Restricted accessResearch articleFirst published online 2017-06
The role of attentional networks in the access to the numerical magnitude of fractions in adults / El rol de las redes atencionales en el acceso a la magnitud numérica de fracciones en adultos
This study explored the relationship between the efficiency of alerting, orienting and executive control networks (attentional executive function) and accessing numerical magnitudes in adults, during a fraction comparison task, presenting pairs of fractions either with (CC) or without (WCC) common components. The results indicate that CC fractions are processed in a componential style, are affected by a whole number bias (WNB) and that performance in this block does not depend on the efficiency of attentional networks. By contrast, pairs of WCC fractions are processed in a holistic way, the WNB interacts with the numerical distance between fractions and performance in this block correlates with the efficiency of attentional orienting and executive control systems. Taken together, our findings show that the efficient selection of information and inhibitory control of intervening variables play an important role in processing fractions, particularly when the task requires the use of more holistic strategies to access the numerical magnitude of the fraction.
Get full access to this article
View all access options for this article.
References
1.
BarrazaP.GómezD. M.OyarzúnF.DartnellP. (2014). Long-distance neural synchrony correlates with processing strategies to compare fractions. Neuroscience Letters, 567, 40–44. doi:10.1016/j.neulet.2014.03.021
2.
BlairC.KnipeH.GamsonD. (2008). Is there a role for executive functions in the development of mathematics ability?Mind, Brain, and Education, 2, 80–89. doi:10.1111/j.1751-228X.2008.00036.x
3.
BonatoM.FabbriS.UmiltàC.ZorziM. (2007). The mental representation of numerical fractions: Real or integer?Journal of Experimental Psychology: Human Perception and Performance, 33, 1410 –1419
4.
CraggL.GilmoreC. (2014). Skills underlying mathematics: The role of executive function in the development of mathematics proficiency. Trends in Neuroscience and Education, 3, 63–68. doi:10.1016/j.tine.2013.12.001
5.
DehaeneS. (1997). The number sense. New York, NY: Oxford University Press.
6.
DehaeneS.KerszbergM.ChangeuxJ. P. (1998). A neuronal model of a global workspace in effortful cognitive tasks. Proceedings of the National Academy of Sciences, 95, 14529–14534. doi:10.1073/pnas.95.24.14529
7.
DeWolfM.VosniadouS. (2015). The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction, 37, 39–49. doi:10.1016/j.learninstruc.2014.07.002
FanJ.McCandlissB. D.SommerT.RazA.PosnerM. I. (2002). Testing the efficiency and independence of attentional networks. Journal of Cognitive Neuroscience, 14, 340–347. doi:10.1162/089892902317361886
11.
FazioL. K.DeWolfM.SieglerR. S. (2016). Strategy use and strategy choice in fraction magnitude comparison. Journal of Experimental Psychology: Learning, Memory, and Cognition, 42, 1–16
12.
GilmoreC.KeebleS.RichardsonS.CraggL. (2015). The role of cognitive inhibition in different components of arithmetic. ZDM, 47, 771–782. doi:10.1007/s11858-014-0659-y
13.
GómezD. M.JiménezA.BobadillaR.ReyesC.DartnellP. (2015). The effect of inhibitory control on general mathematics achievement and fraction comparison in middle school children. ZDM, 47, 801–811. doi:10.1007/s11858-015-0685-4
14.
HampelF. R.RonchettiE. M.RousseeuwP. J.StahelW. A. (2011). Robust statistics: The approach based on influence functions (Vol. 114). New York, NY: John Wiley & Sons.
15.
HofmannW.SchmeichelB. J.BaddeleyA. D. (2012). Executive functions and self-regulation. Trends in Cognitive Sciences, 16, 174–180. doi:10.1016/j.tics.2012.01.006
16.
HollandP. W.WelschR. E. (1977). Robust regression using iteratively reweighted least-squares. Communications in Statistics-Theory and Methods, 6, 813–827. doi:10.1080/03610927708827533
17.
IschebeckA.SchockeM.DelazerM. (2009). The processing and representation of fractions within the brain: An fMRI investigation. NeuroImage, 47, 403–413. doi:10.1016/j.neuroimage.2009.03.041
18.
KolkmanM. E.HoijtinkH. J.KroesbergenE. H.LesemanP. P. (2013). The role of executive functions in numerical magnitude skills. Learning and Individual Differences, 24, 145–151. doi:10.1016/j.lindif.2013.01.004
19.
MeertG.GrégoireJ.NoëlM. P. (2009). Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task. The Quarterly Journal of Experimental Psychology, 62, 1598–1616. doi:10.1080/17470210802511162
20.
MeertG.GrégoireJ.NoëlM. P. (2010). Comparing 5/7 and 2/9: Adults can do it by accessing the magnitude of the whole fractions. Acta Psychologica, 135, 284–292. doi:10.1016/j.actpsy.2010.07.014
21.
MoyerR. S.LandauerT. K. (1967). Time required for Judgements of Numerical Inequality. Nature, 215, 1519–1520. doi:10.1038/2151519a0
22.
NiY.ZhouY. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40, 27–52. doi:10.1207/s15326985ep4001_3
23.
ObersteinerA.Van DoorenW.Van HoofJ.VerschaffelL. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28, 64–72. doi:10.1016/j.learninstruc.2013.05.003
24.
PetersenS. E.PosnerM. I. (2012). The attention system of the human brain: 20 years after. Annual Review of Neuroscience, 35, 73–89. doi:10.1146/annurev-neuro-062111-150525
25.
PosnerM. I.PetersenS. E. (1990). The attention system of the human brain. Annual Review of Neuroscience, 13, 25–42. doi:10.1146/annurev.ne.13.030190.000325
26.
RatcliffR. (1993). Methods for dealing with reaction time outliers. Psychological Bulletin, 114, 510–532. doi:10.1037/0033-2909.114.3.510
27.
RothbartM. K.SheeseB. E.PosnerM. I. (2007). Executive attention and effortful control: Linking temperament, brain networks, and genes. Child Development Perspectives, 1, 2–7. doi:10.1111/cdep.2007.1.issue-1
28.
SchneiderM.SieglerR. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36, 1227–1238
29.
SpruteL.TempleE. (2011). Representations of fractions: Evidence for accessing the whole magnitude in adults. Mind, Brain, and Education, 5, 42–47. doi:10.1111/j.1751-228X.2011.01109.x
30.
VamvakoussiX.Van DoorenW.VerschaffelL. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31, 344–355. doi:10.1016/j.jmathb.2012.02.001
31.
Van HoofJ.LijnenT.VerschaffelL.Van DoorenW. (2013). Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks. Research in Mathematics Education, 15, 154–164. doi:10.1080/14794802.2013.797747
32.
ZhangL.FangQ.GabrielF. C.SzűcsD. (2016). Common magnitude representation of fractions and decimals is task dependent. The Quarterly Journal of Experimental Psychology, 69, 764–780. doi:10.1080/17470218.2015.1052525
