数学认知能力的认知与脑机制理论模型综述

张红川; 董奇

doi:10.16382/j.cnki.1000-5560.2002.01.002

数学认知能力的认知与脑机制理论模型综述

doi: 10.16382/j.cnki.1000-5560.2002.01.002

张红川,
董奇

北京师范大学发展心理研究所，北京 100875

基金项目:

国家攀登计划基金项目 95—专—09

① M. H. Ahcraft, & J. Bttagia(1978). Cognitive Anthmetic: Eridence for Retrieval and Decision Proceses in Mental Addition. Joumnal of Experimenal Paychology : Human Iearning and Mcmory, 4, pp.527 - 538.
②M. H. Asheraf(1982). The Development of Mcntal Arthmetic:A chonometric Approach. Devclopmcntal Review, 2.pp.213 - 236.
③M. H. Ashcraf(1987). Children's Knowledge of Simple Arithumetic: A Developmental Model und Simolation. In J. Bisanz, C.J. Brain- erd & R. Kail(Eds.), Foirmal Models in Developmental Paychology. (pp.302 - 338). Edmontion: University of Alberta.
④ D.F. Benson, & M. B. Denckda(1969). Verbal Paraphasia田a Source of Calculation Disturbance. Archives of Neurology, 21, pp.96 - 102.
⑤ A. B.I. Bemardo(in press). Asymetrice Actiation of Number Codes in Bilinguals: Futher Evidence far the Enoding Complex Mdel of Number Processing. Menory & Cognition.
⑥ M. Brybaert, w. Fias, & M.P. Noe(198). The Whorfian Hypohesis and Numerical Cogition: Is "Twenty- Four”" Procesed in the Same Way田s“Four- and-Twenty"?" Cogition, 66, pp.51 -77.
⑦ J1. D. Cupbell(upulishod). An Encodig-omplx Approach to Number Procesing in Chinese FEnglish Bilinguals.
⑧ R. M. Church, & W. H. Meck(1984).The Numerical Atibute of Stimuli. in H. L. Roitblat, T. C. Bever, & H. s. Terrace(eds). (pp. 445 - 464). Animal Cognition, Hillsdale, N.J. : Erlbaum.
⑨ L. Cipolot(1995). Multiple Routes for Reading words, Why Not Numbers? Evidence from a Case of Arabic Numeral Dyslexa. Cog- nitive Neuropsychology, 12, p.313 - 342. OL. Cohen, S. Dehaene, & P. Verstichel(1994). Number Words and Number Non-words. A Case of Deep Dyslexia Extending to Arnabic Numerals. Brain, 117, pp.267 - 279.
⑩ L. Cohen, s. Dehaene, & P. Verstichel(1994). Number Words and Number Non- words. A Case of Deep Dyslexia Extending to Anbic Numerals. Brain, 117, pp.267 - 279.
⑪ S. Dehaene & L. Cohen(1994). Cerebral Pathways for Calculation: Double Dissociation between Rote Verbal and Quantitative Knowl- edge of Arithmetic. Cortex, 33, pp.219 - 250.
⑫ S. Dehaene(1992). Varieties of numercal abiltes. Cognition, 44, 1 -42.
⑬ S. Dehaene(1996). The Organization of Brain Activations in Number Comparison: Event-related Potentials and the Additive factors Method. Joumal of Cognitive Neuroscience, 8, pp.47- 68.
⑭ S. Dehaene, N. Tzourio, V. Frak, L. Raynaud, L. Cohen, J. Mehler, & B. Mazoyer(1996). Cerebral Activations During Number Multi- plication and Comparison: A PET Study. Neuropsychologia.34, pp.1097- 1106.
⑮ S. Dehaene, E. Spelke, P. Pinal, R. Stanescu, & S. Tsivkin(1999). Soruces of Mathematical Thinking: Behavioral and Brain-imaging Evidence. Science, 284, pp.970- 974.
⑯ S. Dehaene(2001). Precis of the Number Sense. Mind and Languuage, vol 16, 1, pp.16- 36.
⑰ C. Deloche, & X. Seron(1982). From One to 1: An Analysis of a Transcoding Process by Means of Neuropsychological Data. Cogni- tion, 12, pp.119- 149.
⑱ C. Deloche, & K. Willmnes(2000). Cognitive Neuropeychological Models of Adult Calculation and Number Processing: The Role of the Surface Format of Numbers. European Child & Adolescent Paychiatry 9, pp.27 -40.
⑲ M. D. Hauser, P. MacNeilage, & M. Ware(1996). Numerical Representations in Primates. Procedings of National Academy of Science.
⑳ M. McCloskey, A. Caramazza & A. Basili (1985). Cognitive Mechanisms in Number Processing and Calculaytion: Evidence from Dyscalculia. Braain and Cognition, 4, pp. 171- 196.
㉑ M. McCloskey, P. Macaruso & T. Whetstone (1992). The Functional Architecture of Numerical Processing: Defending the Modular Model. InJ. I. D. Campbell (Eds.) Nature and Origins of Mathematical Skills. Series: Advances in Psychology, 91. (pp. 493 - 537). Amserdam: Elsevier.
㉒ J. McNeil & E. K. Warington (1994). Dissociation between Addition and Subtraction with Written Calculation. Neuropsy- chologia，32，pp. 717- 728.
㉓ N. J. van Karskamp & L. Ciplotti (2001). Selective lmpairnent for Addition, Substraction and Mutplication: lmplications for the Organization of Arithmetical Facts. Cortex, 37, pp. 363 - 388.
㉔ M. Pesenti, M. Thioux，X. Seron & A. De Volder (2000). Neuraaanatomical Substrate of Arabic Nuymber Processing, Nu- merical Comparison and Simple Addition: A PET study. Jorunal of Cognitive Neuroscience, 12 (3)，pp. 461 - 479.
㉕ R. S. Siegler & J. Shrager (1984). A Model of Strategy Choice. In C. Sophian (Eds.)，Onigins of cognitive skills (pp. 229 - 294). Hillsdale, NJ: Lawrence Erlbaum Associates.
㉖ C. M. Temple (1991). Procedural Dyscalculia and Number Fact Dyscalculia: Double Dissociation in Developmental Dyscalculia. Cognitive Neuropsychology, 8, pp. 155 - 176.
㉗ E. K. Warrington (1982). The Fractionation of Arthmetical Skills: A Single Case Study. Quarterly Journal of Experimental Psychology, 34A，pp. 31-51.
㉘ K. Wynn (1998). Psychological Foundations of Number: Numerical Competence in Human Infants. Trends in Cogmitive Sci- ences.Vol.2，No. 8，pp. 296- 303.
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出版历程
- 收稿日期: 2001-12-01
- 刊出日期: 2002-03-01

摘要

摘要: 数学认知能力是个体最重要的认知能力之一，也是当前认知神经科学的重点研究课题。近二十余年来，一些研究者分别从不同的視角，采取多种研究手段与技术对数学认知能力、过程及其与脑结构、功能的联系问题进行了较为系统深入的探讨，获得了大量的研究结果，并据此建立了若干数学认知的功能与结构模型。这些理论模型彼此继承，又不断进行着扩展与深化，为数学认知研究奠定了较好的理论基础。本文对其中应用较为广泛的几个理论模型进行了综述，分析了其主要理论观点、研究证据以及尚待改进之处，并对今后的研究工作提出了一些建议。
- 数学认知 /
- 理论模型 /
- McCloskey模型 /
- 三重编码模型 /
- 编码复杂性模型
注释:

1) ① M. H. Ahcraft, & J. Bttagia(1978). Cognitive Anthmetic: Eridence for Retrieval and Decision Proceses in Mental Addition. Joumnal of Experimenal Paychology : Human Iearning and Mcmory, 4, pp.527 - 538.

2) ②M. H. Asheraf(1982). The Development of Mcntal Arthmetic:A chonometric Approach. Devclopmcntal Review, 2.pp.213 - 236.

3) ③M. H. Ashcraf(1987). Children's Knowledge of Simple Arithumetic: A Developmental Model und Simolation. In J. Bisanz, C.J. Brain- erd & R. Kail(Eds.), Foirmal Models in Developmental Paychology. (pp.302 - 338). Edmontion: University of Alberta.

4) ④ D.F. Benson, & M. B. Denckda(1969). Verbal Paraphasia田a Source of Calculation Disturbance. Archives of Neurology, 21, pp.96 - 102.

5) ⑤ A. B.I. Bemardo(in press). Asymetrice Actiation of Number Codes in Bilinguals: Futher Evidence far the Enoding Complex Mdel of Number Processing. Menory & Cognition.

6) ⑥ M. Brybaert, w. Fias, & M.P. Noe(198). The Whorfian Hypohesis and Numerical Cogition: Is "Twenty- Four”" Procesed in the Same Way田s“Four- and-Twenty"?" Cogition, 66, pp.51 -77.

7) ⑦ J1. D. Cupbell(upulishod). An Encodig-omplx Approach to Number Procesing in Chinese FEnglish Bilinguals.

8) ⑧ R. M. Church, & W. H. Meck(1984).The Numerical Atibute of Stimuli. in H. L. Roitblat, T. C. Bever, & H. s. Terrace(eds). (pp. 445 - 464). Animal Cognition, Hillsdale, N.J. : Erlbaum.

9) ⑨ L. Cipolot(1995). Multiple Routes for Reading words, Why Not Numbers? Evidence from a Case of Arabic Numeral Dyslexa. Cog- nitive Neuropsychology, 12, p.313 - 342. OL. Cohen, S. Dehaene, & P. Verstichel(1994). Number Words and Number Non-words. A Case of Deep Dyslexia Extending to Arnabic Numerals. Brain, 117, pp.267 - 279.

10) ⑩ L. Cohen, s. Dehaene, & P. Verstichel(1994). Number Words and Number Non- words. A Case of Deep Dyslexia Extending to Anbic Numerals. Brain, 117, pp.267 - 279.

11) ⑪ S. Dehaene & L. Cohen(1994). Cerebral Pathways for Calculation: Double Dissociation between Rote Verbal and Quantitative Knowl- edge of Arithmetic. Cortex, 33, pp.219 - 250.

12) ⑫ S. Dehaene(1992). Varieties of numercal abiltes. Cognition, 44, 1 -42.

13) ⑬ S. Dehaene(1996). The Organization of Brain Activations in Number Comparison: Event-related Potentials and the Additive factors Method. Joumal of Cognitive Neuroscience, 8, pp.47- 68.

14) ⑭ S. Dehaene, N. Tzourio, V. Frak, L. Raynaud, L. Cohen, J. Mehler, & B. Mazoyer(1996). Cerebral Activations During Number Multi- plication and Comparison: A PET Study. Neuropsychologia.34, pp.1097- 1106.

15) ⑮ S. Dehaene, E. Spelke, P. Pinal, R. Stanescu, & S. Tsivkin(1999). Soruces of Mathematical Thinking: Behavioral and Brain-imaging Evidence. Science, 284, pp.970- 974.

16) ⑯ S. Dehaene(2001). Precis of the Number Sense. Mind and Languuage, vol 16, 1, pp.16- 36.

17) ⑰ C. Deloche, & X. Seron(1982). From One to 1: An Analysis of a Transcoding Process by Means of Neuropsychological Data. Cogni- tion, 12, pp.119- 149.

18) ⑱ C. Deloche, & K. Willmnes(2000). Cognitive Neuropeychological Models of Adult Calculation and Number Processing: The Role of the Surface Format of Numbers. European Child & Adolescent Paychiatry 9, pp.27 -40.

19) ⑲ M. D. Hauser, P. MacNeilage, & M. Ware(1996). Numerical Representations in Primates. Procedings of National Academy of Science.

20) ⑳ M. McCloskey, A. Caramazza & A. Basili (1985). Cognitive Mechanisms in Number Processing and Calculaytion: Evidence from Dyscalculia. Braain and Cognition, 4, pp. 171- 196.

21) ㉑ M. McCloskey, P. Macaruso & T. Whetstone (1992). The Functional Architecture of Numerical Processing: Defending the Modular Model. InJ. I. D. Campbell (Eds.) Nature and Origins of Mathematical Skills. Series: Advances in Psychology, 91. (pp. 493 - 537). Amserdam: Elsevier.

22) ㉒ J. McNeil & E. K. Warington (1994). Dissociation between Addition and Subtraction with Written Calculation. Neuropsy- chologia，32，pp. 717- 728.

23) ㉓ N. J. van Karskamp & L. Ciplotti (2001). Selective lmpairnent for Addition, Substraction and Mutplication: lmplications for the Organization of Arithmetical Facts. Cortex, 37, pp. 363 - 388.

24) ㉔ M. Pesenti, M. Thioux，X. Seron & A. De Volder (2000). Neuraaanatomical Substrate of Arabic Nuymber Processing, Nu- merical Comparison and Simple Addition: A PET study. Jorunal of Cognitive Neuroscience, 12 (3)，pp. 461 - 479.

25) ㉕ R. S. Siegler & J. Shrager (1984). A Model of Strategy Choice. In C. Sophian (Eds.)，Onigins of cognitive skills (pp. 229 - 294). Hillsdale, NJ: Lawrence Erlbaum Associates.

26) ㉖ C. M. Temple (1991). Procedural Dyscalculia and Number Fact Dyscalculia: Double Dissociation in Developmental Dyscalculia. Cognitive Neuropsychology, 8, pp. 155 - 176.

27) ㉗ E. K. Warrington (1982). The Fractionation of Arthmetical Skills: A Single Case Study. Quarterly Journal of Experimental Psychology, 34A，pp. 31-51.

28) ㉘ K. Wynn (1998). Psychological Foundations of Number: Numerical Competence in Human Infants. Trends in Cogmitive Sci- ences.Vol.2，No. 8，pp. 296- 303.

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图 1 图表搜索理论

下载: 全尺寸图片幻灯片

图 2 网络提取理论

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图 3 联结分布理论

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图 4 McCloskey的抽象表征模型

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图 5 三重编码模型

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图 6 三重编码理论的脑结构模型

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表 1 编码复杂性模型的结构示意表

表 2 McCloskey模型、三重编码模型与编码复杂性模型的关系