An EEG Case Study of Arithmetical Reasoning by Four Individuals Varying in Imagery and Mathematical Ability: Implications for Mathematics Education
The main issue of interest here is whether individuals
who differ in arithmetical reasoning ability and levels of imagery ability display different brain activity during the conduct of mental
arithmetical reasoning tasks. This was a case study of four
participants who represented four extreme combinations of Maths –Imagery abilities: ie., low-low, high-high, high-low, low-high respectively. As the Ps performed a series of 60 arithmetical reasoning tasks, 128-channel EEG recordings were taken and the
pre-response interval subsequently analysed using EGI GeosourceTM
software. The P who was high in both imagery and maths ability
showed peak activity prior to response in BA7 (superior parietal cortex) but other Ps did not show peak activity in this region. The
results are considered in terms of the diverse routes that may be employed by individuals during the conduct of arithmetical reasoning
tasks and the possible implications of this for mathematics education.
[1] P. Arnoux, & A. Finkel, Using mental imagery processes for teaching
and research in mathematics and computer science. International Journal of Mathematical Education In Science & Technology, 41, 2229-242, 2010.
[2] Gelman, R. (2006). Young Natural-Number Arithmeticians. Current
Directions In Psychological Science (Wiley-Blackwell), 15(4), 193-197.
[3] L. S. Fuchs, D. Fuch., K. Stuebing, J. M. Fletcher, C. L. Hamlett,, &
W. Lamber. Problem solving and computational skill: Are they shared or
distinct aspects of mathematical cognition? Journal of Educational
Psychology, 100(1), 30-47, 2008.
[4] Khan, F. (1999). The social context of learning mathematics: Stepping
beyond the cognitive framework. Mind, Culture, And Activity, 6(4), 304-
313.
[5] Libertus, M. E., & Brannon, E. M. (2010). Stable individual differences
in number discrimination in infancy. Developmental Science, 13(6),
900-906.
[6] M. Arsalidou, & M. J Taylor. Is 2+2=4? Meta-analyses of brain areas
needed for numbers and calculations. Neuroimage, 54, 2383-2393, 2011.
[7] A. Theodoropoulou, S. Tei, D. Lehmann, P. L. Faber, F. Schlegel, & P.
Milz. EEG frequency band SLORETA sources during mental arithmetic
compared to resting. European Psychiatry, 26, Supplement 1, p. 945,
2011.
[8] Marks, D. F. (1973). Visual imagery differences in the recall of pictures.
British Journal of Psychology, 64, 17-24.
[9] Marks, D. F. (1995). New directions for mental imagery research.
Journal of Mental Imagery, 19, 153-167
[10] X. Cui., C. B. Jeter., D. Yang, P.R. Montague, & D. M. Eagleman,
Vividness of mental imagery: Individual variability can be measured
objectively. Vision Research, 47, 474-478, 2007.
[11] Huang, M. E. (2000). Vivid Visualization in the Experience of Phobia in
Virtual Environments: Preliminary Results. Cyberpsychology &
Behavior, 3, 315-32
[12] McKelvie, S. J., & Demers, E. G. (1979). Individual differences in
reported visual imagery and memory performance. British Journal Of
Psychology, 70, 51-57.
[13] Varga S., K. (2009). Visual imaginative synchrony. Contemporary
Hypnosis, 26, 146-158.
[14] Pascual-Marqui, R. D. (2002). Standardised low resolution
electromagnetic tomography (sLORETA): technical details. Methods
and Findings in Experimental & Clinical Pharmacology, 24, 5-12.
[15] S. Ocklenburg, O. G├╝nt├╝rk├╝n, C. Best. Hemispheric symmetries and
cognitive flexibility: an ERP and SLORETA study. Brain and Cognition,
78, 148-155, 2012.
[16] P. Luu, D. M. Tucker, & R. Stripling. Neural mechanisms for learning
actions in context. Brain Research, 1179, 89-105, 2007.
[17] Venkatraman, V., Ansari, D., & Chee, M. L. (2005). Neural correlates of
symbolic and non-symbolic arithmetic. Neuropsychologia, 43, 744-753.
[18] S. Dehaene, & L. Cohen. Towards an anatomical and functional model
of number processing. Mathematical Cognition, 1(1), 83-120, 1995.
[19] Menon, V., Riveria, S. M., White, C. D., Glover, G. H., & Reiss, A. L.
(2000).Dissociating prefrontal and parietal cortex activation during
arithmetic processing. Neuroimage, 12, 357-365
[20] Pesenti, M. (2000). Neuroanatomical Substrates of Arabic Number
Processing, Numerical Comparison, and Simple Addition: A PET Study.
Journal of Cognitive Neuroscience, 12, 461-479.
[1] P. Arnoux, & A. Finkel, Using mental imagery processes for teaching
and research in mathematics and computer science. International Journal of Mathematical Education In Science & Technology, 41, 2229-242, 2010.
[2] Gelman, R. (2006). Young Natural-Number Arithmeticians. Current
Directions In Psychological Science (Wiley-Blackwell), 15(4), 193-197.
[3] L. S. Fuchs, D. Fuch., K. Stuebing, J. M. Fletcher, C. L. Hamlett,, &
W. Lamber. Problem solving and computational skill: Are they shared or
distinct aspects of mathematical cognition? Journal of Educational
Psychology, 100(1), 30-47, 2008.
[4] Khan, F. (1999). The social context of learning mathematics: Stepping
beyond the cognitive framework. Mind, Culture, And Activity, 6(4), 304-
313.
[5] Libertus, M. E., & Brannon, E. M. (2010). Stable individual differences
in number discrimination in infancy. Developmental Science, 13(6),
900-906.
[6] M. Arsalidou, & M. J Taylor. Is 2+2=4? Meta-analyses of brain areas
needed for numbers and calculations. Neuroimage, 54, 2383-2393, 2011.
[7] A. Theodoropoulou, S. Tei, D. Lehmann, P. L. Faber, F. Schlegel, & P.
Milz. EEG frequency band SLORETA sources during mental arithmetic
compared to resting. European Psychiatry, 26, Supplement 1, p. 945,
2011.
[8] Marks, D. F. (1973). Visual imagery differences in the recall of pictures.
British Journal of Psychology, 64, 17-24.
[9] Marks, D. F. (1995). New directions for mental imagery research.
Journal of Mental Imagery, 19, 153-167
[10] X. Cui., C. B. Jeter., D. Yang, P.R. Montague, & D. M. Eagleman,
Vividness of mental imagery: Individual variability can be measured
objectively. Vision Research, 47, 474-478, 2007.
[11] Huang, M. E. (2000). Vivid Visualization in the Experience of Phobia in
Virtual Environments: Preliminary Results. Cyberpsychology &
Behavior, 3, 315-32
[12] McKelvie, S. J., & Demers, E. G. (1979). Individual differences in
reported visual imagery and memory performance. British Journal Of
Psychology, 70, 51-57.
[13] Varga S., K. (2009). Visual imaginative synchrony. Contemporary
Hypnosis, 26, 146-158.
[14] Pascual-Marqui, R. D. (2002). Standardised low resolution
electromagnetic tomography (sLORETA): technical details. Methods
and Findings in Experimental & Clinical Pharmacology, 24, 5-12.
[15] S. Ocklenburg, O. G├╝nt├╝rk├╝n, C. Best. Hemispheric symmetries and
cognitive flexibility: an ERP and SLORETA study. Brain and Cognition,
78, 148-155, 2012.
[16] P. Luu, D. M. Tucker, & R. Stripling. Neural mechanisms for learning
actions in context. Brain Research, 1179, 89-105, 2007.
[17] Venkatraman, V., Ansari, D., & Chee, M. L. (2005). Neural correlates of
symbolic and non-symbolic arithmetic. Neuropsychologia, 43, 744-753.
[18] S. Dehaene, & L. Cohen. Towards an anatomical and functional model
of number processing. Mathematical Cognition, 1(1), 83-120, 1995.
[19] Menon, V., Riveria, S. M., White, C. D., Glover, G. H., & Reiss, A. L.
(2000).Dissociating prefrontal and parietal cortex activation during
arithmetic processing. Neuroimage, 12, 357-365
[20] Pesenti, M. (2000). Neuroanatomical Substrates of Arabic Number
Processing, Numerical Comparison, and Simple Addition: A PET Study.
Journal of Cognitive Neuroscience, 12, 461-479.
@article{"International Journal of Medical, Medicine and Health Sciences:60147", author = "Mark Rousell and Di Catherwood and Graham Edgar", title = "An EEG Case Study of Arithmetical Reasoning by Four Individuals Varying in Imagery and Mathematical Ability: Implications for Mathematics Education", abstract = "The main issue of interest here is whether individuals
who differ in arithmetical reasoning ability and levels of imagery ability display different brain activity during the conduct of mental
arithmetical reasoning tasks. This was a case study of four
participants who represented four extreme combinations of Maths –Imagery abilities: ie., low-low, high-high, high-low, low-high respectively. As the Ps performed a series of 60 arithmetical reasoning tasks, 128-channel EEG recordings were taken and the
pre-response interval subsequently analysed using EGI GeosourceTM
software. The P who was high in both imagery and maths ability
showed peak activity prior to response in BA7 (superior parietal cortex) but other Ps did not show peak activity in this region. The
results are considered in terms of the diverse routes that may be employed by individuals during the conduct of arithmetical reasoning
tasks and the possible implications of this for mathematics education.", keywords = "Arithmetic, imagery, EEG, education.", volume = "6", number = "11", pages = "595-3", }
