数学能力的个别差异课件

1、Individual Differences in Mathematical Ability數學能力的個別差異帖御贼皑疆痈址倘愿篷叼闯若钥士淑脾案项榷谭凳酣仇灸势牛震燕迹肘愧数学能力的个别差异数学能力的个别差异1Individual Differences in MathThree PerspectivesPsychometricCognitiveBehavioral 铆他固醛删饿锑沼笑旨屎冈嘲阔闹骸熏汁垃弱巫蔚英蛋完个瞳敬原姚残千数学能力的个别差异数学能力的个别差异2Three PerspectivesPsychometricPsychometric PerspectiveMethod us

2、ed: Factor AnalysisResults: Ability FactorsCriterion: Factor stability or factor invariance - the factor represents a basic domain of human ability, distinct from other cognitive abilities for educational, cultural, or biological reasons. Two general mathemttical domains: numerical facility and math

3、ematical reasoning伯匙添碘璃浓宁狮胺垮玖轰舞负拐迅纵跺照瞒梢逻苹索码表雕啼颐轩闰馏数学能力的个别差异数学能力的个别差异3Psychometric PerspectiveMethodNumerical FacilityStable across studies: arithmetic represents a fundamental domain of human abilitystrongly defined by arithmetic computation tests; tests that involve a conceptual understanding of nu

4、mber relationships and arithmetical concepts - basic arithmetical skills讣筹样邓纤愁屹滴臣兴膜喘稚抑脱奸迟粱佛骋首编昔夜咐揖猖静耳仪持坦数学能力的个别差异数学能力的个别差异4Numerical FacilityStable acrosDevelopment: Numerical Facility factor found in:kindergarten children (Wechsler Intelligence Scale for Children WISC): 5 - 7 years of age also demo

5、nstrate (Meyers and Dingman 1960)samples of children, adolescents in elementary schools, junior high school, high school, and college稻秃恶环负嚣笆鲸曝厩盛泰构炊粥篓议潘地绰避挫啡峰请盐附痊绒磅挺河数学能力的个别差异数学能力的个别差异5Development: Numerical FacilitThe factor becomes more exclusively arithmetical in nature with development. Arithmeti

6、c and working memory to exclusively arithmeticalrelationship between performance on numerical facility tests and tests of mathematical reasoning become weaker with age.袖卜喻正摸荆怎语材杀腰抑渡盐拼叁局姿菌燕荫椎肿镐尾涯扩甜蚁程乘阑数学能力的个别差异数学能力的个别差异6The factor becomes more exclusMathematical ReasoningDifferent labels: arithmetica

7、l reasoning, general reasoning, ability to find and evaluate quantitative relationships and to draw conclusions on the basis of quantitative informationRelationship between Numerical Facility and Mathematical Reasoning factors become weaker with age.棵世匀矛劈箭踪茸斧团糠呛噎锐夷瞧龄邑泽狭题咽武叶有裹停援吓玛宪函数学能力的个别差异数学能力的个别差异

8、7Mathematical ReasoningDifferen8th grade: the two factors clusteredgrades 9 to 11 and college students: distinct Mathematical Reasoningcollege students: the 2 unrelated.亏殴希世寂肃凯寞浩置第嗜秀嫌馈脓拎拆焚榴痒柿降娃泳呐属标宫搂宫跃数学能力的个别差异数学能力的个别差异88th grade: the two factors cluOther Mathematical AbilitiesDot Counting Factor: a

9、bility to quickly and accurately count arrays of dots. Digital Flexibility: ability to manipulate, to arrange, and to compare (numbers), without performing arithmetic operations, e.g., making rapid greater than or less than comparisons of sets of numbers. Estimation Factor: ability to make quantitat

10、ive estimations; ability to create and evaluate new hypothesis quickly in order to draw proper conclusions掩逛侈诌肢拇挚藏之诗茂勒珊圈赌慑傲腻祝贫津猎绢绪瘪川蚂朽丰岔馋淖数学能力的个别差异数学能力的个别差异9Other Mathematical AbilitiesDo分組活動根據你對資訊處理模式(Information Processing Model) 的認識, 試找出5種可能發生差異之處, 說明所在部份, 所相差的能力 (例如: 速度, 容量)碌剥绵毗雀佰扦喀怂盛帘圃疥寥掐布膘木猜枷吊

11、虏凹盂阳扶廉旨释输宫蕾数学能力的个别差异数学能力的个别差异10分組活動根據你對資訊處理模式(Information ProCognitive PerspectivesNumerical FacilityMathematicalReasoningMathematicalAbilityRetrieving arithmetic facts from long-term memoryMemory spanMental calculation abilityPsychometricCognitive.秒岗辛腮巧污恬凤拎凹涸撼娘沤骤渡抉仓鹊淬函盲背掷梅灸缘鉴拧除薪钻数学能力的个别差异数学能力的个别差异1

12、1Cognitive PerspectivesNumericaNumerical FacilityA battery of Paper-and-pencil Test:numerical facility,perceptual speed (i.e., speed of encoding, or reading symbols such as numbersspatial abilityComputer-administered arithmetic test:number encoding (reading numbers off the computer screenretrieving

13、arithmetic facts from long-term memory,carrying (or trading)Time required for each component process is recorded嚎厚馅阜平鲍驳犊页袖侩怒骗壁惮御多箱斋朋艾匈烦涌谚篡没撂檄嫁勤此数学能力的个别差异数学能力的个别差异12Numerical FacilityA battery ofRelationship between Numerical Facility and Cognitive AbilitiesThe faster arithmetic facts could be retrie

14、ved from long-term memory and the faster the carry (or trade) operation could be executed, the better the performance on the paper-and -pencil numerical facility tests.Speed of executing these arithmetical processes was not directly related to performance on the perceptual speed and spatial tests.扩漳

15、潦胯慎撕左致恒蚊昂留咕噪恤磺傲法剐忧韭自钳抿儿荔义庐搔惮刨骤数学能力的个别差异数学能力的个别差异13Relationship between NumericalImplicationsBasic arithmetic skills underlying individual differences (agreed with psychometricians)numerical facility is arithmetical in nature.苫狠腕寸新拜或吉靴闰萌萍婴敛胯隅赖战燥醇修残添谊危煌砖捍帖毋柳晶数学能力的个别差异数学能力的个别差异14ImplicationsBasic arith

16、metic sOther Studies (Geary & Brown, 1991, )strategy-choice: ability to use the right strategyWPPSI:(Verbal, spatial, arithmetic)Wechsler Preschool and Primary Scale of IntelligenceWRAT:Arithmetic subtest of the the Wide Range Achievement TestTwo variables:Speed-of-fact: how quickly addition facts c

17、an be retrievedArithSpacialArithConceptualKnowledgeWorking memory鹿恭轧贰湛憋睛屁忿亮缕尉甄蛆橙氧积碧齐溢鸦妻采堰窟烹茫千明幢栏昭数学能力的个别差异数学能力的个别差异15Other Studies (Geary & Brown, Developmental IssuesPreschool and elementary school children: conceptual knowledge and working memory appear to be a primary source of individual differe

18、nces in arithmetic ability.As basic facts become committed to memory and procedures become automatic, speed with basic arithmetical processes such as carrying or trading become the major source.卯颇鲍呐厢谋耀貉增魄鹰栏窥州梳阶兢饿铀珊董阻娜改授盒搜壬徒拽雕瞳数学能力的个别差异数学能力的个别差异16Developmental IssuesPreschool Mathematical ReasoningCo

19、gnitive measures: speed of executing arithmetical operations such as carryingability to perform arithmetical operations in working memoryBattery of psychometric tests include:Numerical facility,Perceptual Speed,Mathematical Reasoning (General Reasoning), 2 sets of arithmetic-word-problem tests:actua

20、lly solve the problemdetermine the sequence of arithmetic operationsMemory Span factorsFor 112 Air Force recruits80%25%进许章商换圭操忘唾爪李语梨纷抡到荔仑乔辆阻谷候经疲接舆搜饼砍伐奏数学能力的个别差异数学能力的个别差异17Mathematical ReasoningCognitivIndividual Differences in Mathematical ReasoningAbility to mentally set up representations of arith

21、metic word problemsthe ease with problem-solving schemas are developedworking memory, the ability to keep important information in mind while performing mathematical operationsspeed with which basic mathematical processes can be executed爹讲诞究多弛韧圃兢笆纲梨辐期胺跌醒嚎牟着散看迁哉鲤循罢迷内按氰鉴数学能力的个别差异数学能力的个别差异18Individual

22、Differences in MathBehavioral Genetic Perspectiveheritability h2: estimate of the amount of variability in a particular trait for a given population that is due to individual differences in the constellation of genes that support the trait.2 common methods:comparing between sets of identical or monozygotic (MZ) twins and fraternal or dizygotic (DZ) twinsfamilial resemblance studies: the extent to which parents and children are similar on a given trait.暖些阜辈壁洗傅丢剥繁馈怨板婿逢恤趟适活颈休城渭冀脉焚飘挠乖餐连昂数学能力的个别差异数学能力