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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.

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.

The following study shows how reparameterizations and constraints of the general linear model can serve to parse quantitative and qualitative aspects of predictors. We demonstrate three different approaches. The study uses data from the High School Longitudinal Study of 2009 on mathematics course-taking and achievement as an example. Results show that all mathematics courses are not equally predictive of math achievement. Thus, taking into account qualitative aspects of mathematics courses is useful. The study ends with a justification of quantifying qualitative aspects of predictors relative to a criterion with extensions to other linear models.

The decisions that teachers make in transforming the curriculum into specific lesson plans determine the real enactment or otherwise of curricular ideals. These decisions are shaped by the resources available and by each teacher's goals and orientations. This exploratory study employs Schoenfeld's decision-making model to examine how resources, goals and orientations influence lesson planning for mathematics problem solving, for different profiles of primary teachers in Chile. To this purpose, a survey was conducted among 40 teachers of varying degrees of ability and experience: some were beginning teachers, others were experienced but had no further training in teaching problem solving and a third group was composed of experienced teachers with specific training in this question. Interviews with two teachers from each profile revealed important differences between the three groups. Beginning teachers relied more heavily on official resources such as the official curriculum and standard textbooks, aligning themselves with school requirements. Experienced teachers with problem solving training demonstrated a strong inclination towards teaching through a problem solving approach. While beginning teachers acknowledged the importance of promoting problem solving strategies, they did not usually adapt problems to the mathematical content or to the age/competence of their students. Interestingly, all three groups under-utilised sections of curricular resources that emphasise the present curricular focus on problem solving. Finally, the study found that experience alone is not enough to develop a problem solving approach and that focused professional development programmes are needed to equip teachers with the necessary skills. In addition, a diagnostic teaching approach should be incorporated into initial teacher training.

Spanish educational curriculum adopts a mathematical process-based approach, which encompasses problem solving, reasoning and proof, communication, connections and representation. A fundamental role in the integration of these processes in mathematics teaching is played by teachers' professional practice of designing tasks. According to this, our aim is to analyze the ways in which pre-service early childhood teachers understand the mathematical processes in the professional practice of designing early algebra tasks and to identify how they intend to promote these processes through the tasks. Content analysis techniques were used to examine the designed tasks. To illustrate the data analysis and results, six tasks are presented. As a result, pre-service early childhood teachers associate problem solving with challenges and questions. They understand problems as unfamiliar situations but ignore the relationships between students and tasks. Moreover, they do not encourage exploration of phases of problem solving and tend to use strategies more suitable for routine tasks. Communication is identified in all the tasks designed, encouraging interaction and discussion. However, only one task explicitly promotes mathematical language. For reasoning and proof, pre-service teachers begin to use questions to elicit explanations and justifications, but do not encourage verification strategies and various modes of reasoning. The process of connections is only present in one task, reflecting the fragmented nature of mathematics teaching. We conclude that the professional practice of designing mathematical tasks is a powerful in teacher education. However, training programs should place greater emphasis on the meaningful use of mathematical processes.

This article analyzes teachers' perceptions and experiences using an educative curriculum designed to promote high levels of mathematical discourse. After participating in 2 days of professional learning, grade 3 teachers implemented a predifferentiated and enriched mathematics unit in their classroom. The curriculum was designed to be educative, meaning that teaching it served as professional learning. During implementation, researchers conducted an observation of each treatment teacher and after implementation was complete teachers participated in a post interview about their experiences. Findings from this qualitative study indicate that after teaching the curriculum teachers understood the value of oral discourse and how to implement it in their classroom and could identify student benefits from participating in this type of curriculum. This study illuminates promising practices that may support teachers in implementing research-based best practices.

A lack of access to a sequence of introductory to top-level curricula in rural schools has widened the achievement disparity between rural and urban students and influenced the number of college degree holders in rural areas. Recently, surging diversity and differentiation in income levels across nonurbanized areas can serve as determinants of the development of academically rigorous course pipelines in rural schools. This study examines differentiation in spatial access to the curriculum ladder for rigorous mathematics in three southern U.S. states during the 2017-18 school year: Alabama, Arkansas, and Mississippi. Policy variations in these states yield different effects on the sequence of rigorous mathematics courses in rural high schools. Given that the mathematics course pipeline reinforces college access, access to academically challenging courses likely outweighs the rural disadvantages of college readiness in non-urban students and the persistence of inequality in public education.

The increased relevancy and importance of quantitative literacy (QL) have called for educational reform in undergraduate mathematics course offerings. However, lack of clear guidelines has led to wide variability in the content and outcomes of math courses meant to address QL. Therefore, having an expert consensus regarding content and outcomes for an undergraduate mathematics course focusing on QL would advance the quantitative literacy initiative in higher education. The authors propose the Delphi Method to aid in developing a framework based on expert opinions. The authors explain the Method and suggest the result of this process should yield a research-based framework that faculty and institutions can use as a resource for QL math courses.

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.

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: 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.

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.

The evolution of mathematics coincided with advancements in its teaching. The 19th and 20th centuries marked a pedagogical revolution in mathematics education. This paper argues that Bruner's (1966) model, Gagné's (1985) taxonomy, innovative teaching methods emphasizing research and problem-solving, and the inclusion of data analysis topics have shaped modern mathematics education. Additionally, the paper explores transformative trends, emphasizing mathematics literacy and the integration of virtual reality (VR) and artificial intelligence (AI) in education. This evolution emphasizes practical, contextually relevant approaches. VR enhances engagement and comprehension of abstract concepts, while AI offers personalized learning experiences, fostering deeper understanding and skill development.

Background: Many studies have been done in the past to compare country-specific curricula to international standards. However, there is an apparent lack of literature that focusses on evaluating the alignment of country-specific early grade mathematics curriculum to the Global Proficiency Framework (GPF) for mathematics. Aim: This study aims to investigate how the domains of the national early grade mathematics curriculum and the Bachelor of Education curriculum for pre-service early grade teachers in the Colleges of Education (CoE) in Ghana align with the GPF for mathematics. Setting: The study was conducted in Ghana using the national early grade and Colleges of Education (CoE) curricula. Method: Document analysis was employed to compare the list of domains in the GPF to the lists of domains in the Ghanaian national early grade mathematics curriculum and the Bachelor of Education curriculum. Results: The results showed an alignment in the list of domains in GPF and the two curricula. The Bachelor of Education curriculum included theories of early-grade numeracy development which was absent in the GPF. The indicators in the two curricula were found to have exceeded the global minimum proficiency levels in the GPF. Conclusion: The results showed an alignment between the GPF and the two curricula signifies that the mathematics curriculum used for teaching early grade learners in Ghana meets international standards and can help learners compete on a global scale in mathematics learning. Contribution: The study provided valuable insights for policy-makers to consider while making decisions about curriculum standards and teacher training programmes. This is a significant step towards enhancing the quality of early grade mathematics education in Ghana.

Recent reform efforts to center issues of equity and social justice in mathematics classrooms have been under fire from the loudest sectors of right-wing media. The hysteria around incorporating social justice issues in mathematics classrooms is captured in the artificial binary: STEM or CRT. In our paper, we examine resistance to reform efforts in mathematics education in artifacts geared towards audiences beyond mathematics education researchers through the lens of whiteness. We analyzed artifacts from the Math Wars of the late 1990's and the current backlash towards mathematics education reform (Math Culture Wars) in California and Florida. We identified fear as a significant mechanism to upholding whiteness in the backlash to mathematics education reforms, particularly centering white fear. By describing how fear is constructed in the artifacts, scholars may find more targeted responses to the backlash by addressing the ideas perpetuated in these artifacts. Still, the field of mathematics education has done little to become more inclusive and just because our agenda is too closely aligned to the status quo, with responses to the backlash being largely absent or tepid. We close with recommendations for action and allyship within the broader field of education to thwart the hysteria against CRT.

This paper offers insights into how mathematics education researchers can learn from preservice teachers (PSTs) by building upon parallels between adapting curriculum-making and designing research. The pandemic created learning opportunities for PSTs to anticipate mathematics curriculum anew and obstacles for researchers to study their pedagogical processes. A multiple case study reveals how PSTs in Year 1 and Year 2 of a Bachelor of Education program reimagined their intended mathematics curriculum to meet the demands of the evolving pandemic context. Viewed through the lens of complexity thinking and conceptions of "currere" and curriculum-making, PSTs' lesson redesigns include new contexts for teaching and learning (e.g., home environment, parental/guardian involvement, materials) that illuminate how curriculum researchers might become more tentative, responsive, and adaptable to unforeseen circumstances.

There is a plethora of textbooks to choose from. While most textbooks contain the same content, teachers need to understand the textbook they have chosen to support their students' learning, as textbooks can significantly impact student learning and teacher instruction. When searching for a way to understand the various textbooks, my research question became, How do calculus textbooks tell the story of definite integrals? My research is in response to the never-ending search for how teachers can select and use their resources. Also, this study contributes to understanding the relationships between stories and knowledge construction using Dietiker's (2015) narrative framework to analyze the written calculus curriculum. I wrote the specific stories of introducing the definite integral as told by five calculus textbooks. Analyzing how the stories developed disclosed the similarities and differences among the texts in teaching definite integrals. The analysis also revealed a variety of avenues to introduce and teach definite integrals, including a focus on the area under the curve, Riemann sums, or the Fundamental Theorem of Calculus, and some implications to the context of physics related to these avenues. These insights provide teachers with a deeper understanding of textbook lessons and the variances that can potentially alter student learning.

This study aims to map the landscape of the importance of previous research on computational thinking (CT) in mathematics learning over the last decade. This research is a literature review research, there are 113 publications collected from the Scopus database which are then analyzed using the bibliometric analysis method assisted by the Vosviewer application. The data taken from the Scopus database was refined so that it became 113 publications. The results of the study show that publications are spread across various continents, including America, Asia, Africa, and Europe. The United States and the United Kingdom are the most influential countries and have high cooperation with other countries in this field. The main conclusion from this study is that computational thinking has an important role in learning mathematics and STEM. The integration of computational thinking in the mathematics curriculum can improve students' understanding of mathematics and help them face the challenges of the digital age. In addition, the development of effective training methods for mathematics teachers as well as the assessment of good computational thinking learning tools and platforms can help improve the effectiveness of computational thinking teaching in mathematics contexts. These innovations will help better understand how computational thinking can be effectively integrated in mathematics learning and prepare students for a future filled with digital technologies.

This study aimed to evaluate the value of justice, one of the 10 core values in the mathematics course curriculum, in the context of an exemplary activity in classroom practice and student interviews, where it was integrated into mathematics learning goals. The case study model was employed. The sample of the study included eight 7th-grade students in the 2018-2019 academic year. An activity prepared about the value of justice and a semi-structured student interview form were used as data collection tools. The data obtained following the implementation of the activity were analyzed using content analysis. Students stated that it was necessary to carry out value-based activities in mathematics classes to understand the importance of the value of justice and to increase social awareness about it. According to the results of the study, it is recommended to plan, implement, and discuss in-class activities in which students can explain their value perceptions according to mathematical problems and actively participate in the process so that their awareness of the value of justice can be increased.

This study investigated the noticing of teachers who teach mathematics at different grade levels in the context of lesson study. The study specifically focused on teachers' noticing during the planning phase of the lesson. For this, the lesson planning phase of a group of four teachers consisting of kindergarten and primary school 1st grade teachers (vertical teacher team) was investigated. Teachers' planning process for the 1st grade level mathematics lesson was the focus in the context of lesson study. We examined categories and subcategories that emerged in the planning phase of the lesson study and noticing levels dealt with those categories. We examined which categories and subcategories emerged in planning and at which noticing levels they dealt with those categories. The results of the study provide comprehensive data on categories and noticing levels of teachers teaching mathematics at different grade levels in the collaborative planning process of a lesson study focusing on improving problem-solving. The results of the study showed that the teachers' noticing was clustered under three categories: curriculum, teaching methods, and conceptual understanding. In terms of noticing levels, the study's results revealed that noticing is performed at the attending to level in all categories. Although less frequently than the attending to level, teachers noticed making sense of level in all the other categories except the curriculum category. Besides, noticing that the deciding to respond level did not occur at any level might be due to the cultural challenges of adaptation of lesson study and the amount of support, we researchers provided teachers as facilitators.

Mathematics is pivotal in the contemporary technology-driven world. However, poor mathematical performance continues to be a concern in many countries. Guided by Mathematics in a Cultural Context (MCC) framework, this article investigates the similarities, differences, and potential reasons behind early numeracy achievement in South Africa and China. Applying a qualitative research approach, selected teachers, parents, and government officials in the two countries were interviewed for their views on the cultural context and pedagogical practices that potentially impact mathematics teaching and learning. The findings confirmed the multifaceted and interconnected nature of mathematics teaching and learning. However, the findings raise questions about the efficacy of certain practices on mathematics learning and achievement, including the teaching approach, the value of different kinds of motivations, and methods to inspire motivation. This finding suggests the importance of practicing key mathematics concepts in building a solid foundation and confidence in mathematics.

This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals using real-world data sets, particularly those related to population growth, which aim to enhance their understanding, sharpen their problem-solving abilities, and cultivate a positive perspective on the real-world relevance of mathematics. Preliminary findings indicate varied levels of QR skill development among students. These results underscore the potential benefits of infusing QR into mathematics courses and provide insights for educators looking to adopt similar strategies in their teaching.

The incorporation of Computer Science teaching in educational systems has increased in recent years. Given international interest, Chile has promoted projects to promote the development of students' digital skills. Focusing on this new educational context, this research reports the results regarding the identification of computational concepts and practices that can be articulated with the contents and skills of the curriculum. of Chilean mathematics. for first grade of primary school based on the use of the Bee-Bot robot. For this, the study followed a qualitative approach, developing a case study of the Chilean study program with the content analysis technique and using, as analysis categories, computational concepts and practices from the field of educational computing. In total, 30 learning objectives of the study program were analyzed. The results indicate that, although there is little articulation between computational concepts and first grade content proposed in the curriculum, there is greater articulation between computational practices and mathematical skills suggested in the Chilean curriculum. It is concluded that Computational Thinking can be developed from the earliest school levels using the Bee-Bot robot (or similar), and this is demonstrated by the structure of the Chilean primary mathematics curricular program.

Attention to the disconnection between culture and mathematics has been addressed then and now (Wilder (in: Graves et al., Proceedings of the international congress of mathematicians, American Mathematical Society, 1950; Liu in Taiwan Journal of Mathematics Education, 8:79-88, 2021b). Recently, studies, workshops, and contests about an approach to relating culture and mathematics, such as incorporating mathematics history or mathematics writings in class, have emerged. However, although the effectiveness of such an approach was proved, employing it as instruction was still significantly ignored, not to mention the approach to creating mathematics literary writings--the goal that the Mathematics-Literature Contest aimed to achieve. Additionally, no empirical studies have systematically assessed the contest, especially from the cultural perspective. Through teachers' and students' perceptions, this qualitative case study aims to examine the impact of mathematics literary writings on the development of mathematics teaching/learning and the mathematics culture represented in the contest. Ten teachers and 20 students were interviewed. Data were analyzed by following Yin's five phases (2016). The study visualizes an evolutionary model of the contest, signifying the development of mathematics culture simultaneously. Results demonstrated that the contest caused teachers and students, who constituted the internal force, to consolidate the mathematics culture, which was enriched by the external force--to reinterpret the connection between mathematics as well as culture and the reform of general education. The developed mathematics culture included elements other than mathematics, such as the Chinese writings and their interactions with mathematics and life experiences. The findings hold implications for mathematics and general education: An interdisciplinary curriculum design can help cultivate teachers' and students' intellectual acumen; higher education communities worldwide must follow the trend.

There are increasingly frequent calls for school mathematics curricula to be informed by robust research evidence. One approach to achieving this is designing evidence-informed learning and teaching resources for the classroom. In this paper, we reflect on our experiences of designing a free and fully resourced complete set of secondary mathematics curriculum materials. We explore in detail the challenges we have encountered in our attempts to apply principles from the cognitive theory of multimedia learning. We focus on tensions we have experienced when simultaneously applying multiple principles and balancing these with other educational considerations. Specifically, we consider trade-offs between redundancy versus clarity, seductive details versus richness, personalisation and emotional design versus abstraction, spatial contiguity and signalling versus parsimony, and pre-training and worked examples versus exploration. We examine the choices and dilemmas we faced, and illustrate our emerging attempts to resolve these tensions through presenting multiple examples from our design work. We conclude with recommendations about how tensions among these design principles might be navigated in curriculum design and we suggest possible avenues for further research in this area.

This study aims to examine the lesson plan development processes and related experiences of prospective teachers, and determine the potential effects their lesson plan development efforts on their perceived TPACK. The research was conducted as part of a 14-week Mathematics Teaching course. During the course, prospective teachers underwent a six-week training program focused on designing technology-supported mathematics lessons, followed by an eight-week period dedicated to developing lesson plans for different topics and objectives within the mathematics curriculum. Data for this case study was collected from sample of 44 prospective teachers through participant diaries, observation notes, interviews, and pre- and post-lesson administration of the Turkish version of Schmidt et al.'s (2009) TPACK scale. Qualitative data was thematically analyzed to complement quantitative analysis using a t-test. The findings indicate that engaging in lesson plan preparation activities during mathematics teaching courses positively influenced prospective teachers' perceived TPACK levels. Specifically, an increase in TPACK levels was observed after attending the course. Furthermore, several factors have been identified that enable prospective teachers' perception of TPACK to be positively affected. These findings suggest the need for technology-supported course design within the mathematics curriculum of teacher training programs. Providing elective courses that offer prospective teachers additional opportunities to develop lesson plans is recommended.

The development of professional digital competencies is an important condition for a meaningful integration of digital technologies in mathematics education. A widely used and empirically studied approach for the professional development of in-service teachers are teacher design teams, in which lessons are collaboratively planned, implemented and reflected. However, this approach has not yet been considered for the collaboration of pre-service and in-service teachers. Therefore, this article examines in a holistic case study mixed teacher design teams composed of pre-service and in-service teachers. A total of 23 interviews were conducted with pre-service and in-service teachers and analyzed by inductive development of categories using the method of qualitative content analysis. The case study shows among other things, that the different prerequisites of the participants can lead to a relatively clear division of roles within the collaboration, which turns out to be suitable for the professionalization of both pre-service and in-service mathematics teachers.

Information technology enhances the nature of mathematics as an empirical discipline, leading to an approach called "experimental mathematics" (EM). It fosters the use of technology-based interactive resources (IRs) in mathematics education, giving mathematics an experimental dimension and reflecting a tension between the empirical-inductive nature of IRs and formal mathematics (FM). Our qualitative research focused on professional development (PD) for IR-based teaching of EM intertwined with FM based on a threefold theoretical framework that combines the mathematical knowledge required by EM, the pedagogical functionality of IRs, and instrumental orchestration. The research analyzed 14 high school teachers' documents generated in the course of a PD program, revealing the evolution of their orientation. We argue that teachers' evolving orientation toward IR-based EM inclusion in school mathematics is the result of meticulous dynamic PD design implementing three key aspects framed by the threefold theoretical framework: teachers playing various roles during the PD, teacher-researcher collaboration, and theoretical support. The beginning of the evolution of the teachers' orientation toward IR-based EM inclusion in school mathematics was made possible by a design grounded in the above theoretical framework and observed through its lens.

This study explored the use of Indigenous storytelling in the planning and teaching of mathematical content. In collaboration with Indigenous and non-Indigenous educators, a culturally inclusive mathematical lesson was developed, implemented, and reviewed in an elementary school in Northern Ontario. This study used a culturally authentic approach to address the current educational issue of diversity within the Ontario curriculum and education system. The results of this study suggested that utilizing Indigenous storytelling for teaching mathematical curricular expectations could benefit both Indigenous and non-Indigenous students. Storytelling can allow students to relate abstract mathematical concepts to their own lived experiences, to be exposed to diverse cultures, and to foster a positive and open learning environment that is conducive to academic and non-academic learning.

In this essay, I examine coloniality as a racializing force within international education curricula. I focus on the British-developed Cambridge Assessment International Education (CAIE) curriculum, previously known as the Cambridge International Education (CIE) curriculum. Using the CAIE as a specific case, I discuss how international curricula serve as vehicles of coloniality and simultaneously reproduce racialized narratives about Sub-Saharan Africans. The persistence of CAIE is implicated in the ongoing project of coloniality, sustaining and reproducing racial hierarchies and the marginalization of Sub-Saharan African communities. I contend that CAIE privileges a singular way of thinking and being in mathematics and uses assessment practices to perpetuate coloniality. By recognizing the ways in which coloniality and racialization are interconnected, we can better understand the complex systems of power and privilege that shape international mathematics curricula.

The mathematical construct of dimension is one of the fundamental ideas for developing a sound understanding of two-dimensional (2D) and three-dimensional (3D) shapes. Yet, research in mathematics education has rarely explored children's understanding of dimension in primary education. This paper explores how year 5/6 (9 to 11 years old) children construct and negotiate their meanings about dimension while engaging in classroom interactions about 2D and 3D shapes during geometry lessons in a New Zealand (NZ) English-medium multilingual primary classroom. Transcribed data of two key moments selected from six audiovisually recorded geometry lessons are presented. The findings suggest that children may use different discursive constructions--"another world", "different ways to go", and "flat vs fat"--to display their meanings about dimension. The findings also suggest that children and teacher participants may use prosodic features of their languages to interactionally construct the meanings of these discursive constructions. The paper discusses these findings in light of current research literature and offers a few implications for curriculum development and future research.

In this convergent mixed methods design study, single-subject and qualitative data were collected concurrently to provide an in-depth picture of the impact of a modified schema-based instructional intervention. The intervention was delivered using instructional trials embedded across general education math lessons and a modified concrete-semi-concrete-abstract instructional sequence. This study investigated the impact of the intervention on the word-problem-solving, strategy use, and concept acquisition of three students with extensive support needs. The paraprofessional-delivered intervention was implemented in elementary general education mathematics classrooms using embedded instruction and focused on teaching students to solve addition and subtraction word-problems. Single-subject data indicated that all three students learned to solve word-problems given concrete materials but needed more time to master the use of semi concrete supports. Qualitative data indicated that students used taught and untaught strategies to solve word-problems, and mastered addition word-problems before subtraction when they were taught simultaneously. Data were integrated in narrative format to explore how strategy use and concept acquisition related to student word-problem-solving performance. Limitations and implications for research are discussed.

Mathematics teaching usually occurs in a "public space"--e.g., a classroom is a public space with rules defining student and teacher roles that cultivate hierarchic relationships. Working in prison with young inmates (18-23 years old) from marginalized populations, we promoted alternative "common spaces" (physical and symbolic) challenging established hierarchies through equal contribution. Such mathematics curriculum employs an antideficit model (Louie et al., 2021) as prisoners co-research their lives with mathematics. Common spaces empower through recognition while enabling identity transformation. Qualitative data from the CoSpIRom [Common Spaces for Integration of Roma Project (http://cospirom.sed.uth.gr).] project explores: (a) whether common spaces, recognition and equal participation can support mathematics literacy while empowering and emancipating young prisoners; and (b) if and how this framework might prepare prospective teachers within contemporary diversity. Bringing together young prisoners and prospective teachers affects both populations. Mathematics curriculum developed through collaboration meets a consistent request from prisoners that educational programs bridge with the outside world as re-entry preparation. Contrasting life stories from prospective teachers operate as alternative models motivating prisoners to rethink their own life stories and self-concepts. Prospective teachers demonstrated significant intercultural communication skill development, empathy and solidarity for marginalized people, reporting important professional identity growth.

The interrogation of often unintended practices of marginalisation has gained focus in research on mathematics teaching and mathematics teacher education throughout the last decades. In this introductory survey paper, work against marginalisation in these contexts of mathematics education is viewed in terms of work towards equity, diversity and inclusion. Based on this interpretation, we present a framework on awareness and practice of equity, diversity and inclusion in mathematics teaching and mathematics teacher education research. We then use this framework and a survey method of mapping review to identify and comment on a selection of studies. As a result, we illustrate three research moves towards equity, diversity and inclusion, in the form of interconnected themes: (1) Widening the understanding of the mathematics and the mathematics education curricula (2) Improving the practice and discussion of mathematics teaching (3) Unpacking ideologies in mathematics teaching and mathematics teacher education. We finally examine the themes and the special issue papers together to foreground commonalities regarding awareness of discriminatory discourses and practices of creating and distributing opportunities for all groups, including those historically and currently marginalised. Despite the important increase of equity-driven principles of awareness, we conclude that mathematics education research on teaching and on teacher education needs more examples of practices whose development has been proved to challenge marginalisation.

Marginalization, widely associated with poverty, inequality, and underdevelopment restricts access to resources, limits freedom of choice, inhibits the development of individual capabilities, and makes it challenging to escape from marginalized circumstances. We examine marginality in mathematics teaching and its complexities in the tightly centralized educational system in the Philippines by identifying the different situations that contribute to how mathematics teachers can be excluded from certain educational practices that would normally fall within their mandate as professional teachers. Adopting Gatzweiler and Baumüller's (Marginality: Addressing the nexus of poverty, exclusion and ecology, Springer:27-40, 2014) framework, we interviewed 15 mathematics teachers from different geographical locations around the country. We identified and organized the drivers of marginality into biophysical and societal causal clusters that enable or constrain teachers to act as professionals. Biophysical causal clusters include mathematics curriculum and mathematics assessments among others while societal causal clusters include various directives, interpretations, and realities surrounding the biophysical causal clusters. Discussions about the complexities brought about by these clusters and how teachers act or respond as they navigate around them are highlighted. Recommendations for concrete de-marginalization actions are offered.

This survey describes the structure of the field of research on curriculum resources in mathematics education in the period from 2018 till 2023. Based on the procedures of a systematic review relevant literature was identified using Web of Science as a database. The included literature was analyzed and categorized according to the type of curriculum resource and the area of study. Seven areas of studies were identified: studies on the role of curriculum resources, content analysis, user studies, studies on the effects of curriculum resources, studies on curriculum resource design, curriculum resources as data, and reviews. The areas were further subdivided into different subcategories based on the research questions of the included papers. The findings show that research on mathematics textbooks is still predominant in the field. The most popular areas of research are content analysis, user studies, studies on design, and studies on effects. Emerging areas are research on students' use of curriculum resources and the employment of user data from digital curriculum resources as data basis in mathematics education research.

Estimation is an essential competence with a developmental role in the learning of various mathematical topics. Yet, as previous studies highlight, this competence is either excluded or ambivalently included in intended curricula around the world. The current study investigates the estimation-related opportunities in the primary curricula of three Eastern Mediterranean countries (Cyprus, Greece, and Turkey). Our analyses are framed by four forms of estimation (computational, measurement, quantity, number line). As with previous studies in other contexts, computational estimation and measurement estimation are extensively addressed in the curricula of Cyprus and Turkey, yet without any meaningful justification for their inclusion. All three curricula fail to recognise the importance of number line estimation and quantity estimation, the two forms with the most significant developmental implications for the later learning of other mathematical concepts and areas of mathematics. Among the three curricula under scrutiny, the Greek is the one with the fewest and most superficial references to estimation. In closing, we discuss the implications of this study and suggestions for future research.

In Sri Lankan advanced level mathematics curriculum, teachers are required only to provide the intuitive idea of the concept of limit. The purpose of this study is to explore the strategies used by mathematics teachers to achieve this. Twelve in-service secondary mathematics teachers working in government and private schools participated in the study. Data was collected through lesson observations and field notes. Video recorded lessons were transcribed and qualitatively analyzed. Teaching-With-Analogy model was used as a guiding framework to evaluate how teachers integrate real-life examples in classrooms. The analysis revealed few appealing approaches as well as various flaws and misconceptions. In fact, seven teachers took deliberate efforts to link the concept to real-life and among them, four teachers gave an intuition on how x approaches a specific value, through real-life scenarios. However, many were not successful in mapping features of the real-life example to the features of the concept. Few teachers superficially and negligently applied irrelevant metaphors, analogies and colloquial terms. There were gaps in teacher knowledge when incorporating real-life connections to the limit concept. We emphasize the importance of teachers being mindful when using real-life examples in fostering intuition since inappropriate choices of examples could contribute to misconceptions.

Very few Lebanese students have been able to perform at the highest level in mathematics and science in TIMSS, leading to the belief that current curricula and/or pedagogies are not supporting our highly able students to realize their potentials. In this research, we investigate how the national Policy documents and the mathematics and science centralized curricula, and textbooks address the needs of highly able students. Teachers' perceptions and role in providing for the educational needs of highly able is also examined. Through qualitative methods, the following data sources were used to address the research aim: policy document analysis, curriculum analysis, and teacher interviews. Findings indicated no specific policy for highly able students in Lebanon and little evidence of curricular provisions and attention to the needs of highly able learners in the mathematics and science national curricula and textbooks. The resultant data also provided important insights into the limited knowledge of teachers in the area of supporting highly able learners. The findings of the current study will inform the efforts of the policy makers and the Ministry of Education faced with the challenge of effectively educating their most able students.

Mathematics includes elements of thinking and communication skills that are essential in a changing world. In this context, thinking and communication skills have a privileged place in the mathematics curriculum (Umay, 2004). This study aims to investigate the learning outcomes of the 2018 middle school mathematics curriculum in terms of mathematical communication skills. The current study employed the document analysis research method. The document analyzed in the study consists of the learning outcomes set in the middle school 5th-8th grade mathematics curriculum, which was updated in the 2018 school year by the Ministry of National Education and is still being implemented. In the study, the researchers developed a "Mathematical Communication Skills Rubric" to examine the learning outcomes set in the middle school 5th-8th grade mathematics curriculum regarding mathematical communication skills. The analysis of the data was carried out with the deductive content analysis approach. In the study, when the learning outcomes in the middle school mathematics curriculum were examined in terms of mathematical communication skills, it was determined that 70% of the total 275 learning outcomes were insufficient. The results show that the learning outcomes of the middle school mathematics curriculum should be rearranged to serve the improvement of mathematical communication skills and that mathematical communication should be structured in more detail regarding the reading, listening, speaking and writing dimensions. [This article includes an extended summary in Turkish.]

This study aims to evaluate mathematics curriculum used in social sciences high schools' preparatory classes based on Stufflebeam (CIPP) evaluation model in terms of context, input, process and product dimensions. With this aim, this study seeks to answer "How is preparatory class mathematics curriculum (PCMC) evaluated in terms of its context, input, process and products?" from the viewpoint of teachers and students. Case study method which is one of qualitative research methods is used in this study. The study is carried out in the first term of 2021-2022 academic year in a social sciences high school which uses National Ministry of Education's curriculum. Participants of the study are 65 students and four mathematics teachers. Mathematics achievement test and interview forms are used as data gathering tools. The results of the study revealed that both teachers and students have critical views of context, input, process and product dimensions of the curriculum; however, the criticisms intensify in process and product dimensions of the curriculum. Another finding of the study is that specific conditions of schools and characteristics of students and teachers have a major impact on commitment to curriculum, teaching-learning processes and learning outcomes. Some recommendations are made for implementers and researchers based on the findings of the study. [This article includes an extended summary in Turkish.]

This study examined the efficacy of an afternoon and weekend academic program called the "Community School Initiative" (CSI) during the COVID-19 pandemic. CSI was offered to racialized students and families from the Jane and Finch community in Toronto which is one of the most under-resourced neighbourhoods in Canada. It involved a partnership between private social enterprise "Spirit of Math" and non-profit organization "Youth Association for Academics, Athletics, and Character Education" (YAAACE). Seven teachers participated in a focus group and 33 students and parents completed a survey to express their experiences attending the CSI. Findings were identified using thematic analysis from a Critical Race Theory paradigm. Key characteristics of effective structural community-programming were identified. The results highlight the importance of access to opportunities in a culturally reflective manner to ensure student success through continuity of care particularly on evenings and weekends involving a team of caring educators.

The aim of the study is to determine the extent to which the root values were included in the middle school mathematics textbooks that were recommended in the 2018 middle school mathematics curriculum by Ministry of National Education (MoNE). In this study, mathematics textbooks were assumed to be an important material in terms of development of students' intention to use root values. The data were collected from ten mathematics textbooks, including two fifth grade, three sixth grade, two seventh grade, and three eighth grades, recommended by MoNE for use in middle schools in the 2019-2020 academic year. A basic qualitative research design was used in the study. To analyze the data a content analysis process was implemented. As a result, it was found that while the values of friendship, self-control, responsibility, patriotism, and benevolence were used in the textbooks in detail and with their first meanings, there was not enough content about the values of justice, honesty, respect, and love and these values were being used differently from their first meanings. It is recommended that the content involving root values should be distributed more homogeneously to the grade levels and values should be used with their first meaning in mathematics textbooks. In addition, there should be more specific information in mathematics textbooks about how to integrate root values into a mathematics classroom.

The effect of symbolic form model on students' interest in logic content of the mathematics curriculum was investigated in this study. The research was guided by three research questions and three hypotheses. The study used a quasi-experimental design. The population of this research was 2,342 SS2 learners in Enugu State, Nigeria. A sample of 172 students was used. Data were collected and analyzed using the SILCMCQ and SPSS software respectively. The symbolic form model in teaching significantly boosted students' interest in logic content of the mathematics curriculum, according to the findings. The study provided recommendations, one of which is that mathematics teachers should use the symbolic form model of instruction to increase students' interest when logic content is taught.

Robust understanding of geometry is important for students' future studies in mathematical sciences, many careers, and for understanding the world around them. Therefore, the aim of this study was to understand the geometric thinking levels of 9th graders in Ghana before they enter the Senior High School. This study used the van Hiele theory (Van Hiele-Geldof, 1957) to understand geometric thinking levels of 400 9th graders in western Ghana. These students were given the van Hiele Geometry Test (VHGT) developed by Usiskin (1982). The results showed that 56.2% of 9th graders demonstrated thinking at the pre-visualization level, 30.75%of the graders attained level 1(visualization), 12.5% reached level 2 and only 0.5% demonstrated level 3 thinking. These findings indicate that students are struggling to meet the Ministry of Education's curriculum standards. Additional analysis points to reasoning about properties of geometric figures using definitions and informal deductive reasoning, instead of relying on visual characteristics of diagrams as a specific obstacle for students. Recommendations are made for improving the teaching and learning geometry based on our findings.