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The implications for instructional practices and curricula for educators working with infants and toddlers are discussed further in Chapter 6. Another way that educators contribute to the cognitive growth of infants and toddlers is through the emotional support they provide Jamison et al. Emotional support of this kind is important not only as a positive.

Moreover, the secure attachments that young children develop with educators contribute to an expectation of adult support that enables young children to approach learning opportunities more positively and confidently. Emotional support and socioemotional development are discussed further later in this chapter. Consider, for example, a parent or other caregiver interacting with a 1-year-old over a shape-sorting toy. The adult may also be using number words to count the blocks as they are deposited.

In this interaction, moreover, the baby is developing both expectations for what this adult is like—safe, positive, responsive—and skills for social interaction such as turn taking. As children further develop cognitively as preschoolers, their growth calls for both similar and different behavior by the adults who work with them. First, they are more consciously aware of their knowledge—much more of their understanding is now explicit. This means they are more capable of deliberately enlisting what they know into new learning situations, although they are not yet as competent or strategic in doing so as they will be in the primary grades.

When faced with a problem or asked a question, they are more capable of offering an answer based on what they know, even when their knowledge is limited. Second, preschoolers are more competent in learning from their deliberate efforts to do so, such as trial-and-error or informal experimentation. Nonetheless, the potential to underestimate the cognitive abilities of young children persists in the preschool and kindergarten years.

A study in kindergarten revealed that teachers spent most of their time in basic content that children already knew, yet the children benefited more from advanced reading and mathematics content Claessens et al. One example is interactive storybook reading, in which children describe the pictures and label their elements while the adult and child ask and answer questions of each other about the narrative.

In each case, dialogic conversation about text. Language and literacy skills are discussed further in a subsequent section of this chapter, as well as in Chapter 6. In a similar manner, board games can provide a basis for learning and extending number concepts. In several experimental demonstrations, when preschool children played number board games specifically designed to foster their mental representations of numerical quantities, they showed improvements in number line estimates, count-on skill, numerical identification, and other important quantitative concepts Laski and Siegler, Other research has shown that instructional strategies that promote higher-level thinking, creativity, and even abstract understanding, such as talking about ideas or about future events, is associated with greater cognitive achievement by preschool-age children e.

These activities also can be integrated into other instructional practices during a typical day. Preschool-age children are developing a sense of themselves and their competencies, including their academic skills Marsh et al.

Their beliefs about their abilities in reading, counting, vocabulary, number games, and other academic competencies derive from several sources, including spontaneous social comparison with other children and feedback from teachers and parents concerning their achievement and the reasons they have done well or poorly.

Primary grade children are using more complex vocabulary and grammar. They are growing in their ability to make mental representations, but they still have difficulty grasping abstract concepts without the aid of real-life references and materials Tomlinson, This is a critical time for children to develop confidence in all areas of life.

Children at this age show more independence from parents and family, while friendship, being liked and accepted by peers, becomes more important. Being in school most of the day means greater contact with a larger world, and children begin to develop a greater understanding of their place in that world CDC, Children understand their own feelings more and more, and learn better ways to describe experiences and express thoughts and feelings. They better understand the consequences of their actions, and their focus on concern for others grows.

They are very observant, are willing to play cooperatively and work in teams, and can resolve some conflicts without seeking adult intervention CDC, Children who are unable to self-regulate have emotional difficulties that may interfere with their learning. Educators in these settings are scaffolding the skills that began to develop earlier, so that children are able to gradually apply those skills with less and less external support.

This serves as a bridge to succeeding in upper primary grades, so if students lack necessary knowledge and skills in any domain of development and learning, their experience during the early elementary grades is crucial in helping them gain those competencies. Building on many of the themes that have emerged from this discussion, the following sections continue by looking in more depth at cognitive development with respect to learning specific subjects and then at other major elements of development, including general learning competencies, socioemotional development, and physical development and health.

These skills and abilities include the general cognitive development discussed above, the general learning competencies that allow children to control their own attention and thinking; and the emotion regulation that allows children to control their own emotions and participate in classroom activities in a productive way the latter two are discussed in sections later in this chapter. Still another important category of skills and abilities, the focus of this section, is subject-matter content knowledge and skills, such as competencies needed specifically for learning language and literacy or mathematics.

Content knowledge and skills are acquired through a developmental process. As children learn about a topic, they progress through increasingly sophisticated levels of thinking with accompanying cognitive components. These developmental learning paths can be used as the core of a learning trajectory through which students can be supported by educators who understand both the content and those levels of thinking. Each learning trajectory has three parts: a goal to develop a certain competence in a topic , a developmental progression children constructing each level of thinking in turn , and instructional activities tasks and teaching practices designed to enable thinking at each higher level.

Learning trajectories also promote the learning of skills and concepts together—an effective approach that leads to both mastery and more fluent, flexible use of skills, as well as to superior conceptual understanding Fuson and Kwon, ; National Mathematics Advisory Panel, See Chapter 6 for additional discussion of using learning trajectories and other instructional practices. Every subject area requires specific content knowledge and skills that are acquired through developmental learning processes. It is not possible to cover the specifics here for every subject area a young child learns.

To maintain a feasible scope, this chapter covers two core subject areas: 1 language and literacy and 2 mathematics. This scope is not meant to imply that learning in other areas, such as science, engineering, social studies, or the arts, is unimportant or less subject specific. Rather, these two were selected because they are foundational for other subject areas and for later academic achievement, and because how they are learned has been well studied in young children compared with many other subject areas.

The development of language and literacy includes knowl-. The following sections address the development of language and literacy skills, including the relationship between the two; the role of the language-learning environment; socioeconomic disparities in early language environments; and language and literacy development in dual language learners.

Language skills build in a developmental progression over time as children increase their vocabulary, average sentence length, complexity and sophistication of sentence structure and grammar, and ability to express new ideas through words Kipping et al. Catts and Kamhi define five features of language that both work independently and interact as children develop language skills: phonology speech sounds of language , semantics meanings of words and phrases , morphology meaningful parts of words and word tenses , syntax rules for combining and ordering words in phrases , and pragmatics appropriate use of language in context.

The first three parameters combined phonology, semantics, and morphology enable listening and speaking vocabulary to develop, and they also contribute to the ability to read individual words. Developing oral communication skills are closely linked to the interactions and social bonds between adults and children. This comprehension begins with pragmatics—the social aspects of language that include facial and body language as well as words, such that infants recognize positive and negative interactions.

Semantics understanding meanings of words and clusters of words that are related soon follows, in which toddlers link objects and their attributes to words. Between the ages of 2 and 4, most children show dramatic growth in language, particularly in understanding the meanings of words, their interrelationships, and grammatical forms Scarborough, Karmiloff and Karmiloff-Smith suggest that children build webs among words with similar semantics, which leads to broader generalizations among classes of related words. Then, as new words arise from conversation, storytelling, and book reading, these words are linked to.

The more often adults use particular words in conversation with young children, the sooner children will use those words in their own speech Karmiloff and Karmiloff-Smith, Research has linked the size of vocabulary of 2-year-olds to their reading comprehension through fifth grade Lee, Book reading stimulates conversation outside the immediate context—for example, children ask questions about the illustrations that may or may not be central to the story.

This introduces new words, which children attach to the features of the illustrations they point out and incorporate into book-centered conversations. This type of language, removed from the here and now, is decontextualized language. Children exposed to experiences not occurring in their immediate environment are more likely to understand and use decontextualized language Hindman et al. Repeated routines also contribute to language development. As books are read repeatedly, children become familiar with the vocabulary of the story and their conversations can be elaborated.

Routines help children with developmental delays acquire language and use it more intelligibly van Kleek, The long-term effect of high-quality teacher—child book-centered interactions in preschool lasted through the end of first grade. New research shows that the effects of interactive reading also hold when adapted to the use of digital media as a platform for decontextualized language and other forms of language development. However, a few studies of e-books also have shown that the bells and whistles of the devices can get in the.

See also the discussion of effective use of technology in instruction in Chapter 6. Alongside developing depth of vocabulary including the meaning of words and phrases and their appropriate use in context , other important parameters of language development are syntax rules for combining and ordering words in phrases, as in rules of grammar and morphology meaningful parts of words and word tenses. Even before the age of 2, toddlers parse a speech stream into grammatical units Hawthorne and Gerken, Long before preschool, most children join words together into sentences and begin to use the rules of grammar i.

Along with these morphemic changes to words, understanding syntax helps children order the words and phrases in their sentences to convey and to change meaning. Before children learn to read, the rules of syntax help them derive meaning from what they hear and convey meaning through speech. Cunningham and Zibulsky , p. Although syntactic understanding develops for most children through conversation with adults and older children, children also use these rules of syntax to extract meaning from printed words. This becomes an important reading skill after first grade, when text meaning is less likely to be supported with pictures.

Construction of sentences with passive voice and other complex, decontextualized word forms are more likely to be found in books and stories than in directive conversations with young children. An experimental study illustrates the role of exposure to syntactic structures in the development of language comprehension Vasilyeva et al.

Four-year-olds listened to stories in active or passive voice. After listening to ten stories, their understanding of passages containing these syntactic structures was assessed. Although students in both groups understood and could use active voice similar to routine conversation , those who listened to stories with passive voice scored higher on comprehension of this structure. Literacy skills follow a developmental trajectory such that early skills and stages lead into more complex and integrated skills and stages Adams, Seminal theories and studies of reading describe an inextricable link between language development and reading achievement e.

Early oral language competencies predict later literacy Pearson and Hiebert, Not only do young children with stronger oral language competencies acquire new language skills faster than students with poorly developed oral language competencies Dickinson and Porche, , but they also learn key literacy skills faster, such as phonemic awareness and understanding of the alphabetic principle Cooper et al. Both of these literacy skills in turn facilitate learning to read in kindergarten and first grade.

Vocabulary development a complex and integrative feature of language that grows continuously and reading words a skill that most children master by third or fourth grade Ehri, are reciprocally related, and both reading words accurately and understanding what words mean contribute to reading comprehension Gough et al. Because comprehending and learning from text depend largely upon a deep understanding of the language used to communicate the ideas and concepts expressed, oral language skills i. For example, children with larger speaking vocabularies in preschool may have an easier time with phoneme awareness and the alphabetic.

Each word a child knows can influence how well she or he understands a sentence that uses that word, which in turn can influence the acquisition of knowledge and the ability to learn new words. A stronger speaking and listening vocabulary provides a deeper and wider field of words students can attempt to match to printed words.

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Being bogged down by figuring out what a given word means slows the rate of information processing and limits what is learned from a sentence. Thus, differences in early vocabulary can have cascading, cumulative effects Fernald et al. The transition from speaking and listening to reading and writing is not a smooth one for many children.

Although a well-developed vocabulary can make that transition easier, many children also have difficulty learning the production and meanings of words. Longitudinal studies of reading disability have found that 70 percent of poor readers had a history of language difficulties Catts et al.

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Using Body Language in Your Presentation [Book]

The oral language and vocabulary children learn through interactions with parents, siblings, and caregivers and through high-quality interactions with educators provide the foundation for later literacy and for learning across all subject areas, as well as for their socioemotional well-being. The language interactions children experience at home and in school influence their developing minds and their understanding of concepts and ideas. The daily talk to which children are exposed and in which they participate is essential for developing their minds—a key ingredient for building their knowledge of the world and their understanding of concepts and ideas.

In turn, this conceptual knowledge is a cornerstone of reading success. The bulk of the research on early linguistic experiences has investigated language input in the home environment, demonstrating the features of. The evidence accumulated emphasizes the importance of the quantity of communicative input i.

This research has particularly relevant implications for educational practices discussed further in Chapter 6. The language environment of the classroom can function as a support for developing the kind of language that is characteristic of the school curriculum—for example, giving children opportunities to develop the sophisticated vocabulary and complex syntax found in texts, beginning at a very early age Schleppegrell, ; Snow and Uccelli, Moreover, advances in cognitive science suggest that it is not enough to be immersed in environments that offer multiple opportunities for exposure to varied and rich language experiences.

Rather, the process also needs to be socially mediated through more knowledgeable persons who can impart their knowledge to the learner; again, social interaction is a critical component of cognitive development and learning. Early childhood settings and elementary classrooms thus not only present opportunities for exposure to varied language- and literacy-rich activities whether written or spoken , but also provide a person who is expert in mediating the learning process—the educator.

For example, Huttenlocher and colleagues found greater syntactic skills in preschoolers exposed to teachers who used more syntactically complex utterances. Another study found for monolingual English-speaking children that fourth-grade reading comprehension levels were predicted by exposure to sophisticated vocabulary in preschool. In classroom studies focused on the linguistic environment, the level of analysis has involved broad measures of language use, such as amount of talk i.

Children are better prepared to comprehend narrative texts they encounter in school if their early language environments provide more exposure to and opportunities to participate in extended discourse. This is because extended discourse and narrative texts share similar patterns for communicating ideas Uccelli et al. Engaging groups of children in effective extended discourse involves asking and discussing open-ended questions and encouraging turn taking, as well as monitoring the group to involve nonparticipating children Girolametto and Weitzman, In addition to using interactive storybook and text reading as a platform for back-and-forth conversations often referred to as interactive or dialogic reading, as described in the preceding section Mol et al.

These findings are consistent with the notion that to promote language learning, different inputs are needed at. Children benefit from hearing simplified speech during very early word learning Furrow et al. With more exposure to language and more advanced vocabulary development, they benefit from speech input that is more complex i. Hoff suggests that if input is too complex, children filter it out without negative consequences—as long as sufficient beneficial input is available to them.

An important consideration in light of these findings is that recent research in early childhood classrooms serving children from low-income backgrounds suggests that daily high-quality language-building experiences may be rare for these children. For example, in a Head Start organization serving large numbers of Latino children a recent observational study found a preschool environment lacking in the frequent and high-quality teacher—child language interactions that are needed to support language and literacy development Jacoby and Lesaux, Literacy instruction was highly routine based and with low-level language structures.

Extended discourse was infrequently used; only 22 percent of observed literacy-based lessons included at least one instance of extended discourse between a teacher and a child or group of children. Instead, teachers asked questions that yielded short answers or linked only to the here and now e. What is the weather today? These features of infrequent extended discourse and predominantly routine-based literacy instruction were remarkably stable across teachers and classrooms.

Using Body Language in Your Presentation by Jerry Weissman

Other research investigating teacher talk in Head Start preschool classrooms has produced similar findings e. This is consistent with findings that there are sizable cultural and socioeconomic differences in high-quality language-promoting experiences in the home and in the classroom environment in early childhood Dickinson, ; Dickinson and Porche, ; Dickinson and Tabors, ; Raikes et al.

At the same time, for children from low-resource backgrounds oral language skills show an even stronger connection to later academic outcomes than for children from high-resource backgrounds. Given these findings, rich linguistic experiences at early ages may therefore be especially important for these children. Even small improvements in the literacy environment can have especially strong effects for children who are raised in low-income households Dearing et al. Improving language environments for young children requires daily learning opportunities that focus on the diversity and complexity of language used with young children.

Extended discourse can take place throughout all activities and in specific interactions, especially using book reading as a platform for back-and-forth conversations. Such studies could advance existing research in at least two ways. In particular, it could further elucidate how language-based social processes in the classroom affect literacy development for the many students who enter schools and other care and education settings with limited proficiency in English.

The majority of published studies focused on language-based interactions are focused on English-only learners, despite the fact that social processes can be experienced differently by different groups, even within the same setting Rogoff and Angelillo, ; Tseng and Seidman, In addition, prior research has measured a two-way process in a largely unidirectional manner—measuring speech only from parent to child or educator to student. More specifically, Justice and colleagues suggest that future research examine teacher—child language interactions in a multidimensional way to explore how syntactic complexity, cognitive demand, and even linguistic form e.

Finally, greater understanding is needed of the ways in which the classroom language processes described in this section might act as a foundational mediator of the efficacy of interventions focused on learning outcomes in other domains and subject areas. This study also found that children with advanced language skills will receive greater benefits from interacting with peers who also have advanced language skills Mashburn et al. In order to achieve these benefits, however, the preschool classrooms need to be designed so that peers can interact with one another, and include activities such as reading books and engaging in play together.

Children with teachers who organize the day with optimal amounts of time for peer-to-peer interactions may achieve greater language growth Mashburn et al. For children whose home language is not the predominant language of their school, educators and schools need to ensure the development of English proficiency. At the same time, children can be helped to both build and maintain their first language while adding language and literacy skills in English Espinosa, In support of this as a long-term goal are the potential advantages of being bilingual, including maintaining a cultural and linguistic heritage and conferring an advantage in the ability to communicate with a broader population in future social, educational, and work environments.

Additionally, an emerging field of research, albeit with mixed results to date, explores potential advantages of being bilingual that are linked more directly to cognitive development, starting in early childhood and extending to preserving cognitive function and delaying the symptoms of dementia in the elderly Bialystok, ; de Bruin et al. Bilingual or multilingual children are faced with more communicative challenges than their monolingual peers. A child who frequently experiences failure to be understood or to understand may be driven to pay more attention to context, paralinguistic cues, and gestures in order to interpret an utterance, and thus become better at reading such cues.

The result may be improved development of theory of mind and understanding of pragmatics Yow and Markman, a,b. In addition, the need to continually suppress one language for another affords ongoing practice in inhibitory or executive control, which could confer advantages on a range of inhibitory control tasks in children and helps preserve this fundamental ability in aging adults Bialystok, ; Bialystok and Craik, ; Bialystok et al. One challenge in the education of dual language learners is that they sometimes are classified along with children with special needs.

One reason for this is the lack of good assessment tools to help distinguish the nature of the difficulties experienced by dual language learners—whether due to a learning disability or to the fact that learning a second language is difficult, takes time, and develops differently in different children Hamayan et al. More information about this study can be found at www. Mathematics knowledge in preschool predicts mathematics achievement even into high school National Mathematics Advisory Panel, ; NRC, ; Stevenson and Newman, Mathematics ability and language ability also are interrelated as mutually reinforcing skills Duncan et al.

Indeed, mathematical thinking reaches beyond competence with numbers and shapes to form a foundation for general cognition and learning Clements and Sarama, ; Sarama et al. Mathematics therefore appears to be a core subject and a core component of thinking and learning Duncan and Magnuson, ; Duncan et al. Given its general importance to academic success Sadler and Tai, , children need a robust foundation in mathematics knowledge in their earliest years.

Multiple analyses suggest that mathematics learning should begin early, especially for children at risk for later difficulties in school Byrnes and Wasik, ; Clements and Sarama, Well before first grade, children can learn the skills and concepts that support more complex mathematics understanding later. Particularly important areas of mathematics for young children to learn include number, which includes whole number, operations, and relations; geometry; spatial thinking; and measurement. Children also need to develop proficiency in processes for both general and specific mathematical reasoning NRC, If given opportunities to learn, young children possess a remarkably broad, complex, and sophisticated—albeit informal—knowledge of mathematics Baroody, ; Clarke et al.

In their free play, almost all preschoolers engage in substantial amounts of premathematical activity. They count objects; compare magnitudes; and explore patterns, shapes, and spatial relations. Preschoolers can also, for example, learn to invent solutions to simple arithmetic problems Sarama and Clements, High-quality mathematics education can help children realize their potential in mathematics achievement Doig et al. However, without such education starting, and continuing throughout, the early years, many children will be on a trajectory in which they will have great difficulty catching up to their peers Rouse et al.

As discussed further in Chapter 6 , early childhood classrooms typically are ill suited to helping children learn mathematics and underestimate their ability to do so. In some cases, children can even experience a regression on some mathematics skills during prekindergarten and kindergarten Farran et al. Mathematics needs to be conceptualized as more than. Without building a robust understanding of mathematics in the early years, children too often come to believe that math is a guessing game and a system of rules without reason Munn, Both education and experience can make a difference, as evidenced by data from the latest international Trends in International Mathematics and Science Study, which added data collection on early mathematics education Mullis et al.

Students with higher mathematics achievement at fourth and sixth grades had parents who reported that they often engaged their children in early numeracy activities and that their children had attended preprimary education and started school able to do early numeracy tasks e. Those children who had attended preschool or kindergarten had higher achievement, while the 13 percent who had attended no preprimary school had much lower average mathematics achievement Mullis et al.

Children move through a developmental progression in specific mathematical domains, which informs learning trajectories as important tools for supporting learning and teaching. Box illustrates the concept of a developmental progression through the example of subitizing , an oft-neglected mathematical goal for young children. Research shows that subitizing, the rapid and accurate recognition of the number in a small group, is one of the main abilities very young children should develop Palmer and Baroody, ; Reigosa-Crespo et al.

Through subitizing, children can discover critical properties of number, such as conservation and compensation Clements and Sarama, ; Maclellan, and develop such capabilities as unitizing and arithmetic. Subitizing is not the only way children think and learn about number.

Counting is the other method of quantification. It is the first and most basic mathematical algorithm and one of the more critical early mathematics competencies Aunola et al. Chapter 6 includes examples from a complete learning trajectory—goal, developmental progression, and instructional activities—for counting Clements and Sarama, For example, very young children possess approximate number systems ANSs that allow them to discriminate large and small sets, determining, for example, whether there are more white or gray dots in the figure below. Six-month-olds can discriminate a ratio, and by 9 months of age, they can also distinguish sets in a ratio e.

Subitizing involves determining and explicitly identifying the exact number of items in a small set. Subitizing ability develops in a stepwise fashion. Between 35 and 37 months, they differentiate between 1 and 2, but not larger numbers. A few months later, at 38 to 40 months, they can identify 3 as well. After about 42 months, they can identify all numbers that they can count, 4 and higher, at about the same time.

However, research in natural, child-initiated settings shows that the development of these abilities can occur much earlier, with children working on 1 and 2 around their second birthday or earlier Mix et al. Babies in the first 6 months of life, and even earlier, can discriminate 1 object from 2, and 2 objects from 3 Antell and Keating, ; Wynn et al.

Thus, even infants can discriminate among and match small configurations of objects, only for these small numbers. Because children cannot discriminate 4 objects from 5 or 6 until the age of about 3 years, some researchers have suggested that infants use an automatic perceptual process that people, including adults, can apply only to small collections up to around 4 objects Chi and Klahr, A developmental progression moves from foundational but pre-explicit quantification to explicit naming of small quantities.

This initially involves only perceptual subitizing Clements, ; Kaufman et al. From their second to third birthdays, most children can name sets of 1 and 2, and then 3 soon thereafter Mix et al. Larger sets are perceived, quantified, and quickly named as the child gains experience. Perceptual subitizing also plays the role of unit-.

Then a qualitative advance is made as conceptual subitizing develops. This involves similarly quantifying 2 parts separately and then combining them, again, quickly, accurately, and without being explicitly aware of the cognitive processing Clements, ; see empirical evidence for such processes in Trick and Pylyshyn, Many theories have been advanced to explain the subitizing process Baroody et al.

A synthesis suggests the following model. The ANS serves as a transition between general, approximate notions of number and one based on an exact, abstract, mental model. Infants quantify collections of rigid objects not sequences of sounds or materials that are nonrigid and noncohesive such as water Huntley-Fenner et al. These quantifications begin as an undifferentiated, innate notion of amount of objects. Object individuation, which occurs early in preattentive processing and is a general, not numerical-only, process , helps lay the groundwork for differentiating discrete from continuous quantity.

For example, by about 6 months of age, infants may represent very small numbers 1 or 2 as individuated objects. To compare quantities, they process correspondences. Initially, these are inexact estimates, depending on the ratio between the sets Johnson-Pynn et al. Once children can represent objects mentally, they also can make exact correspondences between these nonverbal representations and eventually develop a quantitative notion of that comparison e.

Even these correspondences, however, do not imply a cardinal representation of the collection. To complete the subitizing process, children must make word—word mappings between numbers e. They then label small number situations with the corresponding number word, mapping the number word to the numerosity property of the collection.

That is, they begin to establish what mathematicians call a numerical equivalence class. The construction of such schemes probably depends on guiding frameworks and principles developed through interactions with others, such as parents and educators. Ericsson et al. Activities such as teachers challenging students to name the number of dots in a display shown only for seconds have resulted in substantial growth in this ability Baroody et al.

Subitizing ability is not merely a low-level, innate process, but develops considerably and combines with other mental processes. Even though they are limited, subitizing capabilities appear to form a foundation for later connection to culturally based cognitive tools such as number words and the number word sequence and the development of exact and extended number concepts and skills. Functional magnetic resonance imaging and other studies have shown that a neural component of numerical cognition present in the early years may be the foundation for later symbolic numerical development Cantlon et al.

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Subitizing appears to precede and support the development of counting ability and arithmetic skills Eimeren et al. Children who cannot subitize conceptually are handicapped in learning such arithmetic processes. Those who can subitize may be limited to doing so with small numbers at first, but such actions are useful stepping stones to the construction of more sophisticated procedures with larger numbers.

Indeed, lack of this competence may underlie mathematics learning disabilities and difficulties Ashkenazi et al. Children from low-resource communities and those with special needs often lag in subitizing ability, hindering their mathematical development Butterworth, ; Chu et al. Children with special needs in learning mathematics fall into two categories.

Those with mathematical difficulties struggle to learn mathematics for any reason; this category may apply to as many as percent of students Berch and Mazzocco, Those with specific mathematics learning disabilities are more severe cases; these students have a memory or cognitive deficit that interferes with their ability to learn math Geary, This category may apply to about percent Berch and Mazzocco, ; Mazzocco and Myers, In one study, this classification persisted in third grade for 63 percent of those classified as having mathematics learning disabilities in kindergarten Mazzocco and Myers, One consistent finding is that students with mathematics learning disabilities have difficulty retrieving basic arithmetic facts quickly.


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This has been hypothesized to be the result of an inability to store or retrieve facts and impairments in visual-spatial representation. As early as kindergarten, limited working memory and speed of cognitive processing may be problems for these children Geary et al.


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  4. Many young children with learning disabilities in reading show a similar rapid-naming deficit for letters and words Siegel and Mazabel, ; Steacy et al. Another possibility is that a lack of higher-order, or executive, control of verbal material causes difficulty learning basic arithmetic facts or combinations. For example, students with mathematics learning disabilities may have difficulty inhibiting irrelevant associations. One explanation for the difficulty students with mathematics learning disabilities have learning basic arithmetic combinations might be delays in understanding counting.

    These students may not fully understand counting nor recognize errors in counting as late as second grade. Other experts, however, claim that a lack of specific competencies, such as subitizing, is more important Berch and Mazzocco, Some evidence suggests that it is possible to predict which kindergartners are at risk for mathematics learning disabilities based on skill including reading numerals, number constancy, magnitude judgments of one-digit numbers, or mental addition of one-digit numbers Mazzocco and Thompson, However, until more is known, students should be classified as having mathematics learning disabilities only with great caution and.

    Such labeling in the earliest years could do more harm than good Clements and Sarama, It can appear that language is less of a concern in mathematics compared to other subjects because it is assumed to be based on numbers or symbols, but this is not the case Clements et al. In fact, children learn math mainly from oral language, rather than from mathematical symbolism or textbooks Janzen, Vocabulary and knowledge of print are both predictors of later numeracy Purpura et al.

    Similarly, growth in mathematics from kindergarten to third grade is related to both early numerical skills and phonological processing Vukovic, In one study of linguistically and ethnically diverse children aged years, language ability predicted gains in geometry, probability, and data analysis but not in arithmetic or algebra controlling for reading ability, visual—spatial working memory, and gender Vukovic and Lesaux, Thus, language may affect how children make meaning of mathematics but not its complex arithmetic procedures.

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    Moreover, there is an important bidirectional relationship between learning in mathematics and language Sarama et al. Each has related developmental milestones. Children learn number words at the same time as other linguistic labels. Most children recognize by the age of 2 which words are for numbers and use them only in appropriate contexts Fuson, Each also has related developmental patterns, with learning progressing along similar paths. In both, children recognize the whole before its parts. In learning language, this is word before syllable, syllable before rime-onset, and rime-onset before phoneme see also Anthony et al.

    Similarly in mathematics, numbers are first conceptualized as unbreakable categories and then later as composites e. By 6 years old in most cultures, children have been exposed to symbol representations that are both alphabetic and numerical, and they begin to be able to segment words into phonemes and numbers into singletons e.

    The ability to identify the component nature of words and numbers predicts the ability to read Adams, ; Stanovich and Siegel, and to compute Geary, , In addition to these similarities in typical developmental pathways, many children with learn-. Furthermore, there appear to be shared competencies between the two subject areas. Beginning mathematics scores have been shown to be highly predictive of subsequent achievement in both reading and mathematics although beginning reading skills such as letter recognition, word identification, and word sounds were shown to be highly predictive of later reading advanced competencies such as evaluation but not mathematics learning Duncan et al.

    Building Blocks children performed the same as the children in the control group on letter recognition and on three oral language subscales but outperformed them on four subscales: ability to recall key words, use of complex utterances, willingness to reproduce narratives independently, and inference Sarama et al. These skills had no explicit relation to the math curriculum. Similarly, a study of 5- to 7-year-olds showed that an early mathematics and logical-mathematical intervention increased later scores in English by 14 percentile points Shayer and Adhami, Time on task or time on instruction does affect learning, which naturally leads to consideration of potential conflicts or tradeoffs between time spent on different subjects e.

    However, this assumes that mathematics activities will not have a positive effect on language and literacy. Yet as described here, evidence from both educational and psychological research suggests the potential for high-quality instruction in each to have mutual benefits for learning in both subjects.

    Rich mathematical activities, such as discussing multiple solutions and solving narrative story problems, can help lay the groundwork for literacy through language development, while rich literacy activities can help lay the groundwork for mathematics development Sarama et al. For mathematics learning in children who are dual language learners, the language, not just the vocabulary, of mathematics need to be addressed Clements and Sarama, Challenges for dual language learners include both technical vocabulary, which can range in how similar or distinct terms are from everyday language, and the use of complex noun phrases.

    On the other hand, bilingual children often can understand a mathematical idea more readily because, after using different terms for it in different languages, they comprehend that the mathematical idea is abstract, and not tied to a specific term see Secada, At a minimum, their teachers need to connect everyday language with the language of math Janzen, Instructional practices for teaching mathematics with dual language learners are discussed further in Chapter 6. For subject-matter content knowledge and proficiency, children learn best when supported along a trajectory with three components: 1 their understanding of the subject-matter content itself, 2 their progress through predictable developmental levels and patterns of thinking related to their understanding of the content, and 3 instructional tasks and strategies that adults who work with children can employ to promote that learning at each level.

    For example:.

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    Some principles of how children learn along a trajectory hold across subject-matter domains, but there are also substantive differences among subjects in the specific skills children need and in the learning trajectories. Both generalizable principles and subject-specific distinctions have implications for the knowledge and competencies needed to work with children.

    These general learning competencies have been labeled and categorized in various ways. This section examines these competencies as well as their interrelationships with the previously discussed subject-matter domains of language and literacy and mathematics. Several cognitive control processes are important for planning and executing goal-directed activity, which is needed for successful learning e.

    These processes include, for example, short-term and working memory, attention control and shifting, cognitive flexibility changing thinking between different concepts and thinking about multiple concepts simultaneously , inhibitory control suppressing unproductive responses or strategies , and cognitive self-regulation. Other theoretical frameworks exist as well. As with the overall domains of development displayed earlier in Figure , the committee did not attempt to reconcile those different perspectives. This variation in perspectives makes it difficult to parse the literature produced by different fields of research and practice.

    In general, however, executive function appears to improve most rapidly in young children Best et al. Executive function processes appear to be partially dependent on the development of the prefrontal cortex the site of higher-order cognitive processes , notably through the preschool and kindergarten age range Bassett et al. Short-term memory is the ability for short-term recall, such as of a sentence or important details from conversation and reading.

    Working memory allows children to hold in their memory information from multiple sources, whether heard or read, so they can use and link that information. Updating working memory is the ability to keep and use relevant information while engaging in another cognitively demanding task Conway et al. Attention control is the ability to focus attention and disregard distracting stimuli e. Attention shifting and cognitive flexibility are often grouped. Cognitive flexibility is important, for example, for reading Duke and Block, Children who are better able to consider, at the same time, both letter-sound and semantic meaning information about words have better reading comprehension Cartwright, ; Cartwright et al.

    Reading comprehension also appears to improve when children are taught about words with multiple meanings e. In addition, interventions in young children that focus on cognitive flexibility have shown significant benefits for reading comprehension Cartwright, Inhibitory control involves controlling a dominant response e.

    The skill of simple response inhibition withholding an initial, sometimes impulsive, response develops during infancy through toddlerhood. Infants also develop some control of cognitive conflict in tasks in which an. Later in their first year, children can resolve conflict between their line of sight and their line of reaching Diamond, By about 30 months, they can successfully complete a spatial conflict task Rothbart and Rueda, From 3 to 5 years of age, complex response inhibition and response shifting develop, with attention shifting developing at about age 4 Bassett et al.

    The most rapid increase in inhibitory control is between 5 and 8 years of age, although moderate improvements are seen up to young adulthood Best et al. As one example of its importance for mathematics, when the initial reading of a problem is not the correct one, children need to inhibit their impulse to answer incorrectly and carefully examine the problem. Three birds already flew away. How many birds were there from the start? Cognitive self-regulation is what helps children plan ahead, focus attention, and remember past experiences.

    The construct of self-regulation and related concepts have a long history in psychology e. Most recently, researchers and educators have used the broad term self-regulation to refer to the processes involved in intentionally controlling attention, thinking, impulses, emotions, and behavior. In this way, self-regulation can be thought of in relation to several aspects of development, including the cognitive processes discussed here and the social and emotional processes discussed later in this chapter. Developmental psychobiological research and neuroimaging indicate that these subclasses are both neurally and behaviorally distinct while also being related and correlated Bassett et al.

    Together, these types of self-regulation allow children to persevere with tasks even when facing difficulties in problem solving or learning, fatigue, distraction, or decreased motivation Blair and Razza, ; Neuenschwander et al. It is thus unsurprising that. Both cognitive self-regulation and emotional self-regulation discussed later in this chapter contribute to socioemotional development and also play a role in learning.

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