home languages is encouraged in the Foundation Phase, but unfamiliar standardised isiXhosa translations in support materials often contain barriers to understanding and/or distortion in meaning. Aim: The article addresses three questions: (1) To what extent is there fidelity and alignment of the translated isiXhosa materials to the original mathematical meaning? (2) To what extent do the selected terms align with the everyday isiXhosa that learners are accustomed to? (3) What are the implications for future translation of such materials? Setting: Analysis of the isiXhosa translation of a doubling and halving teaching unit and adapted translation for use in a Grade 3 classroom in the Eastern Cape. Methods: This qualitative research uses Toury's Descriptive Translation Studies theory. Results: The findings highlight several ambiguities and incoherent translations. The article advocates for a comprehensive approach to translation, emphasising the importance of maintaining conceptual fidelity and clarity. Conclusion: The authors suggest the need for transliteration techniques in translations to support teacher and learner access to mathematical sense-making. Contribution: This research provides insights for translators of materials and implications for teachers, proposing an approach to translation. In particular, it argues that the involvement of Foundation Phase teachers in the translation of such materials is crucial.

Background: Problem-solving as a vehicle to develop independent thinking skills is mostly underestimated and is often either overlooked or not given adequate attention within the existing South African mathematics curriculum. Consequently, numerous learners often display limited skills or lack skills to adequately crack Mathematics problems by applying methods put forward in class. This generally results in under-achievement. Aim: This study aims to explore and emphasise the problem-solving methods applied by Grade 4 learners involved in solving measurement word problems, and to reveal what transpires when the selected learners apply these methods to arrive at meaningful solutions. Setting: Data were collected from a class of 42 Grade 4 learners at a primary school in Cape Town South Africa. Learners were conveniently selected. Methods: A qualitative case study research design was adopted. Data gathering instruments of the study included observing learners solving, measurement word problem activities and focus group interviews. Results: The study revealed that singular methods were applied by Grade 4 learners, such as, adding, multiplying, creating a sketch or diagram, grouping, dividing, subtracting, logical reasoning, guessing and tabulating values. Conclusion: Grade 4 learners are prone to applying methods such as clustering or organising into groups, tabulating numerical values and logical reasoning were all applying mathematically sound methods. Such learners, however, needed a degree of supervision and instruction to indicate the way in which such methods were applied successfully as these methods were not necessarily dealt with in classroom context or in textbooks. Contribution: The findings emphasise the need for tackling learners' limited problem-solving competencies and accentuate the necessity for greater attention to develop and grow methods for optimal and successful solving of problems in context.

Background: Initial teacher education (ITE) research in South Africa shows gaps in preservice teachers' (PSTs) primary mathematics knowledge. Aim: We study the mental mathematics understandings and teaching experiences of three PSTs who achieved high gains for learners they taught mental mathematics to using the Mental Starters Assessment Project (MSAP) jump strategy materials. Setting: The three PSTs, from one urban university, taught the jump strategy to Grade 3 classes in three different Gauteng schools. Methods: Learner pre- and post-tests around the taught unit provided the basis for categorising the three 'high gain' PSTs. Extended interviews with each PST were then transcribed. Initial grounded analyses of these data were subsequently overlaid with categories drawn from the mathematical knowledge for teaching literature. Results: All three PSTs indicated relatively strong common content knowledge of jump strategies and connected specialised content knowledge. They also exhibited strong awareness of the MSAP content. They differed in how they saw the relationship between fluency, calculation and equivalence tasks. Conclusion: The study's findings indicate the need for more explicit attention to the connection between mental maths fluencies and strategic calculation in ITE. Contribution: The study points to ways in which mental mathematics can be understood and taught for strong learning gains.

Considering the content of history of mathematics textbooks, it's evident that their emphasis is primarily on the illustrative aspects of recurring numerical sequences, with a particular focus on the Fibonacci sequence. Unfortunately, this limited approach results in the neglect of other sequences akin to the Fibonacci numbers, thus rendering the subject challenging for teaching purposes. This study aims to address this gap by offering a concise exploration of the combinatorial aspects of the Padovan numbers, specifically through the concept of a board as initially examined by mathematicians. In line with the research methodology of didactic engineering and the teaching theory of the theory of didactic situations, two problem situations have been developed, centered on the Padovan combinatorial model, thereby contributing to the enrichment of mathematical education within initial teacher training programs. Within this framework, various strategies are introduced that rely on visualization and counting, with the objective of illustrating specific mathematical identities suitable for potential classroom applications.

This study explores how pre-service mathematics teachers build alternative model simulations of real-world scenarios. Inclusion in the formal structures for wealth generation and accumulation is a fervently debated issue in South Africa. Share owning in companies listed on the Johannesburg Stock Exchange (JSE) in South Africa is one of many wealth-building tools. Related discussions evolved on the spread of share ownership among black and white citizens. Two mathematically motivated positions were reported in a newspaper. In one of their mathematics courses, prospective mathematics teachers were presented with the article and asked to reflect on it with the prompt 'Which of these two methods for determining the "number of Black South Africans holding shares on the JSE" would your group support?' Audio- and video-recorded data were collected and subjected to thematic analysis. The themes that emerged from the analysis were economic empowerment, authority of research and trustworthiness of information. The discussions reflected on the complexities and rationalities involved in decision-making of mathematically driven opposing positions on issues of social importance. The mathematically derived results of such issues will eventually be resolved in the political field. The findings revealed that building of alternative mathematical models by pre-service mathematics teachers begins with an explicit problem setting, followed by the development of mathematical models that included real-world problems.