9
Conclusions and Recommendations

Over the past several decades there has been an increased focus on the importance of the preschool period—between ages 3 and 5—in providing children with the opportunities they need to get off to a successful start in formal schooling. Many policy makers are now intent on implementing universal public preschool because of the mounting evidence that high-quality preschool can help ameliorate inequities in educational opportunity and begin to address achievement gaps. The importance of supporting literacy in these early childhood settings is widely accepted, but little attention is given to mathematics. However, research on children’s capacity to learn mathematics, when combined with evidence that early success in mathematics is linked to later success in both mathematics and reading, makes it clear that basic literacy consists of both reading and mathematics. Improvements in early childhood mathematics education can provide young children with the foundational educational resources that are critical for school success. Furthermore, the increasing importance of science and technology in everyday life and for success in many careers highlights the need for a strong foundation in mathematics.

Historically, mathematics has been viewed by many as unimportant to or developmentally inappropriate for young children’s learning experiences. However, the research synthesized in this report makes it clear that these beliefs are unfounded. In the course of normal development, young children develop key mathematical ideas and skills that include counting; adding and subtracting; finding which is more (or less); working with shapes by moving, combining, and comparing them to learn some of their properties; experiencing and labeling spatial terms (e.g., above, below);



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9 Conclusions and Recommendations Over the past several decades there has been an increased focus on the importance of the preschool period—between ages 3 and 5—in providing children with the opportunities they need to get off to a successful start in formal schooling. Many policy makers are now intent on implementing universal public preschool because of the mounting evidence that high-qual- ity preschool can help ameliorate inequities in educational opportunity and begin to address achievement gaps. The importance of supporting literacy in these early childhood settings is widely accepted, but little attention is given to mathematics. However, research on children’s capacity to learn mathematics, when combined with evidence that early success in mathemat- ics is linked to later success in both mathematics and reading, makes it clear that basic literacy consists of both reading and mathematics. Improvements in early childhood mathematics education can provide young children with the foundational educational resources that are critical for school success. Furthermore, the increasing importance of science and technology in ev- eryday life and for success in many careers highlights the need for a strong foundation in mathematics. Historically, mathematics has been viewed by many as unimportant to or developmentally inappropriate for young children’s learning experi- ences. However, the research synthesized in this report makes it clear that these beliefs are unfounded. In the course of normal development, young children develop key mathematical ideas and skills that include counting; adding and subtracting; finding which is more (or less); working with shapes by moving, combining, and comparing them to learn some of their properties; experiencing and labeling spatial terms (e.g., above, below); 1

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2 MATHEMATICS LEARNING IN EARLY CHILDHOOD and understanding length measurement as the number of length units that makes the total; as well as representing and communicating mathematics understanding to others. Relying on a comprehensive review of the research, this report lays out the critical areas that should be the focus of young children’s early mathematics education, explores the extent to which they are currently in- corporated into early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. The committee describes these critical areas of mathematics in terms of teaching- learning paths that can be used to promote optimal learning. Such a path describes the skills and knowledge that are foundational to later learning and lays out a likely sequence of the steps toward greater competence. One can look closely along the path to gauge what children will be able to do next and to design instructional activities that will help them move along the path. The notion of such teaching-learning paths is a framing assump- tion for the conclusions and recommendations of this report. To ensure that all children enter elementary school with the mathemati- cal foundation they need for success, the committee recommends a major national initiative in early childhood mathematics. The success of such an initiative requires that parents, early childhood teachers, policy makers, and communities reconceptualize the way they think about and understand young children’s mathematics. The early childhood education system (e.g., workforce, early childhood programs, and policies) will need to work co- herently together toward this goal. Furthermore, families and communities must also adopt this goal if they are serious about improving children’s mathematics education. In this chapter, the committee summarizes the major conclusions of the report organized around the chapters, articulates the key recommenda- tions that flow from these conclusions, and lays out an agenda for future research. CHILDREN’S COMPETENCE AND POTENTIAL TO LEARN MATHEMATICS The committee’s review of developmental research with infants and toddlers demonstrates that the knowledge and competencies relevant to mathematics are present from early in life. As early as infancy, babies are curious about their world and are able to think about it in mathematical ways. Preverbal number knowledge is shared by humans from diverse cul- tural backgrounds as well as by other species. For example, by 10 months of age, young infants can distinguish a set of two items from a set of three items, and over time they are able to distinguish the number of items in sets with larger numbers. Building on this foundation, young children continue

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 CONCLUSIONS AND RECOMMENDATIONS to expand their knowledge and competence and enjoy their early informal experiences with mathematics, such as spontaneously counting toys, excit- edly asking who has more, or pointing out shapes. Conclusion 1: Young children have the capacity and interest to learn meaningful mathematics. Learning such mathematics enriches their current intellectual and social experiences and lays the foundation for later learning. Knowledge and competencies acquired through everyday experiences provide a starting point for mathematics learning. Infants’ and toddlers’ natural curiosity initially sparks their interest in understanding the world from a mathematical perspective, and the adults and communities that educate and care for them also provide experiences that serve as the basis for further mathematics learning. Children’s everyday environments are rich with mathematics learning opportunities, for example, using relational words, such as more than/less than, and counting and sorting objects by shape or size. These foundational, everyday mathematics experiences can be built on to move children further along in their understanding of math- ematical concepts. Conclusion 2: Children learn mathematics, in part, through everyday experiences in the home and the larger environment beginning in the first year of life. Children need rich mathematical interactions and guidance, both at home and school to be well prepared for the challenges they will meet in formal schooling. Parents, other caregivers, and teachers can play a fundamental role in the organization of learning experiences that support mathematics because they can expose children to mathematically rich envi- ronments and engage them in mathematics activities. For example, parents and caregivers can teach children to see and name small quantities, count, and point out shapes in the world, “Here are two crackers. You have one in each hand. These crackers are square.” One important way that young children’s mathematics learning can be enhanced is through adult support and instruction that is connected to and extends their preexisting mathematics knowledge. For example, a situa- tion in which a young child insists on having “more” teddy bears than his playmate provides an opportunity for the adult to engage the child with a mathematical question (e.g., who has more and how can you find out?). In this instance, the adult can use several key mathematical ideas to help the child understand who has more bears, such as using the number word list to count, 1-to-1 counting correspondence, cardinality (i.e., knowing the total

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 MATHEMATICS LEARNING IN EARLY CHILDHOOD number of items in the set), and comparing the number of bears in the two sets. These kinds of mathematics learning opportunities help children learn to mathematize or engage in processes that involve focusing on the math- ematical aspects of an everyday situation, learn to represent and elaborate a model of the situation, and use that model to solve problems. Conclusion 3: Children need adult support and instruction to build and extend their early knowledge and learn to focus on and elaborate the mathematical aspects of everyday situations—to mathematize. The committee was keenly aware of the influence that developmental and contextual variations have on children’s learning opportunities and the quality of their educational environments both inside and outside the class- room. Understanding individual differences in children’s development—for example, in executive function or in opportunities to learn about math- ematics in their everyday environments—is fundamental to supporting the development of competence in mathematics. Although all children need extensive exposure to mathematics, there is a wide range of individual variation across all domains of learning. This affects the kinds of learning experiences and instruction that individual children need. The need to sup- port early childhood mathematics education in ways that are appropriate for diverse learners and contexts is a theme throughout the committee’s discussion of early childhood mathematics. Conclusion 4: Due to individual variation, which is related to a com- bination of previous experiences, opportunities to learn, and innate ability, some children need more extensive support in mathematics than others. It is important to understand the sources of observed differences in children’s competence and not confuse one source of individual variation for another. For example, low performance might be attributed to a deficit in a child’s ability to learn mathematics, when it actually results from other factors, such as that child’s lack of opportunities to learn mathematics or difficulties stemming from linguistic and cultural barriers between teacher and child. Opportunities to explore the mathematics of everyday life differ de- pending on children’s background, including their socioeconomic status (SES) and cultural group. Mathematics knowledge and skills vary within and between cultural groups due to a variety of factors, including language and relative emphasis placed on mathematics. Cultural, linguistic, and socioeconomic factors interact in complex ways that are difficult to tease apart.

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5 CONCLUSIONS AND RECOMMENDATIONS The committee was particularly concerned about mathematics teaching and learning for children from low socioeconomic backgrounds because of the particular challenges they face that can have an impact on their knowl- edge and competence in mathematics. For example, they may be more likely to attend schools with fewer resources and have less support for mathemat- ics at home. Thus, although children with very low and high mathematics knowledge and competence are found across all SES groups, those with low SES will need particular attention. Importantly, providing young children with high-quality mathematics instruction can help to ameliorate systematic inequities in educational outcomes and later career opportunities. Conclusion 5: Young children in lower socioeconomic groups enter school, on average, with less mathematics knowledge and skill than their higher socioeconomic status peers. Formal schooling has not been successful in closing this gap for low socioeconomic status children. In addition to needing instructional support in mathematics, evidence indicates that young children also need to be supported in their social- emotional development as an integral part of their education. Specifically, during the early education years, children develop general competencies and approaches to learning that include their capacity to regulate their emotions and behavior, to focus their attention, and to communicate effectively with others. In turn, mathematics learning can help to promote the development of these general competencies. Conclusion 6: All learning, including learning mathematics, is facili- tated when young children also are developing skills to regulate their own learning, which includes regulating emotions and behavior, focus- ing their attention, and communicating effectively with others. FOUNDATIONAL AND ACHIEVABLE MATHEMATICS FOR YOUNG CHILDREN On the basis of research evidence about children’s knowledge and competence during the early childhood years, as well as on the established consensus of the early childhood mathematics community (see, for example, the NCTM Curriculum Focal Points), the committee identified two areas of mathematics on which to focus: (1) number, including whole number, operations, and relations, and (2) geometry, spatial thinking, and mea- surement. In each of these areas, the committee offers guidance about the teaching-learning paths based on what is known from developmental and classroom-based research. Each child’s progression along these mathematics teaching-learning paths is a function of his or her own level of develop-

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6 MATHEMATICS LEARNING IN EARLY CHILDHOOD ment as well as opportunities and experiences, including instruction. The teaching-learning paths can provide the basis for curriculum and can be used by teachers to assess where each child is along the path. Although it is true that young children are more competent in math- ematics than many early childhood teachers, parents, and the general public believe, there are limits to what they can do in mathematics. The committee kept this in mind throughout the study process, and thus the teaching-learning paths presented in this report are both foundational and achievable. The first content area is number, including whole number, operations, and relations. Working with number (e.g., learning to count) is the primary goal of many early childhood programs; however, when given the oppor- tunity, children are capable of demonstrating competence in more sophis- ticated mathematics activities related to whole number, operations, and relations. For example, cardinality—knowing how many are in a set—is a key part of children’s number learning. Relations and operations are extensions of understanding number. The relations core consists of such skills as constructing the relations more than, less than, and equal to. The operations core includes addition and subtraction. The second major content area is geometry, spatial thinking, and mea- surement. Children’s foundational mathematics involves geometry or learn- ing about space and shapes in two and three dimensions (e.g., learning to recognize shapes in many different orientations, sizes, and shapes). A fun- damental understanding of shape begins with experiences in which children are shown varied examples and nonexamples and understand attributes of shapes that are mathematically relevant as well as those (e.g., orientation, size) that are not. As children progress along the teaching-learning path, they need opportunities to discuss and describe shapes, and, on the basis of these experiences, they gain abilities to combine shapes into pictures and eventually learn to take apart and put together shapes to create new shapes. Young children also need instructional activities involving spatial orienta- tion and spatial visualization. For example, they can use mental representa- tions of their environment and, on the basis of the representation, model relationships between objects in their environment. Importantly, children’s knowledge of measurement helps them connect number and geometry be- cause measurement involves covering space and quantifying this coverage. Later, children can compare lengths by measuring objects with manipulable units, such as centimeter cubes. Number is particularly important to later success in school mathemat- ics, as number and related concepts make up the majority of mathemat- ics content covered in later grades. However, it is important to point out that concepts related to number (and relations and operations) can also be explored through geometry and measurement. In addition, geometry

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 CONCLUSIONS AND RECOMMENDATIONS and measurement provide rich contexts in which children can deepen their mathematical reasoning abilities. Conclusion 7: Two broad mathematical content areas are particularly important as a focus for mathematics instruction in the early years: (1) number (which includes whole number, operations, and relations) and (2) geometry, spatial thinking, and measurement. In the context of these core content areas, young children should engage in both general and specific thinking processes that underpin all levels of mathematics. These include the general processes of representing, problem solving, reasoning, connecting, and communicating, as well as the more specific processes of unitizing, decomposing and composing, relating and ordering, looking for patterns and structures, and organizing and clas- sifying information. In other words, children should learn to mathematize their world: focusing on the mathematical aspects of an everyday situation, learning to represent and elaborate the quantitative and spatial aspects of a situation to create a mathematical model of the situation, and using that model to solve problems. Conclusion 8: In the context of each of these content areas, young chil- dren should engage in both general and specific mathematical thinking processes as described above and in Chapter 2. THE EARLY CHILDHOOD EDUCATION SYSTEM The early childhood education “delivery system,” which educates and cares for children before kindergarten entry, has a great deal of diversity and is best characterized as a loosely sewn-together patchwork of different kinds of programs and providers that vary widely in the extent to which they articulate and act on their educational missions or are explicitly de- signed to provide education services. Program types range from friends and relatives who care for children in the home through informal arrangements, to large centers staffed by teachers offering a structured curriculum. This diversity in the early childhood education system characterizes the education and care arrangements of young children in the United States today. About 40 percent of young children spend their day in a home-based setting, either with a parent or some other caregiving adult (this percentage includes children in home-based relative and nonrelative care as well as children who do not have any regular early education and care arrange- ments), and about 60 percent are in some kind of center-based care (this includes children in center-based non-Head Start and Head Start settings). Depending on the type of setting, different regulations regarding edu-

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 MATHEMATICS LEARNING IN EARLY CHILDHOOD cational standards or expectations may be in place, which in turn influence the nature and quality of young children’s learning experiences from setting to setting. Increasingly, policy makers are focused on how to provide high- quality preschool education for more children, especially to those whose families cannot afford to pay for it. A number of states are moving toward state-funded preschool education to provide early education and care for these children. Across all settings, there is a need to increase the amount and qual- ity of time devoted to mathematics. Formal settings with an educational agenda represent the greatest opportunity for implementing a coherent, sequenced set of learning experiences in mathematics. For this reason, the committee focused attention on the kind of curriculum and instruction that can be implemented in centers and preschools. The committee gave more limited attention to how to increase support for mathematics in informal settings. These approaches are discussed in the section “Beyond the Educa- tion System.” Curriculum and Instruction Having laid out a vision for optimal teaching-learning paths in early childhood mathematics, the committee turned to the evidence base re- lated to curriculum and instruction. The committee first examined the extent to which the content and learning experiences embodied in the teaching-learning paths are represented in current curricula and preschool classrooms. Next, the committee explored what is known about effective mathematics instruction for young children and what might need to be done to improve existing practice. The committee looked for evidence to address two sets of questions: What is known about how much mathematics in- struction is available currently to children in preschool settings and of what quality? What is known about the best methods of instruction and effective curriculum to teach mathematics to young children? Although few system- atic data exist, the committee was able to identify some useful sources. We conducted original analyses of the standards documents pertaining to early childhood for 49 states and those pertaining to kindergarten for the 10 states with the largest student populations. On the basis of these analyses, the committee concludes: Conclusion 9: Current state standards for early childhood do not, on average, include much mathematics. When mathematics is included, there is a pattern of wide variation among states in the content that is covered. Although standards represent broad guidance from the states regard- ing appropriate content for early childhood settings, they do not provide a

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 CONCLUSIONS AND RECOMMENDATIONS window on what actually occurs in classrooms. For the latter, the commit- tee examined data from a large-scale study of instruction in state-funded preschools drawn from 11 states as well as several, small-scale studies of curriculum. The results show that when mathematics activities are incor- porated into early childhood classrooms, they are often presented as part of an integrated or embedded curriculum, in which the teaching of math- ematics is secondary to other learning goals. This kind of integration occurs when, for example, a storybook has some mathematical content but is not designed to bring mathematics to the forefront, a teacher counts or does simple arithmetic during snack time, or points out the mathematical ideas children might encounter during play with blocks. However, data suggest that heavy reliance on integrated or embedded mathematics activities may contribute to too little time being spent on mathematics in early childhood classrooms. Furthermore, the time that is spent may be on activities in which the integrity and depth of the mathematics is questionable. Few of the existing comprehensive early childhood curriculum approaches provide enough focused mathematics instruction for children to progress along the teaching-learning paths recommended by the committee. Conclusion 10: Most early childhood programs spend little focused time on mathematics, and most of it is of low instructional quality. Many opportunities are therefore missed for learning mathematics over the course of the preschool day. Evidence examined by the committee suggests that instructional time focused on mathematics is potentially more effective than embedded math- ematics. Emerging evidence from a few studies of rigorous mathematics curricula show that children who experience focused mathematics activi- ties in which mathematics teaching is the major goal have higher gains in mathematics and report enjoying mathematics more than those who do not. Furthermore, these studies indicate that a planned, sequenced curriculum can support young children’s mathematical development in a sensitive and responsive manner. Supplemental opportunities to use mathematics during mathematical play, sociodramatic play, and with concrete materials (e.g., blocks, puzzles, manipulatives, interactive computer software) can provide children with the opportunity to “practice” mathematics in a meaningful and engaging context. Conclusion 11: Children’s mathematics learning can be improved if they experience a planned, sequenced curriculum that uses the research- based teaching-learning paths described in this report, as well as inte- grated mathematics experiences (e.g., mathematics in the context of a storybook) that extend mathematical thinking through play, explora- tion, creative activities, and practice.

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0 MATHEMATICS LEARNING IN EARLY CHILDHOOD Effective mathematics curricula use a variety of instructional ap - proaches, such as a combination of individual, small-group, and whole- group activities focused on mathematics that move children along the research-based teaching-learning paths described in this report. Further- more, in all these contexts, intentional teaching enhances the mathematics learning of young children. Intentional teaching varies from teacher-guided activities to responsive feedback that builds on and extends the child’s under- standing. It is also important to engage children in math talk—discussion between adults and children that focuses on mathematics concepts, such as how many objects are in a set or how to arrive at an answer—as this facilitates their mathematical development by increasing the connections they make between mathematics concepts, words, and ideas. It should be noted that the committee does not endorse any specific model or curricu- lum; rather we hope to convey that the research-based principles described in this report should guide choices about development of early childhood mathematics curriculum and instruction. Conclusion 12: Effective early mathematics curricula use a variety of instructional approaches and incorporate intentional teaching. Evidence also indicates that instruction is more effective when it can build on information about the child’s current level of understanding. Such responsive instruction can be accomplished when teachers know how to use formative assessment to guide instruction. Formative assessment is an important component of what teachers need to know to effectively guide children along the mathematics teaching-learning paths. Conclusion 13: Formative assessment provides teachers with informa- tion about children’s current knowledge and skills to guide instruction and is an important element of effective mathematics teaching. Evidence from studies of early childhood education indicates that any approach to curriculum and pedagogy is more effective if undertaken in the context of a positive learning environment. Positive relationships between children and their teachers are a key aspect of high-quality early childhood education. In this kind of classroom, children are provided with a safe and nurturing environment that promotes learning and positive interactions between teachers and peers. Conclusion 14: Successful mathematics learning requires a positive learning environment that fully engages children and promotes their enthusiasm for learning.

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1 CONCLUSIONS AND RECOMMENDATIONS Workforce and Professional Development The early childhood workforce—those who serve both instructional and noninstructional roles in early childhood settings—is central to sup- porting the academic, social, emotional, and physical development of young children. This workforce consists of people who serve in a variety of roles, are located in a variety of settings, and have a wide range of education and training backgrounds. About 24 percent of early childhood workers are in center-based settings, 28 percent are in regulated home-based settings, and about 48 percent work in informal care arrangements outside both of these systems. Although the majority of early childhood professionals work in informal care settings, the majority of children are in center-based settings. Even in a single setting, individuals fill different roles, such as lead teacher, assistant teacher, classroom aide, or program administrator. Level and type of training can vary by both role and setting. For example, family child-care providers may have little or no specific training in early child- hood education, a teachers’ assistant may have some formal coursework, and center-based lead teachers may have a 4-year college degree (or even a graduate degree) with specialization in early childhood. This diversity of roles and educational backgrounds creates challenges for addressing the workforce needs related to supporting early childhood mathematics. Individuals in different roles are likely to need different kinds of knowledge and training to support children’s mathematics. Depending on level of education, there are also likely to be differences in individuals’ knowledge of mathematics, of children’s development in mathematics, and of how to support mathematics learning. In addition, the field of early childhood has historically placed great emphasis on teaching its workforce to support children’s social and emo- tional development, placing less attention on cognitive development and academic domains. Indeed, academic activities, such as mathematics learn- ing, can be a context in which social-emotional development flourishes. In large part, the heavy emphasis on social-emotional development in early childhood is based on misinterpretations of cognitive development theories; that is, the notion of young children engaging in more abstract thinking, such as mathematics, was believed to be at odds with the development and learning of preschool-age children. Research on early childhood mathemat- ics has disproved this notion, but the idea is still pervasive in the field and continues to be a challenge in moving from research to practice. Conclusion 15: Many in the early childhood workforce are not aware of what young children are capable of in mathematics and may not recognize their potential to learn mathematics.

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2 MATHEMATICS LEARNING IN EARLY CHILDHOOD Professional development, which typically provides training to those already in the workforce, can be a vital mechanism for providing teachers with new or updated skills and knowledge that they need and for reach- ing those in the workforce who have little or no formal training. Based on studies at the K-12 level, effective approaches to in-service professional development in mathematics are ongoing, grounded in theory, tied to a cur- riculum, job-embedded, and delivered at least partially onsite by a knowl- edgeable trainer who allows teachers time for reflection. The committee reviewed emerging data from studies conducted in early childhood settings that support these findings. These studies indicate that professional devel- opment focused on understanding children’s developmental progression in mathematics in the context of a research-based curricular sequence can improve teachers’ instructional effectiveness. An effort to provide profes- sional development to teachers is one important component of successfully improving instruction, but sustainable change will also require collabora- tion from administrators, teachers, and parents. Conclusion 16: In-service education of teachers and other staff to support mathematics teaching and learning is essential to effective implementation of early childhood mathematics education. Useful pro- fessional development will require a sustained effort that involves help- ing teachers to (a) understand the necessary mathematics, the crucial teaching-learning paths, and principles of intentional teaching and curriculum and (b) learn how to implement a curriculum. Evidence reviewed by the committee about the formal preparation of early childhood educators (courses taken as part of an associate or under- graduate degree) indicates that there are few opportunities to learn about children’s development in mathematics or how to teach early childhood mathematics. To better prepare early childhood educators in mathematics, additional courses and additional materials in existing courses that cover children’s development in mathematics and mathematics pedagogy are needed. Furthermore, licensure and credentialing systems exert a great deal of influence over the content and experience of pre-service education pro- grams in early childhood, and few incorporate mathematics requirements. Conclusion 17: Pre-service preparation of early childhood educators typically includes few opportunities to learn about children’s math- ematical development or how to support it. Licensure and certifica- tion requirements for credentialing teachers and programs are both potential leverage points for increasing the amount of attention given to supporting mathematics.

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 CONCLUSIONS AND RECOMMENDATIONS In addition to the challenges already outlined regarding the diverse training and settings of the workforce, attracting and retaining qualified in- dividuals to work in early childhood is difficult due to poor compensation, lack of benefits, and high turnover rates in the field. This situation presents an additional challenge to designing pre-service and in-service experiences that can improve early childhood educators’ knowledge of how to support young children’s learning in mathematics. Conclusion 18: Improving the training and knowledge requirements for early childhood teachers will present significant challenges unless exist- ing issues of recruitment, compensation, benefits, and high turnover are also addressed. BEYOND THE EDUCATION SYSTEM A significant number (about 40 percent) of children do not attend cen- ters but instead are educated and cared for by a parent, relative, or another adult in homes. Parents or other caregivers serve as children’s first teachers; evidence reviewed by the committee indicates that they can play a key role in shaping children’s early mathematics learning through such activities as encouraging play with blocks and other manipulatives, teaching number words, playing counting and board games, sorting, classifying, writing, and viewing educational television programs while talking with children about what they are watching. Math talk has been shown to be a particu- larly effective way for adults to support the development of mathematical ideas. In fact, math talk beginning as early as infancy is related to children’s mathematics knowledge at preschool entry. In addition, informal learning environments, such as libraries, museums, and community centers, have the potential to be resources that parents and caregivers can use to engage children in mathematics activities. Conclusion 19: Families can enhance the development of mathematical knowledge and skills as they set expectations and provide stimulating environments. Evidence indicates, however, that low-SES families are less likely than families from higher socioeconomic groups to engage in the kind of prac- tices that promote language and mathematics competence. Although many types of educational programs have been designed to promote the use of these practices with low-SES parents, there is little evidence about the qualities that make such efforts successful. Educational programs for par- ents based on models that place parents in the traditional role of students

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 MATHEMATICS LEARNING IN EARLY CHILDHOOD learning from “experts” have difficulty sustaining family participation long enough to be successful. Conclusion 20: Educational programs for parents have the potential to enhance the mathematical experiences provided by parents; however, there is little evidence about how to design such programs to make them effective. The resources available to parents and other caregivers as well as those available through informal educational environments (e.g., libraries, muse- ums, community centers) can also be an effective mechanism for supporting children’s mathematics learning. Educational television programming and software, for example, can teach children about mathematics. The com- mittee reviewed research on software and educational programs, as well as models of community-based programs that promote mathematics, and concludes: Conclusion 21: Given appropriate mathematical content and adult support, the media (e.g., television, computer software) as well as community-based learning opportunities (e.g., museums, libraries, community centers) can engage and educate young children in math- ematics. Such resources can provide additional mathematics learning opportunities for young children, especially those who may not have access to high-quality early education programs. RECOMMENDATIONS As the committee’s conclusions make clear, there is much work to be done to provide young children with the learning opportunities in math- ematics that they need. Thus, the committee thinks it is critically important to begin an intensive national effort to enhance opportunities to learn mathematics in early childhood settings to ensure that all children enter school with the mathematical foundations they need for academic success. The research-based principles and mathematics teaching-learning paths de- scribed in this report can also reduce the disparity in educational outcomes between children from low-SES backgrounds and their higher SES peers. The research to date about how young children learn key concepts in mathematics has clear implications for practice, yet these findings are not widely known or implemented by early childhood educators or even those who teach early childhood educators. This report has focused on synthesiz- ing and translating this evidence base into a usable form that can be used to guide a national effort. Thus the committee recommends:

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5 CONCLUSIONS AND RECOMMENDATIONS Recommendation 1: A coordinated national early childhood mathemat- ics initiative should be put in place to improve mathematics teaching and learning for all children ages 3 to 6. A number of specific recommendations for action follow from this overarching recommendation. The specific steps and the individuals or or- ganizations that must be involved in enacting them are outlined below. Recommendation 2: Mathematics experiences in early childhood set- tings should concentrate on (1) number (which includes whole num- ber, operations, and relations) and (2) geometry, spatial relations, and measurement, with more mathematics learning time devoted to num- ber than to the other topics. The mathematical process goals should be integrated in these content areas. Children should understand the concepts and learn the skills exemplified in the teaching-learning paths described in this report. In both content areas, sufficient time should be devoted to instruction to allow children to become proficient with the concepts and skills outlined in the teaching-learning paths. In addition, the general and specific math- ematical process goals (see Chapter 2) must be integrated with the content in order to allow children to make connections between mathematical ideas and deepen their mathematical reasoning abilities. This new content focus will require that everyone involved rethink how they view and understand the mathematics that is learned in early childhood. Early childhood learn- ing goals, programs, curricula, and professional development will need to be informed by and adapted to the research-based teaching-learning paths laid out in this report. The committee therefore recommends: Recommendation 3: All early childhood programs should provide high-quality mathematics curricula and instruction as described in this report. Early childhood programs will each need to implement a thoughtfully planned curriculum that includes a sequence of teacher-guided mathemat- ics activities as well as child-focused, teacher-supported experiences. Such curricula must be based on models of instruction that are appropriate for young children and support their emotional and social development as well as their cognitive development. As noted previously, effective mathematics curricula use a variety of instructional approaches and should incorporate opportunities for children to extend their mathematical thinking through play, exploration, creative activities, and practice. Programs will need to review, revise, and align their existing stan-

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6 MATHEMATICS LEARNING IN EARLY CHILDHOOD dards, professional development, curriculum, and materials to achieve the teaching-learning paths for early childhood mathematics education pre- sented in this report. It is especially important that children living in pov- erty receive such high-quality experiences so that they start first grade on a par with children from more advantaged backgrounds. This means that implementation of our recommendations by programs serving economically disadvantaged children, such as Head Start and publicly funded early child- hood programs, is particularly urgent. To make the recommended changes, early childhood programs will need explicit policy directives to do so. To encourage this, the committee recommends: Recommendation 4: States should develop or revise their early child- hood learning standards or guidelines to reflect the teaching-learning paths described in this report. Given the fresh knowledge and perspectives this report affords, it is important that states review their early learning and development stan- dards and guidelines to ensure that they reflect an appropriate emphasis on early mathematics. To that end, we call for all states to examine their early learning and development guidelines, first, to determine that sufficient emphasis is given to the importance of mathematics for young children’s development and, second, to ensure that the mathematics content focuses on (1) number (including whole number, operations, and relations) and (2) geometry, spatial thinking, and measurement. Recommendation 5: Curriculum developers and publishers should base their materials on the principles and teaching-learning paths described in this report. Teachers and early childhood programs need appropriate materials in order to support children’s mathematical development and learning. Cur- riculum developers and publishers who produce materials for curriculum, instruction, and assessment should revise and update them so that they reflect the principles articulated in this report. The success of this overall effort will need to focus on reaching both the existing early childhood workforce and pre-service educators to provide them with skills and knowledge they need to teach mathematics. Thus, we make several recommendations related to teachers and the workforce. Recommendation 6: An essential component of a coordinated national early childhood mathematics initiative is the provision of professional development to early childhood in-service teachers that helps them

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 CONCLUSIONS AND RECOMMENDATIONS (a) to understand the necessary mathematics, the crucial teaching- learning paths, and principles of intentional teaching and curriculum and (b) to learn how to implement a curriculum. Applying teachers’ theoretical knowledge to a curriculum with a strong mathematics component provides them with the opportunity to get feed- back and reflect on the instructional practices that they will actually be im- plementing in the classroom. Professional development should also focus on teachers’ beliefs about children’s mathematics, the activities and resources in the classroom that can promote children’s mathematical development, and their knowledge of curriculum-linked assessment practices. All of these important areas should be included in professional development delivered by a highly qualified teacher educator. To implement high-quality mathematics instruction, the committee also recommends that early childhood educators be taught to use a range of effective instructional strategies in a variety of formats, including whole- group, pair/small-group, and individual work; exploration and practice; and play and focused activities. Serious efforts to improve the preparation of early childhood teachers will need to include the state licensure/certification, accreditation and recogni- tion, and credentialing systems that assess teachers’ competence and program quality. The early childhood mathematics described in this report should be reflected in the core components of these systems and programs. Recommendation 7: Coursework and practicum requirements for early childhood educators should be changed to reflect an increased emphasis on children’s mathematics as described in the report. These changes should also be made and enforced by early childhood organizations that oversee credentialing, accreditation, and recognition of teacher professional development programs. The committee also recognizes the need to go beyond the formal early childhood education system to reach families and communities—both of which have a strong impact on young children’s learning. An important component of reaching all children will need to include strategies aimed at children who are in other settings, such as homes or family child care. Recommendation 8: Early childhood education partnerships should be formed between family and community programs so that they are equipped to work together in promoting children’s mathematics. For example, family education and support programs, such as the Head Start Family and Community Partnerships Program, should include infor-

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 MATHEMATICS LEARNING IN EARLY CHILDHOOD mation that provides guidance to families and communities as to why they should and how they can help children develop key mathematical ideas and skills. Furthermore, professionals working with families should be given training focused on early mathematics knowledge and skills, as well as have access to programs and resources on home-based mathematics activities. To this end, there is a need for development of more resources that can support mathematics in informal settings and through media and technology. Recommendation 9: There is a need for increased informal program- ming, curricular resources, software, and other media that can be used to support young children’s mathematics learning in such settings as homes, community centers, libraries, and museums. FUTURE RESEARCH In its work, the committee conducted a comprehensive review of the existing evidence related to mathematics development and learning in early childhood. As noted, we have determined that the evidence base is robust enough to guide a major national initiative in early mathematics. Yet gaps remain in the knowledge base about children’s mathematics education. We think it is critical that the research base continue to advance in a number of key areas outlined below. Implications for English language learners. Increasingly, early childhood classrooms serve significant numbers of children whose first language is not English; these children will be held to the same expectations for future achievement as children whose home language is English. To date, little published research has investigated the teaching and learning of mathemat- ics with preschool age children who are simultaneously learning English. The committee recommends research be conducted that can help identify the best methods of enhancing the mathematical learning of young children who speak a first language other than English. Research on the role of teachers in proiding effectie instruction. In re- cent years, researchers have made progress in understanding the process of teaching mathematics at the elementary school level. This research stresses the role of teachers’ knowledge and skill including their knowledge of mathematics, their understanding of children’s mathematical thinking and learning and their pedagogical content knowledge (i.e., their knowledge of how to structure the classroom and curriculum and to engage children in activities so that the mathematics is accessible). However, there has been much less attention to similar issues in early childhood settings. Research is needed to determine the extent to which the findings from research in

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 CONCLUSIONS AND RECOMMENDATIONS the higher grades apply to mathematics instruction in early childhood and what might be unique to early childhood. Ealuation of curricula. In the course of our review of early childhood mathematics, it became clear that many of the available curricula have not been rigorously evaluated for effectiveness. High-quality curriculum re- search is needed that tracks the effectiveness of curricula during implemen- tation, using the theories and instructional models that were originally used to guide development of the curriculum. This research must also consider how diversity in children’s backgrounds and across learning environments influences implementation and effectiveness. To achieve these goals, the committee recommends that curriculum research and development move through phases: from early reviews of relevant research to the creation of learning materials to help children along the teaching-learning paths in this report, to cycles of baseline evaluation, and finally to confirmatory evalu- ation using rigorous designs, with all phases integrating quantitative and qualitative methodologies. Research of this type will help ensure that early childhood programs can make informed, evidence-based choices among curricula. Effectie teacher preparation. Much of the recent research on the prepa- ration of early childhood educators has focused on whether the bachelor’s degree is an effective marker for teachers’ competency. While this line of inquiry has been helpful in identifying some of teachers’ skills that are related to positive child learning outcomes, research in the field needs to move beyond the B.A./non-B.A. distinction. The committee recommends that research on the effectiveness of early childhood teachers focus on the content and quality of teacher education programs rather than on whether or not teachers have a bachelor’s degree. Parental inolement. It is unclear why families from low SES back- grounds often do not participate in educational activities and what can be done to promote their involvement in these programs. The committee therefore recommends the conduct of better descriptive studies that exam- ine what parents understand about supporting their children’s mathematics learning and how to promote parents involvement in these efforts. Further- more, if parents do have knowledge about how to support their children’s mathematical development but are not putting this knowledge into practice, it is important that research examine the impediments that stand in the way of their actively promoting early childhood mathematics. Interentions for children with mathematics learning disabilities. Explo- ration of learning difficulties or disabilities in mathematics is a nascent area

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50 MATHEMATICS LEARNING IN EARLY CHILDHOOD of research that needs expansion. Further exploration is needed to better understand what early number competencies are predictive of future success in mathematics. Such research can help identify children at risk for learning difficulties or disabilities in mathematics during the preschool years, de- velop targeted interventions for such children, and test their effectiveness.