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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. [ABSTRACT FROM AUTHOR]

AbstractBecause word problems present mathematical information through a scenario, they are language-intensive and require mathematical and reading comprehension skills to solve them. In addition, they are linguistically complex, which makes them challenging for all learners, especially multilingual learners. Given the rising number of dual-language bilingual programs in the United States—which have the goal of simultaneously supporting content and language learning—it is important to understand the linguistic complexity of word problems and their translations. Therefore, we adopted a sociolinguistic perspective to recognize the inextricable relationship between language and mathematics and conducted a linguistic content analysis of Grades 1 and 4 addition/subtraction word problems in a widely used U.S. elementary curriculum. We analyzed the ways in which word problems were linguistically complex and how complexity differed between English, French, and Spanish translations. We found that word problems were complex due to vocabulary inconsistencies, assumed cultural knowledge, verb tenses, and errors. The French and Spanish translations also had more errors and inconsistencies than the English source text. Findings have implications for curriculum and assessment developers related to multilingual editing and linguistic and contextual consistency, as well as for teachers to support students’ engagement with language and mathematics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this theoretical article, we argue that the imminent collapse of earth systems that sustain life forms calls for mathematics education as a field to reflect on and re-evaluate its priorities and thus practices. We consider both what ecological collapse means for mathematics education and whether mathematics education might offer meaningful gestures in response. We explore how the relationship between the social and the ecological is conceptualised in mathematics education (and other relevant) research and what this implies for mathematics education. We read, in this scholarship, a growing focus on the ecological and conceptualisations of socio-ecological relations between existing entities that are dialectical, or mutually dependent. More rarely, are they seen as entangled and monist, and it is in this thought that we locate our contribution of multi-layered gestures of mathematics education. We describe these, in terms of three broad practices: listening for socio-ecological entanglement; attending to the scales of socio-ecological entanglements; and living entanglement as mathematics educators. We exemplify these gestures through examples of curriculum innovation. This article, a socio-ecological gesture in itself, is written in the spirit of opening a conversation into which we invite others. [ABSTRACT FROM AUTHOR]

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

The post-pandemic adaptation demands technological innovations in sustainable learning to support mathematics curriculums. This research aims to develop the Web-based Window Shopping (WBWS) in high school mathematics curriculum with ADDIE procedure. The data were collected through interviews, questionnaires, and tests. The stages of research comprised analysis, design, development, implementation, and evaluation. The experts' validation test results showed that the aspects of materials and medium achieved an average score of 82,75%. Meanwhile, the trial test results showed that the developed WBWS is worth implementing, with the average percentage of effectiveness reaching 83,33%. The results suggest that the creation of WBWS as a web-based learning model for mathematics curriculum is not only feasible but also meets the educational needs of high school students. Teachers and students can use this web-based learning model as an alternative for implementing the independent curriculum on mathematics learning. [ABSTRACT FROM AUTHOR]

This conceptual paper puts forward the construct termed teacher curriculum competence, which is an amalgamation of theoretical or formal and personal practical teacher knowledge and orientations in relation to curriculum. We situate the competence in institutional, political, and philosophical contexts. Drawing on research related to mathematics curriculum at different stages (i.e. the official, intended, and enacted curriculum) and teacher competence frameworks, we elaborate on how a teacher interacts with curriculum informed by their knowledge and orientations. When working with curriculum, teacher curriculum competence refers to what teachers attend to and how they interpret curriculum, as well as why they make decisions, including when to introduce particular concepts or skills, based on their local students' needs. In addition, we argue that the process of interacting with curriculum helps shape teacher knowledge and orientations. This article is significant for the contribution it makes to conceptualizing teacher curriculum competence in a centralized curriculum system, that is a nationally mandated. Although we use the mathematics discipline as an example, implications for research in promising areas for future studies in this space are also discussed. [ABSTRACT FROM AUTHOR]

This study aims to analyse Grade 8 objectives in the year 2018 Mathematics and Sciences curricula, and the compatibility between the 2021-2022 academic period textbooks of the Ministry of National Education (MEB) and the year 2019, 2020, 2021 and 2022 High School Placement Exam (LGS) questions according to Original Bloom Taxonomy. The 52 objectives specified under Grade 8 Mathematics Curriculum and the 61 objectives specified under Grade 8 Sciences Curriculum as well as the review questions at the end of modules and units of the Mathematic textbooks and Science textbooks were analysed against the 160 LGS questions posed under the science examination section in the years 2019, 2020, 2021 and 2022 in order to gather data. Analysis of Grade 8 Mathematics Curriculum has shown that largest objectives were observed in practice (f= 20) and comprehension (f= 18) stages. Analysis of Grade 8 Sciences Curriculum has shown that objectives in this domain were observed to be at knowledge stage for eight objectives, at comprehension stage for 25 objectives, at practice stage for seven objectives, at analysis stage for three objectives, at synthesis stage for eight objectives and at assessment stage for six objectives. It is found that objectives under both curricula cover multiple cognitive domain stages. Study data has led to identification of no affective objective among mathematics objectives, while two affective and two psychomotor domain objectives were identified among science objectives. Analysis of both curricula reveal that the objectives under the curricula and questions in the textbooks are supportive regarding LGS questions aimed at comprehension and practice stages, but insufficient for questions aimed at analysis and assessment stages which require higher level cognitive skills. [ABSTRACT FROM AUTHOR]

Why do some mathematics lessons captivate high school students and others not? This study explores this question by comparing how the content unfolds in the lessons that students rated highest with respect to their aesthetic affordances (e.g., using terms like "intriguing," "surprising") with those the same students rated lowest with respect to their aesthetic affordances (e.g., "just ok," "dull"). Using a framework that interprets the unfolding content across a lesson as a mathematical story, we examine how some lessons can provoke curiosity or enable surprise. We identify eight characteristics that distinguish captivating lessons and show how some, such as the average number of questions under consideration at any point in the lesson, are strongly related to student aesthetic experiences. In addition, the lessons that students described as more interesting included more instances of misdirection, such as when students' false assumptions provide opportunities for surprising results. These findings point to the characteristics of future lesson designs that could enable more students to experience curiosity and wonder in secondary mathematics classrooms. [ABSTRACT FROM AUTHOR]

In 2010 a mathematics curriculum was introduced in Irish second level schools entitled 'Project Maths' (PM). It aimed to refocus second level mathematics teaching and learning away from an over emphasis on procedural mathematics towards problem solving and real understanding [Department of Education and Skills (DES). (2010). Report of the Project Maths implementation support group. ]. This paper aims to examine the performance of 1st year undergraduate students' procedural and problem solving skills after the introduction of PM. A diagnostic test was developed to determine students' skills in each area and findings demonstrated that students perform statistically significantly better in the procedural skills in mathematics when compared to problem solving skills. These findings raise concerns around the lack of anticipated improved problem solving skills of a cohort of students exposed to this style of teaching and learning. The paper raises discussion surrounding the intended and actual teaching and learning taking place in second level classrooms along with consideration for the potential role of learned helplessness and the literacy issues. Recommendations are made for follow up qualitative research with stakeholders in mathematics education to better understand the 'why' of the results presented here. [ABSTRACT FROM AUTHOR]

The paper reports on updating and integrating two reformed curricula designed in an era of national crises in Greece. In particular, the curriculum design activity of the Leading Coordinators (LCs) is studied under the lenses of Activity Theory and Positioning Theory. Sixteen transcribed videotaped meetings over a period of ten months are analysed to examine LCs' positionings enacted within the design activity as well as the interaction of the latter with other activity systems in situ. LCs' discourse brought to the fore convergent and divergent positionings mainly related to their research identity, occasionally revealing tensions. Research was the dominant activity system that interacted with that of the curriculum design activity, giving rise to contradictions. These were intensified by socio-political implications of the crises and were mainly related to the formation of a shared object for the design activity, its course of development and the activity of other stakeholders. [ABSTRACT FROM AUTHOR]

This work aims to examine how the learning of mathematics in early childhood is developed in different policies, particularly within the processes of formal education and care in early years institutions. A comparative analysis of early mathematics education policies across countries must consider cultural differences, teaching practice, structural differences and institutional framework conditions, as well as the initial training and professional knowledge of teachers and educators. Extracted from the official country regulations, the following pages include some of the main characteristics of the national systems of early childhood education and care (ECEC) in Portugal, Slovenia and Spain, as well as a comparison of the ECEC guidelines concerning mathematics education between these three countries. There is an international consensus on an approach to early mathematics education inspired by realistic mathematics education (RME), i.e., on the importance of working mathematically in context, as well as on the idea of doing so through play, developing the language to communicate mathematical ideas. However, we found that these three aspects are reflected very differently in the official regulations of the three countries: while in Spain the development is very detailed and emphasizes the holistic approach and the role of mathematics in exploring the environment, the Portuguese curriculum emphasizes the role of mathematics as a form of language. The Slovenian curriculum, at last, focuses on the concepts and procedures associated with each mathematical sense. Furthermore, there are structural features concerning the regulation and type of ECEC system that have an influence in the implementation of the curriculum. [ABSTRACT FROM AUTHOR]

Acknowledging evidence that the ability to estimate has major consequences for both later mathematics learning and real-world functionality, this paper examines the national mathematics curriculum for compulsory school for each of Denmark, Norway and Sweden for the estimation-related opportunities it offers children. Framed against four conceptually and procedurally different forms of estimation (computational, measurement, quantity and number line), each of which is implicated differently in the later learning of mathematics, analyses indicated that none of the four forms of estimation were addressed explicitly in the Norwegian curriculum. Expectations of computational and measurement estimation were present in both the Danish and the Swedish curricula, although neither referred to either quantity or number line estimation. Even when estimation-related learning outcomes were articulated, there was no evidence of the processes by which they might be realised. Finally, there were no acknowledgements that estimation may contribute to the learning of other mathematical topics. [ABSTRACT FROM AUTHOR]

The Old Mutual Mathematics Olympiad (OMMO) in Malawi is a national mathematics competition open to all final year secondary school students. In this paper, we analyse the results of the preliminary round of the competition from 2015 to 2020. We developed seven content areas for the OMMO based on core elements of the Malawi secondary school mathematics curriculum. We found that the OMMO is dominated by questions on the core element Number and numeration, particularly topics like number systems, indices and logarithms, linear equations and number patterns. We also analysed the general performance of students in these areas. We found that students performed well in topics like inequalities, trigonometry and mensuration and did very poorly on proportions, sets, coordinate geometry and geometric constructions, among other topics. These findings suggest that mathematics Olympiads can help diagnose areas that are difficult for students and hence enhance the teaching and learning of Mathematics, especially in Malawi and other countries with a similar mathematics curriculum. To take care of under-represented areas, future OMMO examinations need to be structured to adequately cover all the core elements. [ABSTRACT FROM AUTHOR]

Leading undergraduates to study curriculum themes and experience practices that break with the disciplinary and linear logic of the process of educating mathematically motivated the creation of an opportunity to place them in the process of authoring their learning. In this article, we analyze 39 integrative projects conceived from the survey of aspects of reality and social problems of the local reality where students and school are inserted, for which the undergraduates of a class of the Pedagogy course acted as authors. This is a documental analysis study, conducted with the aim of problematizing the curriculum development in Mathematics from integrative projects as a practice in the initial teacher education. The activity of preparing these projects led the undergraduates to consider that the construction of knowledge involved in issues and problems of global or local reality implies study, reorganization and deconstruction of the teacher's image as the sole holder of knowledge. It also indicated the need to invest in specific knowledge of Mathematics and teaching methodologies. [ABSTRACT FROM AUTHOR]

The objective of this research is to analyze the statistical training proposal for mathematics teachers in Venezuela. The use of statistics in everyday life and its usefulness in different areas of knowledge has led to the recognition of its value for the general education of all citizens. For this reason, for several decades now, most countries have included statistics as part of the primary and secondary mathematics curriculum. In any curricular change, the role of the teacher is essential for its success. However, training institutions are also important, which must make adjustments in the curricula to train new generations of teachers to teach the new content. That is why this work reports the analysis of the study plans for the training of mathematics teachers from two Venezuelan universities, with a view to establishing how they aspire to prepare them for the teaching of statistics and probability. The results indicate that the training proposal does not seem to be adequate for future teachers to teach statistics in secondary school. [ABSTRACT FROM AUTHOR]

In recent years, attention has turned to the development of evidenced-based learning progressions/trajectories as a means of identifying the likely paths learners might take in developing a deep, well-connected understanding of key aspects of mathematics. However, the extent to which this work influences what happens in mathematics classrooms varies greatly depending on the prevailing relationship between curriculum, pedagogy and assessment. This article will draw on current policy documents and the literature to challenge current assumptions at the national level about what constitutes a learning progression. It will draw briefly on the results of a recently completed, large-scale study on mathematical reasoning in the middle years of schooling to make a case for evidenced-based learning progressions/trajectories as boundary objects in reconnecting and rebalancing the curriculum, pedagogy and assessment relationship to support reform at scale. [ABSTRACT FROM AUTHOR]

Mathematics curricula have traditionally focused on content knowledge, often in the form of a scope and sequence of increasingly difficult mathematics. The importance of using and applying mathematics is recognised in the current Australian Curriculum Mathematics (AC: M) as 'proficiencies' that are intended to be integrated with the content. There is little support for teachers to develop these proficiencies – reasoning, understanding, problem solving and fluency. Learning progressions are sequences of learning that focus on cognitive processes, and thus provide a useful basis for curriculum development. Using an empirical Statistical Reasoning Learning Progression as an exemplar, a new approach to curriculum development is suggested that links content knowledge with the proficiencies. The outcome is a zone-based, rather than year level based, curriculum that allows teachers to target their teaching, so that students develop increasingly sophisticated understanding of statistics and probability. [ABSTRACT FROM AUTHOR]

Since problem solving became one of the foci of mathematics education, numerous studies have been performed to improve its teaching, develop students' higher-level skills, and evaluate its learning. While these studies usually study specific aspects of problem solving, further research is needed to understand how to address problem solving from a more comprehensive perspective, especially in the curriculum. We therefore ask two questions: What characteristics should problem solving have at each stage of the curriculum enactment process to ensure successful implementation? What role should problem solving have from a global curriculum perspective? To answer these questions, we perform a literature review to identify the roles and characteristics of problem solving that facilitate its successful implementation. Based on qualitative analysis of the data, we organize the results into the following categories: conditions of the education system, curriculum structure, characteristics of the planned curriculum and instructional design, types of problems in the intended curriculum and instructional materials, characteristics of the tasks implemented, classroom management, evaluation, student-related considerations, and teachers' roles during problem solving. We also identify five principles to implement problem solving in teaching mathematics: understanding, reasoning, autonomy, collaboration and affective factors. [ABSTRACT FROM AUTHOR]

The Peruvian basic education and its curriculum have been impacted by the COVID-19 pandemic. As a result, certain trends and phenomena have emerged, which shape the new normality in society and have generated many effects on the mathematics curriculum. For this reason, it is necessary to pose the problem of sketching the orientations of mathematics curriculum for the new situation. In this position paper, I developed an outline based on a description of the problem situation, the demands that the world of work had already been making on the curriculum at the international level, and the research carried out by mathematics education. From these factors, I assert the significant role of critical mathematics education, particularly the motto of reading and writing the world with mathematics. I propose that orientations for the mathematics curriculum in basic education in the new normality should include ethical and political issues, statistical and financial literacy, digital skills as a part of a STEM approach, ethnomathematics from native people, and, finally, a problem-posing and problem-solving approach. In this list, ethical and political issues have primacy. [ABSTRACT FROM AUTHOR]

The local needs and circumstances in curriculum revision often necessitate improvements in the quality of education. However, problems associated with the revision of curricula in developing countries have been observed from a range of perspectives in previous studies. This study investigates the revision process of the intended mathematics curriculum in Mozambique through document analysis of related materials and interviews with people involved in the 2015 curriculum revision. The investigation revealed three points. First, the results of nationwide surveys on academic ability conducted by the Ministry of Education and Human Development (MEHD) as well as interviews of parents and teacher questionnaires significantly affected the curriculum-revision process. Second, aligned with the political regulations, opinions from various social and economic groups worked as one of the main factors behind this process. Finally, the National Institute for Educational Development (INDE) has exhibited a strong initiative throughout the process. The research analysis would form a proposition of a methodology to analyse the curriculum revision process. The findings would be relevant to other African countries in undertaking appropriate curricular revisions. [ABSTRACT FROM AUTHOR]

International examinations such as TIMSS play a major role in determining the quality of the educational process. TIMSS results show that students have various deficiencies. Studies investigating the causes of this failure draw attention to textbooks. In this study it was aimed to examine the objectives in the 2018 mathematics curriculum and the tasks related to the data handling content domain from 4th to 8th grade textbooks according to TIMSS cognitive domains. In addition, similarities and differences the objectives in the curriculum and the tasks in the textbooks have with TIMSS 2019 cognitive domains were examined. Document analysis method was used and content analysis was conducted. The results revealed that the tasks in all the textbooks are predominantly in the cognitive domain of applying, followed by the cognitive domains of knowing and reasoning. In addition, it was determined that the objectives at all grade levels were predominantly concentrated in the cognitive domain of reasoning. Based on the results obtained, some suggestions were given. [ABSTRACT FROM AUTHOR]

This study describes a professional development (PD) program designed to support middle school teachers in effectively integrating robotics in science and mathematics classrooms. The PD program encouraged the teachers to develop their own science and mathematics lessons, aligned with national standards, infused with robotic activities. A multi-week summer PD and sustained academic year follow-up imparted to the teachers the technical knowledge and skills of robotics as well as an understanding of when and how to use robotics in science and mathematics teaching. The goal of this study is to investigate the effects of the robotics-integrated PD program through the changes of teachers' technological-pedagogical-and-content knowledge self-efficacy, the improvement in their content knowledge of robotics in the context of science and mathematics teaching, and their reflections on the PD. The 41 participants consisted of 20 mathematics and 20 science teachers and one teacher who teaches both subjects. Three instruments were administered to the teachers during the PD, and follow-up interviews were conducted to further examine benefits and possible impacts on their teaching resulting from the PD. The data were analyzed by both statistical and qualitative methods to identify the effectiveness of the PD. The findings of the study indicate that the PD program was effective in increasing participants' robotics content knowledge and confidence and outcome expectancy while integrating robotics in their teaching practices. Based on teacher reflections and follow-up interviews, this study offers guidelines for future development of technology-integrated science and mathematics teaching. [ABSTRACT FROM AUTHOR]

Drawing on the Semiotic-cultural approach and the Anthropological theory of the didactic, this paper discusses how exploration of historically framed conceptualizations of mathematical objects can establish bridges between different mathematical areas such as calculus and Euclidean geometry. A classroom intervention study in two secondary mathematics classrooms involving dynamic geometry software tools to support the construction of a parabola and its tangent and aiming at the development of representational flexibility between algebraic/ functional and geometrical approaches, illustrates how students may benefit from participation in such explorations. [ABSTRACT FROM AUTHOR]

In this study, a comparison of the 5th and 6th grade school mathematics curriculum of Turkey and Germany in the context of geometry learning domain has been made, similarities and differences are revealed about the sub-learning domains, learning outcomes, implementation suggestions. This study, in which a qualitative research approach was adopted, is a cross-national comparative education study in terms of its subject and data collected by document analysis were analyzed by descriptive analysis. As a result of the comparisons made in the context of the geometry learning domain, it was seen that the Turkey program has more sub-learning domains, more detail, divided into two grade levels. In the Germany program, it was concluded that sub-learning domains were expressed more simply and generally. The outcomes in the Turkey program presented in more detail including examples of various activities; the outcomes in the Germany program were handled in a more general and unified manner under a single outcome, were decided the activities by teachers. Moreover, it was observed that in terms of processing skill expected from students, the Turkey program is more comprehensive than the Germany program. It was seen that the subjects were presented in relation to concrete models and real life situations as an implementation suggestion in the both countries. In addition, it was observed that the studies compared in terms of mathematics curriculum of Turkey and the other countries most focused on the elements of the program. [ABSTRACT FROM AUTHOR]

This research was carried out in order to identify the problems faced by teachers, school administrators, parents and students regarding the implementation process of the primary school first grade mathematics curriculum, which was put into practice, and to determine the solutions for these problems. The study was designed according to the phenomenology pattern, which is one of the qualitative research patterns. The study group of the research consists of classroom teachers, school administrators, parents and first grade students determined by the maximum diversity sample from central districts of Adana in 2018-2019 academic year. Data were collected through semi-structured interview forms. Content analysis was used in the analysis of the data. As a result of the research, it has been concluded that teachers, school administrators, parents and students have problems from time to time because of the activities, physical conditions and insufficiency of tools in the application of mathematics curriculum. In this context, in order to increase the effectiveness of the program, it has been suggested that the activities should be revised and the physical and infrastructure facilities in schools should be rearranged according to the changing and developing understanding of education. [ABSTRACT FROM AUTHOR]

Algebra, the foundation to higher math learning skills, is integral in our daily lives. Therefore it is important to introduce a system that will help algebra become a part of one's intellectual support system to assist with everyday challenges. Every person, even if lacking a formal math education, uses applications such as addition, subtraction, multiplication and division. Basic demographic data and a math placement test for students seeking entry into college, covering algebra and pre-calculus topics, was administered. A comparison of student experience, nationality and gender differences over their performance on the placement test revealed no significant performance differences between genders. However, differences based on nationality and student experience were found from a 2-T, Kruskal-Wallis and Tukey's Honest Significant Difference test. [ABSTRACT FROM AUTHOR]

Scholars propose that contextual problems can be used to ground students' understanding of mathematical ideas, and recent curricular trends have resulted in a plethora of resources that introduce and develop new mathematical ideas through contextual problems (CPs). Given the tension between this approach and the traditional role of CPs as opportunities to apply, rather than develop, mathematical ideas, there is a need for a common language that teachers, curriculum designers, and scholars can use to learn from each other about the types of tasks that are central to contextual problem-based instruction. To fulfill this need, the author proposes an analytical framework, developed through observations of a contextual problem-based algebra unit. After describing the categories in the framework using examples from the written and enacted lessons, the author uses existing theories and empirical observation to describe the significance of each type of activity for the development of understanding. [ABSTRACT FROM AUTHOR]

We analyze the knowledge of secondary school mathematics teachers on the realization of mathematical processes in their classroom performance to support students' development of mathematical competence. To accomplish this, we identify and describe changes in their knowledge, skills and attitudes related to using mathematical processes in tasks design, aimed to promote school learning, as part of their professional competence. These teachers participated in a training proposal. We observed that they improved their abilities to link skills, mathematical processes and competence, justify this connection and, design and select tasks that attend to this connection. [ABSTRACT FROM AUTHOR]

The authors investigated the effect of a mathematical curriculum (CU) developed based on verbal and practical activities on the mathematical competency (MC) and learning behaviors (LB) of preschool children. In a quasi-experimental design, 60 children (5- to 6-year-old girls) were selected using the accessible sampling method. The children were randomly divided into an experimental group and a control group, and the relevant concepts were taught to the children in both groups. While the control group received the typical kindergarten education based on the usual textbooks and worksheets, the CU was taught to the experimental group. Structural equation modeling was used to model the data and statistical evaluation. The results demonstrated a significant difference between the two groups in MC and LB. The CU significantly improved MC directly, and indirectly through the improvement of LB (i.e., engagement and learning focus, verbal behaviors, and type of activity). [ABSTRACT FROM AUTHOR]

Highlights • The Arc of Learning framework describes how student learning grows over time. • The framework is an ergonomic resource for curriculum design and use. • We report on how the Arc of Learning framework has been used and can be used. Abstract This article explores students' development of deep, connected mathematical understanding through the lens of curriculum design and teacher enactment of problem-based curriculum materials. Rather than emphasizing student learning as passively watching and imitating a set of isolated skills, the Arc of Learning framework highlights ways that student learning can evolve from informal knowledge to more sophisticated reasoning over time. It is an ergonomic resource for curriculum design and use that makes explicit the intentions of the curriculum designers about how students engage in the learning of mathematics over time. Using examples from a problem-centered curriculum, we report on the student learning opportunities provided by connected sequences of problems. We also discuss how it can be used by various stakeholders. [ABSTRACT FROM AUTHOR]

This article aims to present a mapping and analysis of academic research that focuses on the relationships established between teachers of basic education and curriculum materials of mathematics. Thus, we set out to seek the academic productions and publications inherent to this theme. To do so, we performed a mapping, of the Knowledge State type, having as a source of data collections the thesis bank and dissertations of CAPES (Coordination of Improvement of Higher Level Personnel). To ensure the organization and rigor of the analysis, we are inspired by the content analysis method, based on Bardin (2016). The results revealed that the greatest number of researches on this subject is concentrated in the Program of post-graduate studies in Mathematics Education, Catholic University of São Paulo. [ABSTRACT FROM AUTHOR]

Highlights • Tensions occur when designers and users of math curriculum have conflicting goals. • The ergonomic tensions between users and designers of curricula have three forms. • Curricular examples illustrate how the design tensions are mutually influential. • Some designs reduce tension in one dimension to potentially protect reform goals. • To aid math curriculum reform, ergonomics involves teacher supports and obstacles. Abstract Designers of curriculum materials have intentions, which are goals and visions for what will happen in the classroom and the way that mathematics will be experienced by students and a teacher. These perspectives inform design decisions that aim to enable teachers to enact this vision and achieve these goals in expected contexts. Yet teachers and students have their own goals and visions, or different contextual conditions, that may be different from or even at odds with those of the curriculum designers. These potential differences result in design tensions, which reflect the conflicting demands on the curriculum materials. In this article, we call attention to multiple dimensions of design tensions that are central to the broader goals of curriculum reform. [ABSTRACT FROM AUTHOR]

This study traces curricular support for concepts related to infinity and division by zero, in both elementary and secondary mathematics curriculum documents in our province. It was motivated by results of our previous and ongoing work related to transition to post-secondary studies in mathematics, in which we identified consistent gaps and misconceptions around limits and infinity. Our findings are startling in that, in the school curricula, many expected references to concepts related to division by zero, infinity, and limits are simply not present (expected in the sense of being needed to provide essential support for the material which, according to curriculum documents, must be covered). Recommendations for future curriculum revisions are included. [ABSTRACT FROM AUTHOR]

Epistemology is a conceptual template for how we think about the world, and the study of how we come to know the world around us. The world does not dictate unequivocally how to interpret it. This article will explore this position on the fluidity of epistemic constructs through two prominent philosophical perspectives, those being derived from the works of Ludwig Wittgenstein and Michael Foucault, respectively. These insights will be used to more deeply unfold the current situation for Aboriginal students within dominant approaches to mathematics curriculum in Australia, and the subsequent approaches to the inclusion of Aboriginal knowledge and epistemologies. It is suggested that the epistemic constructs most valued and thus credited as conveyors of ‘truth’, and therefore positioned as powerful forms of knowledge within dominant curriculum and education policy, are those derived from Western, Eurocentric origins. This privileging of particular epistemological constructs over others is reinforced unconsciously through the articulation of educational goals deemed most appropriate, or ‘socially just’, for the Aboriginal student population. The place of Aboriginal knowledge within such constructs is therefore reflective of broader ideation around the role of education within society and its failure to challenge existing structures of power and injustice. [ABSTRACT FROM PUBLISHER]

In this study, it has been aimed to determine the example types on the subject of limits that are used in mathematics textbooks that based on subsequent mathematics curriculum. In this way, the reflection of the change emerged in the curriculums on textbooks and also on in-class implementations in an indirect way are tried to be rendered through the examples. Within this framework, the examples on the subject of limits given in the 11th grade mathematics textbook (high school 3rd grade) of the academic year 2000-2001 and 12th grade mathematics textbook taught in the academic years of 2009-2010 and 2015-2016 have been examined. In order to determine the example types on the subject of limits that are used in the textbooks, classification on example types developed by Alkan (2016) has been used. In the direction of the research findings, it has been determined that standard and improving examples are frequently used in the textbooks despite the fact that start up examples and non-examples are rarely used. In addition to this, it has been seen that extreme and counter examples are not used in these books at all. Start up and improving example are used more frequently in the books that were taught in the years of 2009-2010 and 2015-2016 than the books taught in the years of 2000-2001. It has been seen that start up examples are given more place particularly in the academic years of 2015-2016 and the subject of limits is associated with daily life. [ABSTRACT FROM AUTHOR]

This study explores how textbooks function in education. It asked whether opportunities provided in math textbooks to engage in tasks demanding different levels of understanding correlate with students’ achievements on tasks demanding equivalent levels of understanding on a standardized exam. The textbooks evaluated were two 8 th grade mathematics textbooks used by students in the Arab community in Israel, showing that Textbook A makes more cognitive demands than Textbook B. The study correlated textbooks’ cognitive demand with the scores of all 8 th grade students in the Arab community who completed the national math test in 2015 and studied in schools using either Textbook A or B (N = 4040), while attending to mediating variables. The findings show that if a textbook provides the opportunity to engage in tasks demanding higher levels of understanding, students using this book will have higher scores. The study shows that gender and SES play an important role in how opportunities provided in textbooks interact with students’ scores. Many factors influence variations in mathematics achievements within and between nations. The findings illuminate textbooks’ ability to provide opportunities to learn mathematics. As a result, they raise new questions about how teachers use textbooks and about the role of textbooks in promoting access and equity in mathematics education. Although the work explored specific textbooks, its findings shed light on how learning opportunities relate to achievements more generally. [ABSTRACT FROM AUTHOR]

We explore the teacher-curriculum materials relationship as researched theme, highlighting characteristics of the materials and teachers brought to this relationship, as well as concepts underlying it. It is a bibliographical study, in which the production about this relation in the scope of Mathematics Education is discussed. The discussion focuses on the design of curricular materials as sociocultural tools and on the relationship from resources brought by both agents, teacher and materials, relating to the concepts of affordance and agency. Curriculum materials, with their affordances, and professors express their agencies about choices and decisions regarding Mathematics and its teaching, and both agents influence each other when providing student learning situations. [ABSTRACT FROM AUTHOR]

Undergraduate research has become the centerpiece of many institutions of higher education’s efforts to attract and recruit high school graduates. Since 1987, throughout my tenure at Bloomsburg University, I have involved over 20 students in my research. In my experience, there is clear evidence that students of mathematics substantially benefit if they engage in research during their undergraduate studies. Whether the student plans to apply for employment after graduation or continue with graduate studies, the undergraduate research experience has a tremendous effect on the student’s success. In this paper, I will provide some personal insight on my experience in working with undergraduate students. In most cases, my experience has been in working with one student on a long term (one semester or mostly year-long) research problems. I will discuss my approach to identifying students, the type of projects, providing guidance, and finally the challenges that we face in supervising undergraduate research. To exemplify, emphasis will be placed on the status of a recent 1-year research project, which was funded by the Pennsylvania State System of Higher Education, and a senior undergraduate student worked on it for one year. [ABSTRACT FROM AUTHOR]

This study compared the effects of an integrated reform-based curriculum to a subject-specific curriculum on student learning of 19,526 high school algebra students. Using hierarchical linear modelling to account for variation in student achievement, the impact of the reform-based Core-Plus Mathematics curricular materials on student test scores is compared to the subject-specific curriculum. Findings from this study indicate that students enrolled in integrated mathematics outperformed subject-specific students on an Algebra I exam (highly aligned with content), and performed equally on an Algebra II exam (poorly aligned). High minority students in high-need schools demonstrated higher performance when they were enrolled in integrated mathematics. [ABSTRACT FROM AUTHOR]

We present discussions about how teachers interact with math curriculum materials, within a qualitative research. The data collection took place in a focus group, with the participation of eight teachers. The analysis was performed based on Sacristán when analyzing the level of the curriculum presented to the teachers, and on Remillard and Brown when it was about the use that teachers do of the mathematics curriculum materials and its impact on education. Teachers report that the participation in this research project and the use of the materials presented had a great influence in the activities they carried out in the classroom, thatwere better planned and carried out more properly; and pointed out the need of such studies to be part of the teachers' formation. [ABSTRACT FROM AUTHOR]

How teachers read or interpret textbooks, which represent curricula, is important for successful implementation of curricula (the level of reading of knowledge, skills and values in the textbooks that curriculum sets forth for students' learning). This paper aims to investigate how middle school mathematics teachers read mathematics textbooks in the light of goals of middle school mathematics curriculum. To this end, a 5th grade mathematics textbook's segment which covers one learning objective about simplifying and expanding fractions is given to 30 middle school mathematics teachers and they are asked this following question: "What do think that the textbooks writers pay attention for teaching of this learning objective?" The findings reveal that the teachers did not read such mathematical process skills as reasoning, making connection, and communication which were reflected into the learning objective in the textbook. The findings also show that the teachers mainly read the textbooks by "describing what is done", "providing suggestion", and "pointing out short comings" and these suggest that this type of reading is rather superficial as far as the teaching that the curriculum aims to achieve is concerned. The paper draws attention to the issues regarding how the textbook reading skills of mathematics teachers can be developed and presents some implications about textbook research. [ABSTRACT FROM AUTHOR]

This article presents a study on the choice of criteria for the selection of topics to be worked in the Mathematics Curriculum of the High School, that relate mathematics contents to themes of interest. This work is justified by the importance of the Math teacher seek different methodological features for the development of the teaching and learning process, which can be applied in their classes, arousing the curiosity, the attention and the interest of students. From the contributions of Skovsmose (2006), Doll Jr. (1997) and Silva (2009) has been elaborated a classification of the themes of interest that can be developed along the Mathematics Curriculum. This classification can subsidize the teachers in their choice of themes to be developed, for it presents possible mathematics contents that can be worked in each theme. [ABSTRACT FROM AUTHOR]

This paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of mathematics curriculum as story and defines and illustrates the mathematical story elements of mathematical characters, action, setting, and plot. Drawn from literary theory, this framework supports the interpretation of mathematics curriculum as art, able to stimulate the imagination and curiosity of students and teachers alike. In doing so, it is argued, this framework offers teachers and other curriculum designers a conceptual tool that can be used to improve the mathematics curriculum offered to students in terms of both logic and aesthetic. [ABSTRACT FROM AUTHOR]

Through the examination of a collection of macro factors and explanations for racial disparities in mathematics assessment found in the literature, this article takes up these accounts and problematizes the factors by unpacking the assumptions and exposing complexities. We do this using Critical Race Theory (CRT) to reinterpret and call out important blind spots. Essential questions that guided our analysis included: what macro factors has the field identified as influencing or explaining racial disparities in mathematics assessments? What assumptions undergird the field’s conversations about racial disparities in mathematics assessments? In what ways can those assumptions be challenged through CRT to highlight the story of race in the US? Our analysis reveals that the factors fall victim to a meritocratic premise that assumes all students are exposed to equivalent forms and amounts of mathematical knowledge. This assumption effectively locates the problem of assessment within students and not the institutions that are entrusted with providing access to mathematics curricular knowledge that is requisite for success. We conclude by arguing for a call to social action and continued policy measures with a renewed focus on equitable curricular access as an important method to improve the assessment outcomes for racial minority students. [ABSTRACT FROM PUBLISHER]

The purpose of this study is to explore the opinions of mathematics teachers working in high schools on the high school mathematics curriculum that was reformed in 2013. Structured interview method was employed to collect data from nine high school teachers. Content and descriptive analysis were used to analyze the data obtained from the interviews with teachers. Based on the qualitative analysis of data, the teachers favored the reduction in the content and acquisition regulation, but criticized some eliminated content and acceptance the level of readiness of students. The teachers believed the benefit of using compassstraightedge, information and communication technologies. Furthermore, the teachers expected more professional development opportunities, particularly on the use of technology for teaching mathematics before they are hold accountable for the implementation of the new curriculum. [ABSTRACT FROM AUTHOR]

Making real world connections in mathematics curricula and in teaching mathematics is generally viewed favorably within the educational community, however, little empirical research has examined how and why to use real world connections in mathematics education based on the views of experts. This study describes the feasibility of the use of real world connections according to high school mathematics teachers and academicians of mathematics education. Opinions of high school mathematics teachers (n=16) and academicians (n=8) about advantages, disadvantages, and examples of real world connections are elicited and reported. Teachers and academicians report several advantages of the use of real world connections in teaching mathematics as well as its disadvantages and limitations. Suggestions about dealing with limiting factors for using real world connections are also reported. [ABSTRACT FROM AUTHOR]

This article sets out to evaluate the English Early Years Foundation Stage Goal for Numbers, in relation to research evidence. The Goal, which sets out to provide ‘a good foundation in mathematics’, has greater breadth of content and higher levels of difficulty than previous versions. Research suggests that the additional expectations are unachievable by the majority of rising fives, but that a more effective foundation to ensure progress and prevent later difficulties would prioritise number sense with numbers to 10, including subitising, numeral comprehension, relative number size, one more/less than and part–whole relationships. [ABSTRACT FROM PUBLISHER]

Highlights: [•] Curriculum analysis as a line of scholarship can provide insightful information. [•] There are variations across the studies with regard to the analytic methods used. [•] Greater methodological consistency could help support more generalized findings. [•] There is a need to better define and conceptualize reasoning and proving. [•] Student learning opportunities shall be analyzed beyond the intended curriculum. [Copyright &y& Elsevier]