Transcranial Electrical Stimulation and Numerical Cognition

Canadian Journal of Experimental Psychology

Volumn 70, Issue 1, 2016, Pages 41-58

  Sarkar, Amar ^a   Kadosh, Roi Cohen ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

cognitive enhancement; numerical cognition; transcranial DC stimulation; transcranial electrical stimulation; transcranial random noise stimulation

Indexed keywords

BRAIN; BRAIN MAPPING; COGNITION; HUMAN; MATHEMATICS; MEMORY; PATTERN RECOGNITION; PERCEPTIVE DISCRIMINATION; PHOTOSTIMULATION; PHYSIOLOGY; REACTION TIME; TRANSCRANIAL DIRECT CURRENT STIMULATION;

BRAIN; BRAIN MAPPING; COGNITION; DISCRIMINATION (PSYCHOLOGY); HUMANS; MATHEMATICS; MEMORY; PATTERN RECOGNITION, VISUAL; PHOTIC STIMULATION; REACTION TIME; TRANSCRANIAL DIRECT CURRENT STIMULATION;

EID: 84966298454     PISSN: 11961961     EISSN: None     Source Type: Journal    
DOI: 10.1037/cep0000064     Document Type: Article

References (133)

1. Ambrus, G. G., Paulus, W., Antal, A. (2010). Cutaneous perception thresholds of electrical stimulation methods: Comparison of tDCS and tRNS. Clinical Neurophysiology, 121, 1908-1914. http://dx.doi.org/10 .1016/j.clinph.2010.04.020
2. Antal, A., Nitsche, M. A., Kruse, W., Kincses, T. Z., Hoffmann, K.-P., Paulus, W. (2004). Direct current stimulation over V5 enhances visuomotor coordination by improving motion perception in humans. Journal of Cognitive Neuroscience, 16, 521-527. http://dx.doi.org/10.1162/089892904323057263
3. Arsalidou, M., Taylor, M. J. (2011). Is 2-2-4 Meta-analyses of brain areas needed for numbers and calculations. NeuroImage, 54, 2382-2393. http://dx.doi.org/10.1016/j.neuroimage.2010.10.009
4. Bailey, D. H., Hoard, M. K., Nugent, L., Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113, 447-455. http://dx.doi.org/10 .1016/j.jecp.2012.06.004
5. Barth, H., Kanwisher, N., Spelke, E. (2003). The construction of large number representations in adults. Cognition, 86, 201-221. http://dx.doi.org/10.1016/S0010-0277(02)00178-6
6. Beddington, J., Cooper, C. L., Field, J., Goswami, U., Huppert, F. A., Jenkins, R., Thomas, S. M. (2008). The mental wealth of nations. Nature, 455, 1057-1060. http://dx.doi.org/10.1038/4551057a
7. Berryhill, M. E., Jones, K. T. (2012). tDCS selectively improves working memory in older adults with more education. Neuroscience Letters, 521, 148-151.
8. Bindman, L. J., Lippold, O. C. J., Redfearn, J. W. (1964). The action of brief polarizing currents on the cerebral cortex of the rat (1) during current flow and (2) in the production of long-lasting after-effects. The Journal of Physiology, 172, 369-382. http://dx.doi.org/10.1113/jphysiol .1964.sp007425
9. Bolzoni, F., Baczyk, M., Jankowska, E. (2013). Subcortical effects of transcranial direct current stimulation in the rat. The Journal of Physiology, 591, 4027-4042.
10. Booth, J. L., Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79, 1016-1031. http://dx.doi.org/10.1111/j.1467-8624.2008.01173.x
11. Boyke, J., Driemeyer, J., Gaser, C., Büchel, C., May, A. (2008). Training-induced brain structure changes in the elderly. The Journal of Neuroscience, 28, 7031-7035. http://dx.doi.org/10.1523/JNEUROSCI .0742-08.2008
12. Brannon, E. M., Terrace, H. S. (1998). Ordering of the numerosities 1 to 9 by monkeys. Science, 282, 746-749. http://dx.doi.org/10.1126/science .282.5389.746
13. Brem, A. K., Fried, P. J., Horvath, J. C., Robertson, E. M., Pascual-Leone, A. (2014). Is neuroenhancement by noninvasive brain stimulation a net zero-sum proposition NeuroImage, 85, 1058-1068.
14. Butterworth, B., Varma, S., Laurillard, D. (2011). Dyscalculia: From brain to education. Science, 332, 1049-1053. http://dx.doi.org/10.1126/science.1201536
15. Bynner, J., Parsons, S. (1997). Does numeracy matter London: The Basic Skills Agency.
16. Campbell, Z., Zakzanis, K. K., Jovanovski, D., Joordens, S., Mraz, R., Graham, S. J. (2009). Utilizing virtual reality to improve the ecological validity of clinical neuropsychology: An FMRI case study elucidating the neural basis of planning by comparing the Tower of London with a three-dimensional navigation task. Applied Neuropsychology, 16, 295-306. http://dx.doi.org/10.1080/09084280903297891
17. Cantlon, J. F. (2012). Math, monkeys, and the developing brain. Proceedings of the National Academy of Sciences of the United States of America, 109(Suppl. 1), 10725-10732. http://dx.doi.org/10.1073/pnas .1201893109
18. Cantlon, J. F., Brannon, E. M., Carter, E. J., Pelphrey, K. A. (2006). Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology, 4, e125. http://dx.doi.org/10.1371/journal.pbio .0040125
19. Cantlon, J. F., Platt, M. L., Brannon, E. M. (2009). Beyond the number domain. Trends in Cognitive Sciences, 13, 83-91. http://dx.doi.org/10 .1016/j.tics.2008.11.007
20. Cappelletti, M., Barth, H., Fregni, F., Spelke, E. S., Pascual-Leone, A. (2007). rTMS over the intraparietal sulcus disrupts numerosity processing. Experimental Brain Research, 179, 631-642. http://dx.doi.org/10 .1007/s00221-006-0820-0
21. Cappelletti, M., Gessaroli, E., Hithersay, R., Mitolo, M., Didino, D., Kanai, R., Walsh, V. (2013). Transfer of cognitive training across magnitude dimensions achieved with concurrent brain stimulation of the parietal lobe. The Journal of Neuroscience, 33, 14899-14907. http://dx.doi.org/10.1523/JNEUROSCI.1692-13.2013
22. Chaieb, L., Kovacs, G., Cziraki, C., Greenlee, M., Paulus, W., Antal, A. (2009). Short-duration transcranial random noise stimulation induces blood oxygenation level dependent response attenuation in the human motor cortex. Experimental Brain Research, 198, 439-444. http://dx.doi.org/10.1007/s00221-009-1938-7
23. Clemens, B., Jung, S., Zvyagintsev, M., Domahs, F., Willmes, K. (2013). Modulating arithmetic fact retrieval: A single-blind, shamcontrolled tDCS study with repeated fMRI measurements. Neuropsychologia, 51, 1279-1286. http://dx.doi.org/10.1016/j.neuropsychologia .2013.03.023
24. Cohen Kadosh, R. (2013). Using transcranial electrical stimulation to enhance cognitive functions in the typical and atypical brain. Translational Neuroscience, 4, 20-33.
25. Cohen Kadosh, R. (in press). Modulating and enhancing cognition using brain stimulation: Science and fiction. Journal of Cognitive Psychology.
26. Cohen Kadosh, R., Cohen Kadosh, K., Schuhmann, T., Kaas, A., Goebel, R., Henik, A., Sack, A. T. (2007). Virtual dyscalculia induced by parietal-lobe TMS impairs automatic magnitude processing. Current Biology, 17, 689-693. http://dx.doi.org/10.1016/j.cub.2007.02.056
27. Cohen Kadosh, R., Lammertyn, J., Izard, V. (2008). Are numbers special An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation. Progress in Neurobiology, 84, 132-147. http://dx.doi.org/10.1016/j.pneurobio.2007.11 .001
28. Cohen Kadosh, R., Levy, N., O'Shea, J., Shea, N., Savulescu, J. (2012). The neuroethics of non-invasive brain stimulation. Current Biology, 22, R108-R111. http://dx.doi.org/10.1016/j.cub.2012.01.013
29. Cohen Kadosh, R., Soskic, S., Iuculano, T., Kanai, R., Walsh, V. (2010). Modulating neuronal activity produces specific and long-lasting changes in numerical competence. Current Biology, 20, 2016-2020. http://dx.doi.org/10.1016/j.cub.2010.10.007
30. Cordes, S., Gelman, R., Gallistel, C. R., Whalen, J. (2001). Variability signatures distinguish verbal from nonverbal counting for both large and small numbers. Psychonomic Bulletin & Review, 8, 698-707. http://dx.doi.org/10.3758/BF03196206
31. Dehaene, S., Dehaene-Lambertz, G., Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences, 21, 355-361. http://dx.doi.org/10.1016/S0166-2236(98) 01263-6
32. Dehaene, S., Izard, V., Spelke, E., Pica, P. (2008). Log or linear Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science, 320, 1217-1220. http://dx.doi.org/10.1126/science.1156540
33. Dehaene, S., Piazza, M., Pinel, P., Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487-506. http://dx.doi.org/10.1080/02643290244000239
34. Delazer, M., Ischebeck, A., Domahs, F., Zamarian, L., Koppelstaetter, F., Siedentopf, C. M., Felber, S. (2005). Learning by strategies and learning by drill-Evidence from an fMRI study. NeuroImage, 25, 838-849. http://dx.doi.org/10.1016/j.neuroimage.2004.12.009
35. Dockery, C. A., Hueckel-Weng, R., Birbaumer, N., Plewnia, C. (2009). Enhancement of planning ability by transcranial direct current stimulation. The Journal of Neuroscience, 29, 7271-7277. http://dx.doi.org/10 .1523/JNEUROSCI.0065-09.2009
36. Draganski, B., Gaser, C., Busch, V., Schuierer, G., Bogdahn, U., May, A. (2004). Neuroplasticity: Changes in grey matter induced by training. Nature, 427, 311-312. http://dx.doi.org/10.1038/427311a
37. Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428-1446. http://dx.doi.org/10 .1037/0012-1649.43.6.1428
38. Fan, J., McCandliss, B. D., Sommer, T., Raz, A., Posner, M. I. (2002). Testing the efficiency and independence of attentional networks. Journal of Cognitive Neuroscience, 14, 340-347. http://dx.doi.org/10.1162/089892902317361886
39. Fertonani, A., Pirulli, C., Miniussi, C. (2011). Random noise stimulation improves neuroplasticity in perceptual learning. The Journal of Neuroscience, 31, 15416-15423. http://dx.doi.org/10.1523/JNEUROSCI .2002-11.2011
40. Floël, A., Rösser, N., Michka, O., Knecht, S., Breitenstein, C. (2008). Noninvasive brain stimulation improves language learning. Journal of Cognitive Neuroscience, 20, 1415-1422. http://dx.doi.org/10.1162/jocn .2008.20098
41. Fregni, F., Boggio, P. S., Nitsche, M., Bermpohl, F., Antal, A., Feredoes, E., Pascual-Leone, A. (2005). Anodal transcranial direct current stimulation of prefrontal cortex enhances working memory. Experimental Brain Research, 166, 23-30.
42. Fritsch, B., Reis, J., Martinowich, K., Schambra, H. M., Ji, Y., Cohen, L. G., Lu, B. (2010). Direct current stimulation promotes BDNFdependent synaptic plasticity: Potential implications for motor learning. Neuron, 66, 198-204.
43. Gandiga, P. C., Hummel, F. C., Cohen, L. G. (2006). Transcranial DC stimulation (tDCS): A tool for double-blind sham-controlled clinical studies in brain stimulation. Clinical Neurophysiology, 117, 845-850.
44. Geary, D. C., Hoard, M. K., Nugent, L., Byrd-Craven, J. (2008). Development of number line representations in children with mathematical learning disability. Developmental Neuropsychology, 33, 277-299. http://dx.doi.org/10.1080/87565640801982361
45. Gebuis, T., Gevers, W., Cohen Kadosh, R. (2014). Topographic representation of high-level cognition: Numerosity or sensory processing Trends in Cognitive Sciences, 18, 1-3. http://dx.doi.org/10.1016/j.tics .2013.10.002
46. Gebuis, T., Reynvoet, B. (2012). The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology: General, 141, 642-648. http://dx.doi.org/10.1037/a0026218
47. Gibson, E. J., Gibson, J. J., Pick, A. D., Osser, H. (1962). A developmental study of the discrimination of letter-like forms. Journal of Comparative and Physiological Psychology, 55, 897-906. http://dx.doi.org/10.1037/h0043190
48. Girelli, L., Lucangeli, D., Butterworth, B. (2000). The development of automaticity in accessing number magnitude. Journal of Experimental Child Psychology, 76, 104-122. http://dx.doi.org/10.1006/jecp.2000 .2564
49. Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306, 496-499. http://dx.doi.org/10.1126/science .1094492
50. Green, C. S., Bavelier, D. (2003). Action video game modifies visual selective attention. Nature, 423, 534-537. http://dx.doi.org/10.1038/nature01647
51. Halberda, J., Mazzocco, M. M., Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665-668. http://dx.doi.org/10.1038/nature07246
52. Hauser, T. U., Rotzer, S., Grabner, R. H., Mérillat, S., Jäncke, L. (2013). Enhancing performance in numerical magnitude processing and mental arithmetic using transcranial Direct Current Stimulation (tDCS). [Advance online publication]. Frontiers in Human Neuroscience, 7, 244. http://dx.doi.org/10.3389/fnhum.2013.00244
53. Henik, A., Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory & Cognition, 10, 389-395.
54. Holland, R., Leff, A. P., Josephs, O., Galea, J. M., Desikan, M., Price, C. J., Crinion, J. (2011). Speech facilitation by left inferior frontal cortex stimulation. Current Biology, 21, 1403-1407. http://dx.doi.org/10.1016/j.cub.2011.07.021
55. Hubbard, E. M., Piazza, M., Pinel, P., Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435-448. http://dx.doi.org/10.1038/nrn1684
56. Iuculano, T., Cohen Kadosh, R. (2013). The mental cost of cognitive enhancement. The Journal of Neuroscience, 33, 4482-4486. http://dx.doi.org/10.1523/JNEUROSCI.4927-12.2013
57. Iuculano, T., Cohen Kadosh, R. (2014). Preliminary evidence for performance enhancement following parietal lobe stimulation in Developmental Dyscalculia. [Advance online publication]. Frontiers in Human Neuroscience, 8, 38. http://dx.doi.org/10.3389/fnhum.2014.00038
58. Izard, V., Sann, C., Spelke, E. S., Streri, A. (2009). Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences of the United States of America, 106, 10382-10385. http://dx.doi.org/10.1073/pnas.0812142106
59. Jacobson, L., Koslowsky, M., Lavidor, M. (2012). tDCS polarity effects in motor and cognitive domains: A meta-analytical review. Experimental Brain Research, 216, 1-10. http://dx.doi.org/10.1007/s00221-011-2891-9
60. Jaeggi, S. M., Buschkuehl, M., Jonides, J., Perrig, W. J. (2008). Improving fluid intelligence with training on working memory. Proceedings of the National Academy of Sciences of the United States of America, 105, 6829-6833. http://dx.doi.org/10.1073/pnas.0801268105
61. Kasahara, K., Tanaka, S., Hanakawa, T., Senoo, A., Honda, M. (2013). Lateralization of activity in the parietal cortex predicts the effectiveness of bilateral transcranial direct current stimulation on performance of a mental calculation task. Neuroscience Letters, 545, 86-90. http://dx.doi.org/10.1016/j.neulet.2013.04.022
62. Kaufmann, L., Wood, G., Rubinsten, O., Henik, A. (2011). Metaanalyses of developmental fMRI studies investigating typical and atypical trajectories of number processing and calculation. Developmental Neuropsychology, 36, 763-787. http://dx.doi.org/10.1080/87565641 .2010.549884
63. Keeser, D., Meindl, T., Bor, J., Palm, U., Pogarell, O., Mulert, C., Padberg, F. (2011). Prefrontal transcranial direct current stimulation changes connectivity of resting-state networks during fMRI. The Journal of Neuroscience, 31, 15284-15293. http://dx.doi.org/10.1523/JNEUROSCI.0542-11.2011
64. Klein, E., Mann, A., Huber, S., Bloechle, J., Willmes, K., Karim, A. A., Moeller, K. (2013). Bilateral bi-cephalic tDCS with two active electrodes of the same polarity modulates bilateral cognitive processes differentially [corrected]. PLoS ONE, 8, e71607. http://dx.doi.org/10 .1371/journal.pone.0071607
65. Klingberg, T. (2010). Training and plasticity of working memory. Trends in Cognitive Sciences, 14, 317-324. http://dx.doi.org/10.1016/j.tics.2010 .05.002
66. Krause, B., Cohen Kadosh, R. (2013). Can transcranial electrical stimulation improve learning difficulties in atypical brain development A future possibility for cognitive training. Developmental Cognitive Neuroscience, 6, 176-194. http://dx.doi.org/10.1016/j.dcn.2013.04.001
67. Krause, B., Cohen Kadosh, R. (2014). Not all brains are created equal: The relevance of individual differences in responsiveness to transcranial electrical stimulation. [Advance online publication]. Frontiers in Systems Neuroscience, 8, 25. http://dx.doi.org/10.3389/fnsys.2014.00025
68. Krause, B., Márquez-Ruiz, J., Cohen Kadosh, R. (2013). The effect of transcranial direct current stimulation: A role for cortical excitation/inhibition balance [Advance online publication]. Frontiers in Human Neuroscience, 7, 602. http://dx.doi.org/10.3389/fnhum.2013.00602
69. Kuo, M. F., Nitsche, M. A. (2012). Effects of transcranial electrical stimulation on cognition. Clinical EEG and Neuroscience, 43, 192-199. http://dx.doi.org/10.1177/1550059412444975
70. Libertus, M. E., Feigenson, L., Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14, 1292-1300. http://dx.doi.org/10.1111/j .1467-7687.2011.01080.x
71. Libertus, M. E., Odic, D., Halberda, J. (2012). Intuitive sense of number correlates with math scores on college-entrance examination. Acta Psychologica, 141, 373-379. http://dx.doi.org/10.1016/j.actpsy.2012.09.009
72. Link, T., Moeller, K., Huber, S., Fischer, U., Nuerk, H. C. (2013). Walk the number line-An embodied training of numerical concepts. Trends in Neuroscience and Education, 2, 74-84. http://dx.doi.org/10.1016/j.tine .2013.06.005
73. Looi, C. Y., Duta, M., Brem, A.-K., Huber, S., Nuerk, H.-C., Cohen Kadosh, R. (2015). Combining brain stimulation and video gaming to promote long-term transfer and cognitive enhancement. Manuscript submitted for publication.
74. Luber, B., Lisanby, S. H. (2014). Enhancement of human cognitive performance using transcranial magnetic stimulation (TMS). NeuroImage, 85, 961-970. http://dx.doi.org/10.1016/j.neuroimage.2013.06.007
75. MacLeod, C. M. (1991). Half a century of research on the Stroop effect: An integrative review. Psychological Bulletin, 109, 163-203. http://dx.doi.org/10.1037/0033-2909.109.2.163
76. Márquez-Ruiz, J., Leal-Campanario, R., Sánchez-Campusano, R., Molaee-Ardekani, B., Wendling, F., Miranda, P. C., Delgado-Garciá, J. M. (2012). Transcranial direct-current stimulation modulates synaptic mechanisms involved in associative learning in behaving rabbits. Proceedings of the National Academy of Sciences of the United States of America, 109, 6710-6715. http://dx.doi.org/10.1073/pnas.1121147109
77. Meck, W. H., Church, R. M. (1983). A mode control model of counting and timing processes. Journal of Experimental Psychology: Animal Behavior Processes, 9, 320-334. http://dx.doi.org/10.1037/0097-7403.9 .3.320
78. Meinzer, M., Antonenko, D., Lindenberg, R., Hetzer, S., Ulm, L., Avirame, K., Floël, A. (2012). Electrical brain stimulation improves cognitive performance by modulating functional connectivity and task-specific activation. The Journal of Neuroscience, 32, 1859-1866. http://dx.doi.org/10.1523/JNEUROSCI.4812-11.2012
79. Meinzer, M., Jähnigen, S., Copland, D. A., Darkow, R., Grittner, U., Avirame, K., Floël, A. (2014). Transcranial direct current stimulation over multiple days improves learning and maintenance of a novel vocabulary. Cortex, 50, 137-147. http://dx.doi.org/10.1016/j.cortex .2013.07.013
80. Meinzer, M., Lindenberg, R., Antonenko, D., Flaisch, T., Floël, A. (2013). Anodal transcranial direct current stimulation temporarily reverses age-associated cognitive decline and functional brain activity changes. The Journal of Neuroscience, 33, 12470-12478. http://dx.doi.org/10.1523/JNEUROSCI.5743-12.2013
81. Miller, E. K., Cohen, J. D. (2001). An integrative theory of prefrontal cortex function. Annual Review of Neuroscience, 24, 167-202. http://dx.doi.org/10.1146/annurev.neuro.24.1.167
82. Nieder, A., Miller, E. K. (2003). Coding of cognitive magnitude: Compressed scaling of numerical information in the primate prefrontal cortex. Neuron, 37, 149-157. http://dx.doi.org/10.1016/S0896-6273(02)01144-3
83. Nieratschker, V., Kiefer, C., Giel, K., Krüger, R., Plewnia, C. (2015). The COMT val/met polymorphism modulates effects of tDCS on response inhibition. Brain Stimulation, 8, 283-288.
84. Nitsche, M. A., Cohen, L. G., Wassermann, E. M., Priori, A., Lang, N., Antal, A., Pascual-Leone, A. (2008). Transcranial direct current stimulation: State of the art 2008. Brain Stimulation, 1, 206-223. http://dx.doi.org/10.1016/j.brs.2008.06.004
85. Nitsche, M. A., Paulus, W. (2000). Excitability changes induced in the human motor cortex by weak transcranial direct current stimulation. The Journal of Physiology, 527, 633-639. http://dx.doi.org/10.1111/j.1469-7793.2000.t01-1-00633.x
86. Owen, A. M., Hampshire, A., Grahn, J. A., Stenton, R., Dajani, S., Burns, A. S., Ballard, C. G. (2010). Putting brain training to the test. Nature, 465, 775-778. http://dx.doi.org/10.1038/nature09042
87. Parsons, S., Bynner, J. (2005). Does numeracy matter more London: National Research and Development Centre for Adult Literacy and Numeracy.
88. Pascual-Leone, A., Horvath, J. C., Robertson, E. M. (2012). Enhancement of normal cognitive abilities through noninvasive brain stimulation. In R. Chen & J. C. Rothwell (Eds.), Cortical connectivity (pp. 207-249). Berlin: Springer-Verlag. http://dx.doi.org/10.1007/978-3-662-45797-9-11
89. Peretti, C. S., Danion, J. M., Gierski, F., Grangé, D. (2002). Cognitive skill learning and aging: A component process analysis. Archives of Clinical Neuropsychology, 17, 445-459. http://dx.doi.org/10.1093/arclin/17.5.445
90. Piazza, M., Izard, V. (2009). How humans count: Numerosity and the parietal cortex. The Neuroscientist, 15, 261-273. http://dx.doi.org/10 .1177/1073858409333073
91. Piazza, M., Izard, V., Pinel, P., Le Bihan, D., Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547-555. http://dx.doi.org/10.1016/j.neuron.2004.10 .014
92. Piazza, M., Pinel, P., Le Bihan, D., Dehaene, S. (2007). A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron, 53, 293-305. http://dx.doi.org/10.1016/j.neuron .2006.11.022
93. Pica, P., Lemer, C., Izard, V., Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499-503. http://dx.doi.org/10.1126/science.1102085
94. Plewnia, C., Zwissler, B., Längst, I., Maurer, B., Giel, K., Krüger, R. (2013). Effects of transcranial direct current stimulation (tDCS) on executive functions: Influence of COMT Val/Met polymorphism. Cortex, 49, 1801-1807.
95. Price, G. R., Palmer, D., Battista, C., Ansari, D. (2012). Nonsymbolic numerical magnitude comparison: Reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults. Acta Psychologica, 140, 50-57.
96. Priori, A., Hallett, M., Rothwell, J. C. (2009). Repetitive transcranial magnetic stimulation or transcranial direct current stimulation Brain Stimulation, 2, 241-245. http://dx.doi.org/10.1016/j.brs.2009.02.004
97. Reigosa-Crespo, V., Valdés-Sosa, M., Butterworth, B., Estévez, N., Rodríguez, M., Santos, E., Lage, A. (2012). Basic numerical capacities and prevalence of developmental dyscalculia: The Havana Survey. Developmental Psychology, 48, 123-135. http://dx.doi.org/10.1037/a0025356
98. Reis, J., Schambra, H. M., Cohen, L. G., Buch, E. R., Fritsch, B., Zarahn, E., Krakauer, J. W. (2009). Noninvasive cortical stimulation enhances motor skill acquisition over multiple days through an effect on consolidation. Proceedings of the National Academy of Sciences of the United States of America, 106, 1590-1595. http://dx.doi.org/10.1073/pnas.0805413106
99. Renzi, C., Vecchi, T., Silvanto, J., Cattaneo, Z. (2011). Overlapping representations of numerical magnitude and motion direction in the posterior parietal cortex: A TMS-adaptation study. Neuroscience Letters, 490, 145-149.
100. Richardson, F. C., Suinn, R. M. (1972). The Mathematics Anxiety Rating Scale: Psychometric data. Journal of Counseling Psychology, 19, 551-554. http://dx.doi.org/10.1037/h0033456
101. Richmond, L. L., Wolk, D., Chein, J., Olson, I. R. (2014). Transcranial direct current stimulation enhances verbal working memory training performance over time and near transfer outcomes. Journal of Cognitive Neuroscience, 26, 2443-2454. http://dx.doi.org/10.1162/jocn-a-00657
102. Ritchie, S. J., Bates, T. C. (2013). Enduring links from childhood mathematics and reading achievement to adult socioeconomic status. Psychological Science, 24, 1301-1308. http://dx.doi.org/10.1177/0956797612466268
103. Rivera, S. M., Reiss, A. L., Eckert, M. A., Menon, V. (2005). Developmental changes in mental arithmetic: Evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex, 15, 1779-1790. http://dx.doi.org/10.1093/cercor/bhi055
104. Rubinsten, O., Henik, A. (2005). Automatic activation of internal magnitudes: A study of developmental dyscalculia. Neuropsychology, 19, 641-648. http://dx.doi.org/10.1037/0894-4105.19.5.641
105. Rubinsten, O., Henik, A. (2006). Double dissociation of functions in developmental dyslexia and dyscalculia. Journal of Educational Psychology, 98, 854-867. http://dx.doi.org/10.1037/0022-0663.98.4.854
106. Rubinsten, O., Henik, A., Berger, A., Shahar-Shalev, S. (2002). The development of internal representations of magnitude and their association with Arabic numerals. Journal of Experimental Child Psychology, 81, 74-92. http://dx.doi.org/10.1006/jecp.2001.2645
107. Ruffini, G., Fox, M. D., Ripolles, O., Miranda, P. C., Pascual-Leone, A. (2014). Optimization of multifocal transcranial current stimulation for weighted cortical pattern targeting from realistic modeling of electric fields. NeuroImage, 89, 216-225.
108. Sack, A. T., Cohen Kadosh, R., Schuhmann, T., Moerel, M., Walsh, V., Goebel, R. (2009). Optimizing functional accuracy of TMS in cognitive studies: A comparison of methods. Journal of Cognitive Neuroscience, 21, 207-221.
109. Santarnecchi, E., Polizzotto, N. R., Godone, M., Giovannelli, F., Feurra, M., Matzen, L., Rossi, S. (2013). Frequency-dependent enhancement of fluid intelligence induced by transcranial oscillatory potentials. Current Biology, 23, 1449-1453.
110. Sarkar, A., Dowker, A., Kadosh, R. C. (2014). Cognitive enhancement or cognitive cost: Trait-specific outcomes of brain stimulation in the case of mathematics anxiety. The Journal of Neuroscience, 34, 16605-16610.
111. Schmiedek, F., Lövdén, M., Lindenberger, U. (2010). Hundred days of cognitive training enhance broad cognitive abilities in adulthood: Findings from the COGITO study. [Advance online publication]. Frontiers in Aging Neuroscience, 2.
112. Schwarz, W., Ischebeck, A. (2003). On the relative speed account of number-size interference in comparative judgments of numerals. Journal of Experimental Psychology: Human Perception and Performance, 29, 507-522.
113. Shalev, R. S. (2007). Prevalence of developmental dyscalculia. In D. B. Berch & M. M. M. Mazzocco (Eds.), Why is math so hard for some children The nature and origins of mathematical learning difficulties and disabilities (pp. 49-60). Baltimore, MD: Brookes.
114. Shallice, T. (1982). Specific impairments of planning. Philosophical Transactions of the Royal Society of London Series B, Biological Sciences, 298, 199-209. http://dx.doi.org/10.1098/rstb.1982.0082
115. Siegler, R. S., Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75, 428-444.
116. Siegler, R. S., Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237-250. http://dx.doi.org/10.1111/1467-9280.02438
117. Slagter, H. A., Lutz, A., Greischar, L. L., Francis, A. D., Nieuwenhuis, S., Davis, J. M., Davidson, R. J. (2007). Mental training affects distribution of limited brain resources. PLoS Biology, 5, e138. http://dx.doi.org/10.1371/journal.pbio.0050138
118. Snowball, A., Tachtsidis, I., Popescu, T., Thompson, J., Delazer, M., Zamarian, L., Cohen Kadosh, R. (2013). Long-term enhancement of brain function and cognition using cognitive training and brain stimulation. Current Biology, 23, 987-992. http://dx.doi.org/10.1016/j.cub .2013.04.045
119. Snyder, A., Bahramali, H., Hawker, T., Mitchell, D. J. (2006). Savantlike numerosity skills revealed in normal people by magnetic pulses. Perception, 35, 837-845.
120. Stroop, J. R. (1935). Studies of interference in serial verbal reactions. Journal of Experimental Psychology, 18, 643-662. http://dx.doi.org/10 .1037/h0054651
121. Terhune, D. B., Tai, S., Cowey, A., Popescu, T., Cohen Kadosh, R. (2011). Enhanced cortical excitability in grapheme-color synesthesia and its modulation. Current Biology, 21, 2006-2009. http://dx.doi.org/10 .1016/j.cub.2011.10.032
122. Terney, D., Chaieb, L., Moliadze, V., Antal, A., Paulus, W. (2008). Increasing human brain excitability by transcranial high-frequency random noise stimulation. The Journal of Neuroscience, 28, 14147-14155. http://dx.doi.org/10.1523/JNEUROSCI.4248-08.2008
123. Truong, D. Q., Magerowski, G., Blackburn, G. L., Bikson, M., Alonso-Alonso, M. (2013). Computational modeling of transcranial direct current stimulation (tDCS) in obesity: Impact of head fat and dose guidelines. NeuroImage, 2, 759-766.
124. Tseng, P., Hsu, T. Y., Chang, C. F., Tzeng, O. J., Hung, D. L., Muggleton, N. G., Juan, C. H. (2012). Unleashing potential: Transcranial direct current stimulation over the right posterior parietal cortex improves change detection in low-performing individuals. The Journal of Neuroscience, 32, 10554-10561. http://dx.doi.org/10.1523/JNEUROSCI.0362-12.2012
125. Tzelgov, J., Yehene, V., Kotler, L., Alon, A. (2000). Automatic comparisons of artificial digits never compared: Learning linear ordering relations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26, 103-120. http://dx.doi.org/10.1037/0278-7393.26.1.103
126. Villringer, A., Chance, B. (1997). Non-invasive optical spectroscopy and imaging of human brain function. Trends in Neurosciences, 20, 435-442. http://dx.doi.org/10.1016/S0166-2236(97)01132-6
127. Villringer, A., Planck, J., Hock, C., Schleinkofer, L., Dirnagl, U. (1993). Near infrared spectroscopy (NIRS): A new tool to study hemodynamic changes during activation of brain function in human adults. Neuroscience Letters, 154, 101-104. http://dx.doi.org/10.1016/0304-3940(93)90181-J
128. Wagner, T., Valero-Cabre, A., Pascual-Leone, A. (2007). Noninvasive human brain stimulation. Annual Review of Biomedical Engineering, 9, 527-565. http://dx.doi.org/10.1146/annurev.bioeng.9.061206.133100
129. Walsh, V. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7, 483-488. http://dx.doi.org/10.1016/j.tics.2003.09.002
130. Waters-Metenier, S., Husain, M., Wiestler, T., Diedrichsen, J. (2014). Bihemispheric transcranial direct current stimulation enhances effectorindependent representations of motor synergy and sequence learning. The Journal of Neuroscience, 34, 1037-1050. http://dx.doi.org/10.1523/JNEUROSCI.2282-13.2014
131. Weber, M. J., Messing, S. B., Rao, H., Detre, J. A., Thompson-Schill, S. L. (2014). Prefrontal transcranial direct current stimulation alters activation and connectivity in cortical and subcortical reward systems: A tDCS-fMRI study. Human Brain Mapping, 35, 3673-3686. http://dx.doi.org/10.1002/hbm.22429
132. Xu, F., Spelke, E. S. (2000). Large number discrimination in 6-monthold infants. Cognition, 74, B1-B11. http://dx.doi.org/10.1016/S0010-0277(99)00066-9
133. Zamarian, L., Ischebeck, A., Delazer, M. (2009). Neuroscience of learning arithmetic-Evidence from brain imaging studies. Neuroscience and Biobehavioral Reviews, 33, 909-925. http://dx.doi.org/10 .1016/j.neubiorev.2009.03.005