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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]

The connections between citizenship education and mathematics education have been the focus of theoretical development and attention by educators interested in issues of justice, equity, power, criticality, and citizen engagement with societal issues, across schools, universities, and adult education levels. In this survey article, we contribute to new knowledge in the field by identifying and describing three interconnected layers of influence on the praxis of teaching and learning: (1) perspectives from citizenship education and mathematics education (e.g., kinds of citizenship, critical thinking in mathematics education); (2) institutional factors (e.g., policy, curricula, implementation within education systems); and (3) emerging influences (e.g., changing skill demands, innovations from communities of practice). In exploring the connections between citizenship education and mathematics education, we go beyond extant theory development and point to influences such as global disruptions, societal changes, systemic structures at the national and local levels, messaging in the media, and the role of teachers and learners. The holistic analysis of these influences enables identification of tensions and dilemmas, and issues of identity, autonomy, adoption, and systemic change. Together these point to multiple implications for educators, policy makers, and researchers aiming to enable informed and engaged citizens. [ABSTRACT FROM AUTHOR]

Parental involvement in mathematics learning can positively affect student achievement and wellbeing but is challenging to establish and maintain. Asian immigrants make up around 15% of New Zealand's population, yet little is known about these parents' involvement in their child's schooling. To examine the experiences of parental involvement in their child's mathematics learning of East Asian parents, data from semi-structured interviews carried out with eleven parents were considered in light of a common parental involvement framework. Parents' perspectives about the mathematics curriculum were found to come mainly from communication with teachers and observation of their child's learning. Parents desired improved involvement in their children's mathematics learning and better communication with their child's teacher. Implications include that to capitalise on the potential of parental involvement for improving mathematics learning, teachers must prioritise effective communication with parents to enable their involvement. [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]

Properties of arithmetic operations are important in mathematics and play a significant role in elementary school students' learning of mathematics. At the same time, it is quite challenging to help students learn arithmetic operational properties beyond memorization, so that they know when and how to use a specific arithmetic property. This paper reports a study containing two parts to explore students' learning of the Commutative Property of Addition (CPA) as related to the content presentation in textbooks. Part one is to assess selected students' performance on CPA at the end of Grade two, and part two is to explore possible contributions of textbooks to students' performance in Shanghai. Firstly, we evaluated the performance of 41 second-graders on CPA by collecting data through a paper-and-pencil test, which was followed up with individual interviews. Through analyzing how textbooks present and organize this topic, we sought to better understand from a curriculum standpoint how students' performance on CPA is impacted by textbooks. Results revealed that Shanghai textbooks make a positive contribution to students' learning performance. The findings from this study help to shed light on how those textbooks aid student learning, and provide an example for further reflection on student learning of arithmetic operational properties in different curricula. [ABSTRACT FROM AUTHOR]

In this paper we report the results of a study in which we investigated how formal education and shadow education in Taiwan provide students opportunities to learn mathematics. Based on the conceptual framework of Opportunity to Learn (OTL), aspects specific to formal education, including mathematics curriculum, mathematics textbooks, and teachers' competence, and their teaching, were reviewed. Two national projects identified under shadow education were examined. The results revealed significant features of the mathematics curriculum, textbook design, and the quality of mathematics teachers in Taiwan that constitute a lived space where teachers with their knowledge and beliefs, curriculum, textbooks, and school settings, can generate cognitive and affective learning outcomes in students. Further analyses of the two above-mentioned projects showed how Taiwan extended learning opportunities to motivate students to learn and understand school mathematics. Based on the review, challenges were also identified. [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]

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]

This paper examines a didactic phenomenon, a perception that the elements of sets have a common property, e.g. that {1, 2, 3} and {a, b, c} are sets but {1, 2, 3, a, b, c} is not a set. The paper reports manifestations of this phenomenon in one country: across a range of school students in textbooks and in curricula and across pre-service and in-service teachers. The paper considers interpretations of the results under various theoretical frameworks and argues that these interpretations can be synthesized around the anthropological theory of the didactic. The paper ends with implications for what is taught under the name 'mathematics'. [ABSTRACT FROM AUTHOR]

Translating a mathematics lesson from curriculum materials into instruction is not straightforward, and launching, or beginning, a lesson such that students will become productively engaged in the target mathematics is nontrivial. The purpose of the study was to investigate preservice teachers' curricular noticing as they draw upon curriculum materials to design instruction, with a focus on how to launch that lesson. We engaged preservice elementary licensure students at two universities in a four-part process of analyzing mathematics curriculum, planning a lesson, demonstrating their visualization of enactment through animating their lesson launch, and reflecting on the process. Findings indicate that the focal case study pair modified the curricular materials to model mathematical aspects of fractions, adapted the introduction of key academic vocabulary, and introduced materials not mentioned in the curriculum to draw children into the lesson. We discuss implications for preservice teachers' planning of the lesson launch and their curricular noticing. [ABSTRACT FROM AUTHOR]

This study examined and compared the intended mathematics curricula according to topic coverage, focus, coherence, and learning progression in grades 1 – 12 within China and the province of Ontario, Canada. The findings show that the overall topics in the two curricula are similar: Chinese curriculum covers 78 topics out of 79 while the Ontario curriculum covers 76. The two curricula also share a similar general sequence such as topics for transfer stages from numbers to functions by starting with constant mathematics, then variable mathematics, and finally functions. However, the detailed topic design of the 2 curricula differs markedly. The Chinese curriculum includes few topics in each year, a short duration or span of each topic, and a fast-paced topic progression. The Ontario curriculum, in contrast, includes more topics each year, longer duration of many topics, and a small pace of topic progression in grades 1 – 8 and a fast pace of topic progression in grades 9 – 12. Because of different curriculum designs in grades 1 – 12, the intended curriculum may influence students' cognitive structures of mathematics, learning behavior and thinking, learning efficiency and achievement, and teachers' professional development. This calls for more refined and advanced research on the defined list of topics, topic organization, and terms to study curriculum in order to increase student learning opportunities. [ABSTRACT FROM AUTHOR]

This study investigates the teaching and learning of single-digit whole number multiplication in China. Analysis of data from documents, classroom teaching, and semi-structured interviews revealed three salient characteristics of emphasizing oral calculation, calculation speed, and understanding across standards, textbook and classroom practices. It also showed how mathematics teachers enact these features in their teaching practice to help students develop their computational skills. The study particularly elaborates the role played by the nine-times table, or Chengfa Kou Jue Table (CKJ Table) in teaching practices, as well as how teachers treat memorization of CKJ and how understanding of operations contributes to their better understanding the relationship between the two in the teaching process. [ABSTRACT FROM AUTHOR]

Eight middle school mathematics teachers’ perceptions and uses of curriculum materials and the Common Core State Standards for Mathematics (CCSSM) were investigated. Adapting a noticing framework and models of dialogic instruction and direct instruction, teachers’ noticing practices with curriculum materials and the CCSSM when planning, enacting, and reflecting on lessons were examined. Teachers who were committed to implementing the CCSSM and who were using one of two substantively different curriculum programs were purposefully selected. Data sources included multiple forms of interviews and classroom observations. The teaching evidenced three distinct noticing patterns. These patterns indicated that teachers’ curriculum materials were associated with how teachers perceived and enacted the CCSSM. Teaching with a curriculum program that was designed as a thinking device prioritized the Standards for Mathematical Practice of CCSSM evidenced noticing that was consistent with dialogic instruction. Teaching with a curriculum program that was designed as a delivery mechanism prioritized the Content Standards of CCSSM and evidenced noticing consistent with direct instruction. Findings indicated that the designated curriculum and contributed to differing interpretations of CCSSM and served as a lens for noticing. However, a dialogic curriculum program was not sufficient to support dialogic approaches in practice. One pattern showed teachers planning dialogic lessons, but the lesson enactments were not consistent with teachers’ plans, with evidence that the teachers were not aware that their practices differed from dialogic approaches. Implications for research and practice are discussed. [ABSTRACT FROM AUTHOR]

Through the lenses of statistical investigations and cognitive demands, we examined bivariate data tasks offered in US high school mathematics textbook series—a popular representative of three curriculum types: traditional, integrated, and hybrid. We developed a framework grounded in literature of association topics for the inclusion and exclusion of tasks. Using the Guidelines for Assessment and Instruction of Statistics Education (GAISE) framework, textbook tasks were coded for four investigation components (formulate questions, collect data, analyze data, and interpret results) and levels of statistical sophistication, as well as levels of cognitive demand as suggested by the Mathematical Complexity framework. Across the three series 582 statistical association tasks, all components of statistical investigation were evident with different levels of treatment: (a) all questions for statistical investigations were provided by textbook authors; (b) tasks rarely afforded student opportunities to collect data; and (c) nearly all of the tasks required students to analyze data and most required them to interpret results. Tasks in the integrated series were more numerous (n = 246) and required higher levels of mathematical complexity and statistical sophistication than tasks in the traditional and hybrid series. The vast majority of tasks were coded at the GAISE Level B for analyze data and interpret results and moderate level for mathematical complexity. Further analyses show the concordance between the developmental levels for statistical sophistication and mathematical complexity. Suggestions for curriculum development, content analysis, and future research are provided. [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]

A study of school mathematics curriculum enacted by competent teachers in Singapore secondary schools is a programmatic research project at the National Institute of Education (NIE) funded by the Ministry of Education (MOE) in Singapore through the Office of Education Research (OER) at NIE. The main goal of the project is to collect a set of data that would be used by two studies to research the enacted secondary school mathematics curriculum. The project aims to examine how competent experienced secondary school teachers implement the designated curriculum prescribed by the MOE in the 2013 revision of curriculum. It does this firstly by examining the video recordings of the classroom instruction and interactions between secondary school mathematics teachers and their students, as it is these interactions that fundamentally determine the nature of the actual mathematics learning and teaching that take place in the classroom. It also examines content through the instructional materials used—their preparation, use in classroom and as homework. The project comprises a video segment and a survey segment. Approximately 630 secondary mathematics teachers and 600 students are participating in the project. The data collection for the video segment of the project is guided by the renowned complementary accounts methodology while the survey segment adopts a self-report questionnaire approach. The findings of the project will serve several purposes. They will provide timely feedback to mathematics specialists in the MOE, inform pre-service and professional development programmes for mathematics teachers at the NIE and contribute towards articulation of “Mathematics pedagogy in Singapore secondary schools” that is evidence based. [ABSTRACT FROM AUTHOR]

This paper reports on 2 studies that examine how mathematical problem posing is integrated in Chinese and US elementary mathematics textbooks. Study 1 involved a historical analysis of the problem-posing (PP) tasks in 3 editions of the most widely used elementary mathematics textbook series published by People's Education Press in China over 3 decades. Study 2 compared the PP tasks in Chinese and US elementary mathematics textbooks. This allows for the examination of PP tasks from an international comparative perspective, which provides one point of view about the kinds of learning opportunities that are available to students in China and the USA. We found evidence that the inclusion of PP tasks in the Chinese textbook series reflected, to some degree, changes in the curricular frameworks in China. However, the distribution of PP tasks across grade levels and content areas, as well as the variety of types of PP tasks included, suggest a need for greater intentionality in the design and placement of PP tasks in both the Chinese and US textbook series. Findings from the 2 studies reported in this paper not only contribute to our understanding about the inclusion of PP tasks in curriculum both historically and internationally, but also suggest a great need to systematically integrate PP activities into curriculum and instruction. The fact that both Chinese and US curriculum standards have heavily emphasized PP in school mathematics, despite there being only a small proportion of PP activities in both Chinese and US elementary mathematics curricula, suggests the existence of challenges that are delaying the implementation of reform ideas such as problem posing in school mathematics. [ABSTRACT FROM AUTHOR]

As part of a larger effort to improve teacher capacity for high-quality mathematics instruction, we investigated the factors that are associated with different enactment patterns at three levels: contextual (e.g., type and quality of textbook), individual (e.g., teacher knowledge), and teachers' opportunity-to-learn (e.g., professional development experiences). Analysis of 183 teachers' self-reports on their practices revealed three notable findings. First, the factors at the three levels were all found to be significantly related to the different patterns of enacted curriculum. However, the use of quality textbooks and the alignment of teachers' views and instructional goals with curriculum goals were found to be the two factors that are most strongly associated with the enactment pattern of high-level problems and high-level teacher questions in instruction. Furthermore, teachers with the enactment pattern of increasing lower cognitive demand of problems into higher ones tended to rate their curriculum knowledge higher than teachers with the enactment pattern of using low-level problems and teacher questions in their teaching. In particular, deviation from and dissatisfaction with their assigned low-quality textbooks were found to be critical factors that are associated with the enactment pattern of increasing lower cognitive demands of problems in instruction. [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]

We examined the effect of curriculum organization in US high schools where students could freely choose to study mathematics from textbooks that employed one of two types of content organization, an integrated approach or a (traditional) subject-specific approach. The study involved 2,242 high school students, enrolled in either Course 3 or Algebra 2, in 10 schools in 5 geographically dispersed states. Taking account of curriculum implementation and students' prior mathematics learning, we analyzed two end-of-year outcome measures: a test of common objectives and a standardized achievement test. Our hierarchical linear models with three levels showed that students in the integrated curriculum scored significantly higher than those in the subject-specific curriculum on the common objectives test. In both outcome measures, gender and prior achievement were significant student-level predictors. In the standardized achievement test, ethnicity was a moderating factor. At the teacher-level, in addition to curriculum type, teachers' orientation and free and reduced lunch eligibility were significant moderating factors. Opportunity to learn, implementation fidelity, teacher experience, and professional development were not significant predictors. [ABSTRACT FROM AUTHOR]

Educational Standards provide a statement of educational competency goals. How to integrate such goal statements with the instructional core, in ways that promote curricular and instructional coherence and continuity of student learning, is a perennial challenge. In the United States, the Common Core State Standards for Mathematics, or CCSS-M, have been widely adopted, and are claimed to be based on research on learning in general and on learning trajectories in particular. The relationships, however, are tacit and incompletely, and sometimes controversially, articulated. This paper describes a body of work that associates the first nine grades of Standards (K-8) to eighteen learning trajectories and, for each learning trajectory, unpacks, interprets, and fills in the relationships to standards with the goal of bringing the relevant research to teachers (TurnOnCCMath.net). The connections are made using a set of descriptor elements, comprised of conceptual principles, coherent structural links, student strategies, mathematical distinctions or models, and bridging standards. A more detailed description of the learning trajectory for equipartitioning (EQP) shows the detailed research base on student learning that underpins a particular learning trajectory. How curriculum materials for EQP are designed from the learning trajectory completes the analysis, illustrating the rich connections possible among standards, descriptors, an elaborated learning trajectory, and related curricular materials. [ABSTRACT FROM AUTHOR]

The official curriculum for mathematics in Singapore schools is based on a framework that has mathematical problem solving as its primary goal. It is detailed and one may say that the gap between the designated curriculum and teacher intended curriculum is often very narrow. This is so as the main source of instructional materials is textbooks which are very closely aligned with the official national curriculum. There is a dearth of research on the enactment of the curriculum in Singapore schools, with the few research studies done so far appearing to cover only a narrow focus. The author's view is that, even though only a few such studies have been published, schools have always been engaged in small-scale investigations, the findings of which are necessary to guide decisions on matters related to choice of textbooks and pedagogies for improved student learning. Considering all the published research and the investigative work undertaken by educators in Singapore, it may be said that the conceptual model proposed by Remillard and Heck is rigorous. In addition, the issues in this particular issue of ZDM offer educators, both classroom teachers and others, very good perspectives for research on the enactment of the school mathematics curriculum. [ABSTRACT FROM AUTHOR]

This issue of ZDM focuses on research related to the enacted curriculum from various perspectives within the context of the US educational system. In this editorial, we describe the broad view of curriculum enactment taken in this issue, highlighting that we mean more than just how instruction plays out within a classroom. For instance, enactment can occur at a national level as educational goals are enacted into a set of national objectives or standards. Enactment can occur as goals or standards are embedded into written curriculum materials or textbooks, both in terms of teacher guides and materials for students. Enactment can occur as teachers make decisions about how to use their written curriculum materials. Finally, enactment can occur as teachers and students engage and interact with written materials during classroom instruction. We elaborate briefly on these views and then outline the structure of this ZDM issue. [ABSTRACT FROM AUTHOR]

Effective mathematics teachers have a large body of professional knowledge, which is largely undocumented and shared by teachers working in a given country's education system. The volume and cultural nature of this knowledge make it particularly challenging to share curricula and instructional methods between countries. Thus, approaches based on knowledge engineering-designing a software system by interviewing human experts to extract their knowledge and heuristics-are particularly promising for cross-cultural curriculum implementations. Reasoning Mind's Genie 2 system demonstrates the viability of such an approach, bringing elements of Russian mathematics education (known for its effectiveness) to the United States. Genie 2 has been adopted on a large scale, with around 67,000 United States students participating in the 2012-2013 school year. Previously published work (some of it in peer reviewed articles and some in non-peer-reviewed independent evaluations) has associated Genie 2 with high student and teacher acceptance, increases in test scores relative to 'business as usual' conditions, high time on task, and a positive affective profile. Here, we describe for the first time the design, function, and use of the Genie 2 system. Based on this work, we suggest general principles-which collectively represent a proposed methodology-for the design of intelligent tutoring systems intended for cross-cultural transfer of curriculum and instructional methods. [ABSTRACT FROM AUTHOR]

In education, there is a growing interest in the concept of competency especially in vocational training and professional development. The concept is strongly associated with the ability to apply knowledge and skills in effective ways in unanticipated situations. In Sri Lanka, a new competency-based mathematics curriculum was introduced in 2007 for grade 6 and the implementation was completed in 2010 for grade 11 as part of a reform process. The main aim of this implementation was to eliminate previous transmission methods of teaching and to assign a transformational role to the teacher. In this study, I analyzed the suitability of this new curriculum as a competency-based curriculum and examined whether it has achieved its objectives. The results showed that the new curriculum was better in elaborating the subject content and teaching methods. However, in a broader sense, it has not fulfilled its objectives as a competency-based curriculum. The analysis led one to conclude that competency-based teaching and learning approaches were superficially introduced in mathematics education in Sri Lanka. The curriculum documents did not properly reflect their intended objectives. [ABSTRACT FROM AUTHOR]

Insights into teachers’ planning of mathematics reported here were gathered as part of a broader project examining aspects of the implementation of the Australian curriculum in mathematics (and English). In particular, the responses of primary and secondary teachers to a survey of various aspects of decisions that inform their use of curriculum documents and assessment processes to plan their teaching are discussed. Teachers appear to have a clear idea of the overall topic as the focus of their planning, but they are less clear when asked to articulate the important ideas in that topic. While there is considerable diversity in the processes that teachers use for planning and in the ways that assessment information informs that planning, a consistent theme was that teachers make active decisions at all stages in the planning process. Teachers use a variety of assessment data in various ways, but these are not typically data extracted from external assessments. This research has important implications for those responsible for supporting teachers in the transition to the Australian Curriculum: Mathematics. [ABSTRACT FROM AUTHOR]

The present study addresses the impact of the curriculum on primary school children's acquisition of clock-reading knowledge from analog and digital clocks. Focusing on Chinese and Flemish children's clock-reading knowledge, the study is about whether the differences in sequencing of learning and instruction opportunities-as defined by the curriculum-result in differences in accuracy and development of clock-reading knowledge. By means of (1) an in-depth qualitative analysis of the Chinese and Flemish mathematics curriculum standards and textbooks and (2) a quantitative analysis of 11,743 students' accuracy in reading the time, the current study mirrors the differential impact of alternative curriculum designs for primary education. The results of the analyses reveal that Chinese children acquire clock-reading knowledge-for analog and digital clocks-2 years earlier than their Flemish peers, due to a 2-year earlier exposure. Discussing these results, it is argued that the Flemish curriculum tends to underestimate what children are capable of and that clock-reading within the Flemish primary mathematics curriculum builds on dated assumptions and research results. Building on these outcomes, it is argued that curriculum development should be the result of collaborative inquiry involving policy makers, researchers, and teachers. [ABSTRACT FROM AUTHOR]

Research in mathematics education that crosses national boundaries provides new insights into the development and improvement of the teaching and learning of mathematics. In particular, cross-national comparisons lead researchers to more explicit understanding of their own implicit theories about how teachers teach and how children learn mathematics in their local contexts as well as what is going on in school mathematics in other countries. Further, when researchers from multiple countries and regions study collaboratively aspects of teaching and learning of mathematics, the taken-for-granted familiar practices in the classroom can be questioned. Such cross-national comparisons provide opportunities for researchers and educators to probe typical dichotomies such as 'high-performing' versus 'low performing', 'teacher-centred versus student-centred', or even 'East versus West', in searching for similarities and differences in educational policies and practices in different cultural contexts. [ABSTRACT FROM AUTHOR]

The purpose of this study was to explore strategies used by high-achieving 6th grade students in the United Arab Emirates (UAE) to solve basic arithmetic problems involving number sense. The sample for the study consisted of 15 high-achieving boys and 15 high-achieving girls in grade 6 from 2 schools in the Emirate of Abu Dhabi, UAE. Data for the study were collected through individual interviews in which students were presented with 10 basic problems. The results showed that a low percentage of solutions involved aspects of number sense such as appropriate use of benchmarks; using numbers flexibly when mentally computing, estimating, and judging reasonableness of results; understanding relative effect of operations; and decomposing or recomposing numbers to solve problems. It was also found that students were highly dependent on school-taught rules. In many cases, these rules were confused and misused. [ABSTRACT FROM AUTHOR]

Working with Navajo Indian informants in Arizona, USA we became aware of the capabilities of children and adults to find their way in vast and clearly 'chaotic' canyons. One thing we did was describe what people actually did and said about their ways to find the way back home in such contexts. A second one was to use these data in order to build a curriculum book for a bicultural school on the Navajo reservation. We start from this example to ask what the political choices are, which we confront when working with such material: how much mathematics (or is it Mathematics) is needed in daily life? And what mathematics should we promote or develop, without becoming colonialist again? In Section 2, we discuss the meaning and the status of ethnomathematics, proposing that it would be the generic category which allows for a more systematic and comparative study of the whole domain of mathematical practices. In Section 3, we introduce the concept of multimathemacy (after multiliteracy) to discuss the political agenda of ethnomathematics. We argue that multimathemacy should be the basis of the curriculum in order to guarantee optimal survival value for every learner. [ABSTRACT FROM AUTHOR]

Many national and international studies put forward the idea that primary education in Turkey is questionable in many aspects. As a result, the Ministry of National Education changed primary curriculums in 2004 in Turkey. The curriculum for primary mathematics was redeveloped taking into consideration constructivist theory of education. The purpose of this study is to assess the qualities of the 2004 mathematics curriculum using a goal-oriented curriculum evaluation model in which the intrinsic value of the curriculum is examined in terms of its qualities and success depending on teachers’ perspectives, as they are one of the most important elements of the teaching–learning situation. The results show that the qualities of the 2004 mathematics curriculum match the criteria of a constructivist curriculum as set out in the literature. Also, the level of performance expected from the teachers’ perspective as those who instruct in the curriculum is very high. The results point to the fact that the 2004 mathematics curriculum may be considered as a positive change even if there is room for improvement in all aspects. [ABSTRACT FROM AUTHOR]

Computational estimation has not yet established a place in the Kuwaiti national curriculum. An attempt was made to include it during the early 1990s, but it was dropped by the Kuwaiti Ministry of Education because of the difficulties teachers had teaching it. In an effort to provide guidance for reintroducing the concept into the curriculum, this study reports on mathematics teachers’ understanding of the meaning of computational estimation and their views about its significance in the elementary and middle school curricula in Kuwait. Data gathered from 59 elementary and middle schools teachers in Kuwait revealed that more than 60% of teachers equate computational estimation with rounding. While two-thirds of the teachers viewed computational estimation to be an important skill for daily life; only one-fifth (20%) saw it as important in mathematics education. More than half of the teachers either disagreed with the idea of teaching computational estimation or only wanted to teach it in limited situations. Most were concerned about the difficulty of learning computational estimation or feared that teaching computational estimation would cause problems with students’ development of standard algorithms for determining an exact answer. These findings reveal the challenge that mathematics educators face in introducing computational estimation into the mathematics curriculum. In order for computational estimation to be taught in elementary and middle school classrooms, teachers need to understand the concept and its value in education. Teacher education needs to focus on helping teachers better understand the concept of computational estimation and appreciate its value for instruction. [ABSTRACT FROM AUTHOR]

Despite widespread agreement that proof should be central to all students' mathematical experiences, many students demonstrate poor ability with it. The curriculum can play an important role in enhancing students' proof capabilities: teachers' decisions about what to implement in their classrooms, and how to implement it, are mediated through the curriculum materials they use. Yet, little research has focused on how proof is promoted in mathematics curriculum materials and, more specifically, on the guidance that curriculum materials offer to teachers to enact the proof opportunities designed in the curriculum. This paper presents an analytic approach that can be used in the examination of the guidance curriculum materials offer to teachers to implement in their classrooms the proof opportunities designed in the curriculum. Also, it presents findings obtained from application of this approach to an analysis of a popular US reform-based mathematics curriculum. Implications for curriculum design and research are discussed. [ABSTRACT FROM AUTHOR]

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Proof seems to have been losing ground in the secondary mathematics curriculum despite its importance in mathematical theory and practice. The present paper critically examines three specific factors that have lent impetus to the decline of proof in the curriculum: a) The idea that proof need be taught only to those students who intend to pursue post-secondary education, b) the view that deductive proof need no longer be taught because heuristic techniques are more useful than proof in developing skills in reasoning and justification, c) the idea that deductive proof might profitably be abandoned in the classroom in favour of a dynamic visual approach to mathematical justification. The paper concludes that proof should be an essential component in mathematics education at all levels and compatible with both heuristic techniques and dynamic visual approaches. [ABSTRACT FROM AUTHOR]

While there seems to be a general consensus that literacy should include the ability to deal with basic reading, writing, and arithmetic, a view is growing that literacy is in fact more than equipping learners with sets of essential skills (Wells, 1981; Schoenfeld, 1985; Bereiter & Scardamalia, 1987; Cumming, 1990; Wells & Chang-Wells, 1992). Olson (1994) reviews in his book The World on Paper a large number of studies in the field of psychology, sociology, history, and linguistics and concludes that modern literacy in the West is characterized by a new way of looking at written texts and the representation the texts project. In the contemporary East, while many countries including China are striving for economic development and modernization, the question of why science and modernity did not first develop in some oriental cultures such as China, which used to be the most advanced, remains interesting but unanswered. In the light of Olson's discussion regarding literacy and Western modernity, this paper adopts a cognitive-linguistic perspective and examines the social conditions in which ancient Chinese mathematics struggled to develop. Examples and experiences in ancient Chinese mathematical texts are presented to reveal the close relationship between modernity, literacy, and written language. In response to a new interest in a context-rich approach to mathematics teaching, the paper also discusses its implications for the mathematics curriculum. [ABSTRACT FROM AUTHOR]