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Mathematics and Transition to School: International Perspectives

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Abstract

This edited book brings together for the first time an international collection of work focused on two important aspects of any young child’s life – learning mathematics and starting primary or elementary school. The chapters take a variety of perspectives, and integrate these two components in sometimes explicit and sometimes more subtle ways. The key issues and themes explored in this book are: - the mathematical and other strengths that all participants in the transition to school bring to this period of a child’s life; - the opportunities provided by transition to school for young children’s mathematics learning; - the importance of partnerships among adults, and among adults and children, for effective school transitions and mathematics learning and teaching; - the critical impact of expectations on their mathematics learning as children start school; - the importance of providing children with meaningful, challenging and relevant mathematical experiences throughout transition to school; - the entitlement of children and educators to experience assessment and instructional pedagogies that match the strengths of the learners and the teachers; - the importance for the aspirations of children, families, communities, educators and educational organisations to be recognised as legitimate and key determinants of actions, experiences and successes in both transition to school and mathematics learning; and - the belief that young children are powerful mathematics learners who can demonstrate this power as they start school. In each chapter, authors reflect on their work in the area of mathematics and transition to school, place that work within the overall context of research in these fields, predict the trajectory of this work in the future, and consider the implications of the work both theoretically and practically.

Chapters (19)

This edited book brings together for the first time an international collection of work built around two important components of any young child’s life—learning mathematics and starting (primary or elementary) school. The chapters take a variety of perspectives, and integrate these two components in sometimes explicit and sometimes more subtle ways. This chapter provides a theoretical framework for transition to school and investigates possible places for mathematics in that transition. It stresses the importance of considering the strengths of all involved in the transition to school and how these strengths can be used to assist children learn increasingly sophisticated mathematics. The chapter concludes with an analysis of each of the book chapters in terms of their links into the theoretical framework for transition to school and young children’s mathematics learning.
Growing attention to preK mathematics and increased focus on standards in the US may be leading policy makers, administrators, and practitioners down the wrong path when it comes to assessing young children. The temptation to rely on standardised assessment practices may result in misguided understandings about what children actually know about mathematics. As part of a larger study of professional development with teachers focused on culturally and developmentally responsive practices in preK mathematics, we have found that our understanding of children’s mathematical knowledge varies greatly depending on the form (what), context (where), assessor (who), and purpose (why) of assessment. Drawing on findings from three cases, we suggest that in the transition to school, shifting to more a formalised ‘school-type’ assessment is fraught with obstacles that vary greatly by child.
One-to-one interviews have been used extensively in Australia by both researchers and teachers to assess young children’s mathematical understanding. This chapter discusses the use of a one-to-one task based interview developed as part of the Early Numeracy Research Project. The First Year of School Mathematics Interview component has been used in a range of research contexts, both prior to school and in the early years. A recent study, using the interview with children with Down syndrome where the interview was presented in a more flexible manner, raises important questions regarding its use both in research and practice. The opportunities and expectations during the transition to school and how these may be enhanced by the use of one-to-one assessment interviews is also discussed.
Research over the past 10 years has established that many children starting school are more mathematically capable than teachers, mathematics curricula and text book writers assume. This issue and implications arising for children’s transition to school are explored in this chapter through examining data for 125 children who participated in the Australian Let’s Count Longitudinal Evaluation Study in 2012, 1438 children who participated in the Australian Early Numeracy Research Project (ENRP) in 2001, and the new Australian Curriculum—Mathematics. The children’s mathematics knowledge was assessed using the Mathematics Assessment Interview. The findings suggest that large numbers of children in both the Let’s Count preschool group and the ENRP Beginning School group met the new Australian Curriculum—Mathematics Foundation Standard prior to beginning school. This suggests that many children may be inadequately challenged by the mathematics tasks and instruction they experience in their first year of school.
Recent psychological studies as well as research findings in mathematics education highlight the significance of early number skills for the child’s achievement in mathematics at the end of primary school. In this context, the ongoing 3-year longitudinal study discussed in this chapter, investigates the development of early numeracy understanding of 408 children from 1 year prior to school until the end of Grade 1. The study seeks to identify children who struggle with respect to their mathematics learning after the first year of school and compare their achievements with their number concept development 1 year prior to school as well as immediately prior to school entry (Grade 1). Initial findings suggest that children’s understanding and skills with respect to number and counting are important precursors for later school success. The children who were identified as low-achievers in mathematics at the end of Grade 1, also demonstrated less knowledge and skills than their peers prior to school.
Let’s Count is an early mathematics program designed by The Smith Family and researchers from Charles Sturt University and the Australian Catholic University as a means of assisting parents and other family members to help their young children (aged 3–5 years) play with, investigate and learn powerful mathematical ideas. Let’s Count involves early childhood educators in the role of mentors to the parents and family members of the children in their settings, providing assistance in noticing and exploring mathematics in everyday life. In 2011, I was responsible for developing Let’s Count into the form of a distance education subject for offer to students enrolled in an early childhood teacher education degree at Charles Sturt University, as a means of sustaining the Let’s Count initiative and achieving a wider impact on the early childhood community. In this chapter, I report on a project which followed up with former participants in the subject, and the families with whom they have worked, to ascertain the success of the Let’s Count program in bringing together early childhood educators and families to support positive transitions in children’s mathematics education. This chapter explores the ongoing effects of educators’ and families’ engagement with the program, and shares examples of Let’s Count activities in prior-to-school, school, family and community contexts.
Experiences that children have at home can establish a foundation for numeracy learning, and serve as an important transition toward school entry. However, Canadian parents and other caregivers do not often have a good understanding of numeracy learning, they may not be prepared to provide appropriate activities, and some may avoid numeracy activities because of their own negative views of mathematics. Accordingly, when parents and caregivers do focus on academic preparation, they typically emphasise literacy over numeracy activities. In this paper, we describe how children’s home experiences support numeracy learning, in preparation for school. Our research has shown that young children who are involved frequently in numeracy activities in both formal and informal contexts are better prepared for numeracy learning in school than their peers who have fewer numeracy experiences. These results support the view that parents and other caregivers should be encouraged to take an active interest in children’s early learning, and to help children to make appropriate connections between intuitive understandings of numeracy concepts and the formal knowledge that is emphasised in school. Our work has also shown that parents can use their children’s personal interests to foster numeracy knowledge. In this chapter, we summarise our findings, present two extreme cases, and provide recommendations to show how caregivers can be involved in providing stimulating numeracy opportunities for children.
The focus of this chapter is on how teachers respond to children's resources and their mathematical thinking as they transfer from preschool to primary school. The theoretical framework builds on sociocultural theories. The area of investigation is individuals changing their ways of understanding, perceiving, noticing, and thinking as they collaborate with others. Thus, the emphasis is on classroom cultures and learning environments that promote mathematical learning where all children have a voice and are supported to develop their understanding. The methodological approach comprises narrative inquiry and analysis. Through focus group interviews, narratives are gathered from teachers who work with children in preschool and the early primary grades. We learned that what characterises these teachers is their belief that all children can learn mathematics if learning spaces are created that respect the children's resources. The teachers analyse children's mathematical resources and respond to what they bring with them to school as they organise classroom cultures and develop supportive mathematical learning environments. 8.1 Introduction The diversity of pupils in Icelandic schools has increased in the last two decades as pupils with disabilities have entered their neighbourhood schools and immigration has brought in students for whom Icelandic is not their native tongue. These changing social conditions have put increasing pressure on teachers to modify their practices and take into account the diverse group of learners that forms their learning communities. From our earlier research and work as teacher educators, we have learned that many teachers find it challenging to teach mathematics. Their own experience as mathematics learners was typically as passive receivers who practiced rules and procedures, introduced by teachers and textbooks. Teachers lack 119
This chapter considers the relationship between policy and practice in the Early Years Foundation Stage (EYFS) mathematics curriculum in England, with a particular focus on reception-class (RC) children aged 4–5 years. It explores what the policy requires teachers to do in terms of curriculum implementation; what teachers’ views and understanding of the EYFS mathematics curriculum are; and how RC teachers implement EYFS mathematics policy. A case-study design included policy text analysis, interviews with EYFS teachers and observations of EYFS mathematics practice. International comparison studies appeared to have had an important influence on early childhood mathematics policies by creating a top-down pressure for higher standards. Document analysis revealed that despite claims of a reduction and a simplification of early learning goals in the EYFS, in fact the mathematical content had substantially increased. Moreover, the teaching guidance provided to support RC teachers through this change in requirements was wholly inadequate. Tensions in policy text were reflected in mixed and ambivalent views and practices. Whilst RC teachers applauded the principle of a play-based pedagogy in the EYFS, the mathematical content required was regarded as complex and confusing and, in some cases, planned by colleagues teaching the national curriculum to 6–7 year-olds. Observation revealed predominantly child-initiated small-group work with little mathematics in nursery classes for 2–3 year-olds. By 3–4 years, a growing emphasis on large-group work for literacy and numeracy was apparent and by 4–5 years, children were receiving a structured daily mathematics lesson reminiscent of the old National Numeracy Strategy. Hence, teachers brought their own values, experience and understandings to practice. The study revealed the interplay of global influences of educational comparison and national fear of falling standards, with RC teachers and young children caught in a nexus of forces.
Transitions in the early years have substantial effects on children's success in school. Moreover, lack of consideration of continuity and alignment may mislead both researchers and politicians to assume preschool effects ' fade ', when it may be that poor transitions to primary school are to blame. We hypothesise that most present educational contexts are unintentionally and perversely aligned against early interventions. For example, primary curricula assume little mathematical competence, so only low-level skills are taught. Most teachers are required to follow such curricula rigidly and remain unaware that some of their students have already mastered the material they are about to ' teach '. Teachers may be held accountable for getting the largest number of students to pass minimal competency assessments, engendering the belief that higher performing students are 'doing fme'. In this way, we believe the present U.S. educational system unintentionally but insidiously re-opens the gap berween students from low- and higher-resource communities. We conducted a large cluster randomised trial of an intervention that evaluated the persistence of effects of a research-based model for scaling up educational interventions, with one control and rwo intervention conditions. Only the intervention condition that included a follow-through treatment to suppon the transition to the primary grades maintained substantial gains of the pre-K mathematics curriculum.
In this chapter we share the perceptions of a small number of principals, teachers and parents about children’s prior-to-school mathematics. Rather than focusing on the somewhat limited notions of young children’s mathematical experiences reflected in some of the comments of these adults, we position the transition to school as a relational context, recognising it as a time when many and varied beliefs, expectations and understandings come together as a cultural interface. We advocate that working collaboratively at this time has the potential to enhance the experiences of young children and the adults with whom they interact, and to provoke both professional and personal reflection and change, particularly in relation to mathematics education.
This chapter elaborates findings from a longitudinal ongoing cross-cultural study comparing the teacher education and classroom practices in Finland and Sweden. The focus is on the cultural scripts of mathematics instruction during the first school years (ages 6–8). Firstly, we present a description of the contexts of each country concerning primary teacher education and the transition from preschool to school. We then characterise the dominating conceptualisations of the mathematics classroom practices for the early years in both countries, building on several analyses of different data sources. We focus especially on the intricate balance between flexibly building mathematics on pupils’ ideas of familiar everyday phenomena within a thematic teaching style on the one hand, and on the other, the organisation of learning environments strictly based on a predetermined hypothetical learning trajectory. Finally, we discuss our findings in light of the international literature on early mathematics education and transition from preschool to school.
This chapter will discuss the New Zealand [NZ] approach to mathematics in early childhood settings with a particular emphasis on the foundational mathematics that infants and toddlers gain through play. It will describe ways that children’s mathematical knowledge is developed through and with others as they move toward formal schooling. Early years curriculum in NZ encompasses both prior-to school (early childhood) and school education. Early childhood education serves children in education and care services from birth to school entry at (approximately) 5 years of age and is underpinned by Te Whariki, the NZ framework for early childhood. The formal (school) sector is, similarly underpinned by The NZ Curriculum Framework. These two documents are both grounded in constructivist, socio-cultural theory and provide the basis for a seamless transition from EC to school. Mathematics education in NZ has a particular emphasis on the development of numeracy (number knowledge and understandings) through progressions laid out in national frameworks. This emphasis has established the need for early childhood programmes to ensure that very young children are given opportunities to explore foundational mathematics in a variety of ways. However, the challenge for NZ early childhood teachers is twofold: to provide a play-based mathematics curriculum that builds on children’s interests and provides for seamless, child-centred transitions, and to align the informal learning of EC with the more formal requirements of established mathematical transitions.
This chapter describes a 3-year early numeracy project conducted with 15 Australian Aboriginal Community Children’s Services across the state of New South Wales and the Australian Capital Territory. The project involved 66 early childhood educators and 255 children aged 4–5 years in the year prior to formal school. The children were engaged in a preschool Patterns and Early Algebra program previously developed and trialed with young children. Following an interview-based assessment, the Early Mathematical Patterning Assessment (EMPA), educators implemented a 12 week intensive program based on early patterning frameworks that developed young children’s early algebraic and mathematical reasoning, communication and problem-solving skills. Data from children’s progression on the frameworks and interview data from primary school teachers in the year following implementation, provided evidence of the impact of the program not only on children’s mathematics learning but on their transition to school.
The Chinese number system is believed to aid Chinese children in learning mathematics, which may help to explain the differences in mathematics performance between English-speaking and Chinese-speaking children. This chapter discusses Hong Kong Chinese preschool children’s mathematics learning and pre-primary and primary transition from the perspective of language and culture. Hong Kong preschool children have been found to perform better in mathematics compared with their English-speaking peers. Although the Chinese number naming system helps to explain the children’s better performance in learning individual mathematics concepts, this is insufficient in itself to account for the children’s performance. Other factors, such as classroom instruction and cultural beliefs about mathematics learning, may also have an important influence on children’s mathematics performance. Further studies involving teachers have shown that there is top-down pressure for Hong Kong preschools to adopt an academically focused curriculum. The Chinese cultural aspiration for academic success and the quest for a smooth pre-primary and primary transition have led to the use of the traditional drill-and-practice approach for teaching particular advanced mathematics concepts in Hong Kong preschools. The implications of this for early childhood mathematics teaching are discussed.
In recent years, many concepts for early mathematics education have been developed. Taking a closer look at these concepts, it can be seen that they differ considerably in pedagogical background and in quality. During the transition from kindergarten to school, it is extremely important to guarantee consistency and continuity in mathematical learning processes. Therefore, all efforts of early mathematics education should be mathematically correct, ‘intellectually honest’ and ensure that children acquire the essential prerequisites for further mathemati-cal learning. Additionally, mathematical learning should be designed according to children’s specific age. Based on scientific findings, this chapter specifies why early mathematics education in natural learning situations, like play activities, meets these requirements of subject- and child-orientation. Play situations can fos-ter the development of mathematical learning in kindergarten and in school sus-tainably. Results of an intervention study about learning mathematics while play-ing traditional board games (N=95, average age: 4.8 years, control and intervention group) confirm this assumption. The intervention shows significant effects. Video analyses of the play situations illustrate the findings and allow in-vestigating in detail the role of the teachers and the mathematical learning pro-cesses which occurred during the play activities.
The interactions young children have with adults are of great importance in developing children’s mathematical reasoning. The one-to-one mathematical conversations and interactions young children have with their teachers are memorable to children. In their 1st year at school, children can recall their conversations with the teacher, reconstruct their thinking, and reflect on their learning. Children construct mathematical ideas in the course of their interactions with their teacher and classmates. Interactions in whole class settings have been studied. However, not as much has been written about the interactions between teacher and child in one-to-one conversations during the mathematics lessons of young children. This chapter examines the nature of teacher-child mathematical conversations and how they evolve as children move to the generally more formal setting of school. Interactions that challenge children to think mathematically in their transition year to school illustrate the central characteristics of questioning, listening, and thinking. The mathematical pedagogical behaviours that support and facilitate these interactions are noted.
Internationally, mathematising is now a key focus in mathematics education for children aged 3–8 years (Perry and Dockett, Handbook of International Research in Mathematics Education, 2008; National Research Council (NRC), Mathematics Learning in Early Childhood: Paths Towards Excellence and Equity, 2009). For young children mathematising involves going back and forth between abstract mathematics and real situations in the world around them (NRC, Mathematics Learning in Early Childhood: Paths Towards Excellence and Equity, 2009). It helps children to make sense of mathematics by connecting it to their everyday lives. While mathematical thinking processes associated with mathematising begin in early childhood (Paley, Molly is Three: Growing Up in School, 1986; Tizard and Hughes, Young Children Learning, 2002), educators may not always recognise and promote children’s engagement with these processes (Dunphy, International Journal of Early Years Education, 17(1), 3–16, 2009). In this chapter I present examples of children involved in mathematising. The discussion addresses issues that arise in supporting mathematisation during the transition to school, as well as directions for future research.
England’s Foundation Stage (birth to five) encourages children’s interests to be central in developing the curriculum. As children enter school, in the last year of this stage, political and organisational pressures take over forcing teachers to have uneasy pedagogies. From a postructural stance the ‘schoolification’ of the child begins and there is a great divide between the mathematics of the child and that of the school. The literature on transitions exposes curricula dissonance not only in England but across Europe, Australasia and North America. Dialogues from teachers highlight their confusion about how and when to teach calculation and especially mathematical notation. Mathematics becomes more teacher centred with strict objectives. The data from England’s National Assessments continue to show poor achievement in mathematical problem solving in the Foundation Stage. There needs to be a conceptual shift in the teaching of mathematics to young children in English schools to encompass children’s enquiries. This is from a Vygotskian perspective where there is priority given to social and cultural practices stressing the importance of co-participation. This could identify and enhance children’s mathematical problem solving. There is, however, much challenge for teachers not only in understanding children’s own mathematics that involves children’s agency but at the same time they need to confront the organisational walls of opposition.
... An important episode in the mathematical development of children is the transition from informal to formal mathematics (Ginsburg et al. 1998;Gueudet et al. 2016;Perry et al. 2015). Already before the start of formal schooling, children develop a basic understanding of number, counting, and arithmetic (Baroody 1987;Ginsburg 1977;Verschaffel et al. 2017). ...
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The transition from informal to formal mathematics is an important episode in children’s mathematical development. The current study investigated how young children’s computational estimation performance and strategy use develops in this transitional period. The computational estimation performance of 350 children was assessed before the start of formal schooling (i.e., third grade of kindergarten) and again after the start of formal schooling (i.e., first grade of primary school) by means of a computational estimation addition task with manipulatives. Both children’s answer construction and their counting behavior while constructing the answer were observed during task administration. Results showed an age-related increase in children’s estimation accuracy as well as in their proportion of exact answers. Age-related changes in strategy use were also observed. Children demonstrated an increase in their counting behavior while constructing the answer, but no changes in the way the answer was constructed. In both grades, the answer was most often constructed by laying down all manipulatives immediately in one group. These results suggested that children can follow two pathways to solve the estimation problems: (1) relying on the visual representation of the addends without using counting and (2) using the verbal labels provided by the experimenters while using counting. More use of counting in first grade positively influenced children’s estimation accuracy in this grade, suggesting that these children strive for more precision compared to children who do not count.
... We have noted previously that it prompts attention to the relationships and interactions associated with starting school, the characteristics and resources each individual (be they a child, family member, or educator) brings with them to the transition, recognition of the various systems or contexts in which children and families are located, as well as attention to specific events, patterns of interactions and historical context. (Dockett, Petriwskyj, and Perry 2014, 4) Mathematics education plays a role in effective transition to school (Perry, MacDonald, and Gervasoni 2015). In the remainder of this paper, we focus on one preschool mathematics education initiative and the ways in which the PPCT model has provided the theoretical and analytical framework for the initiative. ...
... We have noted previously that it prompts attention to the relationships and interactions associated with starting school, the characteristics and resources each individual (be they a child, family member, or educator) brings with them to the transition, recognition of the various systems or contexts in which children and families are located, as well as attention to specific events, patterns of interactions and historical context. (Dockett, Petriwskyj, and Perry 2014, 4) Mathematics education plays a role in effective transition to school (Perry, MacDonald, and Gervasoni 2015). In the remainder of this paper, we focus on one preschool mathematics education initiative and the ways in which the PPCT model has provided the theoretical and analytical framework for the initiative. ...
Article
Over the last 20 years, the authors have utilised Bronfenbrenner’s ecological and bioecological models as a basis for their work investigating children’s transition to school, including the place of mathematics learning in this transition. The later bioecological model gave increased emphasis to the role of the individual within contexts, the processes that characterised interactions within and across contexts (proximal processes), and the influence of time. This bioecological model outlined four elements – person, process, context and time – which, together, were described as influencing the development of individuals. While the mathematical learning of young children influences, and is influenced by, all four elements of the model, the critical role of proximal processes in this learning is highlighted in this paper. Our aim is to identify how the four elements of the bioecological model, particularly proximal processes, provide a framework to analyse the experiences of the adults – early childhood educators and parents – involved in an early childhood mathematics education intervention designed to promote engagement with mathematics in playful situations. Data are drawn from 35 early childhood educators and 37 parents over 2 consecutive years (2013, 2014) with generally different participants in each year.
... Researchers around the world recognize the importance of the early home environment as a critical starting point for numeracy development (Perry, Macdonald, & Gervasoni, 2015 ). Children who start school without foundational numeracy knowledge, presumably because of varied early learning circumstances, have diffi culty gaining that knowledge and consistently lag behind their peers . ...
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Children’s environments contain a diverse array of actions, objects, events, and conditions that have the potential to influence the development of math skills. The focus of this chapter is on the HOME Inventory and what research using the HOME reveals about relations between children’s home environments and their competence in mathematics. Studies show that socioemotional and structural features of the home are associated with math competence just as are access to learning materials and efforts on the part of parents to provide enriching experiences. Provision of stimulation during the second and third years of life shows a stronger relation to math than does stimulation during early infancy. It also appears that some of the relations are indirect via language and cognitive processing skills. Although research is limited, research using the HOME suggests that the broad affordances of the home environment matter as regards the early development of math competence.
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This chapter presents a critical review and celebration of the most significant Australasian early childhoodEarly childhood mathematics education research that has been published over the period 2016–2019. We utilise the internationally-accepted definition of ‘early childhood’Early childhood as the age range birth to eight years, encompassing prior to school settings, school settings, as well as home and community contextsContext. Eminent scholars in the field have undertaken the research presented in this chapter in conjunction with a range of stakeholders in early childhoodEarly childhood mathematics education, including teachers, families and children. This chapter is structured according to six key themes which emerged from the preliminary analysis and categorisation of the current research across the Australasian region; namely: Mathematics contentMathematics content; CurriculumCurriculum, policyPolicy and assessmentAssessment; Aspects of teaching and learning; Home and prior to schoolHome and prior to school contextcontextsContext; Australian and New Zealand IndigenousIndigenous education; and Emerging areas of researchEmerging areas of research. Indeed, this review highlights several very promising new areas of research, for example: mathematics education for children aged birth to two years; and innovative researchMethodologymethodologiesInnovative research methodologies such as ‘camera glasses’ and ‘trolley cams’ utilised in everyday contextContext. The new areas discussed in this chapter highlight the growing interestInterest in, and opportunities for, research in the early yearsEarly years space. However, with the emergence of new areas of research there has been a decline in other areas such as pattern and algebra, geometry, and length measurement. From the synthesis of the research literature the following findings are evident. First, young children are often capable of mathematical thinking from a very early age, which suggests a mismatch between the intended curriculumCurriculum and children’s capabilities when they start school. Second, the current education policiesPolicy within Australia and New Zealand have yet to bridge the mathematical transitionTransitions from early childhoodEarly childhood settings to school. Third, the contrast between a holistic appreciation of the mathematics surrounding children in prior to school settings is in stark contrast to school settings where mathematics is formalised and segmented and less richly experiential. The chapter concludes with a discussion of recommendations for future research in this field.
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Increasingly, education systems around the world are implementing national curriculum frameworks for early childhood education settings. However, the disciplines of science, technology, engineering, and mathematics are not always explicitly articulated in such frameworks, and consequently, the potential for STEM learning within these frameworks is not always well understood. In this chapter, we offer a counter argument to the “typical” justification of STEM education that it is in nations’ interest to develop a STEM literate workforce in order to be economically competitive on a global level. Instead, we highlight a child-rights perspective for STEM education in the early years, elucidating the potential access to STEM education afforded through national early childhood curriculum frameworks. This chapter interrogates the national early childhood curriculum frameworks of Australia, New Zealand, and Sweden in order to demonstrate how STEM can be made visible in such frameworks.
Article
There is growing international research evidence about young children’s engagement with mathematics education. However, much of this evidence is drawn from children aged four years and upwards. This paper reports findings from a systematic review of peer-reviewed research concerning mathematics education for children aged under four. The majority of the studies took place within an early childhood education service such as a preschool or day care centre, and task-based interviews and standardised assessments were most commonly used. Most of the papers focused on either educators’ knowledge, attitudes and strategies, or children’s mathematical competencies. The literature presents compelling evidence that children do engage in mathematics education prior to four years of age, and that they possess many mathematical competencies. Findings suggest that educators play a critical role in shaping the mathematical learning opportunities available to children; however, there is some uncertainty among educators about how to support young children’s mathematics learning.
Article
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).
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The study aims to explore the specificity of Mathematics pedagogical content knowledge in Early Childhood Education Pedagogy in Initial Teacher Education. It addresses the issue by characterizing student teachers’ perspectives and by analyzing student teachers’ knowledge mobilized in a situation of planning for teaching. The answers to a task developed by students in an Initial Teacher Education program are analyzed in terms of the mathematical knowledge and pedagogical options presented. The results contribute to the discussion in terms of (un)balance between teacher-initiated and child-led activities. The discussion deepens the importance to assert specific/particular ways of teaching in Early Childhood Education, contrasting with the more restricted view of only adult-led moments being teaching. Strong content knowledge and pedagogical content knowledge are valued because of their relevance both at the level of adults’ knowledge needed to support children initiatives and plan curricular/didactic activities and at the level of the knowledge children interact within their daily environment and routine.
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This study aimed at analyzing the development of Ecuadorian children’s early numerical abilities during the Kindergarten year in relation to their SES, the quality of their early mathematics education, and the attended school type. 179 Ecuadorian Kindergartners (18 classrooms, 6 classrooms per school type) were offered a standards-based early numeracy test at both the start and the end of the Kindergarten year. In all classrooms, the quality of early mathematics education was assessed twice via the COEMET instrument. Results first showed rather low scores on the early numeracy test, with only 50% (at the start) up to 70% (at the end) of the items solved correctly, along with large inter-individual differences in these scores. Second, the quality of early mathematics education in the participating classrooms was also rather low. Third, children’s early numerical abilities at Kindergarten entry, SES, and school type predicted children’s early numerical abilities at the end of the school year. The quality of early mathematics education did not contribute to children’s numerical development. We critically discuss our findings in view of optimizing the quality of Ecuadorian early mathematics education as a stepping stone towards enhanced numerical development.
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This edited book brings together an international collection of work on a consistent and growing focus in mathematics education: the need to forge connections in early mathematics learning. Each chapter examines diverse ways that connections can be made, philosophically, theoretically, and pedagogically, illustrating different perspectives and providing provocations for researchers and educators. This chapter introduces themes of connection found in mathematics education and interdisciplinary literature and considers the purpose and value of connection in mathematics learning, specifically for children from birth to eight years. An overview of each of the book chapters and their connections mathematics is also provided.
Article
It is widely believed that teachers' knowledge of students' thinking has a significant impact on teachers' teaching and students' learning. However, there is far less research on how teachers acquire their knowledge of students' thinking before, during, and after lessons. This study is designed to compare the differences between expert and nonexpert mathematics teachers on their behaviors and perceptions related to understanding students' mathematical thinking. Based on 554 Chinese elementary mathematics teachers' responses to a survey, the study found that teachers took actions to understand students' thinking more often when students were learning new topics or encountering difficulties, and they were more likely to do so before lessons than during or after lessons. The comparison revealed that significantly more expert elementary mathematics teachers attempted to understand students' thinking from a variety of perspectives before making the necessary adjustments to their predetermined teaching plans than did nonexpert teachers. Significantly more expert teachers also relied on their own teaching experiences to understand students' thinking. In contrast, significantly more nonexpert teachers claimed that they did not rely on prior teaching experiences because they "did not know how to".
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There has been a great deal written recently about children starting school, particularly primary school. All of the stakeholders in these transitions to school have been considered, along with matters of readiness – for the child, family, educators, schools and communities; adjustment and adaptation; continuity and change in curricula and learning; and the opportunities, aspirations, expectations and entitlements encompassed in the transformation of roles involved. As the children move from their prior-to-school experiences – preschool, child care, home, other out-of-home care – to school, they experience many changes. One of these is often a change from a primarily play-based pedagogical approach in the prior-to-school setting to perhaps a more structured, even formal pedagogy in school. But what about the pedagogies of the transitions themselves? Children do not stop learning and teachers do not stop teaching as children are in the process of transition to school. There are pedagogies of transition employed. This book explores these pedagogies through the work of an international alliance of transitions to school researchers from five countries – Iceland, Scotland and Sweden (European) and Australia and New Zealand (Antipodean). This alliance is named Pedagogies of Educational Transitions – POET.
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Many children in the USA and Canada have access to a wide range of experiences that can support their early numeracy development. Nevertheless, children’s early numeracy knowledge varies considerably in these countries as a function of parents’ education, socioeconomic conditions, parents’ attitudes, beliefs, knowledge about mathematics, and preschool and school educators’ knowledge and experience. In this chapter we provide a selective overview of some of the factors that are related to children’s early numeracy experiences and suggest contexts and circumstances that may facilitate or hinder children’s learning. Parents’ provision of formal and informal opportunities that allow their children to experience number, space, and related concepts and their willingness to engage in meaningful activities may all influence the quality of children’s early experiences. We conclude with suggestions for further research to explore ways in which adults can enhance the home numeracy environments of preschool children.
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This book examines the kinds of transitions that have been studied in mathematics education research. It defines transition as a process of change, and describes learning in an educational context as a transition process. The book focuses on research in the area of mathematics education, and starts out with a literature review, describing the epistemological, cognitive, institutional and sociocultural perspectives on transition. It then looks at the research questions posed in the studies and their link with transition, and examines the theoretical approaches and methods used. It explores whether the research conducted has led to the identification of continuous processes, successive steps, or discontinuities. It answers the question of whether there are difficulties attached to the discontinuities identified, and if so, whether the research proposes means to reduce the gap – to create a transition. The book concludes with directions for future research on transitions in mathematics education.
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Chapter
In this introductory chapter our aim is to set the scene for the following four chapters and situate them within the broad picture of mathematics education research concerning transitions. What kinds of transitions have been considered by mathematics education research? What research questions were studied and which theoretical approaches and associated methods were used? Did the studies lead to the identification of continuous processes, successive steps, or discontinuities? Are difficulties attached to the discontinuities identified, and does the research propose means to reduce those difficulties in order to foster a transition? These are the questions we study in this short literature review.
Chapter
This chapter presents a synthesis of the Australasian early childhood mathematics education research which has been conducted during the review period 2012–2015. “Early childhood education” is taken to be the education of, and for, children aged between birth and 8 years old. The research canvassed in this chapter encompasses a range of early childhood contexts, including home, school, and early childhood education services. Similarly, the research presented in this chapter has been undertaken with a range of stakeholders in early childhood mathematics education, including early childhood and school educators, families, and the children themselves. Consistent with previous reviews, this chapter is structured according to four key themes which have emerged in canvassing the current research: curriculum in early childhood mathematics education; assessment in early childhood mathematics education; content of early childhood mathematics education; and contexts for early childhood mathematics education. This synthesis of research is then used to provide recommendations for future research in this field.
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Book
This book examines the kinds of transitions that have been studied in mathematics education research. It defines transition as a process of change, and describes learning in an educational context as a transition process. The book focuses on research in the area of mathematics education, and starts out with a literature review, describing the epistemological, cognitive, institutional and sociocultural perspectives on transition. It then looks at the research questions posed in the studies and their link with transition, and examines the theoretical approaches and methods used. It explores whether the research conducted has led to the identification of continuous processes, successive steps, or discontinuities. It answers the question of whether there are difficulties attached to the discontinuities identified, and if so, whether the research proposes means to reduce the gap – to create a transition. The book concludes with directions for future research on transitions in mathematics education.
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