J. R. Anderson, J. F. Anderson, J. L. Ferris, J. M. Fincham, J. et al., Lateral inferior prefrontal cortex and anterior cingulate cortex are engaged at different stages in the solution of insight problems, Proceedings of the National Academy of Sciences, vol.106, issue.26, pp.1-6, 2009.
DOI : 10.1073/pnas.0903953106

J. R. Anderson, J. M. Finchamn, Y. Qin, and A. Stocco, A central circuit of the mind, Trends in Cognitive Sciences, vol.12, issue.4, pp.136-143, 2009.
DOI : 10.1016/j.tics.2008.01.006

M. Arsalidou and M. J. Taylor, Is 2+2=4? Meta-analyses of brain areas needed for numbers and calculations, NeuroImage, vol.54, issue.3, 2011.
DOI : 10.1016/j.neuroimage.2010.10.009

D. Badre, Cognitive control, hierarchy, and the rostro???caudal organization of the frontal lobes, Trends in Cognitive Sciences, vol.12, issue.5, 2008.
DOI : 10.1016/j.tics.2008.02.004

D. Badre and A. D. Wagner, Selection, Integration, and Conflict Monitoring, Neuron, vol.41, issue.3, pp.473-487, 2004.
DOI : 10.1016/S0896-6273(03)00851-1

R. S. Blumenfeld, R. , and C. , Dorsolateral Prefrontal Cortex Promotes Long-Term Memory Formation through Its Role in Working Memory Organization, Journal of Neuroscience, vol.26, issue.3, pp.916-925, 2006.
DOI : 10.1523/JNEUROSCI.2353-05.2006

R. S. Blumenfeld, R. , and C. , Prefrontal Cortex and Long-Term Memory Encoding: An Integrative Review of Findings from Neuropsychology and Neuroimaging, The Neuroscientist, vol.1, issue.3, pp.280-291, 2007.
DOI : 10.1093/brain/awg128

E. D. Boorman, T. E. Behrens, and M. F. Rushworth, Counterfactual Choice and Learning in a Neural Network Centered on Human Lateral Frontopolar Cortex, PLoS Biology, vol.21, issue.6, 2011.
DOI : 10.1371/journal.pbio.1001093.s007

M. Brass and D. Y. Von-cramon, Decomposing Components of Task Preparation with Functional Magnetic Resonance Imaging, Journal of Cognitive Neuroscience, vol.21, issue.4, pp.609-620, 2004.
DOI : 10.1038/35082081

T. S. Braver and D. M. Barch, Extracting core components of cognitive control, Trends in Cognitive Sciences, vol.10, issue.12, pp.529-532, 2006.
DOI : 10.1016/j.tics.2006.10.006

J. I. Campbell, Handbook of Mathematical Cognition, 2005.

J. I. Campbell, A. , and S. , Effects of response time deadlines on adults??? strategy choices for simple addition, Memory & Cognition, vol.5, issue.6, pp.988-994, 2002.
DOI : 10.3758/BF03195782

F. Castelli, D. E. Glaser, and B. Butterworth, Discrete and analogue quantity processing in the parietal lobe: A functional MRI study, Proceedings of the National Academy of Sciences, vol.103, issue.12, pp.4693-4698, 2006.
DOI : 10.1073/pnas.0600444103

A. E. Cavanna and M. R. Trimble, The precuneus: a review of its functional anatomy and behavioural correlates, Brain, vol.129, issue.3, pp.564-583, 2006.
DOI : 10.1093/brain/awl004

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, Journal of Cognitive Neuroscience, vol.13, issue.6, pp.617-630, 1162.
DOI : 10.1093/brain/107.3.829

M. Corbetta and G. L. Shulman, Human cortical mechanisms of visual attention during orienting and search, Attention, Space, and Action: Studies in Cognitive Neuroscience, pp.183-198, 1999.
DOI : 10.1098/rstb.1998.0289

S. M. Courtney, L. Petit, J. M. Maisog, L. G. Ungerleider, and J. V. Haxby, An Area Specialized for Spatial Working Memory in Human Frontal Cortex, Science, vol.279, issue.5355, pp.1347-1351, 1998.
DOI : 10.1126/science.279.5355.1347

C. E. Curtis, D. Esposito, and M. , Persistent activity in the prefrontal cortex during working memory, Trends in Cognitive Sciences, vol.7, issue.9, pp.415-423, 2003.
DOI : 10.1016/S1364-6613(03)00197-9

S. Dehaene, The Number Sense, 1999.

S. Dehaene and L. Cohen, Cerebral Pathways for Calculation: Double Dissociation between Rote Verbal and Quantitative Knowledge of Arithmetic, Cortex, vol.33, issue.2, pp.219-250, 1997.
DOI : 10.1016/S0010-9452(08)70002-9

F. Esposito, C. Mulert, and R. Goebel, Combined distributed source and single-trial EEG/fMI modeling: application to effortful decision making processes, Neuroimage, vol.45, 2009.

N. U. Dosenbach, K. M. Visscher, E. D. Palmer, F. M. Miezin, K. K. Wenger et al., A Core System for the Implementation of Task Sets, Neuron, vol.50, issue.5, pp.799-812, 2006.
DOI : 10.1016/j.neuron.2006.04.031

A. Dove, S. Pollmann, T. Schubert, C. J. Wiggins, and D. Y. Von-cramon, Prefrontal cortex activation in task switching: an event-related fMRI study, Cognitive Brain Research, vol.9, issue.1, pp.103-109, 1999.
DOI : 10.1016/S0926-6410(99)00029-4

J. W. French, R. B. Ekstrom, P. , and I. A. , Kit of Reference Tests for Cognitive Factors, 1963.

K. J. Friston, A. P. Holmes, K. J. Worsley, J. B. Polina, C. D. Frith et al., Statistical parametric maps in functional imaging: A general linear approach, Human Brain Mapping, vol.26, issue.4, pp.89-210, 1995.
DOI : 10.1002/hbm.460020402

D. Gandini, P. Lemaire, J. L. Anton, and B. Nazarian, Neural correlates of approximate quantification strategies in young and older adults: An fMRI study, Brain Research, vol.1246, pp.144-157, 2008.
DOI : 10.1016/j.brainres.2008.09.096

URL : https://hal.archives-ouvertes.fr/hal-00346992

S. Göbel, V. Walsh, and M. F. Rushworth, The Mental Number Line and the Human Angular Gyrus, NeuroImage, vol.14, issue.6, p.927, 2001.
DOI : 10.1006/nimg.2001.0927

R. H. Grabner, D. Ansari, K. Koschutnig, G. Reishofer, F. Ebner et al., To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving, Neuropsychologia, vol.47, issue.2, pp.604-608, 2009.
DOI : 10.1016/j.neuropsychologia.2008.10.013

R. H. Grabner, D. Ansari, G. Reishofer, E. Stern, F. Ebner et al., Individual differences in mathematical competence predict parietal brain activation during mental calculation, NeuroImage, vol.38, issue.2, pp.346-356, 2007.
DOI : 10.1016/j.neuroimage.2007.07.041

S. Hodzik and P. Lemaire, Inhibition and shifting capacities mediate adults??? age-related differences in strategy selection and repertoire, Acta Psychologica, vol.137, issue.3, pp.335-344, 2011.
DOI : 10.1016/j.actpsy.2011.04.002

URL : https://hal.archives-ouvertes.fr/hal-00639406

I. Imbo and A. Vandierendonck, The development of strategy use in elementary school children: Working memory and individual differences, Journal of Experimental Child Psychology, vol.96, issue.4, pp.284-309, 2007.
DOI : 10.1016/j.jecp.2006.09.001

R. T. Knight, NEUROSCIENCE: Neural Networks Debunk Phrenology, Science, vol.316, issue.5831, 2007.
DOI : 10.1126/science.1144677

R. T. Knight, M. F. Grabowecky, and D. Scabini, Role of human prefrontal cortex in attention control, Adv. Neurol, vol.66, pp.21-34, 1995.

E. Koechlin and A. Hyafil, Anterior Prefrontal Function and the Limits of Human Decision-Making, Science, vol.318, issue.5850, 2007.
DOI : 10.1126/science.1142995

E. Koechlin, C. Ody, and F. Kouneiher, The Architecture of Cognitive Control in the Human Prefrontal Cortex, Science, vol.302, issue.5648, pp.1181-1185, 2003.
DOI : 10.1126/science.1088545

E. Koechlin and C. Summerfield, An information theoretical approach to prefrontal executive function, Trends in Cognitive Sciences, vol.11, issue.6, 2007.
DOI : 10.1016/j.tics.2007.04.005

T. Klingberg, Development of a superior frontal???intraparietal network for visuo-spatial working memory, Neuropsychologia, vol.44, issue.11, pp.2171-2177, 2006.
DOI : 10.1016/j.neuropsychologia.2005.11.019

P. Lemaire, Cognitive Strategy Variations During Aging, Current Directions in Psychological Science, vol.21, issue.6, pp.363-369, 2010.
DOI : 10.1177/0963721410390354

URL : https://hal.archives-ouvertes.fr/hal-00639413

P. Lemaire, L. Arnaud, and M. Lecacheur, Adults' age-related differences in adaptativity of strategy choices: evidence from computational estimation, Psychol. Aging, vol.19, 2004.

P. Lemaire and M. Lecacheur, Strategy switch costs in arithmetic problem solving, Memory & Cognition, vol.38, issue.3, 2010.
DOI : 10.3758/MC.38.3.322

URL : https://hal.archives-ouvertes.fr/hal-00639411

P. Lemaire, M. Lecacheur, and F. Farioli, Children's strategies in computational estimation, Journal of Experimental Child Psychology, vol.82, issue.4, pp.141-147, 2000.
DOI : 10.1016/S0022-0965(02)00107-8

P. Lemaire and L. Reder, What affects strategy selection in arithmetic? The example of parity and five effects on product verification, Memory & Cognition, vol.16, issue.2, pp.364-382, 1999.
DOI : 10.3758/BF03211420

P. Lemaire and R. S. Siegler, Four aspects of strategic change: Contributions to children's learning of multiplication., Journal of Experimental Psychology: General, vol.124, issue.1, 1995.
DOI : 10.1037/0096-3445.124.1.83

M. C. Lovett, A. , and J. R. , History of Success and Current Context in Problem Solving, Cognitive Psychology, vol.31, issue.2, pp.168-217, 1996.
DOI : 10.1006/cogp.1996.0016

M. C. Lovett and C. D. Schunn, Task representations, strategy variability, and base-rate neglect., Journal of Experimental Psychology: General, vol.128, issue.2, 1999.
DOI : 10.1037/0096-3445.128.2.107

K. Luwel, V. Schillemans, P. Onghena, and L. Vershaffel, Does switching between strategies within the same task involve a cost?, British Journal of Psychology, vol.29, issue.4, pp.753-771, 2009.
DOI : 10.1348/000712609X402801

A. W. Macdonald, J. D. Cohen, and V. A. Stenger, Dissociating the Role of the Dorsolateral Prefrontal and Anterior Cingulate Cortex in Cognitive Control, Science, vol.288, issue.5472, pp.1835-1838, 2000.
DOI : 10.1126/science.288.5472.1835

V. Menon, S. M. Rivera, C. D. White, S. Eliez, G. H. Glover et al., Functional optimization of arithmetic processing in perfect performers, Cognitive Brain Research, vol.9, issue.3, pp.343-345, 2000.
DOI : 10.1016/S0926-6410(00)00010-0

E. K. Miller, The prefrontal cortex and cognitive control, Nature Reviews Neuroscience, vol.1, issue.1, pp.59-65, 2000.
DOI : 10.1038/35036228

C. A. Montojo, C. , and S. M. , Differential Neural Activation for Updating Rule versus Stimulus Information in Working Memory, Neuron, vol.59, issue.1, 2008.
DOI : 10.1016/j.neuron.2008.05.012

B. Pastötter, S. Hanslmayr, and K. Bauml, Conflict processing in the anterior cingulate cortex constrains response priming, NeuroImage, vol.50, issue.4, 2010.
DOI : 10.1016/j.neuroimage.2010.01.095

J. W. Payne, J. R. Bettman, J. , and E. J. , The Adaptive Decision Maker, pp.10-1017, 1993.
DOI : 10.1017/CBO9781139173933

M. Pesenti, L. Zago, F. Crivello, E. Mellet, D. Samson et al., Mental calculation in a prodigy is sustained by right prefrontal and medialtemporal areas, Nat. Neurosci, vol.4, pp.103-107, 1038.

L. Petit and L. Zago, L'attention et la mémoire de travail visuo-spatiales, Cerveau et Pyschologie. Introduction à l'Imagerie Cérébrale Anatomique et Fonctionnelle Houdé, B. Mazoyer, and N. Tzourio-Mazoyer: PUF), pp.377-402, 2002.

M. Petrides, The role of the mid-dorsolateral prefrontal cortex in working memory, Experimental Brain Research, vol.133, issue.1, pp.44-54, 2000.
DOI : 10.1007/s002210000399

M. Piazza, V. Izard, P. Pinel, L. Bihan, D. Dehaene et al., Tuning Curves for Approximate Numerosity in the Human Intraparietal Sulcus, Neuron, vol.44, issue.3, 2004.
DOI : 10.1016/j.neuron.2004.10.014

URL : https://hal.archives-ouvertes.fr/hal-00349682

P. Pinel, M. Piazza, L. Bihan, D. Dehaene, and S. , Distributed and Overlapping Cerebral Representations of Number, Size, and Luminance during Comparative Judgments, Neuron, vol.41, issue.6, pp.983-993, 2004.
DOI : 10.1016/S0896-6273(04)00107-2

URL : https://hal.archives-ouvertes.fr/hal-00349685

L. M. Reder and F. E. Ritter, What determines initial feeling of knowing? Familiarity with question terms, not with the answer., Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.18, issue.3, pp.435-451, 1992.
DOI : 10.1037/0278-7393.18.3.435

K. R. Ridderinkhof, W. P. Van-den-wildenberg, S. J. Segalowitz, C. , and C. S. , Neurocognitive mechanisms of cognitive control: The role of prefrontal cortex in action selection, response inhibition, performance monitoring, and reward-based learning, Brain and Cognition, vol.56, issue.2, pp.129-140, 2004.
DOI : 10.1016/j.bandc.2004.09.016

URL : https://hal.archives-ouvertes.fr/hal-01384907

J. Rieskamp and P. E. Otto, SSL: A Theory of How People Learn to Select Strategies., Journal of Experimental Psychology: General, vol.135, issue.2, pp.207-236, 2006.
DOI : 10.1037/0096-3445.135.2.207

J. K. Roth, J. T. Serences, C. , and S. M. , Neural System for Controlling the Contents of Object Working Memory in Humans, Cerebral Cortex, vol.16, issue.11, pp.1595-1603, 2006.
DOI : 10.1093/cercor/bhj096

J. B. Rowe, I. Toni, O. Josephs, R. S. Frackowiak, and R. E. Passingham, The Prefrontal Cortex: Response Selection or Maintenance Within Working Memory?, Science, vol.288, issue.5471, pp.1656-1660, 2000.
DOI : 10.1126/science.288.5471.1656

M. F. Rushworth, M. P. Noonan, E. D. Boorman, M. E. Walton, and T. E. Behrens, Frontal Cortex and Reward-Guided Learning and Decision-Making, Neuron, vol.70, issue.6, pp.1054-1069, 2011.
DOI : 10.1016/j.neuron.2011.05.014

URL : http://doi.org/10.1016/j.neuron.2011.05.014

C. D. Schunn, L. M. Reder, A. Nhouyavanisvong, D. R. Richards, and P. J. Stroffolino, To calculate or not to calculate: A source activation confusion model of problem familiarity's role in strategy selection., Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.23, issue.1, pp.3-29, 1997.
DOI : 10.1037/0278-7393.23.1.3

A. P. Shimamura, Memory and frontal lobe function, The Cognitive Neurosciences, pp.803-813, 1995.

R. S. Siegler, Cognitive variability, Developmental Science, vol.83, issue.1, 2007.
DOI : 10.1111/j.1467-7687.2007.00571.x

R. S. Siegler and R. Araya, A computational model of conscious and unconscious strategy discovery, Advances in Child Development and Behaviour, pp.1-14, 2005.
DOI : 10.1016/S0065-2407(05)80003-5

R. S. Siegler and P. Lemaire, Older and younger adults' strategy choices in multiplication: Testing predictions of ASCM using the choice/no-choice method., Journal of Experimental Psychology: General, vol.126, issue.1, pp.71-92, 1997.
DOI : 10.1037/0096-3445.126.1.71

O. Simon, L. Cohen, J. F. Mangin, D. L. Bihan, and S. Dehaene, Topographical Layout of Hand, Eye, Calculation, and Language-Related Areas in the Human Parietal Lobe, Neuron, vol.33, issue.3, pp.475-487, 2002.
DOI : 10.1016/S0896-6273(02)00575-5

URL : https://hal.archives-ouvertes.fr/hal-00349713

H. A. Slagter, D. H. Weissman, B. Giesbrecht, J. L. Kenemans, G. R. Mangun et al., Brain regions activated by endogenous preparatory set shifting as revealed by fMRI, Cognitive, Affective, & Behavioral Neuroscience, vol.6, issue.3, pp.175-189, 2006.
DOI : 10.3758/CABN.6.3.175

F. E. Smith, J. , and J. , Neuroimaging analyses of human working memory, Proceedings of the National Academy of Sciences, vol.95, issue.20, pp.12061-12068, 1998.
DOI : 10.1073/pnas.95.20.12061

F. E. Smith, J. , and J. , Storage and Executive Processes in the Frontal Lobes, Science, vol.283, issue.5408, 1999.
DOI : 10.1126/science.283.5408.1657

M. H. Sohn, M. V. Albert, K. Jung, C. S. Carter, A. et al., Anticipation of conflict monitoring in the anterior cingulate cortex and the prefrontal cortex, Proceedings of the National Academy of Sciences, vol.104, issue.25, pp.10330-10334, 2007.
DOI : 10.1073/pnas.0703225104

L. Taconnat, N. Raz, C. Toczé, B. Bouazzaoui, H. Sauzéon et al., Ageing and organisation strategies in free recall: The role of cognitive flexibility, European Journal of Cognitive Psychology, vol.27, issue.2-3, pp.347-365, 2009.
DOI : 10.1037/0012-1649.19.4.513

URL : https://hal.archives-ouvertes.fr/hal-00396200

N. Tzourio-mazoyer, B. Landeau, D. Papathanassiou, F. Crivello, O. Etard et al., Automated Anatomical Labeling of Activations in SPM Using a Macroscopic Anatomical Parcellation of the MNI MRI Single-Subject Brain, NeuroImage, vol.15, issue.1, pp.273-2890978, 2001.
DOI : 10.1006/nimg.2001.0978

K. Uittenhove and P. Lemaire, Sequential Difficulty Effects During Strategy Execution, Experimental Psychology, vol.59, issue.5, pp.295-301, 2012.
DOI : 10.1027/1618-3169/a000157

URL : https://hal.archives-ouvertes.fr/hal-01440382

K. Uittenhove and P. Lemaire, Strategy sequential difficulty effects in Alzheimer patients: A study in arithmetic, Journal of Clinical and Experimental Neuropsychology, vol.135, issue.1, pp.83-89, 2013.
DOI : 10.1027/1618-3169/a000157

URL : https://hal.archives-ouvertes.fr/hal-01439672

K. Uittenhove, C. Poletti, S. Dufau, and P. Lemaire, The time course of strategy sequential difficulty effects: an ERP study in arithmetic, Experimental Brain Research, vol.59, issue.5, pp.1-8, 2013.
DOI : 10.1007/s00221-012-3397-9

URL : https://hal.archives-ouvertes.fr/hal-01152196

M. E. Walton, P. L. Croxson, T. E. Behrens, S. W. Kernneley, and M. F. Rushworth, Adaptive decision making and value in the anterior cingulate cortex, NeuroImage, vol.36, pp.142-154, 2007.
DOI : 10.1016/j.neuroimage.2007.03.029

L. Wang, X. Liu, K. G. Guise, R. T. Knight, J. Ghajar et al., Effective Connectivity of the Fronto-parietal Network during Attentional Control, Journal of Cognitive Neuroscience, vol.18, issue.3, pp.543-553, 2009.
DOI : 10.3758/CABN.4.4.609

L. Zago, M. Pesenti, E. Mellet, F. Crivello, B. Mazoyer et al., Neural Correlates of Simple and Complex Mental Calculation, NeuroImage, vol.13, issue.2, pp.314-3270697, 2000.
DOI : 10.1006/nimg.2000.0697

URL : https://hal.archives-ouvertes.fr/hal-01382905

J. Zbrodoff, L. , and G. , What everyone finds: the problem-size effect, Handbook of Mathematical Cognition, pp.331-345, 2005.

A. Zenon, N. Filali, J. Duhamel, and E. Olivier, Salience Representation in the Parietal and Frontal Cortex, Journal of Cognitive Neuroscience, vol.147, issue.5, pp.918-930, 2010.
DOI : 10.1371/journal.pone.0002219

J. Taillan, E. Ardiale, A. J. Nazarian, B. Félician, O. Lemaire et al., Processes in arithmetic strategy selection: a fMRI study, Frontiers in Psychology, vol.22, issue.343, p.61, 2015.
DOI : 10.1162/jocn.2009.21233

URL : https://hal.archives-ouvertes.fr/hal-01222359

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