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Prove Theorem 6.1.2

A Transition to Advanced Mathematics | 7th Edition | ISBN: 9780495562023 | Authors: Douglas Smith, Maurice Eggen, Richard St. Andre ISBN: 9780495562023 335

Solution for problem 12 Chapter 6.1

A Transition to Advanced Mathematics | 7th Edition

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A Transition to Advanced Mathematics | 7th Edition | ISBN: 9780495562023 | Authors: Douglas Smith, Maurice Eggen, Richard St. Andre

A Transition to Advanced Mathematics | 7th Edition

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Problem 12

Prove Theorem 6.1.2.

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Elise Gan March 24, 2016 Seemingly important vocabulary Emphasized in readings and class Intro to Psychology Study Guide, Test #2 Chapter 7: Memory 7.1 What is Memory • memory = nervous system’s capacity to retain and retrieve skills and knowledge • memory processes information o encoding = occurs at time of learning; processing of info so that it can be stored o storage = retention of the encoded representations over time o consolidation = neural connections that support memory become stronger; encoded information stored in memory; o retrieval = the act of remembering information when needed • memory is the result of brain activity o long-term potentiation (LTP) = strengthening of synaptic connection; makes post-synaptic neurons more easily activated by pre-synaptic neurons § shows how neural plasticity may underlie memory § requires NMDA receptor (glutamate receptor) • opens when nearby neuron fires o medial temporal lobes responsible for formation of new memories o storage of memories in particular brain regions engaged during perception, processing, and analysis o reconsolidation = neural processes involved when memories are recalled then stored again § memories can be changed over time § when reconsolidated memories may differ from original 7.2 How are Memories Maintained over Time • sensory memory = memory system that briefly stores sensory information o lasts only for a fraction of a second o visual sensory memory – iconic memory o auditory sensory memory – echoic memory o enable us to see world as a continuous stream • short-term memory = memory storage system that briefly holds a limited amount of information in awareness • working memory = active processing system that keeps different types of information available for current use o information remains for 20-30 seconds; disappears unless prevented o update working memory with retrieval, transformation and substitution § ex: retrieve number, transform (change) it, keep new number in memory o memory span – capacity of working memory o chunking = organizing information into meaningful units to make easier to remember in working memory • long-term memory = relatively permanent storage of information o separate system from working memory o serial position effect = idea that ability to remember items from a list depends on the order of presentation; two parts § primacy effect – better memory for items at the start of a list § recency effect – better memory for items at the end of a list o memories strengthened with retrieval 7.3 How is Information Organized in Long-Term Memory • long-term storage is based on meaning o perceptual experiences transformed into representations in brain o levels of processing model – more deeply an item is encoded, the more meaning it has and the better it’s remembered o maintenance rehearsal – repeating the item over and over o elaborative rehearsal – encodes information in more meaningful ways; thinking about item conceptually • schema = cognitive structures that help perceive, organize, process, and use information o help understand events in the world o can bias how information is encoded § many schemas influenced by culture • information is stored in association networks o networks of association – set of theories about memory organization o Allan Collins and Elizabeth Loftus (1975) § item’s features linked as to identify item § each unit of information is a node § each node connected to other nodes § activating one node increases likelihood that associated nodes will become active o spreading activation models – stimuli in working memory activate specific nodes • retrieval cues = anything that helps a person or animal remember information stored in long-term memory o encoding specificity principle = idea that any stimulus encoded along with an experience can later trigger a memory for the experience § context-dependent memory – when the recall situation is similar to the encoding situation § state-dependent memory – memory enhanced when a person’s internal states match during encoding and recall • mnemonics = learning aids, strategies, and devices that improve recall through the use of retrieval cues o method of loci (memory palace) – information associated with sequential locations (familiar rooms/locations) 7.4 What are the Different Long-Term Memory Systems • implicit memory = system underlying conscious memories o classical conditioning o procedural memory = involves motor skills and other behavioral habits § riding a bike § gets harder when a person thinks about it • explicit memory = system underlying conscious memories o declarative memory = cognitive information retrieved from explicit memory; knowledge that can be declared o episodic memory = memory of a person’s past experiences o semantic memory = knowledge of facts independent of experience § may not remember where learned • prospective memory = remembering to do something at some future time 7.5 When Does Memory Fail • forgetting is the inability to retrieve memory from long-term storage • methods of savings – relearning is easier than original learning because of savings • amnesia = deficit in long-term memory due to brain injury, disease, etc. o retrograde amnesia = lose past memories (don’t usually lose everything) o anterograde amnesia = lose ability to form new memories • seven sins of memory: transience, blocking, absentmindedness, persistence, misattribution, bias, and suggestibility o transience = memory decay; forgetting over time § proactive interference = old information interferes with the retrieval of new information § retroactive interference = new information interferes with the retrieval of old information o blocking = temporary inability to remember something § tip-of-the-tongue phenomenon – people experience frustration when they try to recall specific words and cannot o absentmindedness = inattentive or shallow encoding of events § major cause is not paying attention o persistence = continual recurrence of unwanted memories § ex: PTSD 7.6 How Are Long-Term Memories Distorted • memory bias = changing of memories over time so they become consistent with current beliefs/attitudes • flashbulb memories = vivid episodic memories in which people first learn of a surprising and consequential or emotionally arousing event • emotional memory – emotionally arousing events/stimuli are remembered better than non-arousing events • source misattribution = memory distortion; people misremember time, place, etc. involved with a memory • source amnesia = when a person has a memory for an event, but can’t remember where s/he encountered the information • cryptomnesia = a person thinks s/he has come up with a new idea, but really just can’t remember its source • suggestibility = development of biased memories from misleading information o Elizabeth Loftus (1974) § participants asked to estimate speed of cars in an accident • different verbs used to describe crash o “smashed,” “hit,” etc. • one week later, people told that cars “smashed” reported broken glass when there wasn’t any • people have false memories o they can arise even when people are confident about accuracy o often grow out of normal cognitive tendencies and processes • repressed memories are controversial Chapter 9: Human Development 9.1 What Factors Shape Infancy • each person grows/matures at about same periods in life span o prenatal period – begins with conception and ends with birth o infancy – birth to around 2 years o childhood – end of infancy to somewhere between 11 and 14 o adolescence – end of childhood to to somewhere between 18 and 21 o adulthood – end of adulthood to death • development starts in the womb o zygote – first cell of a new life o embryo – 2 weeks to 2 months; organs begin to form o fetus – after 2 months; heart beats; body continues to form o synaptic pruning = process where synaptic connections in brain that are used are preserved and those that are not used are lost o teratogens = agents that harm the embryo or fetus § fetal alcohol syndrome (FAS) • biology and environment influence motor development o newborns born with various reflexes § grasping reflex § rooting reflex – baby turns head and sucks § sucking reflex o dynamic systems theory = view that development is a self-organizing process; new forms of behavior emerge through consistent interactions between a biological being and cultural and environmental contexts • infants are prepared to learn o interact socially through imitation o have good senses (except sight) § parents usually hold babies close to face § test sight using preferential-looking technique o infantile amnesia = inability to remember events from early childhood § people may piece together fake memories from stories they have heard about their childhoods • infants develop attachments o attachment = strong emotional connection that persists over time and circumstance § motivates both parents and infants to stay in close contact § 4 to 6 weeks, most infants smile socially § children cry to compel caregivers to feed/comfort them § parents slip easily into baby talk § occurs across species § animals need emotional bonds and comfort o other animals, like ducks, imprint § Harlow’s monkeys • monkeys sought out furry “monkey” when scared/wanted to be comforted o different attachment styles § Ainsworth’s Strange Situation • caregiver brings infant into room, stranger enters, then caregiver leaves § secure attachment = 60-65% of children • infant plays happily when caregiver is there • infant is distressed when caregiver leaves • infant react positively when caregiver returns • prefers caregiver to stranger § insecure attachment = 35-40% of children • avoidant – 20% o infant does not get upset when caregiver leaves o shows no preference for caregiver/stranger o doesn’t seek comfort upon reunion • ambivalent/anxious – 15% o anxious even when caregiver is present o inconsolable even with reunion o both seeks and resists contact with caregiver § securely attached infants often become: • more socially competent in elementary school • less disruptive/aggressive • more likely to be seen as leaders in adolescence 9.2 How Do Children Learn About the World • Piaget emphasizes stages of cognitive development o assimilation = new information is placed into existing schema o accommodation = new experience causes us to revise schema o sensorimotor stage = birth to 2 years § month 1, all about reflexes § months 2-4, accidents happen and get repeated § only after 4 months, infants try to manipulate world around § year 2 devoted to trial and error § takes 15-18 months to differentiate self from others § master object permanence at end • realize objects exist out of sight o preoperational stage = 2-7 years § start to show more abstract, sophisticated thought • fantasy play § learn how to use language to describe objects that aren’t in front of them § base judgments on appearance, not logic § perspective still fairly egocentric o concrete operational stage = 7-12 years § development of logical reasoning § realize actions are reversible § still focused on concrete objects they can act on, instead of abstract/hypothetical reasoning o formal operational stage = 12 years and up § abstract thought § can logically deduce and test hypothesis § long-term planning is possible o criticisms: § assumes all children perform similarly when in same stage § assumes kids go through stages in same order § Piaget may have underestimated kids’ cognitive abilities • kids can grasp math and numbers o if more motivation, more accuracy • children learn from interacting with others o theory of mind = ability to understand that other people have mental states that influence their behavior • moral development begins in childhood o moral reasoning depends on cognitive processes o moral emotions enhance moral reasoning § empathy – understanding another person’s emotional state § sympathy – involves feeling for other people o Lawrence Kohlberg’s stage theory § preconventional level = earliest level of moral development; self-interest and event outcomes determine what is moral § conventional level = strict adherence to societal rules and the approval of others determine what is moral § postconventional level = decisions about morality depend on abstract principles and the value of all life o social intuitionist model = idea that moral judgments reflect people’s initial and automatic emotional responses 9.3 What Changes During Adolescence • puberty = onset of sexual maturity that marks beginning of adolescence o adolescent growth spurt o development of primary sex characteristics o development of secondary sex characteristics o teenagers act on impulses more § limbic system matures faster than frontal cortex • a sense of identity forms o three major changes cause teens to question who they are § transformation of physical appearance § sophistication of cognitive abilities § heightened societal pressure to prepare for future o gender identity = personal beliefs about whether one is male or female o gender roles = characteristics associated with males and females because of cultural influence or learning § impact gender identity § impact gender schemas – how we perceive behaviors § same behaviors often viewed differently for males and females § children bombarded with information about gender roles from a very young age § children pick up on gender expectations as they grow up • peers and parents help shape the adolescent self o compare strengths and weaknesses to peers o adolescents use peer groups to help feel sense of belonging/acceptance o outside observers place teenagers into cliques o family and peers play complimentary roles in a person’s life 9.4 What Brings Meaning in Adulthood • adults are affected by life transitions o pursue career goals, make long-term commitments, etc. o middle aged people cannot drink as much alcohol or eat as much unhealthy food o happily married people usually healthier • transition to old age can be satisfying o elderly contribute much to modern society § ex: federal judges, celebrities, etc. o older adults often suffer from dementia § causes thinking, memory, and behavior to deteriorate progressively § Alzheimer’s – minor memory impairments to more serious difficulties such as forgetting daily routines o socioemotional selectivity theory – as people age, they see time as limited and prioritize positive emotions • cognition changes with age o observed deficits among older people § lower working memory capacity § short-term memory decreases more than long-term § recall is harder than recognition § decrease in memory more pronounced for negative than for positive items o through adolescence and adulthood, cognitive abilities increase o even for older people, being in good health and keeping socially active increases cognitive skills o some cognitive tendencies increase with age § wisdom § crystallized intelligence • specific knowledge, reasoning strategies, vocabulary Chapter 10: Emotion and Motivation 10.1 What are Emotions • emotion = immediate, specific negative or positive response to environmental events or internal thoughts o mood – longer lasting emotional states, can be positive or negative, often “objectless” § can’t usually identify source • emotions vary in valence and arousal o primary emotions = innate, evolutionarily adaptive, and universal § anger, fear, sadness, disgust, happiness, surprise, and contempt o secondary emotions = blends of the primary emotions o circumplex model of emotions – emotions plotted along two continuums: valence (x-axis) and arousal (y-axis) § valence – how negative or positive they are § arousal – generic term for physiological activation • emotions have a physiological component o limbic system involved § amygdala, insula, etc. • three theories of emotion o James-Lange theory of emotion = people perceive specific patterns of bodily responses and as a result feel emotion § facial feedback hypothesis – facial expressions trigger emotions o Cannon-Bard theory = information about emotional stimuli sent simultaneously to the cortex and the body and results in emotional experience and bodily reactions at the same time o Schachter-Singer two-factor theory = label applied to physiological arousal results in the experience of an emotion § people seek source or arousal § whatever person believes cause emotion will determine label 10.2 How are Emotions Adaptive • emotions serve cognitive functions o people anticipate future emotional states to make decision o affect-as-information theory – people use current moods to make judgments and appraisals o somatic markers = bodily reactions that arise from the emotional evaluation of an action’s consequences § gut feeling • facial expressions communicate emotion o people across cultures make very similar facial expressions • display rules = rules learned through socialization that dictate which emotions are suitable in different situations o more appropriate for women to show emotion than men • emotions strengthen interpersonal relations o humans are social animals o guilt strengthens social bonds § shows that people care about their relationships § discourages people from doing things that could affect relationships § can be used to manipulate others § shows knowledge of mistakes 10.3 How are People Motivated • motivation = process that energizes, guides, and maintains behavior towards a goal • drives motivate the satisfaction of needs o need = state of deficiency; biological or social o Maslow’s Hierarchy of Needs § need hierarchy = arrangement of needs; basic survival needs must be met before people can satisfy higher needs • physiological, safety, belonging/love, esteem, self- actualization • self-actualization = pinnacle of Maslow’s hierarchy; when one’s personal dreams and aspirations have been attained o drive = psychological state that motivates an organism to satisfy a need by creating arousal o homeostasis = tendency for bodily functions to maintain equilibrium o Yerkes-Dodson law = psychological principle that performance on challenging tasks increases with arousal up to a moderate level § after that, arousal impairs performance § when graphed, looks like a semi-circle • people are motivated by incentives o incentives = external objects/goals that motivate behaviors o extrinsic motivation = motivation to perform an activity because of the external goals toward which that activity is directed o intrinsic motivation = motivation to perform an activity because of the value/pleasure associated with that activity § may satisfy curiosity o self-determination theory – people are motivated to satisfy needs for competence, related to others, and autonomy § sense of personal control § extrinsic rewards may reduce intrinsic value o self-perception theory – people seldom aware of their specific motives o Freud, pleasure principle – people seek pleasure and avoid pain § approach motivations – seek out stimuli associated with pleasure § avoidance motivation – avoid negative outcomes • people set goals to achieve o self regulation – people change behavior to reach personal goals o self-efficacy – expectation that your efforts will lead to success o achievement motive – desire to do well relative to standards o delayed gratification – postponing immediate gratification in pursuit of long term goals • people have a need to belong o need to belong theory = theory that need for interpersonal attachments is a fundamental motive; evolved for adaptive purposes o humans more successful in groups 10.4 What Motivates Eating • many physiological factors influence eating o when ventromedial region of hypothalamus damaged: § hyperphagia – extreme weight gain; overeating o when outer/lateral region of hypothalamus damaged: § aphagia – extreme weight loss o glucostatic theory – bloodstream monitored for glucose levels; animals become hungry when glucose deficient o lipostatic theory – proposes set-point for body fat o hormone leptin involved in fat regulation • eating influenced by time and taste o people eat at certain times because they learned to o sight and smell of tasty foods make people feel hungry § similar to Pavlov o people more inclined to eat when presented with variety of flavors § sensory-specific satiety – decreased reward value of food if eaten over and over • culture plays a role o what people will eat depends on personal experience and cultural beliefs o cuisine – local norms for what to eat and how to prepare it o what parents eat affects what children eat 10.5 What Motivates Sexual Behavior • biology influences sexual behavior o sex hormones released from gonads o neurotransmitters can affect various aspects of sexual response o hormones on circadian cycle for men § testosterone levels higher in morning o hormones on menstrual cycle for women § approximately ever 28 days o sexual response cycle = four-stage pattern of physiological and psychological responses during sexual activity § excitement – people contemplate/begin engaging in sexual behaviors § plateau – physiological aspects increase; frenzied phase § orgasm – involuntary muscle contractions § resolution – slow return to normal state of arousal; refractory period for men • cultural scripts and rules shape sexual interactions o sexual scripts – cognitive beliefs about how a sexual experience should be enacted § encouraged by media o double standard for number of sexual partners o sexual strategies theory = theory that women and men have evolved distinct mating strategies because they faced different adaptive problems § maximize probability of passing on genes § women tend to be more cautious because more responsibility • people differ in sexual orientations o homosexuality seen as deviant in Western cultures o exposure to hormones in prenatal environment may have effect o hypothalamus may be related to sexual orientation Chapter 11: Health and Well-Being 11.1 What Affects Health • health psychology = field that integrates research on health and on psychology; psychological principles to promote health and well-being • well-being = positive state that includes striving for optimal health and life satisfaction • biopsychosocial model = health and illness result from a combination of factors: biological, behavioral, and social • different lifestyles contribute to health differences • obesity and maladaptive eating habits have many health consequences o body mass index (BMI) = ratio of body weight to height; used to measure obesitry § doesn’t take into account age, sex, bone structure, or body fat distribution § people with low BMIs but large amounts of abdominal fat are more at risk than people with high BMIs who have fat distributed more evenly o a variety of food can contribute to overeating § can lead to obesity § people also eat more if portions are larger o obesity runs in families o obese people seen as less intelligent, less productive, and less socially adept in Western cultures § obesity seen as luxury in some African cultures o many people try to diet § because of inconsistencies, people will easily regain weight back after restrictive eating o disordered eating § anorexia nervosa = eating disorder; excessive fear of becoming fat; restricting energy intake to stay light • often view selves as fat even when extremely skinny § bulimia nervosa = eating disorder; binge eating and inappropriate compensatory behaviors, like purging § binge-eating disorder = binge eating that causes significant distress • usually engage in binge-eating at least once a week, but do not purge § eating disorders tend to run in families • smoking is leading cause of death o most smokers being in childhood or adolescence § see adults/idols smoking and see it as the adult thing to do § maybe think it will make them tough and cool o second-hand smoke from cigarettes affects people around smokers o electronic cigarettes § obtain nicotine but not as harmful as regular cigarettes § doesn’t cause second-hand smoke o quitting smoking § many people use nicotine replacement or medication • doesn’t usually work that well § many people quit cold turkey • exercise has numerous benefits o if exercise more, more health benefits o enhances growth of new neurons and the production of synaptic connections 11.2 What is Stress • stress = unpleasant state of arousal when someone perceives that an event threatens our ability to cope effectively • stressor = something in environment that is perceived as threatening or demanding and produces stress o major life stressors - death or threat of death, major life events, o daily hassles – small day-to-day annoyances • coping response = any attempt to avoid, escape from, or minimize a stressor • stress has physiological components o hypothalamic-pituitary-adrenal (HPA) axis = body system involved in stress responses § hypothalamus à pituitary gland à adrenal glands • releases cortisol • sex differences in how people respond to stressors o fight-or-flight response = physiological preparedness of animals to deal with danger by either fighting or fleeing o end-and-befriend response = females’ tendency to protect and care for their offspring and form social alliances o oxytocin = hormone involved in mothers bonding to newborns • general adaptation syndrome = consistent pattern of responses to stress o three stages § alarm – emergency reaction that prepares body to fight or flee § resistance – body prepares for longer defense from stressor § exhaustion – physiological and immune systems fail 11.3 How Does Stress Affect Health • over long term stress negatively affects health • stress disrupts immune system o immune system = body’s mechanism for dealing with invading microorganisms § made up of three types of specialized white blood cells called lymphocytes • B cells – produce antibodies • T cells – involved in attacking intruders directly • natural killer cells – kill viruses, attack tumors • stress increases risk of heart disease o increased heart rate and blood pressure, increased epinephrine and norepinephrine, increased ischemia can lead to risk of cardiac events o Type A behavior = pattern of behavior characterized by competitiveness, achievement orientation, aggressiveness, etc. § more likely to have heart disease § hostility most toxic factor, most likely to contract heart disease o Type B behavior = pattern of behavior characterized by noncompetitive, relaxed, accommodating behavior • coping reduces the negative health effects of stress o primary appraisals = part of coping process; involves making decisions about whether a stimulus is stressful, benign, or irrelevant o secondary appraisals = part of coping process; involves evaluating response options and choosing coping behaviors o anticipatory coping happens before the onset of a future stressor o emotion-focused coping = type of coping; people try to prevent having an emotional response to a stressor § ex: avoidance, distancing oneself from outcomes, drinking, etc. o problem-focused coping = type of coping; people take direct steps to conform or minimize a stressor o positive reappraisal – cognitive process; people focus on possible good things in his/her current situation o downward comparisons – comparing oneself to those worse off o creation of positive events – strategy of giving positive meaning to ordinary events o some people stress resistant – capable of adapting to life changes § called hardiness – commitment, challenge, and control o some people more resilient – better able to cope in adversity o broaden-and-build theory – positive emotions prompt people to consider novel solutions to their problems 11.4 Can a Positive Attitude Keep People Healthy • positive psychology emphasizes well-being o happiness has 3 components: § positive emotion and pleasure § engagement in life § a meaningful life • being positive has health benefits • social support is associated with good health o people with social support experience less stress overall o buffering hypothesis = when others provide emotional support, recipient is better able to cope with stressful events o marriage can be good for health § troubled marriages may increase stress and decrease health o trusting others is associated with better health § hormone oxytocin increases trust § well-being increases with increase in social bonds • spirituality contributes to well-being § people can find meaning and purpose in their lives through faith Chapter 13: Personality 13.1 Where Does Personality Come from • personality = characteristic thoughts, emotional responses, and behaviors that are relatively stable in an individual over time and across circumstance • personality trait = a pattern of thought, emotion, and behavior that’s relatively consistent over time and across situations • biological factors play important role in personality o genes, brain structures, and neurochemistry • personality is rooted in genetics o identical twins are much more similar than fraternal twins o identical twins raised apart are still very similar o children raised together but who were not related were not any more alike than two random people • temperaments are evident in infancy o temperaments = biological tendencies to feel/act in certain ways § broader than personality traits o activity level – overall amount of energy/behavior a person exhibits o emotionality – describes the intensity of emotional reactions o sociability – general tendency to affiliate with others • there are long-term implications of temperaments o socially inhibited children were much more likely to be anxious, depressed, unemployed, etc. o shyness has a biological and social component § one quarter of behaviorally inhibited children are not shy later in childhood • usually when parents are supportive • personality is adaptive o groups whose members have diverse skills have selective advantage over groups whose members have limited skills § ex: may be advantageous to have group members that are adventure seeking and that are cautious 13.2 What Are the Theories of Personality • psychodynamic theory = development through management of unconscious conflicts, Freudian o conscious level – thoughts people are aware of o preconscious level – content that isn’t currently in awareness, but that could be brought to awareness o unconscious level – material that mind cannot easily retrieve o Freud also proposed a structural model of personality § id = most basic level; submerged in unconscious; operates according to pleasure principle • libido – force that drives pleasure principle § superego = brake of id; largely unconscious; develops in childhood; internalization of parental and societal standards § ego = mediates between id and superego; tries to satisfy id while adhering to superego; operates according to reality principle • defense mechanisms = unconscious mental strategies that the mind uses to protect itself from anxiety o psychosexual stages = developmental stages that correspond to distinct libidinal urges; progression affects personality § oral stage – birth to 18 months; seek pleasure through mouth § anal stage – 2 to 3 years; learn to control bowels § phallic stage – 3 to 5 years; discover pleasure of rubbing genitals, not sexual § latency stage – suppress libidinal urges § genital stage – attain mature attitudes about sexuality and adulthood § people can get fixated at a stage, can have oral, anal-retentive, etc. personalities • personality reflects learning and cognition o behavior function of person’s expectancies and values o internal locus of control –believe people bring about own rewards o external locus of control – believe rewards come from outside forces o personal constructs – personal theories of how world works o cognitive-social theories – personal beliefs, expectancies, and interpretations of social situations shape behavior and personality o cognitive-affective personality system (CAPS) – people’s personalities often fail to predict behaviors across different circumstances o self-regulatory capacities – relative ability to set personal goals, evaluate progress, and adjust behavior • humanistic approaches = personality develops as people strive for personal growth and self-understanding o unconditional positive regard – parents should accept and prize children no matter how they behave • trait approach = focuses on how individuals differ in personality dispositions o perform factor analysis – grouping items according to similarities o traits vary from person to person along a continuum o five-factor theory = idea that personality can be described using five factors: openness to experience, conscientiousness, extraversion, agreeableness, and neuroticism § each factor is a higher-order trait and is made of lower-order traits § emerge across cultures and age o biological trait theory – personality traits had two major dimensions § introversion/extraversion • personality rooted in two motivational functions o behavioral approach system (BAS) = brain system involved in the pursuit of incentives or reward o behavioral inhibition system (BIS) = brain system sensitive to punishment; inhibits behavior that might lead to danger or pain 13.3 How Stable is Personality • people are inconsistent o situationism = theory that behavior is determined more by situations than by personality traits o how much a trait predicts behavior depends on three factors § centrality of trait • central traits more consistent than secondary § aggregation of traits over time • if behaviors are averaged across situations § type of trait being evaluated • behavior is influenced by the interaction of personality and situations o strong situations tend to mask differences in personality § ex: elevators, religious services, etc. o weak situations tend to reveal differences in personality § ex: parks, bars, parties, etc. o interactionists = behavior determined jointly by situations and underlying dispositions • personality traits relatively stable over time o basic tendencies – traits determined largely by biology; very stable o characteristic adaptations – adjustments to situational demands • development and life events alter personality traits o people have more self-control and emotional stability when older o personality changes occur as result of expectations and experiences associated with age-related roles § ex: becoming a spouse, parent, etc. • culture influences personality o Western cultures emphasize independence while Eastern cultures emphasize relations with other people o self-reports often don’t match cultural stereotypes o women and men very similar personality-wise § differences support common stereotypes § sex difference larger in countries that advocate gender equality 13.4 How is Personality Assessed • personality refers to both unique and common characteristics o idiographic approaches = person-centered approaches to assessing personality; focuses on individual lives; individual is unique § central traits – important for how individuals define selves § secondary traits – less descriptive or not applicable o nomothetic approaches = focus on how common characteristics vary from person to person • researchers use multiple methods to assess personality o unconscious processes, life history data, behavioral data, self-reports o projective measures = personality tests that examine unconscious processes by having people interpret ambiguous stimuli § idea is that people will reveal unconscious parts or personality § Rorschach inkblot test – people shown random inkblots and are asked to describe what they look like § Thematic Apperception Test (TAT) – people shown pictures and are asked to tell a story o objective measures = personality tests that relatively directly assess personality through self-report or observer ratings § may target specific traits § can assess many traits § California Q-Sort – people given cards and are asked to sort them into categories; accurate/inaccurate statements about self • observers show accuracy in trait judgments

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Textbook: A Transition to Advanced Mathematics
Edition: 7
Author: Douglas Smith, Maurice Eggen, Richard St. Andre
ISBN: 9780495562023

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Prove Theorem 6.1.2