Early Childhood Mathematical Reasoning

Early Childhood Mathematical Reasoning

Early Childhood Mathematical Reasoning
Mathematical reasoning, like literacy, builds on informally acquired knowledge. Between 14 and 16 months, toddlers display a beginning grasp of ordinality , or order relationships between quantities—for example, that 3 is more than 2, and 2 is more than 1. And 2-year-olds often indicate without counting that a set of items has “lots,” “many,” or “little” in relation to others (Ginsburg, Lee, & Boyd, 2008 ). By the time children turn 3, most can count rows of about five objects, although they do not yet know exactly what the words mean. For example, when asked for one, they give one item, but when asked for two, three, four, or five, they usually give a larger, but incorrect, amount. Nevertheless, 2½- to 3½-year-olds understand that a number word refers to a unique quantity—that when a number label changes (for example, from five to six), the number of items should also change (Sarnecka & Gelman, 2004 ).

By age 3½ to 4, most children have mastered the meaning of numbers up to 10, count correctly, and grasp the vital principle of cardinality —that the last number in a counting sequence indicates the quantity of items in a set (Geary, 2006a ). Mastery of cardinality increases the efficiency of children’s counting. Early Childhood Mathematical Reasoning.

Around age 4, children use counting to solve arithmetic problems. At first, their strategies are tied to the order of numbers as presented; to add 2 + 4, they count on from 2 (Bryant & Nunes, 2002 ). But soon they experiment with other strategies and eventually arrive at the most efficient, accurate approach—in this example, beginning with the higher digit. Around this time, children realize that subtraction cancels out addition. Knowing, for example, that 4 + 3 = 7, they can infer without counting that 7 – 3 = 4 (Rasmussen, Ho, & Bisanz, 2003 ). Grasping basic arithmetic rules facilitates rapid computation, and with enough practice, children recall answers automatically.

When adults provide many occasions for counting, comparing quantities, and talking about number concepts, children acquire these understandings sooner (Ginsburg, Lee, & Boyd, 2008 ). Math proficiency at kindergarten entry predicts math achievement years later, in elementary and secondary school (Duncan et al., 2007 ; Romano et al., 2010 ).

As with emergent literacy, children from low-SES families begin kindergarten with considerably less math knowledge than their economically advantaged agemates—a gap due to differences in environmental supports. In an early childhood math curriculum called Building Blocks, materials that promote math concepts and skills enable teachers to weave math into many preschool daily activities, from building blocks to art and stories (Clements & Sarama, 2008 ). Compared with agemates randomly assigned to other preschool programs, low-SES preschoolers experiencing Building Blocks showed substantially greater year-end gains in math concepts and skills, including counting, sequencing, and arithmetic computation.

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This board game helps preschoolers acquire basic math knowledge by affording many opportunities to count, compare quantities, and talk about number concepts. Early Childhood Mathematical Reasoning.

ASK YOURSELF
REVIEW Describe a typical 4-year-old’s understanding of mental activities, noting both strengths and limitations.

CONNECT Cite evidence on the development of preschoolers’ memory, theory of mind, and literacy and mathematical understanding that is consistent with Vygotsky’s sociocultural theory.

APPLY Lena wonders why her son’s preschool teacher provides extensive playtime in learning centers instead of formal lessons in literacy and math skills. Explain to Lena why adult-supported play is the best way for preschoolers to develop academically.

REFLECT Describe informal experiences important for literacy and math development that you experienced while growing up. How do you think those experiences contributed to your academic progress in school?

image14 Individual Differences in Mental Development
Five-year-old Hal sat in a testing room while Sarah gave him an intelligence test. Some of Sarah’s questions were verbal. For example, she showed him a picture of a shovel and said, “Tell me what this is”—an item measuring vocabulary. She tested his memory by asking him to repeat sentences and lists of numbers back to her. To assess Hal’s spatial reasoning, Sarah used nonverbal tasks: Hal copied designs with special blocks, figured out the pattern in a series of shapes, and indicated what a piece of paper folded and cut would look like when unfolded (Roid, 2003 ; Wechsler, 2002 ). Early Childhood Mathematical Reasoning.

Sarah knew that Hal came from an economically disadvantaged family. When low-SES and certain ethnic minority preschoolers are bombarded with questions by an unfamiliar adult, they sometimes react with anxiety. Also, such children may not define the testing situation in achievement terms but, instead, may settle for lower performance than their abilities allow. Sarah spent time playing with Hal before she began testing and encouraged him while testing was in progress. Under these conditions, low-SES preschoolers improve in performance (Bracken, 2000 ).

The questions Sarah asked Hal tap knowledge and skills that not all children have equal opportunity to learn. In Chapter 9 , we will take up the hotly debated issue of cultural bias in mental testing. For now, keep in mind that intelligence tests do not sample all human abilities, and performance is affected by cultural and situational factors (Sternberg, 2005 ). Nevertheless, test scores remain important: By age 6 to 7, they are good predictors of later IQ and academic achievement, which are related to vocational success in industrialized societies. Let’s see how the environments in which preschoolers spend their days—home, preschool, and child care—affect mental test performance.

Applying What We Know Features of a High-Quality Home Life for Preschoolers: The HOME Early Childhood Subscales
Subscale

Sample Item

Cognitive stimulation through toys, games, and reading material

Home includes toys that teach colors, sizes, and shapes.

Language stimulation

Parent converses with child at least twice during observer’s visit.

Organization of the physical environment

All visible rooms are reasonably clean and minimally cluttered.

Emotional support: parental pride, affection, and warmth

Parent spontaneously praises child’s qualities or behavior twice during observer’s visit.

Parent caresses, kisses, or hugs child at least once during observer’s visit.

Stimulation of academic behavior

Child is encouraged to learn colors.

Parental modeling and encouragement of social maturity

Parent introduces interviewer to child.

Opportunities for variety in daily stimulation

Family member takes child on one outing (picnic, shopping) at least every other week.

Avoidance of physical punishment

Parent neither slaps nor spanks child during observer’s visit.

Sources: Bradley, 1994; Bradley et al., 2001.

Home Environment and Mental Development
A special version of the Home Observation for Measurement of the Environment (HOME), covered in Chapter 5 , assesses aspects of 3- to 6-year-olds’ home lives that support mental development (see Applying What We Know above). Preschoolers who develop well intellectually have homes rich in educational toys and books. Their parents are warm and affectionate, stimulate language and academic knowledge, and arrange interesting outings. They also make reasonable demands for socially mature behavior—for example, that the child perform simple chores and behave courteously toward others. And these parents resolve conflicts with reason instead of physical force and punishment (Bradley & Caldwell, 1982 ; Espy, Molfese, & DiLalla, 2001 ; Roberts, Burchinal, & Durham, 1999 ). Early Childhood Mathematical Reasoning.

As we saw in Chapter 2 , these characteristics are less often seen in low-SES families. When parents manage, despite low education and income, to obtain high HOME scores, their preschoolers do substantially better on tests of intelligence and measures of language and emergent literacy skills (Berger, Paxson, & Waldfogel, 2009 ; Foster et al., 2005 ; Mistry et al., 2008 ). And in a study of low-SES African-American 3- and 4-year-olds, HOME cognitive stimulation and emotional support subscales predicted reading achievement four years later (Zaslow et al., 2006 ). These findings highlight the vital role of home environmental quality in children’s mental development.

Preschool, Kindergarten, and Child Care
Children between ages 2 and 6 spend even more time away from their homes and parents than infants and toddlers do. Largely because of the rise in maternal employment, over the past several decades the number of young children enrolled in preschool or child care has steadily increased to more than 60 percent in the United States (U.S. Census Bureau, 2012b ).

A preschool is a program with planned educational experiences aimed at enhancing the development of 2- to 5-year-olds. In contrast, child care refers to a variety of arrangements for supervising children. With age, children tend to shift from home-based to center-based programs. Many children, however, experience several types of arrangements at once (Federal Interagency Forum on Child and Family Statistics, 2011 ).

The line between preschool and child care is fuzzy. In response to the needs of employed parents, many U.S. preschools, as well as most public school kindergartens, have increased their hours from half to full days (U.S. Department of Education, 2012b ). At the same time, good child care should provide the same high-quality educational experiences that an effective preschool does. Early Childhood Mathematical Reasoning.

Types of Preschool and Kindergarten.
Preschool and kindergarten programs range along a continuum from child-centered to teacher-directed. In child-centered programs , teachers provide a variety of activities from which children select, and much learning takes place through play. In contrast, in academic programs , teachers structure children’s learning, teaching letters, numbers, colors, shapes, and other academic skills through formal lessons, often using repetition and drill.

Despite evidence that formal academic training in early childhood undermines motivation and emotional well-being, preschool and kindergarten teachers have felt increased pressure to take this approach. Young children who spend much time passively sitting and completing worksheets display more stress behaviors (such as wiggling and rocking), have less confidence in their abilities, prefer less challenging tasks, and are less advanced in motor, academic, language, and social skills at the end of the school year (Marcon, 1999a ; Stipek et al., 1995 ). Follow-ups reveal lasting effects through elementary school in poorer study habits and achievement (Burts et al., 1992 ; Hart et al., 1998 , 2003 ). These outcomes are strongest for low-SES children.

A special type of child-centered approach is Montessori education, devised a century ago by Italian physician Maria Montessori, who originally applied her method to poverty-stricken children. Features of Montessori schooling include materials specially designed to promote exploration and discovery, child-chosen activities, and equal emphasis on academic and social development (Lillard, 2007 ). In an evaluation of public preschools serving mostly urban minority children in Milwaukee, researchers compared students randomly assigned to either Montessori or other classrooms (Lillard & Else-Quest, 2006 ). Five-year-olds who had completed two years of Montessori education outperformed controls in literacy and math skills, false-belief understanding, concern with fairness in solving conflicts with peers, and cooperative play with classmates.

Early Intervention for At-Risk Preschoolers.
In the 1960s, as part of the “War on Poverty” in the United States, many intervention programs for economically disadvantaged preschoolers were initiated in an effort to address learning problems before formal schooling begins. The most extensive of these federal programs, Project Head Start , began in 1965. A typical Head Start center provides children with a year or two of preschool, along with nutritional and health services. Parent involvement is central to the Head Start philosophy. Parents serve on policy councils, contribute to program planning, work directly with children in classrooms, attend special programs on parenting and child development, and receive services directed at their own emotional, social, and vocational needs. Currently, Head Start serves about 904,000 children and their families across the nation (Head Start Bureau, 2010 ).

More than two decades of research have established the long-term benefits of preschool intervention. The most extensive of these studies combined data from seven interventions implemented by universities or research foundations. Results showed that poverty-stricken children who attended programs scored higher in IQ and achievement than controls during the first two to three years of elementary school. After that, differences declined (Lazar & Darlington, 1982 ). But on real-life measures of school adjustment, children and adolescents who had received intervention remained ahead. They were less likely to be placed in special education or retained in grade, and a greater number graduated from high school. Early Childhood Mathematical Reasoning.

A separate report on one program—the High/Scope Perry Preschool Project—revealed benefits lasting well into adulthood. Two years’ exposure to cognitively enriching preschool was associated with increased employment and reduced pregnancy and delinquency rates in adolescence. At age 27, those who had attended preschool were more likely than no-preschool controls to have graduated from high school and college, have higher earnings, be married, and own their own home—and less likely to have been involved with the criminal justice system (see Figure 7.12 ). In the most recent follow-up, at age 40, the intervention group sustained its advantage on all measures of life success, including education, income, family life, and law-abiding behavior (Schweinhart, 2010 ; Schweinhart et al., 2005 ).

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Project Head Start provides children from poverty-stricken families with preschool education and nutritional and health services. High-quality early educational intervention has benefits lasting into adulthood.

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FIGURE 7.12 Some outcomes of the High/Scope Perry Preschool Project on follow-up at age 27.
Although two years of a cognitively enriching preschool program did not eradicate the effects of growing up in poverty, children who received intervention were advantaged over no-intervention controls on all measures of life success when they reached adulthood.

(Adapted from Schweinhart, 2010; Schweinhart et al., 2005.)

Do effects on school adjustment of these well-designed and well-delivered programs generalize to Head Start and other community-based preschool interventions? Findings are similar, though not as strong. Head Start preschoolers, who are more economically disadvantaged than children in other programs, have more severe learning and behavior problems. And quality of services often does not equal that of model university-based programs (Barnett, 2011 ). But interventions of high quality are associated with diverse, long-lasting favorable outcomes, including higher rates of high school graduation and college enrollment and lower rates of adolescent drug use and delinquency (Garces, Thomas, & Currie, 2002 ; Love et al., 2006 ; Mashburn, 2008 ).

A consistent finding is that gains in IQ and achievement test scores from attending Head Start and other interventions quickly dissolve. In the Head Start Impact Study, a nationally representative sample of 5,000 Head Start 3- and 4-year-olds was randomly assigned to one year of Head Start or to a control group that could attend other types of preschool programs (U.S. Department of Health and Human Services, 2010d ). By year’s end, Head Start 3-year-olds exceeded controls in vocabulary, emergent literacy, and math skills; 4-year-olds in vocabulary, emergent literacy, and color identification. But except for language skills, academic advantages were no longer evident by end of first grade.

What explains these disappointing results? Head Start children typically enter inferior public schools in poverty-stricken neighborhoods, which undermine the benefits of preschool education (Brooks-Gunn, 2003 ; Ramey, Ramey, & Lanzi, 2006 ). An exception is the Chicago Child–Parent Centers—a program emphasizing literacy intervention and parent involvement that began at age 3 and continued through third grade—in which gains in academic achievement were still evident in junior high school (Reynolds & Temple, 1998 ). Early Childhood Mathematical Reasoning.

Still, the improved school adjustment that results from attending a one- or two-year Head Start program is impressive. Program effects on parents may contribute: The more involved parents are in Head Start, the better their child-rearing practices and the more stimulating their home learning environments—factors positively related to preschoolers’ task persistence and year-end academic, language, and social skills (Marcon, 1999b ; McLoyd, Aikens, & Burton, 2006 ; Parker et al., 1999 ).

Head Start is highly cost-effective when compared with the cost of providing special education, treating criminal behavior, and supporting unemployed adults. Economists estimate a lifetime return to society of $300,000 to $500,000 on an investment of about $17,000 per preschool child—a potential total savings of many billions of dollars if every poverty-stricken preschooler in the United States were enrolled (Heckman et al., 2010 ). Because of limited funding, however, only 60 percent of poverty-stricken 3- and 4-year-olds attend some type of preschool program, with Head Start serving just half of these children (Magnuson & Shager, 2010 ).

Child Care.
We have seen that high-quality early intervention can enhance the development of economically disadvantaged children. As noted in Chapter 5 , however, much U.S. child care lacks quality. Preschoolers exposed to substandard child care, especially for long hours, score lower in cognitive and social skills and higher in behavior problems (Belsky, 2006 ; Lamb & Ahnert, 2006 ; NICHD Early Child Care Research Network, 2003b , 2006 ). Externalizing difficulties are especially likely to endure through middle childhood and into adolescence after extensive exposure to mediocre case (Belsky et al., 2007b ; Vandell et al., 2010 ).

In contrast, good child care enhances cognitive, language, and social development, especially for low-SES children—effects that persist into elementary school and, for academic achievement, adolescence (Belsky et al., 2007b ; Burchinal, Vandergrift, & Pianta, 2010 ; NICHD Early Child Care Research Network, 2006 ; Vandell et al., 2010 ). And in a study that followed very-low-income children over the preschool years, center-based care was more strongly associated with cognitive gains than were other child-care arrangements, probably because centers are more likely to provide a systematic educational program (Loeb et al., 2004 ).

Applying What We Know on the following page summarizes characteristics of high-quality early childhood programs, based on standards for developmentally appropriate practice devised by the U.S. National Association for the Education of Young Children. These standards offer a set of worthy goals as the United States strives to upgrade child-care and educational services for young children.

Educational Media
Besides home and preschool, young children spend much time in another learning environment: electronic media, including both television and computers. In the industrialized world, nearly all homes have at least one television set, and most have two or more. And more than 90 percent of U.S. children live in homes with one or more computers, 80 percent of which have an Internet connection, usually a high-speed link (Rideout, Foehr, & Roberts, 2010 ; U.S. Census Bureau, 2012b ). Early Childhood Mathematical Reasoning.

Educational Television.
Sammy’s favorite TV program, Sesame Street, uses lively visual and sound effects to stress basic literacy and number concepts and puppet and human characters to teach general knowledge, emotional and social understanding, and social skills. Today, Sesame Street is broadcast in more than 140 countries, making it the most widely viewed children’s program in the world (Sesame Workshop, 2009 ).

Time devoted to watching children’s educational programs is associated with gains in early literacy and math skills and academic progress in elementary school (Ennemoser & Schneider, 2007 ; Linebarger et al., 2004 ; Wright et al., 2001 ). Consistent with these findings, one study reported a link between preschool viewing of Sesame Street and other similar educational programs and getting higher grades, reading more books, and placing more value on achievement in high school (Anderson et al., 2001 ).

Sesame Street has modified its previous rapid-paced format in favor of more leisurely episodes with a clear story line. Children’s programs with slow-paced action and easy-to-follow narratives, such as Arthur & Friends, The Magic School Bus, and Wishbone, lead to more elaborate make-believe play in early childhood and to greater recall of program content and gains in vocabulary and reading skills in the early school grades than programs that simply provide information (Linebarger & Piotrowski, 2010 ; Singer & Singer, 2005 ). Narratively structured educational TV eases processing demands, freeing up space in working memory for applying program content to real-life situations. Early Childhood Mathematical Reasoning.

Applying What We Know Signs of Developmentally Appropriate Early Childhood Programs
Program Characteristics

Signs of Quality

Physical setting

Indoor environment is clean, in good repair, and well-ventilated. Classroom space is divided into richly equipped activity areas, including make-believe play, blocks, science, math, games and puzzles, books, art, and music. Fenced outdoor play space is equipped with swings, climbing equipment, tricycles, and sandbox.

Group size

In preschools and child-care centers, group size is no greater than 18 to 20 children with two teachers.

Caregiver–child ratio

In preschools and child-care centers, teacher is responsible for no more than 8 to 10 children. In child-care homes, caregiver is responsible for no more than 6 children.

Daily activities

Children select many of their own activities and learn through experiences relevant to their own lives, mainly in small groups or individually. Teachers facilitate children’s involvement, accept individual differences, and adjust expectations to children’s developing capacities.

Interactions between adults and children

Teachers move among groups and individuals, asking questions, offering suggestions, and adding more complex ideas. Teachers use positive guidance techniques, such as modeling and encouraging expected behavior and redirecting children to more acceptable activities.

Teacher qualifications

Teachers have college-level specialized preparation in early childhood development, early childhood education, or a related field.

Relationships with parents

Parents are encouraged to observe and participate. Teachers talk frequently with parents about children’s behavior and development.

Licensing and accreditation

Child-care setting, whether a center or a home, is licensed by the state. Voluntary accreditation by the National Association for the Education of Young Children ( www.naeyc.org/academy ) or the National Association for Family Child Care ( www.nafcc.org ) is evidence of an especially high-quality program.

Source: Copple & Bredekamp, 2009.

Despite the spread of computers, television remains the dominant form of youth media. The average U.S. 2- to 6-year-old watches TV programs and videos from 1½ to 2? hours a day. In middle childhood, viewing time increases to an average of 3½ hours a day, before declining slightly in adolescence (Rideout, Foehr, & Roberts, 2010 ; Rideout & Hamel, 2006 ). Early Childhood Mathematical Reasoning.

Low-SES, African-American, and Hispanic children are more frequent viewers, perhaps because few alternative forms of entertainment are available in their neighborhoods or affordable for their parents. Also, parents with limited education are more likely to engage in practices that heighten TV viewing, including leaving the TV on all day and eating family meals in front of it (Rideout, Foehr, & Roberts, 2010 ). About one-third of U.S. preschoolers and 70 percent of school-age children and adolescents have a TV set in their bedroom; these children spend from 40 to 90 more minutes per day watching than agemates without one (Rideout & Hamel, 2006 ).

Does extensive TV viewing take children away from worthwhile activities? Persistent background TV distracts infants and preschoolers from their play, diminishing time spent in focused attention and involvement with a set of toys (Courage & Howe, 2010 ). The more preschool and school-age children watch prime-time shows and cartoons, the less time they spend reading and interacting with others and the poorer their academic skills (Ennemoser & Schneider, 2007 ; Huston et al., 1999 ; Wright et al., 2001 ). Whereas educational programs can be beneficial, watching entertainment TV—especially heavy viewing—detracts from children’s school success and social experiences.

Learning with Computers.
More than one-fourth of 4- to 6-year-olds use a computer regularly, with preschoolers of higher-SES parents having greater computer access (Calvert et al., 2005 ). And because computers can have rich educational benefits, many early childhood classrooms include computer learning centers. Kindergartners who use computers to draw or write produce more elaborate pictures and text, make fewer writing errors, and edit their work much as older children do. And combining everyday and computer experiences with math manipulatives is especially effective in promoting math concepts and skills (Clements & Sarama, 2003 ). Early Childhood Mathematical Reasoning.

Simplified computer languages that children can use to make designs or build structures introduce them to programming skills. As long as adults support children’s efforts, computer programming promotes improved problem solving and metacognition because children must plan and reflect on their thinking to get their programs to work. Furthermore, while programming, children are especially likely to help one another and to persist in the face of challenge (Nastasi & Clements, 1994 ; Resnick & Silverman, 2005 ).

As with television, children spend much time using computers for entertainment purposes, especially game playing. Both media are rife with gender stereotypes and violence. We will consider their impact on emotional and social development in the next chapter.

ASK YOURSELF
REVIEW What findings indicate that child-centered rather than academic preschools and kindergartens are better suited to fostering academic development?

CONNECT Compare outcomes resulting from preschool intervention programs with those from interventions beginning in infancy (see page 173 in Chapter 5 ). Which are more likely to lead to lasting cognitive gains? Explain.

APPLY Your senator has heard that IQ gains resulting from Head Start do not last, so he plans to vote against additional funding. Write a letter explaining why he should support Head Start.

REFLECT How much and what kinds of TV viewing and computer use did you engage in as a child? How do you think your home media environment influenced your development?

image17 Language Development
Language is intimately related to virtually all cognitive changes discussed in this chapter. Between ages 2 and 6, children make momentous advances in language. Their remarkable achievements, as well as their mistakes along the way, reveal their active, rule-oriented approach to language learning. Early Childhood Mathematical Reasoning.

Vocabulary
At age 2, Sammy had a spoken vocabulary of about 250 words. Buy age 6 he will have acquired around 10,000 words (Bloom, 1998 ). To accomplish this feat, Sammy acquired about five new words each day. How do children build their vocabularies so quickly? Research shows that they can connect new words with their underlying concepts after only a brief encounter, a process called fast-mapping . Preschoolers can even fast-map two or more new words encountered in the same situation (Wilkinson, Ross, & Diamond, 2003 ).

Types of Words.
Children in many Western and non-Western language communities fast-map labels for objects especially rapidly because these refer to concepts that are easy to perceive. When adults point to, label, and talk about an object, they help the child figure out the word’s meaning (Gershoff-Stowe & Hahn, 2007 ). Soon children add verbs (go, run, broke), which require more complex understandings of relationships between objects and actions. Children learning Chinese, Japanese, and Korean—languages in which nouns are often omitted from adult sentences, while verbs are stressed—acquire verbs more readily than their English-speaking agemates (Kim, McGregor, & Thompson, 2000 ; Tardif, 2006 ). Gradually, preschoolers add modifiers (red, round, sad). Among those that are related in meaning, first they make general distinctions (big–small), then more specific ones (tall–short, high–low, wide–narrow) (Stevenson & Pollitt, 1987 ).

To fill in for words they have not yet learned, children as young as age 3 coin new words using ones they already know—for example, “plant-man,” for a gardener, “crayoner” for a child using crayons. Preschoolers also extend language meanings through metaphor—like the 3-year-old who described a stomachache as a “fire engine in my tummy” (Winner, 1988 ). Young preschoolers’ metaphors involve concrete sensory comparisons: “Clouds are pillows,” “Leaves are dancers.” Once vocabulary and general knowledge expand, children also appreciate nonsensory comparisons: “Friends are like magnets,” “Time flies by” (Keil, 1986 ; Özçaliskan, 2005 ). As a result, young children sometimes communicate in amazingly vivid and memorable ways. Early Childhood Mathematical Reasoning.

Strategies for Word Learning.
Preschoolers figure out the meanings of new words by contrasting them with words they already know. How do they discover which concept each word picks out? One speculation is that early in vocabulary growth, children adopt a mutual exclusivity bias—the assumption that words refer to entirely separate (nonoverlapping) categories (Markman, 1992 ). Consistent with this idea, when 2-year-olds hear the labels for two distinct novel objects (for example, clip and horn), they assign each word correctly, to the whole object and not just a part of it (Waxman & Senghas, 1992 ).

Indeed, children’s first several hundred nouns refer mostly to objects well-organized by shape. And learning of nouns based on the perceptual property of shape heightens young children’s attention to the distinctive shapes of other objects (Smith et al., 2002 ; Yoshida & Smith, 2003 ). This shape bias helps preschoolers master additional names of objects, and vocabulary accelerates. Early Childhood Mathematical Reasoning.

Once the name of a whole object is familiar, on hearing a new name for the object, 2- and 3-year-olds set aside the mutual exclusivity bias. For example, if the object (bottle) has a distinctively shaped part (spout), children readily apply the new label to it (Hansen & Markman, 2009 ). Still, mutual exclusivity and object shape cannot account for preschoolers’ remarkably flexible responses when objects have more than one name. Children often call on other components of language in these instances.

According to one proposal, preschoolers figure out many word meanings by observing how words are used in the structure of sentences (Gleitman et al., 2005 ; Naigles & Swenson, 2007 ). Consider an adult who says, “This is a citron one,” while showing the child a yellow car. Two- and 3-year-olds conclude that a new word used as an adjective for a familiar object (car) refers to a property of that object (Hall & Graham, 1999 ; Imai & Haryu, 2004 ). As preschoolers hear the word in various sentence structures (“That lemon is bright citron”), they refine its meaning.

Young children also take advantage of rich social information that adults frequently provide, while drawing on their own expanding ability to infer others’ intentions, desires, and perspectives (Akhtar & Tomasello, 2000 ). In one study, an adult performed an action on an object and then used a new label while looking back and forth between the child and the object, as if inviting the child to play. Two-year-olds concluded that the label referred to the action, not the object (Tomasello & Akhtar, 1995 ). By age 3, children can even use a speaker’s recently expressed desire (“I really want to play with the riff”) to figure out the label belonging to one of two novel objects (Saylor & Troseth, 2006 ).

Adults also inform children directly about which of two or more words to use—by saying, for example, “You can call it a sea creature, but it’s better to say dolphin.” Preschoolers’ vocabularies grow more quickly when they have parents who provide such clarifying information (Callanan & Sabbagh, 2004 ).

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Young children rely on any useful information available to add to their vocabularies. As he makes a bird feeder, this preschooler attends to a variety of perceptual, social, and linguistic cues to grasp the meanings of unfamiliar words, such as pine cone, spread, dip, bird seed, and munching sparrow. Early Childhood Mathematical Reasoning.

Explaining Vocabulary Development.
Children acquire vocabulary so efficiently and accurately that some theorists believe that they are innately biased to induce word meanings using certain principles, such as mutual exclusivity (Lidz, Gleitman, & Gleitman, 2004 ; Woodward & Markman, 1998 ). But critics point out that a small set of built-in, fixed principles cannot account for the flexible manner in which children master vocabulary (Deák, 2000 ). And many word-learning strategies cannot be innate because children acquiring different languages use different approaches to mastering the same meanings.

An alternative view is that vocabulary growth is governed by the same cognitive strategies that children apply to nonlinguistic information. According to one account, children draw on a coalition of cues—perceptual, social, and linguistic—which shift in importance with age (Golinkoff & Hirsh-Pasek, 2006 , 2008 ). Infants rely solely on perceptual features. Toddlers and young preschoolers, while still sensitive to perceptual features (such as object shape), increasingly attend to social cues—the speaker’s direction of gaze, gestures, and expressions of desire and intention (Hollich, Hirsh-Pasek, & Golinkoff, 2000 ; Pruden et al., 2006 ). And as language develops further, linguistic cues—sentence structure and intonation (stress, pitch, and loudness)—play larger roles.

Preschoolers are most successful at figuring out new word meanings when several kinds of information are available (Saylor, Baldwin, & Sabbagh, 2005 ). Researchers have just begun to study the multiple cues that children use for different kinds of words and how their combined strategies change with development.

Grammar
Between ages 2 and 3, English-speaking children use simple sentences that follow a subject–verb–object word order. Children learning other languages adopt the word orders of the adult speech to which they are exposed.

Basic Rules.
Studies of children acquiring diverse languages reveal that their first use of grammatical rules is piecemeal—limited to just a few verbs. As children listen for familiar verbs in adults’ speech, they expand their own utterances containing those verbs, relying on adult speech as their model (Gathercole, Sebastián, & Soto, 1999 ; Lieven, Pine, & Baldwin, 1997 ). Sammy, for example, added the preposition withto the verb open (“You open with scissors”) but not to the word hit (“He hit me stick”). Early Childhood Mathematical Reasoning.

To test preschoolers’ ability to generate novel sentences that conform to basic English grammar, researchers had them use a new verb in the subject–verb–object form after hearing it in a different construction, such as passive: “Ernie is getting gorped by the dog.” The percentage of children who, when asked what the dog was doing, could respond, “He’s gorping Ernie,” rose steadily with age. But not until age 3½ to 4 could the majority of children apply the subject–verb–object structure broadly, to newly acquired verbs (Chan et al., 2010 ; Tomasello, 2003 , 2006 ).

Once children form three-word sentences, they make small additions and changes to words that enable them to express meanings flexibly and efficiently. For example, they add -s for plural (cats), use prepositions (in and on), and form various tenses of the verb to be (is, are, were, has been, will). English-speaking children master these grammatical markers in a regular sequence, starting with those that involve the simplest meanings and structures (Brown, 1973 ; de Villiers & de Villiers, 1973 ).

When preschoolers acquire these markers, they sometimes overextend the rules to words that are exceptions—a type of error called overregularization . “My toy car breaked” and “We each have two foots” are expressions that appear between ages 2 and 3 (Maratsos, 2000 ; Marcus, 1995 ).

Complex Structures.
Gradually, preschoolers master more complex grammatical structures, although they do make mistakes. In first creating questions, 2- to 3-year-olds use many formulas: “Where’s X?” “Can I X?” (Dabrowska, 2000 ; Tomasello, 1992 , 2003 ). Question asking remains variable for the next couple of years. An analysis of one child’s questions revealed that he inverted the subject and verb when asking certain questions but not others (“What she will do?” “Why he can go?”) The correct expressions were the ones he heard most often in his mother’s speech (Rowland & Pine, 2000 ). And sometimes children produce errors in subject–verb agreement (“Where does the dogs play?”) and in subject case (“Where can me sit?”) (Rowland, 2007 ).

Similarly, children have trouble with some passive sentences. When told, “The car was pushed by the truck,” young preschoolers often make a toy car push a truck. By age 5, they understand such expressions, but full mastery of the passive form is not complete until the end of middle childhood (Lempert, 1990 ; Tomasello, 2006 ).

Nevertheless, preschoolers’ grasp of grammar is remarkable. By age 4 to 5, they form embedded sentences (“I think he will come”), tag questions (“Dad’s going to be home soon, isn’t he?”), and indirect objects (“He showed his friend the present”). As the preschool years draw to a close, children use most of the grammatical constructions of their language competently (Tager-Flusberg & Zukowski, 2009 ). Early Childhood Mathematical Reasoning.

Explaining Grammatical Development.
Evidence that grammatical development is an extended process has raised questions about Chomsky’s nativist theory (to review, see page 174 in Chapter 5 ). Some experts believe that grammar is a product of general cognitive development—children’s tendency to search for consistencies and patterns of all sorts. These information-processing theorists believe that children notice which words appear in the same positions in sentences and are similarly combined with other words (Chang, Dell, & Bock, 2006 ; Tomasello, 2003 , 2011 ). Over time, they group words into grammatical categories and use them appropriately in sentences.

Still other theorists, while also focusing on how children process language, agree with the essence of Chomsky’s theory. One idea proposes that the grammatical categories into which children group word meanings are innate—present at the outset (Pinker, 1999 ). Critics, however, point out that children’s early word combinations do not show a grasp of grammar. Still another theory holds that children do not start with innate knowledge but, rather, have a special language-making capacity—a set of procedures for analyzing the language they hear, which supports the discovery of grammatical regularities (Slobin, 1985 , 1997 ). Controversy persists over whether a universal language-processing device exists or whether children who hear different languages devise unique strategies (Lidz, 2007 ; Marchman & Thal, 2005 ).

Conversation
Besides acquiring vocabulary and grammar, children must learn to engage in effective and appropriate communication. This practical, social side of language is called pragmatics , and preschoolers make considerable headway in mastering it.

As early as age 2, children are skilled conversationalists. In face-to-face interaction, they take turns and respond appropriately to their partners’ remarks (Pan & Snow, 1999 ). With age, the number of turns over which children can sustain interaction and their ability to maintain a topic over time increase. By age 4, children adjust their speech to fit the age, sex, and social status of their listeners. For example, in acting out roles with hand puppets, they use more commands when playing socially dominant and male roles (teacher, doctor, father) but speak more politely and use more indirect requests when playing less dominant and female roles (student, patient, mother) (Anderson, 2000 ). Early Childhood Mathematical Reasoning.

Preschoolers’ conversational skills occasionally do break down—for example, when talking on the phone. Here is an excerpt from one 4-year-old’s phone conversation with his grandfather:

Grandfather:

How old will you be?

John:

Dis many. [Holding up four fingers.]

Grandfather:

Huh?

John:

Dis many. [Again holding up four fingers.] (Warren & Tate, 1992 , pp. 259–260)

Young children’s conversations appear less mature in highly demanding situations in which they cannot see their listeners’ reactions or rely on typical conversational aids, such as gestures and objects to talk about. But when asked to tell a listener how to solve a simple puzzle, 3- to 6-year-olds give more specific directions over the phone than in person, indicating that they realize the need for more verbal description on the phone (Cameron & Lee, 1997 ). Between ages 4 and 8, both conversing and giving directions over the phone improve greatly. Telephone talk provides yet another example of how preschoolers’ competencies depend on the demands of the situation.