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Published in: Behavioral and Brain Functions 1/2018

Open Access 01-12-2018 | Research

Magnitude processing of symbolic and non-symbolic proportions: an fMRI study

Authors: Julia Mock, Stefan Huber, Johannes Bloechle, Julia F. Dietrich, Julia Bahnmueller, Johannes Rennig, Elise Klein, Korbinian Moeller

Published in: Behavioral and Brain Functions | Issue 1/2018

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Abstract

Background

Recent research indicates that processing proportion magnitude is associated with activation in the intraparietal sulcus. Thus, brain areas associated with the processing of numbers (i.e., absolute magnitude) were activated during processing symbolic fractions as well as non-symbolic proportions. Here, we investigated systematically the cognitive processing of symbolic (e.g., fractions and decimals) and non-symbolic proportions (e.g., dot patterns and pie charts) in a two-stage procedure. First, we investigated relative magnitude-related activations of proportion processing. Second, we evaluated whether symbolic and non-symbolic proportions share common neural substrates.

Methods

We conducted an fMRI study using magnitude comparison tasks with symbolic and non-symbolic proportions, respectively. As an indicator for magnitude-related processing of proportions, the distance effect was evaluated.

Results

A conjunction analysis indicated joint activation of specific occipito-parietal areas including right intraparietal sulcus (IPS) during proportion magnitude processing. More specifically, results indicate that the IPS, which is commonly associated with absolute magnitude processing, is involved in processing relative magnitude information as well, irrespective of symbolic or non-symbolic presentation format. However, we also found distinct activation patterns for the magnitude processing of the different presentation formats.

Conclusion

Our findings suggest that processing for the separate presentation formats is not only associated with magnitude manipulations in the IPS, but also increasing demands on executive functions and strategy use associated with frontal brain regions as well as visual attention and encoding in occipital regions. Thus, the magnitude processing of proportions may not exclusively reflect processing of number magnitude information but also rather domain-general processes.
Literature
1.
go back to reference Gigerenzer G. Calculated risk: how to know when numbers deceive you. New York: Simon & Schuster; 2002. Gigerenzer G. Calculated risk: how to know when numbers deceive you. New York: Simon & Schuster; 2002.
2.
go back to reference Siegler RS, Fazio LK, Bailey DH, Zhou X. Fractions: the new frontier for theories of numerical development. Trends Cogn Sci. 2013;17:13–9.CrossRefPubMed Siegler RS, Fazio LK, Bailey DH, Zhou X. Fractions: the new frontier for theories of numerical development. Trends Cogn Sci. 2013;17:13–9.CrossRefPubMed
3.
go back to reference NMAP. Foundations for success: the final report of the National Mathematics Advisory Panel. Washington, DC: US Department of Education; 2008. NMAP. Foundations for success: the final report of the National Mathematics Advisory Panel. Washington, DC: US Department of Education; 2008.
4.
go back to reference Rau MA, Aleven V, Rummel N, Rohrbach S. Sense making alone doesn’t do it: fluency matters too! ITS support for robust learning with multiple representations. In: Cerri S, Clancey W, Papadourakis G, Panourgia K, editors. Intell. Tutoring Syst. 7315th ed. Berlin/Heidelberg: Springer; 2012. p. 174–84. Rau MA, Aleven V, Rummel N, Rohrbach S. Sense making alone doesn’t do it: fluency matters too! ITS support for robust learning with multiple representations. In: Cerri S, Clancey W, Papadourakis G, Panourgia K, editors. Intell. Tutoring Syst. 7315th ed. Berlin/Heidelberg: Springer; 2012. p. 174–84.
5.
go back to reference Rau MA, Aleven V, Rummel N. Successful learning with multiple graphical representations and self-explanation prompts. J Educ Psychol. 2015;107:30–46.CrossRef Rau MA, Aleven V, Rummel N. Successful learning with multiple graphical representations and self-explanation prompts. J Educ Psychol. 2015;107:30–46.CrossRef
6.
go back to reference Gabriel F, Coche F, Szucs D, Carette V, Rey B, Content A. Developing children’s understanding of fractions: an intervention study. Mind Brain Educ. 2012;6:137–46.CrossRef Gabriel F, Coche F, Szucs D, Carette V, Rey B, Content A. Developing children’s understanding of fractions: an intervention study. Mind Brain Educ. 2012;6:137–46.CrossRef
7.
go back to reference Nieder A. Counting on neurons: the neurobiology of numerical competence. Nat Rev Neurosci. 2005;6:177–90.CrossRefPubMed Nieder A. Counting on neurons: the neurobiology of numerical competence. Nat Rev Neurosci. 2005;6:177–90.CrossRefPubMed
8.
go back to reference Piazza M, Pinel P, Le Bihan D, Dehaene S. A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron. 2007;53:293–305.CrossRefPubMed Piazza M, Pinel P, Le Bihan D, Dehaene S. A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron. 2007;53:293–305.CrossRefPubMed
9.
go back to reference Pinel P, Dehaene S, Rivière D, Le Bihan D. Modulation of parietal activation by semantic distance in a number comparison task. Neuroimage. 2001;14:1013–26.CrossRefPubMed Pinel P, Dehaene S, Rivière D, Le Bihan D. Modulation of parietal activation by semantic distance in a number comparison task. Neuroimage. 2001;14:1013–26.CrossRefPubMed
10.
go back to reference Dehaene S, Piazza M, Pinel P, Cohen L. Three parietal circuits for number processing. Cogn Neuropsychol. 2003;20:487–506.CrossRefPubMed Dehaene S, Piazza M, Pinel P, Cohen L. Three parietal circuits for number processing. Cogn Neuropsychol. 2003;20:487–506.CrossRefPubMed
11.
go back to reference Moyer RS, Landauer TK. Time required for judgements of numerical inequality. Nature. 1967;215:1519–20.CrossRefPubMed Moyer RS, Landauer TK. Time required for judgements of numerical inequality. Nature. 1967;215:1519–20.CrossRefPubMed
12.
go back to reference Meert G, Grégoire J, Noël M-P. Rational numbers: componential versus holistic representation of fractions in a magnitude comparison task. Q J Exp Psychol. 2009;62:1598–616.CrossRef Meert G, Grégoire J, Noël M-P. Rational numbers: componential versus holistic representation of fractions in a magnitude comparison task. Q J Exp Psychol. 2009;62:1598–616.CrossRef
13.
go back to reference Arsalidou M, Taylor MJ. Is 2+2=4? Meta-analyses of brain areas needed for numbers and calculations. Neuroimage. 2011;54:2382–93.CrossRefPubMed Arsalidou M, Taylor MJ. Is 2+2=4? Meta-analyses of brain areas needed for numbers and calculations. Neuroimage. 2011;54:2382–93.CrossRefPubMed
14.
go back to reference Bugden S, Price GR, McLean DA, Ansari D. The role of the left intraparietal sulcus in the relationship between symbolic number processing and children’s arithmetic competence. Dev. Cogn. Neurosci. 2012;2:448–57.CrossRefPubMed Bugden S, Price GR, McLean DA, Ansari D. The role of the left intraparietal sulcus in the relationship between symbolic number processing and children’s arithmetic competence. Dev. Cogn. Neurosci. 2012;2:448–57.CrossRefPubMed
15.
go back to reference Jolles D, Supekar K, Richardson J, Tenison C, Ashkenazi S, Rosenberg-Lee M, et al. Reconfiguration of parietal circuits with cognitive tutoring in elementary school children. Cortex. 2016;83:231–45.CrossRefPubMedPubMedCentral Jolles D, Supekar K, Richardson J, Tenison C, Ashkenazi S, Rosenberg-Lee M, et al. Reconfiguration of parietal circuits with cognitive tutoring in elementary school children. Cortex. 2016;83:231–45.CrossRefPubMedPubMedCentral
16.
go back to reference Pinel P, Piazza M, Le Bihan D, Dehaene S. Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron. 2004;41:983–93.CrossRefPubMed Pinel P, Piazza M, Le Bihan D, Dehaene S. Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron. 2004;41:983–93.CrossRefPubMed
17.
go back to reference Menon V, Rivera SM, White CD, Glover GH, Reiss AL. Dissociating prefrontal and parietal cortex activation during arithmetic processing. Neuroimage. 2000;12:357–65.CrossRefPubMed Menon V, Rivera SM, White CD, Glover GH, Reiss AL. Dissociating prefrontal and parietal cortex activation during arithmetic processing. Neuroimage. 2000;12:357–65.CrossRefPubMed
18.
go back to reference Fias W, Menon V, Szucs D. Multiple components of developmental dyscalculia. Trends Neurosci. Educ. 2013;2:43–7.CrossRef Fias W, Menon V, Szucs D. Multiple components of developmental dyscalculia. Trends Neurosci. Educ. 2013;2:43–7.CrossRef
19.
go back to reference Menon V. Arithmetic in the child and adult brain. In: Dowker A, editor. Cohen Kadosh R. Oxford Handb. Numer. Cogn. Oxford: Oxford University Press; 2015. p. 502–30. Menon V. Arithmetic in the child and adult brain. In: Dowker A, editor. Cohen Kadosh R. Oxford Handb. Numer. Cogn. Oxford: Oxford University Press; 2015. p. 502–30.
20.
go back to reference Ansari D, Garcia N, Lucas E, Hamon K, Dhital B. Neural correlates of symbolic number processing in children and adults. Neuroreport. 2005;16:1769–73.CrossRefPubMed Ansari D, Garcia N, Lucas E, Hamon K, Dhital B. Neural correlates of symbolic number processing in children and adults. Neuroreport. 2005;16:1769–73.CrossRefPubMed
21.
go back to reference Ansari D. Effects of development and enculturation on number representation in the brain. Nat. Rev. Neurosci. 2008;9:278–91.CrossRefPubMed Ansari D. Effects of development and enculturation on number representation in the brain. Nat. Rev. Neurosci. 2008;9:278–91.CrossRefPubMed
22.
go back to reference van Dijck J-P, Gevers W, Fias W. Numvbers are associated with different types of spatial information depending on the task. Cognition. 2009;113:248–53.CrossRefPubMed van Dijck J-P, Gevers W, Fias W. Numvbers are associated with different types of spatial information depending on the task. Cognition. 2009;113:248–53.CrossRefPubMed
23.
go back to reference Majerus S, D’Argembeau A, Martinez Perez T, Belayachi S, Van der Linden M, Collette F, et al. The commonality of neural networks for verbal and visual short-term memory. J. Cogn. Neurosci. 2010;22:2570–93.CrossRefPubMed Majerus S, D’Argembeau A, Martinez Perez T, Belayachi S, Van der Linden M, Collette F, et al. The commonality of neural networks for verbal and visual short-term memory. J. Cogn. Neurosci. 2010;22:2570–93.CrossRefPubMed
24.
go back to reference Hitch GJ. Role of short-term working memory in mental arithmetic. Cogn. Psychol. 1978;10:302–23.CrossRef Hitch GJ. Role of short-term working memory in mental arithmetic. Cogn. Psychol. 1978;10:302–23.CrossRef
25.
go back to reference Cohen Kadosh R, Henik A, Rubinstein O, Mohr H, Dori H, Van de Ven V, et al. Are numbers special? The comparison systems of the human brain investigated by fMRI. Neuropsychologia. 2005;43:1238–48.CrossRefPubMed Cohen Kadosh R, Henik A, Rubinstein O, Mohr H, Dori H, Van de Ven V, et al. Are numbers special? The comparison systems of the human brain investigated by fMRI. Neuropsychologia. 2005;43:1238–48.CrossRefPubMed
26.
go back to reference Kaufmann L, Koppelstaetter F, Delazer M, Siedentopf C, Rhomberg P, Golaszewski S, et al. Neural correlates of distance and congruity effects in a numerical Stroop task, an event-related fMRI study. Neuroimage. 2005;25:888–98.CrossRefPubMed Kaufmann L, Koppelstaetter F, Delazer M, Siedentopf C, Rhomberg P, Golaszewski S, et al. Neural correlates of distance and congruity effects in a numerical Stroop task, an event-related fMRI study. Neuroimage. 2005;25:888–98.CrossRefPubMed
27.
go back to reference Ansari D, Grabner RH, Koschutnig K, Reishofer G, Ebner F. Individual differences in mathematical competence modulate brain responses to arithmetic errors: an fMRI study. Learn. Individ. Differ. 2011;21:636–43.CrossRef Ansari D, Grabner RH, Koschutnig K, Reishofer G, Ebner F. Individual differences in mathematical competence modulate brain responses to arithmetic errors: an fMRI study. Learn. Individ. Differ. 2011;21:636–43.CrossRef
28.
go back to reference Dehaene S, Spelke ES, Pinel P, Stanescu R, Tsivkin S. Sources of mathematical thinking: behavioral and brain-imaging evidence. Science. 1999;284:970–4.CrossRefPubMed Dehaene S, Spelke ES, Pinel P, Stanescu R, Tsivkin S. Sources of mathematical thinking: behavioral and brain-imaging evidence. Science. 1999;284:970–4.CrossRefPubMed
29.
go back to reference Grabner RH, Ansari D, Koschutnig K, Reishofer G, Ebner F, Neuper C. To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia. 2009;47:604–8.CrossRefPubMed Grabner RH, Ansari D, Koschutnig K, Reishofer G, Ebner F, Neuper C. To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia. 2009;47:604–8.CrossRefPubMed
30.
go back to reference Bloechle J, Huber S, Bahnmueller J, Rennig J, Willmes K, Cavdaroglu S, et al. Fact learning in complex arithmetic - the role of the angular gyrus revisited. Hum. Brain Mapp. 2016;37:3061–79.CrossRefPubMed Bloechle J, Huber S, Bahnmueller J, Rennig J, Willmes K, Cavdaroglu S, et al. Fact learning in complex arithmetic - the role of the angular gyrus revisited. Hum. Brain Mapp. 2016;37:3061–79.CrossRefPubMed
31.
go back to reference Chochon F, Cohen L, van de Moortele PF, Dehaene S. Differential contributions of the left and right inferior parietal lobules to number processing. J. Cogn. Neurosci. 1999;11:617–30.CrossRefPubMed Chochon F, Cohen L, van de Moortele PF, Dehaene S. Differential contributions of the left and right inferior parietal lobules to number processing. J. Cogn. Neurosci. 1999;11:617–30.CrossRefPubMed
32.
go back to reference Dehaene S. The organization of brain activations in number comparison: event-related potentials and the additive-factors method. J. Cogn. Neurosci. 1996;8:47–68.CrossRefPubMed Dehaene S. The organization of brain activations in number comparison: event-related potentials and the additive-factors method. J. Cogn. Neurosci. 1996;8:47–68.CrossRefPubMed
33.
go back to reference Piazza M, Izard V, Pinel P, Le Bihan D, Dehaene S. Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron. 2004;44:547–55.CrossRefPubMed Piazza M, Izard V, Pinel P, Le Bihan D, Dehaene S. Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron. 2004;44:547–55.CrossRefPubMed
34.
go back to reference Venkatraman V, Ansari D, Chee MWL. Neural correlates of symbolic and non-symbolic arithmetic. Neuropsychologia. 2005;43:744–53.CrossRefPubMed Venkatraman V, Ansari D, Chee MWL. Neural correlates of symbolic and non-symbolic arithmetic. Neuropsychologia. 2005;43:744–53.CrossRefPubMed
35.
go back to reference Sokolowski HM, Fias W, Mousa A, Ansari D. Common and distinct brain regions in both parietal and frontal cortex support symbolic and nonsymbolic number processing in humans: A functional neuroimaging metaanalysis. Neuroimage. 2017;146:376–94.CrossRefPubMed Sokolowski HM, Fias W, Mousa A, Ansari D. Common and distinct brain regions in both parietal and frontal cortex support symbolic and nonsymbolic number processing in humans: A functional neuroimaging metaanalysis. Neuroimage. 2017;146:376–94.CrossRefPubMed
36.
go back to reference Holloway ID, Price GR, Ansari D. Common and segregated neural pathways for the processing of symbolic and nonsymbolic numerical magnitude: an fMRI study. Neuroimage. 2010;49:1006–17.CrossRefPubMed Holloway ID, Price GR, Ansari D. Common and segregated neural pathways for the processing of symbolic and nonsymbolic numerical magnitude: an fMRI study. Neuroimage. 2010;49:1006–17.CrossRefPubMed
37.
go back to reference Eger E, Sterzer P, Russ MO, Giraud AL, Kleinschmidt A. A supramodal number representation in human intraparietal cortex. Neuron. 2003;37:719–25.CrossRefPubMed Eger E, Sterzer P, Russ MO, Giraud AL, Kleinschmidt A. A supramodal number representation in human intraparietal cortex. Neuron. 2003;37:719–25.CrossRefPubMed
38.
go back to reference Ansari D, Dhital B, Siong SC. Parametric effects of numerical distance on the intraparietal sulcus during passive viewing of rapid numerosity changes. Brain Res. 2006;1067:181–8.CrossRefPubMed Ansari D, Dhital B, Siong SC. Parametric effects of numerical distance on the intraparietal sulcus during passive viewing of rapid numerosity changes. Brain Res. 2006;1067:181–8.CrossRefPubMed
39.
go back to reference Delazer M, Ischebeck A, Domahs F, Zamarian L, Koppelstaetter F, Siedentopf C, et al. Learning by strategies and learning by drill - evidence from an fMRI study. Neuroimage. 2005;25:838–49.CrossRefPubMed Delazer M, Ischebeck A, Domahs F, Zamarian L, Koppelstaetter F, Siedentopf C, et al. Learning by strategies and learning by drill - evidence from an fMRI study. Neuroimage. 2005;25:838–49.CrossRefPubMed
40.
go back to reference Ischebeck A, Koschutnig K, Reishofer G, Butterworth B, Neuper C, Ebner F. Processing fractions and proportions: An fMRI study. Int. J. Psychophysiol. 2010;77:227.CrossRef Ischebeck A, Koschutnig K, Reishofer G, Butterworth B, Neuper C, Ebner F. Processing fractions and proportions: An fMRI study. Int. J. Psychophysiol. 2010;77:227.CrossRef
41.
go back to reference Ischebeck A, Schocke M, Delazer M. The processing and representation of fractions within the brain. An fMRI investigation. Neuroimage. 2009;47:403–13.CrossRefPubMed Ischebeck A, Schocke M, Delazer M. The processing and representation of fractions within the brain. An fMRI investigation. Neuroimage. 2009;47:403–13.CrossRefPubMed
42.
go back to reference Jacob SN, Nieder A. Notation-independent representation of fractions in the human parietal cortex. J. Neurosci. 2009;29:4652–7.CrossRefPubMed Jacob SN, Nieder A. Notation-independent representation of fractions in the human parietal cortex. J. Neurosci. 2009;29:4652–7.CrossRefPubMed
43.
go back to reference Jacob SN, Nieder A. Tuning to non-symbolic proportions in the human frontoparietal cortex. Eur. J. Neurosci. 2009;30:1432–42.CrossRefPubMed Jacob SN, Nieder A. Tuning to non-symbolic proportions in the human frontoparietal cortex. Eur. J. Neurosci. 2009;30:1432–42.CrossRefPubMed
44.
go back to reference Siegler RS, Fuchs L, Jordan NC, Gersten R, Ochsendorf R. The center for improving learning of fractions: a progress report. In: Chinn S, editor. Routledge Int. Handb. Dyscalculia Math. Learn. Difficulties. New York: Routledge; 2015. p. 292–303. Siegler RS, Fuchs L, Jordan NC, Gersten R, Ochsendorf R. The center for improving learning of fractions: a progress report. In: Chinn S, editor. Routledge Int. Handb. Dyscalculia Math. Learn. Difficulties. New York: Routledge; 2015. p. 292–303.
45.
go back to reference Rau MA, Aleven V, Rummel N. Interleaved practice in multi-dimensional learning tasks: which dimension should we interleave? Learn Instr. 2013;23:98–114.CrossRef Rau MA, Aleven V, Rummel N. Interleaved practice in multi-dimensional learning tasks: which dimension should we interleave? Learn Instr. 2013;23:98–114.CrossRef
46.
go back to reference Rau MA, Aleven V, Rummel N. Intelligent tutoring systems with multiple representations and self-explanation prompts support learning of fractions. In: Dimitrova V, Mizoguchi R, Du Boulay B, editors. 14th Int. Conf. Artif. Intell. Educ. Amsterdam: IOS Press; 2009. p. 441–8. Rau MA, Aleven V, Rummel N. Intelligent tutoring systems with multiple representations and self-explanation prompts support learning of fractions. In: Dimitrova V, Mizoguchi R, Du Boulay B, editors. 14th Int. Conf. Artif. Intell. Educ. Amsterdam: IOS Press; 2009. p. 441–8.
47.
go back to reference Matthews PG, Chesney DL. Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes. Cogn Psychol. 2015;78:28–56.CrossRefPubMed Matthews PG, Chesney DL. Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes. Cogn Psychol. 2015;78:28–56.CrossRefPubMed
48.
go back to reference Common Core State Standards Initiative. Common Core State Standards for Mathematics 2010. http://www.corestandards.org/. Accessed cited 6 Mar 2018. Common Core State Standards Initiative. Common Core State Standards for Mathematics 2010. http://​www.​corestandards.​org/​.​ Accessed cited 6 Mar 2018.
49.
50.
go back to reference Baayen RH, Davidson DJ, Bates DM. Mixed-effects modeling with crossed random effects for subjects and items. J Mem Lang. 2008;59:390–412.CrossRef Baayen RH, Davidson DJ, Bates DM. Mixed-effects modeling with crossed random effects for subjects and items. J Mem Lang. 2008;59:390–412.CrossRef
51.
52.
go back to reference Barr DJ, Levy R, Scheepers C, Tily HJ. Random effects structure for confirmatory hypothesis testing: keep it maximal. J Mem Lang. 2013;68:255–78.CrossRef Barr DJ, Levy R, Scheepers C, Tily HJ. Random effects structure for confirmatory hypothesis testing: keep it maximal. J Mem Lang. 2013;68:255–78.CrossRef
53.
go back to reference R Core Team. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing; 2015. R Core Team. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing; 2015.
54.
go back to reference Bates D, Maechler M, Bolker B, Walker S. Fitting linear mixed-effects models using lme4. J Stat Softw.67:1–48. Bates D, Maechler M, Bolker B, Walker S. Fitting linear mixed-effects models using lme4. J Stat Softw.67:1–48.
55.
go back to reference Judd CM, Westfall J, Kenny DA. Treating stimuli as a random factor in social psychology: a new and comprehensive solution to a pervasive but largely ignored problem. J Pers Soc Psychol. 2012;103:54–69.CrossRefPubMed Judd CM, Westfall J, Kenny DA. Treating stimuli as a random factor in social psychology: a new and comprehensive solution to a pervasive but largely ignored problem. J Pers Soc Psychol. 2012;103:54–69.CrossRefPubMed
56.
go back to reference Singmann H, Bolker B, Westfall J. afex: analysis of factorial experiments. R package version 0.2015. p. 13–145. Singmann H, Bolker B, Westfall J. afex: analysis of factorial experiments. R package version 0.2015. p. 13–145.
57.
go back to reference Hothorn T, Bretz F, Westfall P. Simultaneous inference in general parametric models. Biom J. 2008;50:346–63.CrossRefPubMed Hothorn T, Bretz F, Westfall P. Simultaneous inference in general parametric models. Biom J. 2008;50:346–63.CrossRefPubMed
58.
go back to reference Benjamini Y, Hochberg Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B. 1995;57:289–300. Benjamini Y, Hochberg Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B. 1995;57:289–300.
59.
go back to reference Nichols T, Brett M, Andersson J, Wager T, Poline JB. Valid conjunction inference with the minimum statistic. Neuroimage. 2005;25:653–60.CrossRefPubMed Nichols T, Brett M, Andersson J, Wager T, Poline JB. Valid conjunction inference with the minimum statistic. Neuroimage. 2005;25:653–60.CrossRefPubMed
60.
go back to reference Eickhoff SB, Stephan KE, Mohlberg H, Grefkes C, Fink GR, Amunts K, et al. A new SPM toolbox for combining probabilistic cytoarchitectonic maps and functional imaging data. Neuroimage. 2005;25:1325–35.CrossRefPubMed Eickhoff SB, Stephan KE, Mohlberg H, Grefkes C, Fink GR, Amunts K, et al. A new SPM toolbox for combining probabilistic cytoarchitectonic maps and functional imaging data. Neuroimage. 2005;25:1325–35.CrossRefPubMed
61.
go back to reference Mussolin C, Noel MP, Pesenti M, Grandin C, De Volder A. Neural correlates of the numerical distance effect in children. Front Psychol. 2013;4:1–9.CrossRef Mussolin C, Noel MP, Pesenti M, Grandin C, De Volder A. Neural correlates of the numerical distance effect in children. Front Psychol. 2013;4:1–9.CrossRef
62.
go back to reference Dehaene S, Cohen L. Towards an anatomical and functional model of number processing. Math Cogn. 1:83–120. Dehaene S, Cohen L. Towards an anatomical and functional model of number processing. Math Cogn. 1:83–120.
63.
go back to reference Dehaene S, Cohen L. Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex. 1997;33:219–50.CrossRefPubMed Dehaene S, Cohen L. Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex. 1997;33:219–50.CrossRefPubMed
64.
go back to reference DeWolf M, Chiang JN, Bassok M, Holyoak KJ, Monti MM. Neural representations of magnitude for natural and rational numbers. Neuroimage. 2016;141:304–12.CrossRefPubMed DeWolf M, Chiang JN, Bassok M, Holyoak KJ, Monti MM. Neural representations of magnitude for natural and rational numbers. Neuroimage. 2016;141:304–12.CrossRefPubMed
65.
go back to reference Cohen Kadosh R, Walsh V. Numerical representation in the parietal lobes: Abstract or not abstract? Behav. Brain Sci. 2009;32:313–28.CrossRefPubMed Cohen Kadosh R, Walsh V. Numerical representation in the parietal lobes: Abstract or not abstract? Behav. Brain Sci. 2009;32:313–28.CrossRefPubMed
66.
go back to reference Dehaene S. The number sense: How the mind creates mathematics. Oxford: Oxford University Press; 1997. Dehaene S. The number sense: How the mind creates mathematics. Oxford: Oxford University Press; 1997.
68.
69.
go back to reference Leibovich T, Katzin N, Harel M, Henik A. From, “sense of number” to “sense of magnitude”: The role of conitnuous magnitudes in numerical cognition. Behav. Brain Sci. 2017;40:e164.CrossRefPubMed Leibovich T, Katzin N, Harel M, Henik A. From, “sense of number” to “sense of magnitude”: The role of conitnuous magnitudes in numerical cognition. Behav. Brain Sci. 2017;40:e164.CrossRefPubMed
70.
71.
go back to reference Rosenberg-Lee M, Tsang JM, Menon V. Smybolic, numeric, and magnitude representations in the parietal cortex. Behav. Brain Sci. 2009;32:350–1.CrossRef Rosenberg-Lee M, Tsang JM, Menon V. Smybolic, numeric, and magnitude representations in the parietal cortex. Behav. Brain Sci. 2009;32:350–1.CrossRef
72.
go back to reference Shuman M, Kanwisher N. Numerical magnitude in the human parietal lobe: tests of representational generality and domain specificity. Neuron. 2004;44:557–69.CrossRefPubMed Shuman M, Kanwisher N. Numerical magnitude in the human parietal lobe: tests of representational generality and domain specificity. Neuron. 2004;44:557–69.CrossRefPubMed
73.
go back to reference Culham JC, Brandt SA, Cavanagh P, Kanwisher N, Dale AM, Tootell RB. Cortical fMRI activation produced by attentive tracking of moving targets. J. Neurophysiol. 1998;80:2657–70.CrossRefPubMed Culham JC, Brandt SA, Cavanagh P, Kanwisher N, Dale AM, Tootell RB. Cortical fMRI activation produced by attentive tracking of moving targets. J. Neurophysiol. 1998;80:2657–70.CrossRefPubMed
74.
go back to reference Culham JC, Kanwisher N. Neuroimaging of cognitive functions in human parietal cortex. Curr. Opin. Neurobiol. 2001;11:157–63.CrossRefPubMed Culham JC, Kanwisher N. Neuroimaging of cognitive functions in human parietal cortex. Curr. Opin. Neurobiol. 2001;11:157–63.CrossRefPubMed
75.
go back to reference Klein E, Moeller K, Nuerk H-C, Willmes K. On the neuro-cognitive foundations of basic auditory number processing: an fMRI study. Behav. brain Funct. 2010;6:42.CrossRefPubMedPubMedCentral Klein E, Moeller K, Nuerk H-C, Willmes K. On the neuro-cognitive foundations of basic auditory number processing: an fMRI study. Behav. brain Funct. 2010;6:42.CrossRefPubMedPubMedCentral
76.
go back to reference Rosenberg-Lee M, Chang TT, Young CB, Wu S, Menon V. Functional dissociations between four basic arithmetic operations in the human posterior parietal cortec: A cytoarchitectonic mapping study. Neuropsychologia. 2011;49:2592–608.CrossRefPubMedPubMedCentral Rosenberg-Lee M, Chang TT, Young CB, Wu S, Menon V. Functional dissociations between four basic arithmetic operations in the human posterior parietal cortec: A cytoarchitectonic mapping study. Neuropsychologia. 2011;49:2592–608.CrossRefPubMedPubMedCentral
77.
go back to reference MacDonald AW, Cohen JD, Stenger VA, Carter CS. Dissociating the role of the dorsolateral prefrontal and anterior cingulate cortex in cognitive control. Science. 2000;288:1835–8.CrossRefPubMed MacDonald AW, Cohen JD, Stenger VA, Carter CS. Dissociating the role of the dorsolateral prefrontal and anterior cingulate cortex in cognitive control. Science. 2000;288:1835–8.CrossRefPubMed
79.
go back to reference Huettel AS, Guzeldere G, McCarthy G. Dissociating the neural mechanisms of visual attention in charge of detection using functional MRI. J. Cogn. Neurosci. 2001;13:1006–18.CrossRefPubMed Huettel AS, Guzeldere G, McCarthy G. Dissociating the neural mechanisms of visual attention in charge of detection using functional MRI. J. Cogn. Neurosci. 2001;13:1006–18.CrossRefPubMed
80.
go back to reference Hester R, Fassbender C, Garavan H. Individual differences in error processing: A review and reanalysis of three event-related fMRI studies using GO/NOGO task. Cereb. Cortex. 2004;14:986–94.CrossRefPubMed Hester R, Fassbender C, Garavan H. Individual differences in error processing: A review and reanalysis of three event-related fMRI studies using GO/NOGO task. Cereb. Cortex. 2004;14:986–94.CrossRefPubMed
81.
go back to reference Castelli F, Glaser DE, Butterworth B. Discrete and analogue quantity processing in the parietal lobe: a functional MRI study. Proc. Natl. Acad. Sci. U. S. A. 2006;103:4693–8.CrossRefPubMedPubMedCentral Castelli F, Glaser DE, Butterworth B. Discrete and analogue quantity processing in the parietal lobe: a functional MRI study. Proc. Natl. Acad. Sci. U. S. A. 2006;103:4693–8.CrossRefPubMedPubMedCentral
82.
go back to reference Piazza M, Mechelli A, Price CJ, Butterworth B. Exact and approximate judgements of visual and auditory numerosity: An fMRI study. Brain Res. 2006;1106:177–88.CrossRefPubMed Piazza M, Mechelli A, Price CJ, Butterworth B. Exact and approximate judgements of visual and auditory numerosity: An fMRI study. Brain Res. 2006;1106:177–88.CrossRefPubMed
83.
go back to reference Alivisatos B, Petrides M. Functional activation of the human brain during mental rotation. Neuropsychologia. 1997;35:111–8.CrossRefPubMed Alivisatos B, Petrides M. Functional activation of the human brain during mental rotation. Neuropsychologia. 1997;35:111–8.CrossRefPubMed
84.
go back to reference Jordan K, Heinze H-J, Lutz K, Kanowski M, Jäncke L. Cortical Activations during the Mental Rotation of Different Visual Objects. Neuroimage. 2001;13:143–52.CrossRefPubMed Jordan K, Heinze H-J, Lutz K, Kanowski M, Jäncke L. Cortical Activations during the Mental Rotation of Different Visual Objects. Neuroimage. 2001;13:143–52.CrossRefPubMed
85.
go back to reference Klein E, Suchan J, Moeller K, Karnath HO, Knops A, Wood G, et al. Considering structural connectivity in the triple code model of numerical cognition: differential connectivity for magnitude processing and arithmetic facts. Brain Struct. Funct. 2016;221:979–95.CrossRefPubMed Klein E, Suchan J, Moeller K, Karnath HO, Knops A, Wood G, et al. Considering structural connectivity in the triple code model of numerical cognition: differential connectivity for magnitude processing and arithmetic facts. Brain Struct. Funct. 2016;221:979–95.CrossRefPubMed
86.
go back to reference Peterson BS, Kane MJ, Alexander GM, Lacadie C, Skudlarski P, Leung H-C, et al. An event-related functional MRI study comparing interference effects in the Simon and Stroop tasks. Cogn. Brain Res. 13:427–40. Peterson BS, Kane MJ, Alexander GM, Lacadie C, Skudlarski P, Leung H-C, et al. An event-related functional MRI study comparing interference effects in the Simon and Stroop tasks. Cogn. Brain Res. 13:427–40.
87.
go back to reference Lui X, Banich MT, Jacobson BL, Tanabe JL. Common and distinct neural substrates of attentional control in an integrated Simon and spatial Stroop task as assessed by event-related fMRI. Neuroimage. 2004;22:1097–106.CrossRef Lui X, Banich MT, Jacobson BL, Tanabe JL. Common and distinct neural substrates of attentional control in an integrated Simon and spatial Stroop task as assessed by event-related fMRI. Neuroimage. 2004;22:1097–106.CrossRef
88.
go back to reference Supekar K, Menon V. Developmental maturation of dynamic causal control signals in higher-order cognition: a neurocognitive network model. PLoS Comput. Biol. 2012;8:1002374.CrossRef Supekar K, Menon V. Developmental maturation of dynamic causal control signals in higher-order cognition: a neurocognitive network model. PLoS Comput. Biol. 2012;8:1002374.CrossRef
89.
go back to reference Wagner AD, Desmond JE, Glover GH, Gabrieli JDE. Prefrontal cortex and recognition memory: functional-MRI evidence for context-dependent retrieval processes. Brain. 1998;121:1985–2002.CrossRefPubMed Wagner AD, Desmond JE, Glover GH, Gabrieli JDE. Prefrontal cortex and recognition memory: functional-MRI evidence for context-dependent retrieval processes. Brain. 1998;121:1985–2002.CrossRefPubMed
90.
go back to reference Bunge SA, Kahn I, Wallis JD, Miller EK, Wagner AD. Neural circuits subserving the retrieval and maintenance of abstract rules. J. Neurophysiol. 2003;90:3419–28.CrossRefPubMed Bunge SA, Kahn I, Wallis JD, Miller EK, Wagner AD. Neural circuits subserving the retrieval and maintenance of abstract rules. J. Neurophysiol. 2003;90:3419–28.CrossRefPubMed
91.
go back to reference Taillan J, Ardiale E, Anton JL, Nazarian B, Félician O, Lemaire P. Processes in arithmetic strategy selection: a fMRI study. Front. Psychol. 2015;6:1–12.CrossRef Taillan J, Ardiale E, Anton JL, Nazarian B, Félician O, Lemaire P. Processes in arithmetic strategy selection: a fMRI study. Front. Psychol. 2015;6:1–12.CrossRef
92.
go back to reference Somers DC, Dale AM, Seiffert AE, Tootell RBH. Functional MRI reveals spatially specific attentional modulation in human primary visual cortex. Proc. Natl. Acad. Sci. U. S. A. 2006;96:1663–8.CrossRef Somers DC, Dale AM, Seiffert AE, Tootell RBH. Functional MRI reveals spatially specific attentional modulation in human primary visual cortex. Proc. Natl. Acad. Sci. U. S. A. 2006;96:1663–8.CrossRef
93.
go back to reference Wood G, Nuerk HC, Willmes K. Neural representations of two-digit numbers: A parametric fMRI study. Neuroimage. 2006;29:358–67.CrossRefPubMed Wood G, Nuerk HC, Willmes K. Neural representations of two-digit numbers: A parametric fMRI study. Neuroimage. 2006;29:358–67.CrossRefPubMed
94.
go back to reference Müller NG, Kleinschmidt A. Dynamic interaction of object-and space-based attention in retinotopic visual areas. J. Neurosci. 2003;23:9812–6.CrossRefPubMed Müller NG, Kleinschmidt A. Dynamic interaction of object-and space-based attention in retinotopic visual areas. J. Neurosci. 2003;23:9812–6.CrossRefPubMed
95.
go back to reference Raij T, Uutela K, Hari R. Audiovisual integration of letters in the human brain. Neuron. 2000;28:617–25.CrossRefPubMed Raij T, Uutela K, Hari R. Audiovisual integration of letters in the human brain. Neuron. 2000;28:617–25.CrossRefPubMed
96.
go back to reference Van Atteveldt N, Formisano E, Goebel R, Blomert L. Integration of letters and speech sounds in the human brain. Neuron. 2004;43:271–82.CrossRefPubMed Van Atteveldt N, Formisano E, Goebel R, Blomert L. Integration of letters and speech sounds in the human brain. Neuron. 2004;43:271–82.CrossRefPubMed
97.
go back to reference Ainsworth S. DeFT: A conceptual framework for considering learning with multiple representations. Learn. Instr. 2006;16:183–98.CrossRef Ainsworth S. DeFT: A conceptual framework for considering learning with multiple representations. Learn. Instr. 2006;16:183–98.CrossRef
98.
go back to reference Lortie-Forgues H, Tian J, Siegler RS. Why is learning fraction and decimal arithmetic so difficult? Dev. Rev. 2015;38:201–21.CrossRef Lortie-Forgues H, Tian J, Siegler RS. Why is learning fraction and decimal arithmetic so difficult? Dev. Rev. 2015;38:201–21.CrossRef
99.
go back to reference Obersteiner A, Dresler T, Bieck SM, Moeller K. Understanding Fractions: Integrating Results from Mathematics Education, Cognitive Psychology, and Neuroscience. In: Norton A, Alibali MW, editors. Constr. Number - Merging Perspect. from Psychol. Math. Educ. Heidelberg: Springer; 2018. Obersteiner A, Dresler T, Bieck SM, Moeller K. Understanding Fractions: Integrating Results from Mathematics Education, Cognitive Psychology, and Neuroscience. In: Norton A, Alibali MW, editors. Constr. Number - Merging Perspect. from Psychol. Math. Educ. Heidelberg: Springer; 2018.
100.
go back to reference Swan M. Dealing with misconceptions in mathematics. In: Gates P, editor. Issues Math. Teach. London: Routledge/Falmer; 2001. p. 147–65. Swan M. Dealing with misconceptions in mathematics. In: Gates P, editor. Issues Math. Teach. London: Routledge/Falmer; 2001. p. 147–65.
Metadata
Title
Magnitude processing of symbolic and non-symbolic proportions: an fMRI study
Authors
Julia Mock
Stefan Huber
Johannes Bloechle
Julia F. Dietrich
Julia Bahnmueller
Johannes Rennig
Elise Klein
Korbinian Moeller
Publication date
01-12-2018
Publisher
BioMed Central
Published in
Behavioral and Brain Functions / Issue 1/2018
Electronic ISSN: 1744-9081
DOI
https://doi.org/10.1186/s12993-018-0141-z

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