数学能力的个别差异课件.ppt

1、Individual Differences in Mathematical Ability數學能力的個別差異1Three 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2Psychometric Perspective Method used:Factor Analysis Results:Ability Factors Criterion:Factor stability or factor i

2、nvariance-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 reasoning3Numerical Facility Stable across studies:arithmetic represents a funda

3、mental domain of human ability strongly defined by arithmetic computation tests;tests that involve a conceptual understanding of number relationships and arithmetical concepts-basic arithmetical skills4 Development:Numerical Facility factor found in:kindergarten children(Wechsler Intelligence Scale

4、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 college5 The factor becomes more exclusively arithmetical in nature with development.Arithmetic and working memory to exclusively arit

5、hmetical relationship between performance on numerical facility tests and tests of mathematical reasoning become weaker with age.6Mathematical Reasoning Different labels:arithmetical reasoning,general reasoning,ability to find and evaluate quantitative relationships and to draw conclusions on the ba

6、sis of quantitative information Relationship between Numerical Facility and Mathematical Reasoning factors become weaker with age.7 8th grade:the two factors clustered grades 9 to 11 and college students:distinct Mathematical Reasoning college students:the 2 unrelated.8Other Mathematical Abilities D

7、ot 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.Estimation Factor:ability to make

8、 quantitative estimations;ability to create and evaluate new hypothesis quickly in order to draw proper conclusions9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)10Cognitive PerspectivesNumerical FacilityMathematicalReasoningMathematicalAbilityRetrieving arith

9、metic facts from long-term memoryMemory spanMental calculation abilityPsychometricCognitive.11Numerical FacilityA battery of Paper-and-pencil Test:numerical facility,perceptual speed(i.e.,speed of encoding,or reading symbols such as numbers spatial abilityComputer-administered arithmetic test:number

10、 encoding(reading numbers off the computer screen retrieving arithmetic facts from long-term memory,carrying(or trading)Time required for each component process is recorded12Relationship between Numerical Facility and Cognitive Abilities The faster arithmetic facts could be retrieved from long-term

11、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.13Implications Basic arit

12、hmetic skills underlying individual differences(agreed with psychometricians)numerical facility is arithmetical in nature.14Other Studies(Geary&Brown,1991,)strategy-choice:ability to use the right strategyWPPSI:(Verbal,spatial,arithmetic)Wechsler Preschool and Primary Scale of IntelligenceWRAT:Arith

13、metic subtest of the the Wide Range Achievement TestTwo variables:Speed-of-fact:how quickly addition facts can be retrievedArithSpacialArithConceptualKnowledgeWorking memory15Developmental Issues Preschool and elementary school children:conceptual knowledge and working memory appear to be a primary

14、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.16Mathematical ReasoningCognitive measures:speed of executing arithmetical oper

15、ations such as carrying ability 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:actually solve the problem determine the sequence of arithme

16、tic operationsMemory Span factorsFor 112 Air Force recruits80%25%17Individual Differences in Mathematical Reasoning Ability to mentally set up representations of arithmetic word problems the ease with problem-solving schemas are developed working memory,the ability to keep important information in m

17、ind while performing mathematical operations speed with which basic mathematical processes can be executed18Behavioral Genetic Perspective heritability 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

18、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.19Numerical Facility Median h2 across several studies:.45 V

19、andenbery(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(DeFries)one half of the variability in arithmetical ability is due to genetic factors.20Mathematical Reasoning h2=.27 across several studies(Vandenberg)MZ and DZ h2=.36 to.66 a small to moderate proportion of individual differences in mathematical reasoning ability are due to genetic factors.21