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89 Cards in this Set
- Front
- Back
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Counting |
• By age 3, children acquire a means to count, meaning precisely establishing the number of objects in sets largest than three. • Many 3-year-olds can count ten objects. • Many 5-year-olds can count to 100. • There are cultural differences in the counting level attained by young children. • Not until the age of 5 do most children know the relative sizes of the numbers between 1 and 10 and can say which is more, 4 or 6 oranges. The ability to do so is known as numerical ordering. |
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Five Counting Principles Attributable to Preschoolers |
• One-to-one correspondence: Each object should be labeled by a single number word. • Stable order: The numbers should always be recited in the same order. (1,2,3) • Cardinality: The number of objects in the set corresponds to the last number stated. (one, two three.... there are 3 apples). • Order irrelevance: Objects can be counted left to right, right to left, or in any other order. (as long as you still say 1,2,3) • Abstraction: Any set of discrete objects or events can be counted. (can apply to any objects in the world). |
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Counting procedures |
(a) incorrect counting -counted 4, but there are only 3 items. -Pointed to items -counted one twice
(b) unusual but correct counting -order irrelevant -did not count from left to right |
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Early Arithmetic Concepts |
Kindergarten children have some concept of number - count and determine which of two quantities is larger |
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Piaget & concrete operational ability |
Piaget proposed that addition and subtraction require inversion reversibility (concrete operational ability) If 5 +3 = 8 then by the logical rule of inversion, 8 - 3 must equal 5
-Must be able to have this reversibility to be able to say they have a Arithmetic ability. -says that children do NOT have this ability yet |
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Piaget Proposed 3 stages of understanding |
Stage 1 - children relied on spatial arrangements of the objects (said there were different numbers of objects in the two combinations) Stage 2 - could solve the task but only after counting the objects Stage 3 - could solve the task without having to count the objects |
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Children’s Math Learning |
• Regardless of culture & gender, children come to school with great variation in math ability • Early math skill strongly predictive of later math skill
-Counting and Arithmetic go hand-in-hand, but are still a different
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Early Math Skills |
– Counting, including from numbers other than 1 – Recognizing numerals – Adding & subtracting – Comparing numerical magnitudes |
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Cultural differences in Mathematics |
Academic performance by American and Asian School children: -Not a huge difference at first grade level -5th grade, you can start to see that taiwan & japan pass the US in math
-China far above US in counting level |
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Cultural differences in Mathematics: school age & preschool |
School Age: - more sophisticated mix of strategies - cultural differences in instruction style - parental attitudes toward education - more practice in and out of classroom
Prior to School Age (Preschool): Miller et al - base-ten differences (ex: 11 through 19 is harder to remember) Chang & Sandhofer - numerical language input to children |
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Gender Differences in Mathematics |
-Magnitude of gender differences has declined during past several decades (effect size pre 1973 = .31 post 1973 = .14)
-Elementary school - gender differences small & often non-significant; what effects there are favor girls
-Differences in mathematics favoring males first seen in high school increasing some in college and adulthood
-Gender differences are greater at the highest ability levels with males much more likely than females to be represented among the top percentiles of mathematics ability |
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Gender differences at the Extremes |
Verbal and mathematics SAT scores of 7th and 8th graders selected to participate in John Hopkins program for mathematically skilled youth Top 5% of mathematics ability Consistent gender differences favoring boys
Ratio of boys to girls scoring 420 or more SAT Math 1.5:1 Ratio of boys to girls scoring 600 or more SAT Math 4:1 Ratio of boys to girls scoring 700 or more SAT Math 13:1 |
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Why gender differences? |
• Different strategies • Social factors |
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Different Strategies |
• Boys more flexible in using more strategies for solving problems • Male advantage on some spatial cognition skills is related to performance in math portion of SAT test |
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Social Factors |
• Teachers, parents and peers have negative feelings about mathematically talented girls • Girls vs. boys historically depicted in storybooks, movies, etc. • Early numerical input different for boys v. girls • Girls tend to drop off from boys in junior high & high school |
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Why are gender differences decreasing over time? |
1. Girls taking more mathematics courses in high school than before 2. Tests have changed - Test makers attempting to minimize gender differences in their tests, although evidence to the contrary |
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Causes of Early Differences |
• Differences in innate ability • Differences in number experience & numerical language input • Associated with SES & parent education |
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Math Experience & Numerical Input |
Practice with number line games can improve children’s math performance (ex: shutes & ladders) • Help children understand magnitude because higher numbers = – More moves & more distance traveled – More number names heard – More time since game began |
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Number Board Games |
Playing for only four 15-20 minute sessions over two weeks led to significant gains in: – Number line estimates
• Playing for only four 15-20 minute sessions over two weeks led to significant gains in: – Number line estimates – Comparing magnitudes (“Which is bigger, 4 or 6?”) – Counting from 1-10 – Identifying printed numerals 1-10 • Gains persisted for at least several weeks after the game play |
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What is language? |
• Language consists of the use of symbols to represent, transmit, and store meaning and/or information. • These symbols are organized and systematic patterns of sounds, visual representations, and movements. • The purpose of language is to communicate information and meaning to others. |
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Components of language: |
Phonemes • The smallest unit of sound • Vowels & consonants
Morphemes • The smallest, meaningful unit of sound • Words and meaningful parts of words (e.g., suffixes, prefixes)
Syntax • How the order of words makes meaning |
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Developing Language |
0-4 months: Receptive language: associating sounds with facial movements & learning word boundaries in speech 4 months: Productive language: babbling in multilingual sounds & gestures 10 months: Babbling sounds more like parents’/household’s language 12 months: One-word stage: understanding & beginning to say many nouns 18-24 months: Two-word stage: adding verbs & making sentences but missing words (“See bird! Go park!”) 24+ months: Speaking full sentences & understanding complex sentences |
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Word Learning: Input Matters |
• Language input plays a key role in word learning. • Quantity of language input matters
Two ways to measure quantity: • Tokens (i.e., frequency) • Types |
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Token vs Types |
token: the number of time you said "dog"
types: the words associated with dog, such as "fur" "collar" etc, |
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Quality of language input matters too |
• Children learn words better when parents provide language input that matches up with other social or attentional cues
-Ex: visual cues while talking about something |
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Word Learning: Nouns |
Learning words is a challenge • Ex: cup
To learn a noun, • 1) must associate the noun with the object • 2) generalize the noun to other similar objects |
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Word learning: Nouns cont |
• To study how kids learn words, researchers make-up novel words and novel objects • We use novel words and novel objects to be able to make sure that kids have never heard these words or seen these objects before coming into the lab
• Hearing words in different contexts helps you generalize (and learn) words |
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Why does hearing words in same and different context help kids learn words? |
• Because hearing a word in some of the same context helps kids associate the word with the object • And hearing that word in different contexts also helps kids generalize that word to other similar objects |
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Concrete nouns |
• Concrete nouns are one of the first kinds of words kids learn • By 30 months of age, the average child knows approx. 590 words, of which approx. 60% are concrete nouns • But learning words with unclear, abstract referents are harder to learn—and take longer to learn—than concrete nouns |
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Word Learning: Adjectives |
• Knowing more nouns can make learning adjectives harder • Nouns bias you to attend to the whole object • To learn adjectives, you need to attend to features of the object |
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Morphological Development |
In English, we change the meaning of words by changing the morphology of that word • Example: To indicate that something happened in the past, we use the morphological marker, –ed • To walk --> Walked • To look ---> Looked |
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Morphological Development |
• 1) Lack of morphological change • “Kitty!” • 2) Use morphological change • “Kitties!” • 3) Overgeneralize morphological change • “Kittieses!” • 4) Learn morphological change • “Kitties!” |
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Language Learning & Cognitive Development |
• Learning language makes it easier to think about complex things • Language can represent abstract or difficult concepts • Learning language can also affect your cognition and perception • Example from earlier: learning nouns biases you to pay attention to whole objects, as opposed to features of objects |
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category learning |
• Word learning can affect category learning • English-speaking children tend to show a shape bias when learning object categories • BUT what nouns children know affects how much they show a shape bias when learning categories • The more nouns for solid objects children know, the more they show a shape bias • The more nouns for non-solid, amorphous things children know, the less they show a shape bias |
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Bilingual Language Development |
• Kids become bilingual in many ways Examples: • 2 bilingual parents • Home language & community language • Home language & school language • 2 monolingual parents & foreign language caregiver |
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Learning Two Languages |
• Bilingual children’s language learning is more variable than how monolingual kids learn language. • Children learning 2 languages go through many of the same language learning processes as monolingual kids. • They’re just learning 2 languages instead of 1. • Bilingual children tend to start speaking little later than monolingual children. |
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• Why do bilingual children start talking later than monolingual children? |
Bilingual children must learn… • different people speak different languages • 2 separate vocabularies • there are multiple words for the same thing |
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Bilingualism & Cognitive Development |
• Children who speak two (or more) languages have extra advantages in cognitive development compared to children who speak only one language • Bilingual children tend to be better at inhibiting attention & behaviors AND shifting their attention from one thing to another |
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Take-home Points |
• Children rapidly learn words in the first couple of years of life • The quantity and quality of language input children receive has direct impact on their language learning • Nouns tend to be learned first • Adjective and words with unclear referents are harder to learn • Morphological development happens in a specific pattern • Bilingual children have the added task of learning translation equivalents • Language learning has effects on cognitive development |
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Critical Period for hypothesis |
Theory that there is a biologically driven period in which language acquisition must occur.
Ex: cases of Victor, the Wild Child of Aveyron, and Genie support the critical period hypothesis |
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Critical Period for Language Development |
language develops readily between the birth and puberty, and language acquisition is more difficult and less successful after puberty. • However, it may not be a window that closes at puberty, but age related gradual decline |
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Critical Period? |
• Critical period: – begins and ends abruptly – period beyond which a phenomenon will not appear • Sensitive period: – begins and ends gradually – period of maximal sensitivity • Window of opportunity: – popular metaphor – introduced by P. Bateson, 1978 in his critique |
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Are critical periods critical for early childhood education? |
• The notion of a window of opportunity opening in early childhood, and then closing, never to open again, evoked a powerful visual image in the mid-1990s. • It galvanized scientific and popular media to attend to the problems of early childhood education. |
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Word Learning |
• Until 18 months, children acquire the ability to use words slowly, attaining a vocabulary of about 50 words. • From 18 months to 5 or 6 years, word production ability accelerates rapidly. – Word Spurt – Fast Mapping |
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Fast Mapping |
First Exposure “This is a boat.” Child Learns 1. Label applies to this boat 2. Label |
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Causes for Individual Differences |
• Gender • Birth Order • Language Input – Socio-economic Status – Mother’s Education • Genetics • Language Skills – e.g., phonological memory |
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Language Development in Childhood |
• High growth rate Word learning begins extremely slowly but accelerates quickly • 10,000 words by 1st grade 5.5 per day from 1.5 to 6 yrs
• 40,000 words by 5th grade 20.5 per day from 1st to 5th grade |
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Morphemes |
• Morphemes = the smallest unit of meaning – Two types • Free morphemes – Words – Grammatical morphemes » Articles (a, an, the) » Prepositions (in, on, with, to, from) • Bound morphemes – Prefixes (e.g., Un-, Re-, Pre-) – Suffixes (e.g., -ing, -s, -ed) |
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14 grammatical morphemes & their order of acquisition |
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Morphological Development |
• Order of morpheme development is similar for all English-speaking children – But differences across cultures • A year or more may pass between the first time a child uses a morpheme and when the child masters it • Many morphemes are not used until 3 years old |
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Errors Occurring in Early Word Learning |
• Underextension • Overextension |
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Underextension |
Children often use a word in a very restricted fashion (e.g., “Child-basic level”) – Knows “duck” only in some contexts |
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Overextension |
Children often use a word in too broad a manner (e.g., overgeneralization) – Uses “ball” to refer to all round things |
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Examples of Young Children’s Overextension of Meaning |
Ball: ball, balloon, marble, apple, egg Cat: cat, cat’s usual location on top of TV when absent Moon: moon, half-moon-shaped lemon slice, circular chrome dial on dishwasher, half a Cheerio, hangnail Snow: snow, white flannel bed pad, white puddle of milk on floor Baby: own reflection in mirror, framed photograph of self, framed photograph of others |
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Syntax (Grammar) |
• A system of rules for combining words into sentences – “John ate the apple” not “Ate apple John” |
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Grammar Comprehension |
• 12 months - know what word combinations in their language sound like – “John ate the apple” not “Ate apple John” • 16/18 months - know the meaning of basic sentences – “Mommy threw the ball to Daddy” vs. “Daddy threw the ball to Mommy” |
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Transition from One-Word Speech |
1. Vertical Constructions 2. Unanalyzed Word Combinations 3. “Word + Jargon” Combinations |
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Vertical Constructions |
Before children produce two-word utterances, some children utter successive single-word utterances that seem to be related to each other in meaning in the same way that the words in a two-word utterances are. • Two words that go together separated by a pause • CHILD: Ow. • CHILD: Eye. |
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Unanalyzed Word Combinations |
• Multiword phrases that have been memorized together • “Iwanna,” “Idontknow,” “goodgirl” |
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“Word + Jargon” Combinations |
Real words inserted into strings of jargon • “Blah blah blah bottle.” • “mumble mumble mumble cookie?” • Usually produced by babies who have been producing long strings of jargon since their babbling days (“Jargon Babies” vs. “Word Babies”) |
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Two-Word Combinations |
• Children begin combining words at about 18 months • Two word combinations have a similar structure across cultures • Children’s first word combinations often miss function words and bound morphemes that mark plural, possessive, or tense. – E.g., “Daddy shirt,” “Off TV” |
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Two-Word Combinations |
• 8 Relational Meanings 1. Agent + Action: “Daddy sit” 2. Action + Object: “drive car” 3. Agent + Object: “Mommy sock” 4. Agent + Location: “Mommy chair 5. Entity + Location: “toy floor” 6. Possessor + Possession: “my teddy” 7. Entity + Attribute: “crayon big” 8. Demonstrative + Entity: “this telephone” |
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Two-Word Combinations |
• Two-word combinations are also called telegraphic speech • Combinations become generative when the child can use words in his vocabulary in different combinations – “Daddy sit” and “Mommy sit” – “Baby shoes” and “Baby play” |
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Language is Generative |
• Mental grammar allows new language combinations • Mental grammar contains: – Abstract categories (noun, verb, adjective, etc.) – Rules for combining them • This creates endless opportunities for word combinations |
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Sentence Forms |
• Order of development 1. Declarative Sentences: “Mommy sit” 2. Negative Sentences: “I don’t want it” 3. Questions: “Can I go?” Depends on development of auxiliary verbs (can, will, do) 4. Complex Sentences: “I don’t know if he is going to school today.” |
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Negative Sentences |
• Order of development 1. “No / Not” at the beginning or end of the sentence: “No wear mittens” 2. “No / Not” in the right position but no auxiliaries: “I no want mittens” 3. Auxiliary in the correct location: “I don’t wear mittens” “I’m not wearing mittens” |
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Yes / No Questions |
1. Intonation Only “Kitty stand up?” 2. Auxiliary Inserted “Does the kitty stand up?” |
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Wh- Questions |
1. External Wh- Word “Where Mommy going?” 2. Auxiliary Inserted “Where Mommy is going?” 3. Subject - Auxiliary Inversion “Where is Mommy going?” |
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How do children learn grammar? |
Some theories – Rule Learning – Usage Based Learning – Corrections |
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Exceptions to Rules |
• There are exceptions to language rules – E.g., feet instead of foots • Overregularization Errors – A child’s error making an irregular part of language regular |
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Usage Based Learning |
• The idea that children do not learn rules • Rather, they learn from every day language input • Perhaps through statistical learning? |
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Corrections |
Corrections of children’s incorrect grammatical utterances • Child: I felled down. • Mother: You fell down. |
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Controversy Over Corrections |
Child: Nobody don’t like me. Mom: No, say “nobody likes me.” Child: Nobody don’t like me. (This is repeated several times.) Mom: No, now listen carefully. Say “nobody likes me.” Child: Oh! Nobody don’t likes me. |
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Measuring Grammatical Development |
Grammatical development is measured by the child’s MLU (Mean Length Utterance) – MLU = the average number of morphemes produced in the child’s utterances |
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Mean Length Utterance (MLU) |
How to calculate MLU – Count the number of morphemes in each utterance – Add these numbers together to get a total – Divide this total by the total number of utterances
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MLU Example |
1. daddy sleep-ing 3 2. baby eat banana-s 4 3. no 1 4. I want it 3 5. no talk-s there 4
Morphemes: 3+4+1+3+4= 15 MLU: 15/5= 3 This child has an average of 3 morphemes per utterance |
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MLU Stages |
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Children’s Emergent Literacy |
• Primary language skills – Speaking & listening • Secondary language skills – Reading & writing |
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Chronology of Reading (Chall) |
Stage 0 (birth - first grade) reading prerequisites Stage 1 (first & second grade) phonological recoding skill Stage 2 (second & third grade) fluent reading Stage 3 (fourth - eighth grade) reading to learn Stage 4 (high school) comprehending multiple viewpoints in written text |
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Individual Differences in the Development of Literacy |
Literacy can develop at drastically different rates Causes for individual differences – Genetics – Prior Language Skills • Language Input – Related to Parent SES & education • Language Level – Language skills build on language skills • Phonological Awareness – Literacy Experience • Exposure to reading • Letter knowledge • Knowledge about print |
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Phonological Awareness (Lieberman) |
4 & 5 year olds Tap once for each sound in a short word At = 2 Cat =3 None of 4 year olds and only a few 5 year olds performed accurately Predicts early reading achievement quite accurately |
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Individual Differences in the Development of Literacy |
Reciprocal relationship between language & literacy • Early experience has long term effects!
-The more number of books children have access to, the higher literacy they tend to have |
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Books & Literacy |
Average reading literacy scores of fourth-grade students by number of books reported at home and country |
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Teaching Children to Read |
1. Bottom up process - Phonics method emphasizes the individual components of reading; often independent of meaningful context - sounding out words - memorizing small, frequent words: the, in, and
2. Top down process - Whole word approach teaches visual retrieval and focuses on goals, background, and expectations determine what is selected from text
Instruction in the early grades often emphasizes one over the other |
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Simultaneous Bilingualism |
• Phonology – Children retain the ability to hear phonological contrasts for both languages • Semantics – Bilingual children appear to violate the Mutual Exclusivity Assumption, because they accept two words from the same thing if they believe them to be from different languages • Grammar – Bilingual children lag behind monolingual children in grammatical development |
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Simultaneous Bilingualism |
• How and when do children know they are learning two languages? • How do they differentiate between the languages? • Learning two languages is a more difficult task than one, so it may take longer • The amount of input in both languages is important to determining the course of development |
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Sequential Bilingualism |
• Children’s acquisition of second language may take years and be more difficult than first language acquisition • Language acquisition may include making many errors • There may be trade-offs in the first language when learning the second |
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Sequential Bilingualism |
Individual factors that affect second language learning: – Skills in first language – Phonological memory – Personality – Motivation – Age |
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Benefits of Bilingualism |
• Cognitive benefits – Executive function / attentional control – Working memory • Metalinguistic skills • Can potentially delay onset of Alzheimer’s |
