Log in to StudySoup
Get Full Access to Intermediate Algebra - 6 Edition - Chapter 7.1-7.5 - Problem Integrated review
Join StudySoup for FREE
Get Full Access to Intermediate Algebra - 6 Edition - Chapter 7.1-7.5 - Problem Integrated review

Already have an account? Login here
Reset your password

Use rational exponents to simplify each radical.23 8x6

Intermediate Algebra | 6th Edition | ISBN: 9780321785046 | Authors: Elayn El Martin-Gay ISBN: 9780321785046 180

Solution for problem Integrated Review Chapter 7.1-7.5

Intermediate Algebra | 6th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Intermediate Algebra | 6th Edition | ISBN: 9780321785046 | Authors: Elayn El Martin-Gay

Intermediate Algebra | 6th Edition

4 5 1 269 Reviews
Problem Integrated Review

Use rational exponents to simplify each radical.23 8x6

Step-by-Step Solution:
Step 1 of 3

INTELLIGENCE 1. What are the major differences between psychometric approaches to intelligence (Spearman’s “g”, Cattell and Horn’s fluid and crystallized intelligence, and Guillford’s Structures of the intellect model), Sternberg’s, and Gardner’s approaches to intelligence » Spearman’s g: o General intelligence factor  Mental energy (g factor influences everything we do)  Impacts performance on all tasks o Specific factors  Related to specific Tasks » Cattell and Horn’s fluid and crystallized intelligence: o Fluid Intelligence (the answers to everyday type of problems)  Relatively culture free  Increases until early adulthood or so o Crystallized Intelligence (the facts we are learning)  Influenced by education  Increases throughout the lifespan (at least middle adulthood) o Fluid intelligence influences crystallized intelligence o Fluid tests correlate with one another more than crystallized tests. » Guilford’s Structure of the Intellect Model: o 180 Mental Factors o 3 Dimensions  Sternberg’s Successful Intelligence o The ability to adapt to, shape, and select environments to accomplish one’s goals and those of the one’s society and culture. o Use strengths to minimize weaknesses o Overall, intelligence depends on how we do in our environment. o Practical abilities, creative abilities, and analytical abilities are not hierarchically related (no g) but they can work together. o People should be taught in the style that matches their strengths. » Sternberg’s 3 Types of Intelligence: o Practical Abilities  Reasoning about everyday problems  E.g., conflict resolution o Creative Abilities  Reasoning in novel circumstances  E.g., creating “clean-up”, a fun game o Analytical Abilities  Traditional intelligence test measures  E.g., Language, math, spatial » Sternberg et al. (1996) // Study o Students attend a 4-week summer psychology course o Instruction either matches or mismatches their strengths  Practical: What are the implications of infantile amnesia for the legal system  Creative: Design an experiment to test a theory regarding infantile amnesia.  Analytic: Compare and contrast theories related to infantile amnesia o Findings:  Matching strengths made a difference!  For each individual, only moderate correlations between their analytical, practical, and creative abilities  Gardner’s Theory of Multiple Intelligences o 8 – 10 autonomous intellectual competencies o These interact to produce a diverse mix of talents  Sternberg vs. Gardner: Contention o Gardner has suggested Sternberg’s theory is too similar to Spearman’s g o Sternberg suggests little research to support Gardner.  Sternberg vs. Gardner: Agreement o Sternberg/Gardner – schools focus on teaching children how they learn best.  Child with good spatial skills = charts and graphs.  Child high in social skills = discussion and group work. 2. What is positive manifold What approach to intelligence does positive manifold support  Psychometric Theories: Support  Positive Manifold: High correlations between scores on different cognitive tasks (e.g., grades, test performance, information processing speed, and speed of neural transmission)  Caveats: o Higher correlations between IQ test scores and cognitive tasks for lower and average IQ scores than higher IQ scores. o Develops after age 2 3. What is a mental age quotient What do we do to calculate IQ today  Mental Age Quotient (IQ = Mental Age/Chronological Age x100) o Problems:  IQ may decrease with age as adult  Age 6 and age 10 with the same mental age quotient very different  Deviation IQ (what we use today) o Mean of 100 o Standard Deviation +/- 15 o +s and –s for deviation IQs 4. What are the best predictors during infancy of later IQ scores (especially for infants at risk) o Infants:  Faster habituation correlates with later IQ  Especially for infants at risk  Different from short attention span  Visual recognition memory correlates with later IQ o Versus IQ, Infant Measures may relate to:  PROCESSING SPEED  INHIBITION o From age 8, correlations on IQ tests are high. (Lower between infancy and 5 years.) o The closer together tests taken, the higher the correlation o Scores are NOT constant 5. Are IQ scores stable across development How do we know  McCall, Appelbaum, & Hogarty, 1973 o Main findings:  Not just practice effects  Scores are not constant, but some rank order stability beyond age 8  Note: about 16 percent of the sample did not show a consistent pattern. Lots of room for change! 6. To what extent do genetic and environmental factors predict intelligence With regard to this issue, how does the US differ from other wealthy nations  GENETICS: o Higher correlation for IQ in identical twins versus fraternal twins  Identical twins ~ .86  Fraternal twins ~ .60  Siblings ~ .50 o BUT by adulthood little IQ correlation o Why  Non-shared environmental influences  ENVIRONMENT: o “institutionalization studies” infants who are separated from their mother’s and receive little stimulation  Genetics, Environment, SES, and the US o Recent meta-analytic data examines role of genetics and environment BY nation (10,000 sets of twins) o Find… (definitely suggests concept of intelligence is not fixed)  US clear support for moderately sized Gene X SES interaction: genetic variance plays more of a role in high SES and environmental variance plays role in low SES  In Western Europe and Australia, Gene X SES interaction not there (or reversed; Netherlands)  Replicate: genetic influences on intelligence increase with age and shared environmental influences decrease o Interpretation  National differences in concepts of letter and number are taught  Public education quality more broadly  Medical ad educational access  Macrosocietal characteristics (e.g., upward social mobility) o Those who are adopted before age two, are typically found to have higher IQ scores than those who are raised in orphanages (suggests age is an environmental component) 7. What is the Flynn effect  Flynn Effect o Average IQ has been increasing over last 50 years o Why  Daily life is more challenging  Better nutrition 8. Interventions have been developed to help children at risk. What are some of the findings for different programs related to IQ (e.g., Head Start and the Abecedarian Project)  Head Start & Similar Programs o Preschool program (short) o Most show short-term IQ gains o BUT  few kids end up in special classes or held back  Programs often increase social competence and self-esteem  Abecedarian Project: o Very complete program: Intellectual, medical, and nutritional enrichment from infancy through preschool o Long-term 5-point IQ boost o MORE to success than IQ  The Mozart Effect o Claim: Listening to IQ boosts IQ by 8 or 9 points o Research: college students that listened to 10 minutes of Mozart did better on a paper folding task than college students that sat in 10 minutes of silence  Finding hard to replicate 9. How do people differ in terms of IQ How do risk factors relate to this question  RACE and ETHNICITY: o IQ scores differ among groups:  Asian-American scores are higher than those of any other group in the United States.  The average IQ of Euro-American children is 10-15 points higher than that of African-American children. o BUT THAT IS NOT THE WHOLE STORY! 1. Statistical averages, not individual scores. 2. Millions of ethnic minorities have higher IQs than that of the average Euro-American child. 3. When researchers control for risk factors, effects of race and ethnicity generally go away.  RISK FACTORS: o Head of household unemployed o Mother did not complete high school o At least four kids in the family o No father in the home o Rigidity in parents’ beliefs about child development o Maternal anxiety and depression 10.Is brain size related to intelligence - Brain size correlates weakly with intelligence - BUT: o Women’s brains smaller than men o Neanderthals had large brains o Correlation is small 11.What has research found regarding self-fulfilling prophecies in elementary school education (e.g., teacher expectations of children’s “potential to thrive”)  Self-fulfilling Prophecy  “maze bright” vs. “maze dull” rats (expectation of how the rat should perform affected their performance)  Do teacher EXPECTATIONS influence student LEARNING  Method:  Start of school year, students in grades 1 to 6 administered nonverbal intelligence test (TOGA)  Teachers told: “Harvard Test of Inflected Acquisition” that predicted academic “blooming”  Teachers told that 20% of children showed would show “unusual intellectual gains” during school year  BUT students were actually randomly assigned  Administer IQ test 8 months later  Bottom line:  Expectancies translated to the classroom, particularly for younger grades  Implications  If you were given a list of students at the start of a school, some were “gifted” and others had learning/behavioral disabilities, how would that impact behavior  Some later research:  Teacher expectations may lead to more positive interactions that influence students to enjoy school more  Findings for expectancies extended to a variety of settings 12.What is a fixed versus a growth mindset How can we encourage a growth mindset  Fixed vs. Growth Mindset  How children and adults think about learning influences how well they learn and how they bounce back from obstacles. 1. Fixed mindset: failure due to a lack of ability 2. Growth mindset: failure due to a lack of effort  How to encourage a growth mindset: o Instead of praising ABILITY, praise EFFORT  “You are a fantastic baseball player” vs. “You connected with the ball much better this time” o Tell stories about achievements through hard work. o When a child receives a poor grade, try to focus on effort and future actions. o Talk to children as they get older about how they can “strengthen” their brains. o Demonstrate to children that you think learning is important. 13.What are executive functioning skills What are some of the ways this has been measured What are the main findings (Refer to the marshmallow task; research by Moffitt an colleagues, and the review by Blair, 2016). Can we teach self-control skills  Executive Functioning Skills, including self-control  Working Memory: ability to hold information in mind and mentally work with it  Inhibition: ability to control one’s impulses, attention, and emotions  Cognitive flexibility: ability to change perspectives, adjust priorities based on new information o Delay of gratification task o 4 year old child given a treat o Child told that experimenter will leave room for a while and kid has two choices:  Wait for experimenter to return = 2 treats  Ring a bell = get 1 treat o The better children were at delaying gratification, the better they were at:  explaining ideas  paying attention  coping with stress  SATs (around 200 points higher) years later!!  How do we delay o Distraction – shift our attention elsewhere o Cognitively Reframe – “Think Cold, Think Cognitive”  Preschoolers directed to think “hot” thoughts about a control item were able to wait about 17 minutes on average to earn their reward.  Developmental Changes in strategies to delay o 4 yo often choose the least effective strategies o As they begin to use better strategies able to wait longer o The value of abstract thoughts (i.e., cool thoughts) is later developing, often not occurring until 3 to 6 grade. o Criticisms of the marshmallow task  Moffit et al., 2001  Self-control composite o What was the purpose of the study Looking at the extension to which self control scores predicted as far as intelligence, etc. o What type of study was it Longitudinal o How was the study conducted o Main findings:  Longitudinal research examining nine different measures of self control during the first decade of life finds that, controlling for SES and intelligence, self control in childhood is related to many factors such as health, wealth, and crime  Criticisms  Why do the researchers argue that we should take a “targeted approach” to addressing self-control o “Early childhood interventions that enhances self control is likely to bring greater return on investment than harm reduction programs targeting adolescents alone.” o Argue we should TARGET self-control in early childhood versus developing lots of programs for adolescents that address common problems (e.g., drugs, teen pregnancy, truancy, anger management,…)  Blair, 2016  Neurobiology o Subcortical regions (often from stress response) signal prefrontal cortex to direct our attention o Moderate stimulation facilitates EF o Too much stimulation overstimulation o Too little stimulation inhibits neural activity  Self regulation o Recursive at first: Primarily outside of conscious awareness during infancy and toddlerhood (“top- down”) o Grow older, more conscious (“bottom-up”) o STILL early and later EF seems to be connected  Individual differences in EF (visual memory, emotional reactivity) predict later EF  Measurement difficult and somewhat unreliable. Why o Poor at measuring construct of EF o EF poorly defined or operationalized o EF changes  In poverty o Because situations of poverty are often stressful, hormone levels can be altered in ways that alter the stress response. o Protective factors through:  Positive parenting  Supportive relationship with mother o Also, changes our need and want for food.  Training works  Bottom Lines: EF Skills I. CRUCIAL for success in school, on the job, in friendships, in marriage, for mental and physical health, etcetera II. Malleable: Improve over time and with some interventions T/F: An individual with an overall IQ score of 100 is well above average. FALSE T/F: The size of one’s brain correlates with intelligence. TRUE. READING, WRITING, ARITHEMETIC 1. What are some differences between languages that have the potential to influence the development of literacy skills What makes some languages easier to learn than others What is the basic pattern of development for phonological awareness How do we know (how is this tested) Know terms such as phonological complexity, grain size, orthographic transparency, and onsets and rhymes.  Literacy Languages are represented differently o Phonological Complexity: Grain Size o Phonemes o Syllables o Morphemes o Orthographic Transparency  Phonological Awareness: » Syllables o Tapping/counting tasks o Same different task o Deletion task (take away a syllable; Party > “part”) o Blending task (adding a syllable; Sis + ter > sister) » Similar results across languages, with 3 y o performing above chance » = Syllable awareness prior to literacy teaching » Onsets & Rhymes o Oddity task o Same different task o Blending (h + at = “hat”) o Nursery rhyme completion (very early on) » Onsets and rhyme awareness prior to literacy teaching across languages » Phonemes o Tapping/counting tasks » Phonemic awareness a result of literacy teaching, particularly letters » Cross cultural differences related to orthographic transparency (English has terrible OT) & phonological structure o CVC: “mom” “house” o CV: “mama” “casa” » Children in US need about a year of phonics training to start mapping sounds  PA: Bottom lines o Developmental sequence of phonological skills appears language universal  Syllables  onset/rhyme  phonemes o Phonemic awareness depends on literacy training and varies across languages 2. Discuss children’s developing understanding of reading What types of training improve reading skills  READING in US o Birth-1st grade: prerequisites for reading o 1st-2nd grade: phonological recoding skill o 2nd-3rd grade: reading fluently, learning so-so th th o 4 – 8 grade: learn information from reading, not as good at perspective taking o High school on: begin understanding info from multiple viewpoints **Preschool correlates with later reading skills  Training to improve reading skills o Phonological awareness (tapping sounds) + letter-sound training (connecting sound to letter) o Not learn the alphabet as early as possible  Kindergarteners’’ ability to name letters is related to reading scores, but training children to name letters does not predict reading scores 3. What is dyslexia  `Dyslexia o Common misconception:  Letter perception (orientation matters) nd rd  Typically by 2 /3 grade o Difficulties with phonological representations of sound structure of words o Pragmatically: Children with wide vocabularies and high IQ that struggle with reading and spelling 4. Discuss writing development. What changes in children’s ability to draft responses Why might children write better, more complex essays when dictating them or using a computer than when writing them by hand  WRITING o Writing development: Overview  2-3 y.o. children know writing direction  Invented spelling  Phonological understanding leads to better spelling  Improved perspective taking leads to better writing o Knowledge-telling strategy (elementary school)  Answer questions directly by writing down information as it is retrieved from memory (short, concise, and unintelligible) o Knowledge-transforming strategy (adolescence)  Deciding what information to convey and how to convey it o Does decreasing working memory demands improve writing  4 and 6 graders compose essay in 1 of 3 conditions (best essays for standard dictation) 5. What is one common weakness in how children and adults review work What are some ways to help improve revision skills  Revising: o Children and adults have difficulty identifying weaknesses in texts o Often focus on fixing surface-level errors (e.g., spelling) than meaning-based o Training on perspective taking helps o Using word processing programs helps 6. What types of abilities do infants have in terms of number  Number  Infants:  Can do simple addition and subtraction  Can notice changes in the number of times a puppet jumps too  Connect sounds to visual images  Infants prefer cross-modal congruence  Infants can do simple addition and subtraction**really important study - clip  Can also do some “addition” with large numbers  Make decisions about more and less with large numbers o YET toddlers struggle can’t answer these types of questions verbally 7. What are analog magnitude representations What are the basic processes for math and how do those relate to the differences that we see for infants, toddlers, and young children Explain “Weber’s law” and subitizing in your response.  Mathematical Development o Linguistic system o Visually based code o Analog Magnitude Representation  System in which numbers are coded as “approximates” (better sense of what smaller numbers are) versus exact  Follows Weber’s law: ratio sensitive (easier to detect a difference between 5 and 100 vs 5 and 6)  Adults, infants, and animals all use AMR at times…  …STILL to explain simple math: Subitizing  3, 4, & 5 to decide which row has more squares  Children more successful when ratio 1:2 than 2:3  Counting did not affect success rate  Many studies corroborate basic findings  Neuroimaging supports the idea of separate systems  EEG (better temporal info as far as timing) data supports the idea of ratio sensitivity  Math: o Kindergarten:  Single-digit addition and subtraction (finger counting) o 2 to 4 grade  Multiplication o Inversion (a + b – b = )  4 to 5 years with objects only  6 to 9 years o 3 or 4 graders struggle with Mathematical Equality (3+4+5=__ + 5) o Children develop strategies to help them learn these skills  Retrieval – high confidence  Back-up strategy – low confidence o Individual Differences:  Use 1st grade math test to divide kids into 3 groups  Not so good students: made errors  Good students: fewer errors, faster, used retrieval more  Perfectionists: Equally accurate, but perfectionists used backup strategies instead of retrieval much more often. Very strict confidence criterion needed for retrieval. 8. What are the basic counting principles How does early counting develop What debate remains regarding children’s representation of larger numbers  Counting o Counting Principles:  One-One (only one word per object)  Ordinality (assign numbers in the same order)  Cardinality (last count indicates numbers in the set) o Early Counting:  “Give a number” task  Find: o Grabbers o Counters  Conclusions: o Shifts around 3.5 o Differences in counting for small vs. large numbers  Longitudinal follow-up: ads tasks  “How many”  “Point to X”  Find: kids learn 1, 2, 3 then larger numbers  Debate regarding representation of larger numbers  Cultural Differences:  Age 3 - children in the US can generally count to 10.  There are cultural differences in the counting level attained by young children. 9. When do children use backup strategies and when do they use retrieval from st memory  1 grade 10.How can context play a role in children’s ability to solve math problems (i.e., classroom versus competition, children in Brazil, fractions) o Common Problems:  Context of a Problem: children have problems generalizing  9- to 15- y.o. Brazilian children succeeded in problems with sale but not numbers  US kids more sophisticated strategies in academic contest than games  Fractions: Estimate the answer to the following problem. You will not have time to solve the problem using paper and pencil. 11.What are some common misconceptions about preschool readiness How can we help children succeed in academics o Misconceptions 1: It is best for them to know as much as possible (i.e., my child is smart because she knows X)  WE CAN’T KNOW EVERYTHING o Misconception 2: It is best for them to learn things as early as possible (i.e., my child is smart because she learned to do this at X age)  Academic Preschools: » 4 year olds attending Pre-K programs tested with lots of different types of measures (Hyson et al., 1990)  Compare “high” versus “low” academic  Find:  No significant differences in academic ability  Small difference for anxiety, with children attending high academic programs showing more test anxiety.  Low academic children more likely to have a positive attitude towards school » Earlier is not necessarily better » “It may be developmentally prudent to let children explore the world at their own pace rather than to impose our adult timetables and anxieties on them.” o Misconception 3: Children need lots of toys, books, and activities to fully succeed (i.e., more money = better life).  How do we help children succeed in academics o Good health and physical well-being o Social and emotional preparation o Language and general knowledge  Has familiarity with letters, numbers, shapes, and colors  Is encouraged to notice opposites, make comparisons  Is encouraged to ask questions  Has opportunities to draw, dance, hear music, hear books » Blocks…a case study - Low-income children given blocks show increases in verbal skills 6 months later THEORIES & WRAP-UP Piaget 1. Explain the learning processes described by Piaget: assimilation, accommodation, equilibration. o Learning Processes:  Assimilation  Accommodation  Equilibration 2. Know Piaget’s proposed stages of cognitive development and the substages for infancy including the milestones reached at each stage as well as the approximate age ranges.  Sensorimotor Period:  0 – 2 years  Understanding of the world increases dramatically » Knowledge develops via action » Gradual differentiation of self from environment » Gradual growth of intention 1. Modification of reflexes (0 – 1 month)  Child understands environment through inborn reflexes.  Begin modifying reflexes. 2. Primary circular reactions (1 – 4 mo)  Actions more coordinated, combining reflexes.  Try to recreate pleasing events exactly 3. Secondary circular reactions (4 – 8 mo)  Interested in objects, not just their own body  Repeat action to trigger response  “Out of sight, out of mind” 4. Coordination of secondary circular reactions (8 – 12 mo)  Coordinating multiple actions AKA means-ends behavior  Grasping some aspects of object permanence 5. Tertiary circular reactions (12 – 18 mo)  Deliberately varying behaviors that produce interesting outcomes 6. Beginnings of representational thought (18 – 24 mo)  Start understanding symbols and representations  First signs of pretend play and deferred imitation  Preoperational Period:  2 – 7 years  Development of symbolic understanding and language use  Engage in pretend play, think about the past  BUT suffer from egocentrism and centration » Egocentrism: Children limited in ability to take the perspective of others o Tested with 3-mountain task (understanding we have different visual perspectives) » Centration: focus on one aspect of a problem, neglecting others o Tested with conservation  “Do I have more, do you have more, or are they the same” o Tested with physics: “toy train task” 1. Piaget said children were egocentric through early childhood » BUT, other researchers have found differently i. False belief around 4 or so ii. Drawing rotation… iii. … iv. … 2. Piaget said children didn’t understand conservation » BUT, why else might they fail o Improving performance on conservation tasks  Concrete Operational Period:  7 - 11 years  Begin to think logically about world (e.g., pass conservation task with number and liquid)  Grasp length, volume, time  Can solve multiple classification problems  BUT, don’t think abstractly o Difficulty with hypothetical reasoning problems o Difficulty using systematic approaches to solving some problems (e.g., chemistry problems)  Haphazard (versus systematic)  Stop gathering evidence too soon  Formal Operational Period:  12 years and up  Understand abstract concepts, logic, hypothetical thinking 3. How did Piaget underestimate infant’s understanding of object permanence, symbolic understanding, and deferred imitation  Different Perspectives (Piaget underestimated infants) 1. Piaget said that infants don’t understand object permanence until 8 – 12 months, with full fledged at 18 m.o. » BUT, recent research finds differently o The Object Concept (Assignment 1)  Reaching tasks – some aspects by 8 to 12 months  Violation of expectation tasks – between 3.5 and 12 months  Some 3.5 m babies look longer at impossible event. Most 5 m.o. look longer at impossible event. o Criticisms of violation of expectations:  Passive ask  Familiarity preference  Lingering visual memory trace (i.e., perceptual vs. “thinking”) o Bottom line: Understanding object permanence is gradual, not sudden 2. Piaget said infants don’t understand symbols until 18 to 24 months » BUT, infants can use language before then. (first words around 12 mos) 3. Piaget said infants can’t do deferred imitation until 18 to 24 months » BUT, other researchers have found differently o 9 month old infants can imitate someone’s actions a day later o 14 m.o. imitate based on actors apparent goal (already know what the intent is) 4. Define Piaget’s views about egocentrism and conservation. How did Piaget test these abilities What does research say about them today  Different Perspectives 1. Piaget said that acquiring conservation should be universal » BUT, some cross-cultural differences  Mexican children making pottery understand it earlier  Children in cultures without formal education understand it later » And not all conservation solved at once 2. Piaget said that kids can’t do logical reasoning » BUT, kids this age CAN do it if experts or taught some strategies 5. According to Piaget, how do children struggle with abstract thinking during the concrete operational stage What evidence suggests that Piaget may not have been quite right (i.e., acquiring conservation universal Are there times children CAN do logical reasoning)  Different Perspectives 1. Piaget said children shift to this stage all at once » BUT, children and teens (and sometimes adults) are less consistent 2. Piaget said this was the final stage of cognitive development » BUT, some don’t reach this stage at all 6. Does Piaget’s description of the formal operations stage may not tell the whole story 7. What were Piaget’s major contributions to cognitive development o Contributions: 1. Founding the field of cognitive development 2. Conceptualizing development as active and constructive (children want to learn; we should let them) 3. Exploring new methods (scientific approach to studying kids) 4. Getting a good “gist” of cog dev processes, especially with older children Vygotsky 1. Know internalization of social shared processes and zone of proximal development.  Development depends on what is learned from others  Internalization of socially shared processes: » Intermental level: other people » Intramental level: self  Zone of proximal development: (area in-between Actual and Potential development levels); amount of extra reasoning they would be able to do with little help » ZPD Example: o Sorting dollhouse furniture o 3 and 5 y.o. helped a puppet move dollhouse furniture into a house; one group got help (their mom), other got scaffolding o Found: performance on the new hard task was better for children who had help from mom throughout the task opposed to children who just got feedback at the end. They can do more extra reasoning when they are helped throughout the process. 2. How did Vygotsky characterize the connection between language and thought  Developmental milestone reached when children linked cognition and language (language helps refines and strengthens their cognition skills to organize their thoughts, activities, etc.)  Starts with egocentric/private speech  Reaches inner speech (self-talk you do in your head) » Helps remove themselves from the immediate context to detach themselves to see what’s beyond 3. Support and critique Whorf’s linguistic relativity hypothesis. Use research to support your ideas.  Linguistic Relatively Hypothesis (“Whorf”) o Object gender study:  Native Spanish and German speakers asked to describe items that have opposite genders in the two languages  Provide different types of adjectives, suggesting language influence thought  BUT Alternative explanations  Cultural differences, no language per se  Weird questions  Limited influence on thought itself (not tested on higher order thoughts) o Object categorization:  Yucatec Maya - nouns often refer to material  English - nouns sometimes refer to shape  Differences in categorizing objects o Evidence against “Whorf”:  Languages can be translated  Not having a word in a language does not mean a lack of understanding of the concept  Example: Hopi Indian language (does not refer to time, (don’t refer to past, present and future) but doesn’t mean they don’t understand the concept) 4. What are cultural tools How do they help us Give an example (i.e., sign- assisted memory study conducted by Vygotsky).  In addition to language, psychological functioning mediated by cultural tools:  Technical tools (using a hammer, a computer, etc.)  Psychological tools – Sign systems  A Vygotsky Experiment: o Explored natural memory (perceptual) vs. sign-assisted memory (mediated by symbols, hints) o First task: baseline (of do they know their colors) » “What color is the floor” o Second task: two forbidden colors o Third task: different forbidden colors WITH cards to “help them win” » Kind of like the game “Taboo” o Conclusions: there is a development in sign-assisted memory (using a tool – the cards in front of them)  Helpful for children between 8 and 13 (but not 5 – 6)  Not needed for adults, as if they have their own internal “mental” signs 5. Describe how functioning can be mediated by cultural tools (e.g., alphabet song, abacus).  Other tools too… o Psychological functioning mediated by cultural tools (e.g., “alphabet song”, abacus (in learning addition and subtraction)); suggesting that those cultural tools ARE really important! 6. What are the similarities and differences between Vygotsky’s Sociocultural Theory and Piaget’s Theory Piaget vs. Vygotsky  Piaget: o Focus: Individual child o Context is important for eliciting thoughts in the child (more involved as the child as an active learner)  Vygotsky: o Focus: Child in context o Child’s thinking cannot be separated from context (how they grow up is inherently important for a child) Where are we going Wrap-up 1. What is the competent infant perspective Neuroconstructivism Connectionism o Competent Infant Perspective:  Naïve Physics  Naïve Biology: understanding of the kinds of thing in the world; things die, living vs. non-living, etc.  Naïve Psychology: understanding of self; self-aware o Neuroconstructivism: Explains mechanisms of change by considering biological constraints on neural activation patterns that impact development o Connectionism: Computational modeling of learning via “neural networks”. Provide “input” to units of a network and each yield output – a numerical function. 2. What are some important contributions of cognitive neuroscience o Old and new models o Account for interaction between environment and biological constraints o Recognize MANY learning mechanisms o Cognitive neuroscience important but needs to connect to behavior/development 3. Know the 6 big questions/answers as discussed in class. 1. Are some capabilities innate Yes; development starts in the womb… - But more than not, nature and nurture are extremely intertwined - Ex: Language (universal to specific), analog numbering representation (children have an approximate number sense that seems to potentially increase mathematical abilities) 2. Does development progress through stages - More often than not, it’s continuous 3. How does change occur  Lots of ways! o Biological changes o Habituation and conditioning (children to prefer to look at something slightly different) o Social learning (Vgotsky) o Information-processing mechanisms (as something becomes more automatic, it becomes easier for us to do something else as well) o Domain-specific learning mechanisms (the whole object concept) 4. How do changes in brain contribute to cognitive development - Development of prefrontal cortex  more sophisticated thinking, planning, and metacognition - Brain plasticity 5. How does the social world contribute to cognitive development - Social interaction and culture impact how children think - Scaffolding: structuring how children think 6. How do individuals differ - Figure out general developmental trends before being able to understand individual differences! - Development is an ACTIVE exploratory process (idea of executive functioning skills and that they can be learned); self- regulation and executive function skills are linked to many other things beyond intelligence

Step 2 of 3

Chapter 7.1-7.5, Problem Integrated Review is Solved
Step 3 of 3

Textbook: Intermediate Algebra
Edition: 6
Author: Elayn El Martin-Gay
ISBN: 9780321785046

This full solution covers the following key subjects: . This expansive textbook survival guide covers 90 chapters, and 8410 solutions. This textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. Since the solution to Integrated Review from 7.1-7.5 chapter was answered, more than 237 students have viewed the full step-by-step answer. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046. The answer to “Use rational exponents to simplify each radical.23 8x6” is broken down into a number of easy to follow steps, and 8 words. The full step-by-step solution to problem: Integrated Review from chapter: 7.1-7.5 was answered by , our top Math solution expert on 12/23/17, 04:59PM.

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Use rational exponents to simplify each radical.23 8x6