The Stability of Memory Rules Associative with the Mathematical Thinking Core

Full Text (PDF, 303KB), PP.24-30

Views: 0 Downloads: 0


Xiuzhen Wang 1,* Weiquan Gu 1

1. Harbin Normal University, Acheng District, Harbin City, 150301, China

* Corresponding author.


Received: 20 Oct. 2010 / Revised: 5 Nov. 2010 / Accepted: 6 Dec. 2010 / Published: 8 Feb. 2011

Index Terms

Stability, core system, Boolean rule, stabilized memory, fMRI


Activation of how and where arithmetic operations are displayed in the brain has been observed in various number-processing tasks. However, it remains poorly understood whether stabilized memory of Boolean rules are associated with background knowledge. The present study reviewed behavioral and imaging evidence demonstrating that Boolean problem-solving abilities depend on the core systems of number-processing. The core systems account for a mathematical cultural background, and serve as the foundation for sophisticated mathematical knowledge. The Ebbinghaus paradigm was used to investigate learning-induced changes by functional magnetic resonance imaging (fMRI) in a retrieval task of Boolean rules. Functional imaging data revealed a common activation pattern in the left inferior parietal lobule and left inferior frontal gyrus during all Boolean tasks, which has been used for number-processing processing in former studies. All other regional activations were tasks-specific and prominently distributed in the left thalamus, bilateral parahippocampal gyrus, bilateral occipital lobe, and other subcortices during contrasting stabilized memory retrieval of Boolean tasks and number-processing tasks. The present results largely verified previous studies suggesting that activation patterns due to number-processing appear to reflect a basic anatomical substrate of stability of Boolean rules memory, which are derived from a network originally related to the core systems of number-processing.

Cite This Paper

Xiuzhen Wang, Weiquan Gu, "The Stability of Memory Rules Associative with the Mathematical Thinking Core", International Journal of Modern Education and Computer Science(IJMECS), vol.3, no.1, pp.24-30, 2011. DOI:10.5815/ijmecs.2011.01.04


[1]C. Tomasi, “Past performance and future results,” Nature, vol. 428, pp. 378, 2004.
[2]V. Kostrubiec, J. Tallet, and P.G. Zanone, “How a new behavioral pattern is stabilized with learning determines its persistence and flexibility in memory,” Exp. Brain. Res. vol. 170, pp. 238–244, 2006.
[3]S. Dehaene, M. Piazza, P. Pinel, and L. Cohen, “Three parietal circuits for number processing,” Cogn. Neuropsychol. vol. 20, pp. 487–506, 2003.
[4]L. Feigenson, S. Dehaene, and E. Spelke, “Core systems of number,” Trends Cogn. Sci. vol. 8, pp. 307–314, 2004.
[5]D. Ansari, “Effects of development and enculturation on number representation in the brain,” Nat. Rev. Neurosci. vol. 9, pp. 278–291, 2008.
[6]S. Dehaene, E. Spelke, P. Pinel, R. Stanescu, and S. Tsivkin, “Sources of mathematical thinking: behavioral and brain-imaging evidence,” Science, vol. 284, pp. 970–974, 1999.
[7]V. Dormal, M. Andres, M. Pesenti, “Dissociation of numerosity and duration processing in the left intraparietal sulcus: a transcranial magnetic stimulation study,” Cortex, vol. 44, pp. 462–469, 2008.
[8]O. Gruber, P. Indefrey, P. Steinmetz, and A. Kleinschmidt, “Dissociating neural correlates of cognitive components in mental calculation,” Cereb Cortex, vol. 11, pp. 350–359, vol.2001.
[9]G. Mandler, and B.J. Shebo, “Subitizing: an analysis of its component processes,” J. Exp. Psychol. Gen. vol. 111, pp. 1–21, 1982.
[10]L. Trick, and Z.W. Pylyshyn, “Why are small and large numbers enumerated differently? A limited capacity preattentive stage in vision,” Psychol. Rev. vol. 101, pp. 80–102, 1994.
[11]A. Ischebeck, L. Zamarian, K. Egger, M. Schocke, and M. Delazer, “Imaging early practice effects in arithmetic,” NeuroImage, vol. 36, pp. 993–1003, 2007.
[12]M. Delazer, and T. Benke, “Arithmetic facts without meaning,” Cortex, vol. 33, pp. 697–710, 1997.
[13]R.S. Siegler, “Emerging Minds: The Process of Change in Children’s Thinking,” New York: Oxford University Press, 1996.
[14]H. Ebbinghaus, “Memory: A contribution to experimental psychology” New York: Columbia University Press, 1993.
[15]F.I.M. Craik, and E. Tulving, “Depth of processing and the retention of words in episodic memory,” J. Exp. Psychol. vol. 104, pp. 268–294, 1975.
[16]X.Z. Wang, N. Zhong, S.F. Lu, C.N. Liu, and W.Q. Gu, “Parietal cortex and information granularity in labile and stable learning,” NeuroReport, vol. 21(2), pp. 123-126, 2010.
[17]M.H. Sohn, M.V. Albert, K. Jung, C.S. Carter, and J.R. Anderson, “Anticipation of conflict monitoring in the anterior cingulate cortex and the prefrontal cortex,” PNAS, vol. 104, pp. 10330–10334, 2007.
[18]K.J. Friston, A.P. Holmes, J.B. Poline, P.J. Grasby, S.C.R. Willisams, R.S.J. Frackowiak, and R.Turner, “Analysis of fMRI time-series revisited,” NeuroImage, vol. 2, pp. 45–53, 1995.
[19]J. Talairach, and P. Tournoux, “Co-planar stereotaxic atlas of the human brain,” Thieme Medical Publishers, New York, 1988.
[20]J. Lancaster, P. Kochunov, M. Woldorff, M. Liotti, L. Parsons, L. Rainey, D. Nickerson, and P. Fox, “Automatic talairach labels for functional activation sites,” NeuroImage, vol. 11, pp. S483, 2000.
[21]T.C. Rickard, S.G. Romero, G. Basso, C. Wharton, S. Flitman, and J. Grafman, “The calculating brain: an fMRI study,” Neuropsychologia, vol. 38, pp. 325–335, 2000.
[22]O. Simon, F. Kherif, G. Flandin, J.B. Poline, D. Riviere, J.F. Mangin, D. Le Bihan, and S. Dehaene, “Automatized clustering and functional geometry of human parietofrontal networks for language, space, and number,” Neuroimage, vol. 23, pp.1192–1202, 2004.
[23]M. Delazer, F. Domahs, L. Bartha, C. Brenneis, A. Lochy, T. Trieb, and T. Benke, “Learning complex arithmetic–an fMRI study,” Cogn. Brain. Res. vol. 18, pp. 76–88, 2003.
[24]K. Kucian, T. Loenneker, T. Dietrich, M. Dosch, E. Martin, and M. von Aster, “Impaired neural networks for approximate calculation in dyscalculic children: a functional MRI study,” Behav. Brain. Funct. vol. 2, pp. 31, 2006.
[25]V. Prabhakaran, B. Rypma, and J.D.E. Gabrieli, “Neural substrates of mathematical reasoning: a functional magnetic resonance imaging study of neocortical activation during performance of the necessary arithmetic operations test,” Neuropsychol. vol. 15, pp. 115–127, 2001.
[26]L. Zago, M. Pesenti, E. Mellet, F. Crivello, B. Mazoyer, and N. Tzourio-Mazoyer, “Neural correlates of simple and complex mental calculation,” NeuroImage, vol. 13, pp. 314–327, 2001.
[27]E. Mayer, M. Reicherts, G. Deloche, L. Willadino-Braga, I. Taussik, M. Dordain, M. Van Der Linden, and J-M. Annoni, “Number processing after stroke: Anatomoclinical correlations in oral and written codes,” J. Int. Neuropsychol. Soc. vol. 9, pp. 899–912, 2003.
[28]F. Chochon, L. Cohen, P.F. van de Moortele, and S. Dehaene, “Differential contributions of the left and right inferior parietal lobules to number processing,” J. Cogn. Neurosc. vol. 11, pp. 617–630, 1999.
[29]L. Zamarian, E. Stadelmann, H.C. Nürk, N. Gamboz, J. Marksteiner, and M. Delazer, “Effects of age and mild cognitive impairment on direct and indirect access to arithmetic knowledge,” Neuropsychologia, vol. 45, pp. 1511–1521, 2007.
[30]O. Simon, J.F. Mangin, L. Cohen, D. Le Bihan, and S. Dehaene, “Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe,” Neuron, vol. 33, pp. 475–487, 2002.
[31]T. Fehr, C. Code, and M. Herrmann, “Common brain regions underlying different arithmetic operations as revealed by conjunct fMRI–BOLD activation,” Brain Res. vol. 1172, pp. 93–102, 2007.
[32]J. Whalen, M. McCloskey, R.P. Lesser, and B. Gordon, “Localizing arithmetic processes in the brain, evidence from a transient deficit during cortical stimulation,” J. Cogn. Neurosci. vol. 9, pp. 409–417, 1997.
[33]H. Thogi, K. Saitoh, H. Takahashi, K. Ustugisawa, H. Yonezawa, K. Hatano, and T. Sasaki, “Agraphia and acalculia after a left prefrontal infarction,” J. Neurol. Neurosurg. Psychiatry, vol. 58, pp. 629–632, 1995.
[34]N.U.F. Dosenbach, K.M. Visscher, E.D. Palmer, F.M. Miezin, K.K. Wenger, H.C. Kang, E.D. Burgund, A.L. Grimes, B.L. Schlaggar, and S.E. Petersen, “A core system for the implementation of task sets,” Neuron, vol. 50, pp. 799–812, 2006.
[35]P. Andrés, and M. Van der Linden, “Are central executive functions working in patients with focal frontal lesions?” Neuropsychologia, vol. 40, pp. 835–845, 2002.
[36]J. Jonides, “How does practice makes perfect?” Nat. Neurosc. vol. 7, pp. 10–11, 2004.
[37]E.M. Meintjes, S.W. Jacobson, C.D. Molteno, J.C. Gatenby, C. Warton, C.J. Cannistraci, J.C. Gore, and J.L. Jacobson, “An fMRI study of magnitude comparison and exact addition in children,” Magnetic Resonance Imaging , vol. 28, pp. 351–362, 2010.
[38]G. Foley, “Understanding Adult Education and Training,” Second Edition. Sydney: Allen & Unwin, 2002.