数学能力的个别差异ppt课件

1、Individual Differences in Mathematical Ability數學才干的個別差異Three Perspectives Psychometric Cognitive Behavioral 0 0101020203030404050506060707080809090第一季第一季第二季第二季第三季第三季第四季第四季東部東部中部中部北部北部Psychometric Perspective Method used: Factor Analysis Results: Ability Factors Criterion: Factor stability or factor

2、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 mathematical reasoningNumerical Facility Stable across studies: arithmetic represents

3、 a fundamental domain of human ability strongly defined by arithmetic computation tests; tests that involve a conceptual understanding of number relationships and arithmetical concepts - basic arithmetical skills Development: Numerical Facility factor found in: kindergarten children (Wechsler Intell

4、igence Scale for Children WISC): 5 - 7 years of age also demonstrate (Meyers and Dingman 1960) samples of children, adolescents in elementary schools, junior high school, high school, and college The factor becomes more exclusively arithmetical in nature with development. Arithmetic and working memo

5、ry to exclusively arithmetical relationship between performance on numerical facility tests and tests of mathematical reasoning become weaker with age.Mathematical Reasoning Different labels: arithmetical reasoning, general reasoning, ability to find and evaluate quantitative relationships and to dr

6、aw conclusions on the basis of quantitative information Relationship between Numerical Facility and Mathematical Reasoning factors become weaker with age. 8th grade: the two factors clustered grades 9 to 11 and college students: distinct Mathematical Reasoning college students: the 2 unrelated.Other

7、 Mathematical Abilities Dot Counting Factor: ability 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

8、. Estimation Factor: ability to make quantitative estimations; ability to create and evaluate new hypothesis quickly in order to draw proper conclusions分組活動 根據他對資訊處理方式(Information Processing Model) 的認識, 試找出5種能够發生差異之處, 說明所在部份, 所相差的才干 (例如: 速度, 容量)Cognitive PerspectivesNumerical FacilityMathematicalRea

9、soningMathematicalAbilityRetrieving arithmetic facts from long-term memoryMemory spanMental calculation abilityPsychometricCognitive.Numerical FacilityA battery of Paper-and-pencil Test:numerical facility,perceptual speed (i.e., speed of encoding, or reading symbols such as numbersspatial abilityCom

10、puter-administered arithmetic test:number encoding (reading numbers off the computer screenretrieving arithmetic facts from long-term memory,carrying (or trading)Time required for each component process is recordedRelationship between Numerical Facility and Cognitive Abilities The faster arithmetic

11、facts could be retrieved 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 spee

12、d and spatial tests.Implications Basic arithmetic skills underlying individual differences (agreed with psychometricians) numerical facility is arithmetical in nature.Other Studies (Geary & Brown, 1991, )strategy-choice: ability to use the right strategyWPPSI:(Verbal, spatial, arithmetic)Wechsle

13、r Preschool and Primary Scale of IntelligenceWRAT:Arithmetic subtest of the the Wide Range Achievement TestTwo variables:Speed-of-fact: how quickly addition facts can be retrievedArithSpacialArithConceptualKnowledgeWorking memoryDevelopmental Issues Preschool and elementary school children: conceptu

14、al knowledge and working memory appear to be a primary source of individual differences 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.Mathematical Reasoning

15、Cognitive 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:act

16、ually solve the problemdetermine the sequence of arithmetic operationsMemory Span factorsFor 112 Air Force recruits80%25%Individual Differences in Mathematical Reasoning Ability to mentally set up representations of arithmetic word problems the ease with problem-solving schemas are developed working

17、 memory, the ability to keep important information in mind while performing mathematical operations speed with which basic mathematical processes can be executedBehavioral Genetic Perspective heritability h2: estimate of the amount of variability in a particular trait for a given population that is

18、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) twins familial resemblance studies: the extent to which parents and children are similar on a given trait.Numerical Facility Median h2 across several studies: .45 Vandenbery (1966) individual numerical facility tests such as addition: .43 - .58 Vandenbery (1962) elementary grades in arithmetic: .66 (Husen) arithmetical skills of parents and children +ve correlated