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  • Ahmad, K., Casey, M., & Bale, T. (2002). Connectionist simulation of quantification skills. Connection Science, 14 (3), 165201.
  • Ansari, D., & Dhital, B. (2006). Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: an event-related functional magnetic resonance imaging study. Journal of Cognitive Neuroscience, 18 (11), 18201828.
  • Ansari, D., Garcia, N., Lucas, E., Hamon, K., & Dhital, B. (2005). Neural correlates of symbolic number processing in children and adults. NeuroReport, 16 (16), 17691773.
  • Ashby, F.G., & Valentin, V.V. (2007). Computational cognitive neuroscience: building and testing biologically plausible computational models of neuroscience, neuroimaging, and behavioral data. in M.J. Wenger & C. Schuster (Eds.), Statistical and process models for cognitive neuroscience and aging (pp. 1558). Mahway, NJ: Erlbaum.
  • Baroody, A.J. (1999). The roles of estimation and the commutativity principle in the development of third graders’ mental multiplication. Journal of Experimental Child Psychology, 74, 513.
  • Barth, H., Beckmann, L., & Spelke, E.S. (2008). Nonsymbolic, approximate arithmetic in children: abstract addition prior to instruction. Developmental Psychology, 44 (5), 14661477.
  • Barth, H., Mont, K.L., Lipton, J., Dehaene, S., Kanwisher, N., & Spelke, E. (2006). Non-symbolic arithmetic in adults and young children. Cognition, 98, 199222.
  • Billock, V.A., & Tsou, B.H. (2011). To honor Fechner and obey Stevens: relationships between psychophysical and neural nonlinearities. Psychological Bulletin, 137 (1), 118.
  • Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D. (2006). Complex networks: structure and dynamics. Physics Reports, 424 (4–5), 175308.
  • Booth, J.L., & Siegler, R.S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41 (6), 189201.
  • Brannon, E.M., & Roitman, J. (2003). Nonverbal representations of time and number in animals and human infants. In W. Meck (Ed.), Functional and neural mechanisms of interval timing (pp. 143182). New York: CRC Press.
  • Brannon, E.M., & Terrace, H.S. (1998). Ordering of the numerosities 1 to 9 by monkeys. Science, 282 (5389), 746749.
  • Brown, T.T., Lugar, H.M., Coalson, R.S., Miezin, F.M., Petersen, S.E., & Schlaggar, B.L. (2005). Developmental changes in human cerebral functional organization for word generation. Cerebral Cortex, 15 (3), 275290.
  • Cantlon, J.F., Brannon, E.M., Carter, E.J., & Pelphrey, K.A. (2006). Functional imaging of numerical processing in adults and 4-yr-old children. PLoS Biology, 5, 117.
  • Cantlon, J.F., Libertus, M.E., Pinel, P., Dehaene, S., Brannon, E.M., & Pelphrey, K.A. (2008). The neural development of an abstract concept of number. Journal of Cognitive Neuroscience, 21 (11), 22172229.
  • Casey, B.J., Galvan, A., & Hare, T.A. (2005). Changes in cerebral functional organization during cognitive development. Current Opinion in Neurobiology, 15 (2), 239244.
  • Casey, B.J., Giedd, J.N., & Thomas, K.M. (2000). Structural and functional brain development and its relation to cognitive development. Biological Psychology, 54 (1–3), 241257.
  • Cavada, C., & Goldman-Rakic, P.S. (1989). Posterior parietal cortex in rhesus monkey: II. Evidence for segregated corticocortical networks linking sensory and limbic areas with the frontal lobe. Journal of Comparative Neurology, 287 (4), 422445.
  • Chafee, M.V., & Goldman-Rakic, P.S. (2000). Inactivation of parietal and prefrontal cortex reveals interdependence of neural activity during memory-guided saccades. Journal of Neurophysiology, 83, 15501566.
  • Clearfield, M.W., & Mix, K.S. (1999). Number versus contour length in infants’ discrimination of small sets. Psychological Science, 10 (5), 408411.
    Direct Link:
  • Cohen Kadosh, R., & Henik, A. (2006). A common representation for semantic and physical properties. Experimental Psychology, 53 (2), 8794.
  • Cohen Kadosh, R., & Walsh, V. (2009). Numerical representation in the parietal lobes: abstract or not abstract? Behavioral and Brain Sciences, 32 (3–4), 313373.
  • Dehaene, S. (2007). Symbols and quantities in parietal cortex: elements of a mathematical theory of number representation and manipulation. In P. Haggard, Y. Rossetti & M. Kawato (Eds.), Sensorimotor foundations of higher cognition, volume XXII of Attention and Performance (pp. 527574). Cambridge, MA: Harvard University Press.
  • Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude McCloskey s model. Journal of Experimental Psychology: General, 122 (3), 371396.
  • Dehaene, S., & Changeux, J. (1993). Development of elementary numerical abilities: a neuronal model. Journal of Cognitive Neuroscience, 5 (4), 390407.
  • Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20 (3–6), 487506.
  • Diester, I., & Nieder, A. (2008). Complementary contributions of prefrontal neuron classes in abstract numerical categorization. Journal of Neuroscience, 28 (31), 77377747.
  • Durston, S., Davidson, M.C., Tottenham, N., Galvan, A., Spicer, J., Fossella, J.A., & Casey, B.J. (2006). A shift from diffuse to focal cortical activity with development. Developmental Science, 9 (1), 18.
  • Eger, E., Sterzer, P., Russ, M.O., Giraud, A.-L., & Kleinschmidt, A. (2003). A supramodal number representation in human intraparietal cortex. Neuron, 37 (4), 719725.
  • Elman, J.L. (1993). Learning and development in neural networks: the importance of starting small. Cognition, 48 (1), 7199.
  • Fechner, G.T. (1966). Elemente der Psychophysik [Elements of psychophysics] (H.E. Adler, Trans.). New York: Holt, Rinehart, & Winston. (Original work published 1860)
  • Gaillard, W.D., Hertz-Pannier, L., Mott, S.H., Barnett, A.S., LeBihan, D., & Theodore, W.H. (2000). Functional anatomy of cognitive development: fMRI of verbal fluency in children and adults. Neurology, 54, 180185.
  • Gelman, R., & Gallistel, C.R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.
  • Göbel, S., Calabria, M., Farnè, A., & Rossetti, Y. (2006). Parietal rTMS distorts the mental number line: simulating ‘spatial’ neglect in healthy subjects. Neuropsychologia, 44, 860868.
  • Goldstone, R.L. (1998). Perceptual learning. Annual Review of Psychology, 49, 585612.
  • Halberda, J., Mazzocco, M.M.M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455 (7213), 665668.
  • Hubbard, T.L. (2005). Representational momentum and related displacements in spatial memory: a review of the findings. Psychonomic Bulletin & Review, 12 (5), 822851.
  • Huntley-Fenner, G. (2001). Children’s understanding of number is similar to adults’ and rats’: numerical estimation by 5–7-year-olds. Cognition, 78 (3), B27B40.
  • Johnson, K.O., Hsiao, S.S., & Yoshioka, T. (2002). Neural coding and the basic law of psychophysics. Neuroscientist, 8, 111121.
  • Jordan, K.E., & Brannon, E.M. (2006). The multisensory representation of number in infancy. Proceedings of the National Academy of Sciences, USA, 103 (9), 811.
  • Knops, A., Viarouge, A., & Dehaene, S. (2009). Dynamic representations underlying symbolic and nonsymbolic calculation: evidence from the operational momentum effect. Attention, Perception, & Psychophysics, 71 (4), 803821.
  • Libertus, M.E., Fiegenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14 (6), 12921300.
  • Lindemann, O., & Tira, M.D. (2011). Operational momentum in numerosity production judgments of multi-digit number problems. Zeitschrift für Psychologie / Journal of Psychology, 219 (1), 5057.
  • Lourenco, S.F., & Longo, M.R. (2010). General magnitude representation in human infants. Psychological Science, 21 (6), 873881.
  • Luce, R.D., Green, D.M., & Weber, D.L. (1976). Attention bands in absolute identification. Perception & Psychophysics, 20, 4954.
  • McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: operational momentum in nonsymbolic arithmetic. Perception & Psychophysics, 69 (8), 13241333.
  • McCrink, K., & Wynn, K. (2009). Operational momentum in large-number addition and subtraction by 9-month-olds. Journal of Experimental Child Psychology, 103 (4), 400408.
  • McNeil, N.M., & Alibali, M.W. (2004). You’ll see what you mean: students encode equations based on their knowledge of arithmetic. Cognitive Science, 28, 451466.
  • Mareschal, D., & Johnson, S.P. (2002). Learning to perceive object unity: a connectionist account. Developmental Science, 5 (2), 151172.
  • Meck, W.H., & Church, R.M. (1983). A mode control model of counting and timing processes. Journal of Experimental Psychology: Animal Behavior Processes, 9 (3), 320334.
  • Miller, J.A., & Kenyon, G.T. (2007). Extracting number-selective responses from coherent oscillations in a computer model. Neural Computation, 19 (7), 17661797.
  • Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H.-C. (2009). Children’s early mental number line: logarithmic or decomposed linear? Journal of Experimental Child Psychology, 103 (4), 503515.
  • Nieder, A., & Dehaene, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32, 185208.
  • Nieder, A., Diester, I., & Tudusciuc, O. (2006). Temporal and spatial enumeration processes in the primate parietal cortex. Science, 313, 14311435.
  • Nieder, A., Freedman, D., & Miller, E.K. (2002). Representation of quantity of visual items in the primate prefrontal cortex. Science, 297 (September), 17081711.
  • Nieder, A., & Merten, K. (2007). A labeled-line code for small and large numerosities in the monkey prefrontal cortex. Journal of Neuroscience, 27 (22), 59865993.
  • Nieder, A., & Miller, E.K. (2003). Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex. Neuron, 37 (1), 149157.
  • Nieder, A., & Miller, E.K. (2004). Aparieto-frontal network for visual numerical information in the monkey. Proceedings of the National Academy of Sciences of the USA, 101, 74577462.
  • Opfer, J.E., & Siegler, R.S. (2007). Representational change and children’s numerical estimation. Cognitive Psychology, 55 (3), 169195.
  • Pearson, J., Roitman, J.D., Brannon, E.M., Platt, M.L., & Raghavachari, S. (2010). A physiologically-inspired model of numerical classification based on graded stimulus coding. Frontiers in Behavioral Neuroscience, 4, 1.
  • Pesenti, M., Thioux, M., Samson, D., Bruyer, R., & Seron, X. (2000). Number processing and calculation in a case of visual agnosia. Cortex, 36, 377400.
  • Piaget, J. (1954). The construction of reality in the child. New York: Basic Books.
  • Platt, J.K., & Johnson, D. (1971). Localization of position within a homogenous behavior chain: effects of error contingencies. Learning and Motivation, 2, 386414.
  • Prather, R.W., & Alibali, M.W. (2011). Children’s acquisition of arithmetic principles: the role of experience. Journal of Cognition and Development, 12 (3), 332354.
  • Quintana, J., Fuster, J.M., & Yajeya, J. (1989). Effects of cooling parietal cortex on prefrontal units in delay tasks. Brain Research, 503 (1), 100110.
  • Recanzone, G.H., Schreiner, C.E., & Merzenich, M.M. (1993). Plasticity in the frequency rep- resentation of primary auditory cortex following discrimination training in adult owl monkeys. Journal of Neuroscience, 13, 87103.
  • Robinson, K.M., & Ninowski, J.E. (2003). Adults’ understanding of inversion concepts: how does performance on addition and subtraction inversion problems compare to performance on multiplication and division inversion problems? Canadian Journal of Experimental Psychology, 57 (4), 321330.
  • Roitman, J.D., Brannon, E.M., & Platt, M.L. (2007). Monotonic coding of numerosity in macaque lateral intraparietal area. PLOS Biology, 5 (8), 16721682.
  • Rubia, K., Overmeyer, S., Taylor, E., Brammer, M., Williams, S.C., Simmons, A., Andrew, C., & Bullmore, E.T. (2000). Functional frontalisation with age: mapping neurodevelopmental trajectories with fMRI. Neuroscience and Biobehavioral Reviews, 24 (1), 1319.
  • Saarinen, J., & Levi, D.M. (1995). Perceptual learning in vernier acuity: what is learned? Vision Research, 35, 519527.
  • Santens, S., & Gevers, W. (2008). The SNARC effect does not imply a mental number line. Cognition, 108 (1), 263270.
  • Sawamura, H., Shima, K., & Tanji, J. (2002). Numerical representation for action in the parietal cortex of the monkey. Nature, 415 (6874), 918922.
  • Schlaggar, B.L., Brown, T.T., Lugar, H.M., Visscher, K.M., Miezin, F.M., & Petersen, S.E. (2002). Functional neuroanatomical differences between adults and school-age children in the processing of single words. Science, 296 (5572), 14761479.
  • Schutte, A.R., Spencer, J.P., & Schöner, G. (2003). Testing the dynamic field theory: working memory for locations becomes more spatially precise over development. Child Development, 74 (5), 13931417.
  • Siegler, R.S., & Booth, J.L. (2004). Development of numerical estimation in young children. Child Development, 75, 428444.
  • Siegler, R.S., & Opfer, J.E. (2003). The development of numerical estimation. Psychological Science, 14, 237243.
    Direct Link:
  • Simmering, V.R., Schutte, A.R., & Spencer, J.P. (2008). Generalizing the dynamic field theory of spatial cognition across real and developmental time scales. Brain Research, 1202, 6886.
  • Spencer, J.P., Simmering, V.R., Schutte, A.R., & Schöner, G. (2007). What does theoretical neuroscience have to offer the study of behavioral development? Insights from a dynamic field theory of spatial cognition. In J. Plumert & J.P. Spencer (Eds.), The emerging spatial mind (pp. 320361). Oxford: Oxford University Press.
  • Spencer, J.P., Thomas, M.S.C., & McClelland, J.L. (Eds.) (2009). Toward a unified theory of development. Oxford: Oxford University Press.
  • Song, S., Miller, K.D., & Abbott, L.F. (2000). Competitive Hebbian learning through spike-timing-dependent synaptic plasticity. Nature Neuroscience, 3 (9), 919926.
  • Stevens, J.C., & Marks, L.E. (1980). Cross-modality matching functions generated by magnitude estimation. Perception & Psychophysics, 27 (5), 379389.
  • Stevens, S.S. (1957). On the psychophysical law. Psychological Review, 64 (3), 153181.
  • Tang, Y., Zhang, W., Chen, K., Feng, S., Ji, Y., Shen, J., Reiman, E., & Liu, Y. (2006). Arithmetic processing in the brain shaped by cultures. Proceedings of the National Academy of Sciences of the United States of America, 103 (28), 1077510780.
  • Uttal, D.H., Scudder, K.V., & Deloache, J.S. (1997). Manipulatives as symbols: a new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 18, 3754.
  • Verguts, T., & Fias, W. (2004). Representation of number in animals and humans: a neural model. Journal of Cognitive Neuroscience, 16, 14931504.
  • Walsh, V. (2003). A theory of magnitude: common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7 (11), 483488.
  • Westermann, G., & Mareschal, D. (2004). From parts to wholes : mechanisms of development in infant visual object processing. Infancy, 5 (2), 131151.
  • Whalen, J.W., McCloskey, M., Lesser, R., & Gordon, B. (1997). Localizing arithmetic processes in the brain. Journal of Cognitive Neuroscience, 9 (3), 409417.
  • Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749750.
  • Yang, T., & Maunsell, J.H.R. (2004). The effect of perceptual learning on neuronal responses in monkey visual area V4. Journal of Neuroscience, 24 (7), 16171626.
  • Zorzi, M., Stoianov, I., & Umiltà, C. (2004). Computational modeling of numerical cognition. In J.I.D. Campbell (Ed.), The handbook of mathematical cognition (pp. 6784). Hove: Psychology Press.