数字加工过程中数量表征方式的ERP研究
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摘要
数量表征是数字认知领域的核心问题,对于数字加工过程中数量以何种方式进行表征这一问题在理论上存在着两种对立的观点。一种观点认为,数字加工依赖于单一、抽象的数量编码表征,即数量表征不受数字符号形式的影响；另一种观点则认为,数字的数量表征依赖于数字的表面形式(surface format),即数量表征受数字符号形式影响,并不存在抽象的数量表征。上述两种观点都得到了大量的研究证据。通过分析以往相互矛盾的实验结果可以发现,在这两类相互冲突的实验中,其数量表征任务往往属不同层次的加工。笔者据此假设,不同的加工层次中数量可能以不同的方式进行表征。基于这一假设,笔者选取数量简单比较与加法运算这两种代表不同数量表征加工水平的任务,尝试从数量表征加工层次的角度入手,采用记录事件相关电位的方法,对数量表征方式作进一步探讨。
本研究包括三个实验。实验1以阿拉伯数字和麻将点数为刺激材料,采用延迟匹配S1-S2范式,考察了在数量比较加工过程中,数量是否以依赖于数字表面形式的编码方式表征。实验2选取与实验1相同的刺激材料,采用延迟判断任务(delayed verification task)范式,探讨了在数字运算过程中(以加法运算为例),数量是否以单一、抽象的编码方式表征。实验3以阿拉伯数字、麻将点数以及汉字数字为刺激材料,采用与实验2相同的任务范式,进一步检验数字运算过程中(以加法运算为例),数量是否以单一、抽象的编码方式表征。
本研究主要获得以下结论：
(1)数字加工过程中数量的表征方式受数量加工水平的影响。当任务只需要进行浅层次的数量加工时,不同符号形式的数字以依赖于表面形式的方式表征；当任务需要进行深层次的数量加工时,则以单一、抽象的方式表征。
(2)数量的抽象表征可能以接近阿拉伯数字的形式(或阿拉伯数字形式)存在。
Magnitude representation is one of the most important questions in number cognition. There are two opposing views on magnitude representation in the numerical processing. Some researchers assume that numerical processing relies on a single, abstract magnitude representation, that is, the magnitude representation is independent of numerical notations. While others deny the existence of a unitary abstract magnitude representation and argue that magnitude representation is dependent on surface format of numbers. Each hypothesis has received considerable amount of supporting evidence. From the conflicting results, we find that the level of magnitude representation is different in previous studies. Therefore, we suppose the representation of magnitude is influenced by the level of magnitude processing in different tasks. According to this hypothesis, we attempt to further investigate the representation of magnitude by recording event-related potentials, with numerical comparison and addition tasks selected to represent two different levels of magnitude representation.
This study included three experiments. Adopting a delayed match-to-sample paradigm, the first experiment investigated whether the representation of magnitude depended on the surface format of the numbers, with the Arabic numbers and non-symbolic dots (similar to those on the faces of a mahjong) selected as materials. In the second experiment, the same materials as the first experiment were used, while a delayed verification task paradigm was adopted, in order to investigate whether the representation of magnitude is independent of numerical notations in arithmetic tasks, such as addition tasks. In the third experiment, the same task paradigm as in the second experiment was adopted while the Arabic numbers, Mandarin numbers and non-symbolic dots were adopted as materials. We further explored whether magnitude was indeed represented in an abstract fashion
The main findings of this study are as follows:
(1) The magnitude representation will be influenced by the level of magnitude processing in different tasks. In some tasks accessible to shallow processing, the representation of magnitude depends on the surface format of the numbers. While in other tasks a deep level of processing is needed, magnitude is represented in a single, abstract representation.
(2) The single, abstract magnitude code might be in the form of Arabic format or at least close to Arabic format.
本研究包括三个实验。实验1以阿拉伯数字和麻将点数为刺激材料,采用延迟匹配S1-S2范式,考察了在数量比较加工过程中,数量是否以依赖于数字表面形式的编码方式表征。实验2选取与实验1相同的刺激材料,采用延迟判断任务(delayed verification task)范式,探讨了在数字运算过程中(以加法运算为例),数量是否以单一、抽象的编码方式表征。实验3以阿拉伯数字、麻将点数以及汉字数字为刺激材料,采用与实验2相同的任务范式,进一步检验数字运算过程中(以加法运算为例),数量是否以单一、抽象的编码方式表征。
本研究主要获得以下结论：
(1)数字加工过程中数量的表征方式受数量加工水平的影响。当任务只需要进行浅层次的数量加工时,不同符号形式的数字以依赖于表面形式的方式表征；当任务需要进行深层次的数量加工时,则以单一、抽象的方式表征。
(2)数量的抽象表征可能以接近阿拉伯数字的形式(或阿拉伯数字形式)存在。
Magnitude representation is one of the most important questions in number cognition. There are two opposing views on magnitude representation in the numerical processing. Some researchers assume that numerical processing relies on a single, abstract magnitude representation, that is, the magnitude representation is independent of numerical notations. While others deny the existence of a unitary abstract magnitude representation and argue that magnitude representation is dependent on surface format of numbers. Each hypothesis has received considerable amount of supporting evidence. From the conflicting results, we find that the level of magnitude representation is different in previous studies. Therefore, we suppose the representation of magnitude is influenced by the level of magnitude processing in different tasks. According to this hypothesis, we attempt to further investigate the representation of magnitude by recording event-related potentials, with numerical comparison and addition tasks selected to represent two different levels of magnitude representation.
This study included three experiments. Adopting a delayed match-to-sample paradigm, the first experiment investigated whether the representation of magnitude depended on the surface format of the numbers, with the Arabic numbers and non-symbolic dots (similar to those on the faces of a mahjong) selected as materials. In the second experiment, the same materials as the first experiment were used, while a delayed verification task paradigm was adopted, in order to investigate whether the representation of magnitude is independent of numerical notations in arithmetic tasks, such as addition tasks. In the third experiment, the same task paradigm as in the second experiment was adopted while the Arabic numbers, Mandarin numbers and non-symbolic dots were adopted as materials. We further explored whether magnitude was indeed represented in an abstract fashion
The main findings of this study are as follows:
(1) The magnitude representation will be influenced by the level of magnitude processing in different tasks. In some tasks accessible to shallow processing, the representation of magnitude depends on the surface format of the numbers. While in other tasks a deep level of processing is needed, magnitude is represented in a single, abstract representation.
(2) The single, abstract magnitude code might be in the form of Arabic format or at least close to Arabic format.
引文
Ansari, D., Fugelsang, J. A., Dhital, B.,& Venkatraman, V. (2006). Dissociating response conflict from numerical magnitude processing in the brain:An eventrelated fMRI study. Neurolmage,32,799-805.
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Barsalou, L. W. (1999). Perceptual symbol systems. Behavioral and Brain Sciences, 22,577-660.
Barsalou, L. W. (2003). Abstraction in perceptual symbol systems. Philosophical Transactions of the Royal Society B:Biological Sciences,358,1177-1187.
Barsalou, L. W., Santos, A., Simmons, W. K.,& Wilson, C. D. (2008). Language and simulation in conceptual processing. In:Symbols, embodiment, and meaning,ed. M. De Vega, A. M. Glenberg & A. C. Graesser. Oxford University Press,245-283.
Benson, D. F.,& Denckla, M. B. (1969). Verbal Paraphasia as a source of Calculation Disturbance. Archives of Neurology,21,96-102.
Blankenberger, B.,& Vorberg, D. (1997). The Single-Format Assumption in Arithmetic Fact Retrieval. Journal of Experimental Psychology:Learning, Memory, and Cognition 23,721-738.
Butterworth, B. (1999). The mathematical brain. Macmillan.
Campbell, J. I. D.,& Clark, J. M. (1988). An encoding-complex view of cognitive number processing:Comment on McCloskey, Sokol,& Goodman. Journal of Experimental Psychology:General 117,204-214.
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Origins of Mathematical Skills, Elsevier, Amsterdam,539-556.
Campbell, J. I. D.,& Epp, L. J. (2004). An Encoding-Complex Approach to Numerical Cognition in Chinese-English Bilinguals. Canadian Journal of Experimental Psychology,58(4),229-244.
Campbell., J. I. D. (1994). Architectures for numerical cognition. Cognition,53,1-44.
Cantlon, J. F., Libertus, M. E., Pinel, P., Dehaene, S., Brannon, E. M.,& Pelphrey, K. A. (2009). The Neural Development of an Abstract Concept of Number. Journal of Cognitive Neuroscience,27(11),2217-2229.
Cohen./, DBKDHQH6,&KRFKRQ),/HKHrHFy.6,& 1 DFFDFKH/(2000)./DQJuDJHDQG calculation within the parietal lobe:a combined cognitive, anatomical and fMRI study.38,1426-1440.
Csepe.V, Szucs.D,& Honbolygo.F (2003). Number-word reading as a challenging task in dyslexia. International Journal of Psychophysiology,51,69-83.
Dehaene, S. (1992). Varieties of numerical abilities. Cognition 44,1-42.
Dehaene, S.,& Akhavein, R. (1995). Attention, automaticity, and levels of representation in number processing. Journal of Experimental Psychology: Learning, Memory,and Cognition,21,314-326.
Dehaene, S., Bossini, S.,& Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology. Genera,l(122), 371-396.
Dehaene, S., Dupoux, E.,& Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology:Human Perception and Performance,16(3), 626-641.
Dehaene, S., Spelke, E., Pinel, P., Stanescu, R.,& Tsivkin, S. (1999). Sources of mathematical thinking:Behavioral and brain-imaging evidence. Science, 284(970-974).
Dresler, T., Obersteiner, A., Schecklmann, M., Vogel, A. C. M, Ehlis, A. C., Richter, M. M., et al. (2009). Arithmetic tasks in different formats and their influence on behavior and brain oxygenation as assessed with near-infrared
spectroscopy (NIRS):a study involving primary and secondary school children. Journal of Neural Transmission,116(12).
Folstein, J. R.,& Petten, C. V. (2008). Influence of cognitive control and mismatch on the N2 component of the ERP:A review. Psychophysiology,45(1),152.
Hung, Y. H., Hung, D. L., Tzeng, O. J. L.,& Wu, D. H. (2008). Flexible spatial mapping of different notations of numbers in Chinese readers. Cognition, 106(3),1441-1450.
Ito, Y.,& Hatta, T. (2003). Semantic processing of Arabic, Kanji, and Kana numbers: Evidence from interference in physical and numerical size judgments. Memory and Cognition 37(3),360-368.
Kadosh, R. C. (2008). Numerical representation:Abstract or non-abstract? Quarterly Journal of Experimental Psychology, 61(8),1160-1168.
Kadosh, R. C., Kadosh, K. C., Linden, D. E. J., Gevers, W., Berger, A.,& Henik, A. (2007). The brain locus of interaction between number and size:A combined functional magnetic resonance imaging and event-related potential study. Journal of Cognitive Neuroscience 19,957-970.
Kadosh, R. C.,& Walsh, V. (2007). Dyscalculia. Current Biology,17,946-947.
Kaufmann, L., Koppelstaetter, F., Delazer, M., Siedentopf, C., Rhomberg,P., Golaszewski, S., et al. (2005). Neural correlates of distance and congruity effects in a numerical Stroop task:An event-related fMRI study. Neurolmage, 25,888-898.
Koechlin, E., Naccache, L., Block, E.,& Dehaene, S. (1999). Primed numbers:Exploring the modularity of numerical representations with masked and unmasked semantic priming. Journal of Experimental Psychology: Human Perception and Performance,25(6),1882-1905.
Kucian, K., Aster, M. V., Loenneker, T., Dietrich, T.,& Martin, E. (2008). Development of neural networks for exact and approximate calculation:A FMRI study. Developmental Neuropsychology,33(447-473).
Lee, K. M. (2000). Cortical areas differentially involved in multiplication and subtraction:A functional magnetic resonance imaging study and correlation
with a case of selective acalculia. Annals of Neurology,48,657-661.
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Mao.W,& Wang.Y.P (2008). The active inhibition for the processing of visual irrelevant conflict information. International Journal of Psychophysiology,67, 47-53.
McCloskey, M. (1992). Cognitive mechanisms in numerical processing:evidence from acquired dyscalculia. Cognition,44,107-157.
McCloskey, M., Aliminosa, D.,& Sokol, S. M. (1991). Facts, rules and procedures in normal calculation:evidence from multiple single-patient studies of impaired arithmetic fact retrieval. Brain and Cognition,17,154-203.
McCloskey, M., Caramazza, A.,& Basili, A. (1985). Cognitive mechanisms in number processing and calculation:evidence from dyscalculia. Brain and Cognition,4,171-196.
Menon, V., Rivera, S. M., White, C. D., Glover, G. H.,& Reiss, A. L. (2000). Dissociating prefrontal and parietal cortex activation during arithmetic processing. Neurolmage,4,357-365.
Mestre, C. F.,& Vaid, J. (1993). Activation of number facts in bilinguals. Memory and Cognition,27,809-818.
Moyer, R. S.,& Landauer, T. K. (1967). Time required for judgments of numerical inequality Nature,215,1519-1520.
Nuerk, H. C., Weger, r.,& Willmes, K. (2002). A unit-decade compatibility effect in German number words. Current Psychology Letters:Behaviour, Brain, and Cognition,2,19-38.
Paivio, A. (1971). Imagery and mental processes. Holt, Rinehart,& Winston.
Peters, E., Slovic, P., Vastfjall, D.,& Mertz, C. K. (2008). Intuitive numbers guide decisions. Judgment and Decision Making,3,619-635.
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Pinel, P., Dehaenea, S., Rivieres, D.,& Bihan, D. L. (2001). Modulation of Parietal Activation by Semantic Distance in a Number Comparison Task. Neurolmage, 14(5),1013-1026
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Ansari, D.,& Holloway, I. (2008). Common and segregated neural pathways for the processing of symbolic and non-symbolic numerical magnitude:Evidence from children and adults.. Poster presented at IPSEN-Cell Exciting Biologies: Biology of Cognition, Chantilly, France.
Barsalou, L. W. (1999). Perceptual symbol systems. Behavioral and Brain Sciences, 22,577-660.
Barsalou, L. W. (2003). Abstraction in perceptual symbol systems. Philosophical Transactions of the Royal Society B:Biological Sciences,358,1177-1187.
Barsalou, L. W., Santos, A., Simmons, W. K.,& Wilson, C. D. (2008). Language and simulation in conceptual processing. In:Symbols, embodiment, and meaning,ed. M. De Vega, A. M. Glenberg & A. C. Graesser. Oxford University Press,245-283.
Benson, D. F.,& Denckla, M. B. (1969). Verbal Paraphasia as a source of Calculation Disturbance. Archives of Neurology,21,96-102.
Blankenberger, B.,& Vorberg, D. (1997). The Single-Format Assumption in Arithmetic Fact Retrieval. Journal of Experimental Psychology:Learning, Memory, and Cognition 23,721-738.
Butterworth, B. (1999). The mathematical brain. Macmillan.
Campbell, J. I. D.,& Clark, J. M. (1988). An encoding-complex view of cognitive number processing:Comment on McCloskey, Sokol,& Goodman. Journal of Experimental Psychology:General 117,204-214.
Campbell, J. I. D.,& Clark, J. M. (1992). Cognitive number-processing:an encoding-complex perspective, in:J.I.D. Campbell (Ed,). The Nature and
Origins of Mathematical Skills, Elsevier, Amsterdam,539-556.
Campbell, J. I. D.,& Epp, L. J. (2004). An Encoding-Complex Approach to Numerical Cognition in Chinese-English Bilinguals. Canadian Journal of Experimental Psychology,58(4),229-244.
Campbell., J. I. D. (1994). Architectures for numerical cognition. Cognition,53,1-44.
Cantlon, J. F., Libertus, M. E., Pinel, P., Dehaene, S., Brannon, E. M.,& Pelphrey, K. A. (2009). The Neural Development of an Abstract Concept of Number. Journal of Cognitive Neuroscience,27(11),2217-2229.
Cohen./, DBKDHQH6,&KRFKRQ),/HKHrHFy.6,& 1 DFFDFKH/(2000)./DQJuDJHDQG calculation within the parietal lobe:a combined cognitive, anatomical and fMRI study.38,1426-1440.
Csepe.V, Szucs.D,& Honbolygo.F (2003). Number-word reading as a challenging task in dyslexia. International Journal of Psychophysiology,51,69-83.
Dehaene, S. (1992). Varieties of numerical abilities. Cognition 44,1-42.
Dehaene, S.,& Akhavein, R. (1995). Attention, automaticity, and levels of representation in number processing. Journal of Experimental Psychology: Learning, Memory,and Cognition,21,314-326.
Dehaene, S., Bossini, S.,& Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology. Genera,l(122), 371-396.
Dehaene, S., Dupoux, E.,& Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology:Human Perception and Performance,16(3), 626-641.
Dehaene, S., Spelke, E., Pinel, P., Stanescu, R.,& Tsivkin, S. (1999). Sources of mathematical thinking:Behavioral and brain-imaging evidence. Science, 284(970-974).
Dresler, T., Obersteiner, A., Schecklmann, M., Vogel, A. C. M, Ehlis, A. C., Richter, M. M., et al. (2009). Arithmetic tasks in different formats and their influence on behavior and brain oxygenation as assessed with near-infrared
spectroscopy (NIRS):a study involving primary and secondary school children. Journal of Neural Transmission,116(12).
Folstein, J. R.,& Petten, C. V. (2008). Influence of cognitive control and mismatch on the N2 component of the ERP:A review. Psychophysiology,45(1),152.
Hung, Y. H., Hung, D. L., Tzeng, O. J. L.,& Wu, D. H. (2008). Flexible spatial mapping of different notations of numbers in Chinese readers. Cognition, 106(3),1441-1450.
Ito, Y.,& Hatta, T. (2003). Semantic processing of Arabic, Kanji, and Kana numbers: Evidence from interference in physical and numerical size judgments. Memory and Cognition 37(3),360-368.
Kadosh, R. C. (2008). Numerical representation:Abstract or non-abstract? Quarterly Journal of Experimental Psychology, 61(8),1160-1168.
Kadosh, R. C., Kadosh, K. C., Linden, D. E. J., Gevers, W., Berger, A.,& Henik, A. (2007). The brain locus of interaction between number and size:A combined functional magnetic resonance imaging and event-related potential study. Journal of Cognitive Neuroscience 19,957-970.
Kadosh, R. C.,& Walsh, V. (2007). Dyscalculia. Current Biology,17,946-947.
Kaufmann, L., Koppelstaetter, F., Delazer, M., Siedentopf, C., Rhomberg,P., Golaszewski, S., et al. (2005). Neural correlates of distance and congruity effects in a numerical Stroop task:An event-related fMRI study. Neurolmage, 25,888-898.
Koechlin, E., Naccache, L., Block, E.,& Dehaene, S. (1999). Primed numbers:Exploring the modularity of numerical representations with masked and unmasked semantic priming. Journal of Experimental Psychology: Human Perception and Performance,25(6),1882-1905.
Kucian, K., Aster, M. V., Loenneker, T., Dietrich, T.,& Martin, E. (2008). Development of neural networks for exact and approximate calculation:A FMRI study. Developmental Neuropsychology,33(447-473).
Lee, K. M. (2000). Cortical areas differentially involved in multiplication and subtraction:A functional magnetic resonance imaging study and correlation
with a case of selective acalculia. Annals of Neurology,48,657-661.
LeFevre, J.A., Bisanz, J.,& Mrkonjic, L. (1988). Cognitive arithmetic:Evidence for obligatory activation of arithmetic facts. Memory & Cognition,16(1),45-53.
Macarsuo, P., McCloskey, M.,& Aliminosa, D. (1993). The functional architecture of the cognitive numerical-processing system:Evidence from a patient with multiple impairments. Cognitive Neuropsychology,10,341-376.
Mao.W,& Wang.Y.P (2007). Various conflicts from ventral and dorsal streams are sequentially processed in a common system. Experimental Brain Research, 177,113-121.
Mao.W,& Wang.Y.P (2008). The active inhibition for the processing of visual irrelevant conflict information. International Journal of Psychophysiology,67, 47-53.
McCloskey, M. (1992). Cognitive mechanisms in numerical processing:evidence from acquired dyscalculia. Cognition,44,107-157.
McCloskey, M., Aliminosa, D.,& Sokol, S. M. (1991). Facts, rules and procedures in normal calculation:evidence from multiple single-patient studies of impaired arithmetic fact retrieval. Brain and Cognition,17,154-203.
McCloskey, M., Caramazza, A.,& Basili, A. (1985). Cognitive mechanisms in number processing and calculation:evidence from dyscalculia. Brain and Cognition,4,171-196.
Menon, V., Rivera, S. M., White, C. D., Glover, G. H.,& Reiss, A. L. (2000). Dissociating prefrontal and parietal cortex activation during arithmetic processing. Neurolmage,4,357-365.
Mestre, C. F.,& Vaid, J. (1993). Activation of number facts in bilinguals. Memory and Cognition,27,809-818.
Moyer, R. S.,& Landauer, T. K. (1967). Time required for judgments of numerical inequality Nature,215,1519-1520.
Nuerk, H. C., Weger, r.,& Willmes, K. (2002). A unit-decade compatibility effect in German number words. Current Psychology Letters:Behaviour, Brain, and Cognition,2,19-38.
Paivio, A. (1971). Imagery and mental processes. Holt, Rinehart,& Winston.
Peters, E., Slovic, P., Vastfjall, D.,& Mertz, C. K. (2008). Intuitive numbers guide decisions. Judgment and Decision Making,3,619-635.
Piazza, M., Pinel, P., Bihan, D. L.,& Dehaene, S. (2007). A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron, 53(2),293-305.
Pinel, P., Dehaenea, S., Rivieres, D.,& Bihan, D. L. (2001). Modulation of Parietal Activation by Semantic Distance in a Number Comparison Task. Neurolmage, 14(5),1013-1026
Pinel, P., Piazza, M., Bihan, D. L.,& Dehaene, S. (2004). Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron,41(6),983-993.
Richard, T. C., Romero, S. G., Basso, G, Wharton, C., Flitman, S.,& Grafman, J. (2000). The calculating brain:An fMRI study. Neuropsychologia,38,325-335.
Rivers-Batiz, F. L. (1992). Quantitative literacy and the likelihood of employment among young Adults in the r nited States. Journal of Human Resources,27, 213-218.
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