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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Mathematics Education in South Africa continues to face complex, multifaceted challenges, but as data from this study show, there is reason for hope. The Western Cape Education Department recently implemented the Green Shoots Maths Curriculum Online (MCO) program in 500 of its primary schools. An ABC classification of affective, behavioural, and cognitive learning gain was used to analyse the learning gain for learners, parents, and teachers who use the Green Shoots Maths Curriculum Online (MCO) program. As part of a larger longitudinal Education Design Research project, data in this study were produced through self-reported surveys, MCO usage data, Grade 6 learners' assessment results, and project documentation. Benefits from technology interventions such as the MCO project, tend to be unevenly distributed between resource-rich and resource-poor schools. Findings from this study however indicate that the learning gains for learners, parents and teachers were distributed across all types of schools since learners, parents, and teachers in all these contexts are accessing and using the program. The results from the study may benefit policymakers and education departments who wish to roll out similar programmes, school, and district leaders who manage short and long-term implementations, and teachers and learners wanting to use comparable programs such as this.

Fractions remain one of the most difficult topics to convey to students. Thus, employing professional development programs known for improving the teaching and learning process, such as lesson study, is deemed necessary. This study aims to assess and analyze the strengths and weaknesses of the implemented research lesson using the Mathematical Quality of Instruction (MQI) rubric. This standardized observation tool evaluates the quality of a mathematical instruction. Results indicated that the strengths of the implemented research lesson were demonstrated in the fluent utilization of mathematical language under the domain Richness of Mathematics and the minimal instances of teacher's error and imprecision. On the other hand, weaknesses were observed in student participation under the domains of 'Common Core Aligned Student Practice' and 'Working with Students' in Mathematics. Implications for educators and the various educational processes include among others the importance of lesson preparation, teaching students to articulate ideas explicitly and the continuous use lesson study as a professional learning community.

The research reported in this paper analyses teaching dilemmas experienced by four in-service teachers in the context of a reform-oriented teaching approach for primary mathematics called Developmental Education in Mathematics (DEM). The findings exemplify three teaching dilemmas: Whether to tell students how to solve a challenging task; what to do when students are bored with an important task; and trying to keep the pace of the lesson while supporting all students in the classroom. Importantly, the origins of these dilemmas were found to lie in internal tensions between the components of the DEM system, which the teachers had implemented. Finally, the implications for development of curricular material, implementation of reform-oriented teaching approaches, and the professional development of teachers are discussed.

Equal representation as a social issue is about the participation of one social group, in a particular context, in proportion to the numbers in the group within the total population. The proportion of women in parliament, and of the participation rate of students of lower socioeconomic status in higher education, are examples. The aims of this paper are to set such issues in a school-mathematics context and to increase awareness of the potential of mathematics to connect with social issues. Mathematically, the setting involves the ways in which a fraction can be represented by other fractions having a lower numerator and denominator.

Foundation and Year 1/2 teachers at Saint Martin de Porres Primary School, a Catholic School in Laverton, Melbourne have been collaborating with a team of researchers from Monash University on a four-year project led by Professor Peter Sullivan and colleagues. The teachers have been trialling and implementing a series of lesson sequences as part of an Australian Research Council grant. The project focused on Exploring Mathematical Sequences of Connected, Cumulative and Challenging Tasks (EMC[superscript 3]) (Sullivan et al., 2023). Throughout the project, Dr. Sharyn Livy made regular school visits to work with the teachers and assisted them when implementing the approaches and lesson structure for teaching with challenging tasks (Sullivan et al., 2020a; Sullivan et al., 2020b). To support teaching and student learning the Foundation and Year 1/2 teachers met fortnightly to plan for mathematics. With the guidance of Sharyn and the mathematics leader Elise, the teachers extended their approaches for planning lessons when teaching with challenging tasks. This article shares planning and assessment practices that have evolved over several years to effectively support the implementation of sequences of challenging tasks at this school.

This article describes the experiences of two Cree elementary school teachers who taught school mathematics through place-based education (PBE) in a Treaty 6 First Nations community in the Canadian prairie province of Saskatchewan. Using narrative inquiry, we discuss the teachers' understandings of Indigenizing school mathematics in relation to their Cree identities and PBE, their difficulties and successes in addressing curricular outcomes, and their recommendations for other teachers wishing to take up a similar practice. As described in this article, this research expands upon our existing work in which we sought to provide more nuance and substance around the meaning and practice of Cree Indigenizing school mathematics in the specific context of Treaty 6 Saskatchewan.

STEM (Science, Mathematics, Engineering and Technology) education has widely been considered to have the potential to prepare students with 21st-century skills. Though the Government of Bangladesh (GoB) is concerned with developing human resources for the 21st-century, STEM education has not yet achieved a strong position in the national curriculum system. This study aims to provide a guideline to the GoB to take necessary steps to integrate STEM initiatives aligned with the current science and mathematics curriculum. Adopting a literature survey on the integrated STEM approach, document analysis (primary math and science curriculum, textbook, and teachers' guide of grade 3, 4, and 5) and semi-structured interviews of the primary mathematics teachers, head teachers, STEM experts and curriculum developers of Bangladesh, a framework of integrated STEM approach for primary level has been developed. Besides, the study identified some chapters from science and mathematics textbooks where there are some scopes to integrate the STEM approach and also developed some STEM activities for grade 3, 4, and 5 as future guidelines to the practitioners. This study contributes to the field of STEM-focused primary education in the context of Bangladesh by offering practical guidelines for academic institutions, curriculum developers, teachers' trainers, and policy makers of the country.

Students at the elementary level should have opportunities to critique the world through mathematics and to see themselves as capable doers of mathematics. The lesson described in this article prompted students to consider how to use mathematics to organize an emergency evacuation. In this article, the authors show how small changes to a task provided in a mandated mathematics curriculum can open students to do rich mathematics while considering social and environmental implications.

By utilizing targeted professional learning and predifferentiated, tiered, and enriched mathematics curriculum, teachers gained an understanding of differentiation of content and the value of differentiating content for their students. They also reported a stronger understanding of how to differentiate content in the classroom. However, several barriers to differentiation were also reported, which may provide educational researchers and professional learning coordinators further information about what hinders teachers' application of differentiated strategies, despite increased understanding and existing positive perceptions.

Primary education students with autism spectrum disorder may present difficulties when solving arithmetical problems. Therefore, this exploratory and descriptive single case study aims to verify the suitability of a methodology based on modified conceptual models so that a student with autism spectrum disorder understands and correctly solves direct (multiplication) and inverse (division) Cartesian product problems. The study was carried out within an inclusive educational environment and consisted of baseline, training, follow-up, generalization and maintenance. The results show a functional relationship between independent and dependent variables, the student learned to solve this type of problems, generalized his learning by successfully solving two-step problems (an addition and a multiplication) and maintained what he had learned 5 weeks after the last training session. The student employed pictorial representations, the odometer strategy and counting strategies to solve the problems raised in the follow-up, generalization and maintenance sessions. Limitations and future lines of work are also discussed.

Teaching through problem-solving (TTP) is an approach that helps develop learners', critical thinking, creative thinking, communication collaborative, and computational (5Cs) skills. This approach provides an opportunity for the teachers to maximise metacognition resulting in quality of instruction. This research study aims to determine the process of strengthening the teaching and learning of Mathematics through problem-solving using the "neriage" perspective. Two elementary public schools with different context were used as subjects in this research investigation: with regular curriculum and special curriculum. Pre-post-test design was employed and the quantitative data were analysed using two-tailed t-Test. Grounded theory was used to measure the qualitative component of the research study and axial coding-decoding method was applied to qualitatively analyse the patterns and themes. It was found out that on both types of curriculum, those students that were given intervention performed significantly better than those that were not given intervention. Hence, the TTP approach as an intervention initiative is an effective teaching strategy both in special and regular curriculum. Moreover, regardless of the type curriculum, or whether given intervention or not, students performed significantly better in the posttest. Hence, the instruction, whether with the aid of intervention or not, students' achievements improved significantly.

Much of the mathematics that children experience in school neglect the skills increasingly needed for citizenship, particularly the power of complex data to investigate and make sense of the world. We draw on the relatively new field of data science as a multi-disciplinary approach to investigate problems through analysis of massive, non-standard, incongruous and/or messy data. Our exploratory qualitative study had as its research question: What can children learn about citizenship when they engage with data science? The case study in this paper illustrated ways that children's learning about citizenship were enriched through an age-appropriate data science investigation. The study analysed classroom video from a Year 4 classroom (aged 9-10) over six lessons that integrated curricula in digital technologies, health, and mathematics. In these lessons, the children generated and analysed non-standard data and debated social, well-being and privacy issues as they considered their activities in cyberspace. The video data were analysed using a framework based on critical citizenship education literature that examined dimensions of power, collective engagement, individual responsibility and action. Three key findings emerged. First, the case study highlighted skills in citizenship education developed through data science, positioning children as agents and advocates. Second, the study showed how a complex data investigation in citizenship education was achievable with primary children through meaningful curriculum integration. This is important given that problems that citizens address are typically interdisciplinary. Finally, the findings revealed a gap between data science skills and those developed in the mathematics curriculum, and recommend ways that the maths curriculum could be updated.

This study was conducted to determine the degree of relationship that exists between learners' level of comprehension and solving skills on mathematical word problems of grades four to six learners in Kang-iras Elementary School. It attempted to establish a relationship between the learners' level of comprehension and solving skills. This research study employed the correlational method of research. This research design is appropriate for this research because its primary purpose is to determine the degree of the relationship between the learners' level of comprehension and solving skills of the word problems. Lomax and Li (2009) stressed that correlational research investigates a range of factors, including the nature of the relationship between two or more variables and the theoretical model that might be developed and tested to explain these resultant correlations. From the gathered data, the following findings are, the comprehension level of the learners in Kang-iras Elementary School being studied is at Frustration Level. For each specific skill, only in the literal interpretation skill the learners had been classified at instructional level while for the other two skills, the learners are at frustration level. Majority of the learners are at a frustration level. The level of word problem solving skills in mathematics of the respondents is classified as non-proficient. All three skills indicators used revealed that the respondents are non-proficient. The learners have not mastered word problem-solving. Comprehension skills could not predict the mathematical word problem-solving skills of the learners. There is weak correlation between the variables and the relationship between the two variables is insignificant. There are other factors affecting word problem skills among learners. Some are identified as follows: instructional strategies and methods, learners' motivation and concentration, learner's arithmetic ability, learning facilities or instructional materials, curriculum and teacher's competency. From the findings of the study, it was established that comprehension level is not an indicator of the learners' solving skills and there are other factors that could affect solving mathematical word problems. Solving skill is independent of comprehension skills and the variables studied are not related. Thus, it can be concluded that comprehension is not the only factor that could affect word problem-solving skills but there are more other factors and these factors may be assessed and taken into consideration.