Selective Interference of Finger Movements on Basic Addition and Subtraction Problem Solving
Abstract
Fingers offer a practical tool to represent and manipulate numbers during the acquisition of arithmetic knowledge, usually with a greater involvement in addition and subtraction than in multiplication. In adults, brain-imaging studies show that mental arithmetic increases activity in areas known for their contribution to finger movements. It is unclear, however, if this truly reflects functional interactions between the processes and/or representations controlling finger movements and those involved in mental arithmetic, or a mere anatomical proximity. In this study we assessed whether finger movements interfere with basic arithmetic problem solving, and whether this interference is specific for the operations that benefit the most from finger-based calculation strategies in childhood. In Experiment 1, we asked participants to solve addition, subtraction, and multiplication problems either with their hands at rest or while moving their right-hand fingers sequentially. The results showed that finger movements induced a selective time cost in solving addition and subtraction but not multiplication problems. In Experiment 2, we asked participants to solve the same problems while performing a sequence of foot movements. The results showed that foot movements produced a nonspecific interference with all three operations. Taken together, these findings demonstrate the specific role of finger-related processes in solving addition and subtraction problems, suggesting that finger movements and mental arithmetic are functionally related.
References
(2010). The role of the dorsal visual processing stream in tool identification. Psychological Science, 21, 772–778.
(2010). Neural reuse: A fundamental organizational principle of the brain. Behavioral and Brain Sciences, 33, 245–266.
(2012). Common substrate for mental arithmetic and finger representation in the parietal cortex. NeuroImage, 62, 1520–1528.
(2007). Contribution of motor circuits to counting. Journal of Cognitive Neuroscience, 19, 563–576.
(2010). Creating number semantics through finger movement perception. Cognition, 115, 46–53.
(2011). Finger-number interaction: An ideomotor account. Experimental Psychology, 58, 287–292.
(2010). Response-effect compatibility of finger-numeral configurations in arithmetical context. The Quarterly Journal of Experimental Psychology, 63, 16–22.
(1987). The development of counting strategies for single-digit addition. Journal for Research in Mathematics Education, 18, 41–157.
(2001). The arithmetic tie effect is mainly encoding-based. Cognition, 82, B15–B24.
(1997). Attentional resources in timing: Interference effects in concurrent temporal and nontemporal working memory tasks. Perception & Psychophysics, 59, 1118–1140.
(1999). A head for figures. Science, 284, 928–929.
(2002). Calculation, culture, and the repeated operand effect. Cognition, 86, 71–96.
(2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299–315.
(1988). Acquisition of mental multiplication skill; Evidence for the transition between counting and retrieval strategies. Cognition and Instruction, 5, 323–345.
(2011). A hand full of numbers: A role for offloading in arithmetics learning? Frontiers in Psychology, 2, 368. doi: 10.3389/fpsyg.2011.00368
(2011). The role of vision in the development of finger-number interactions: Finger-counting and finger-monitoring in blind children. Journal of Experimental Child Psychology, 109, 525–539.
(1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83–120.
(2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487–506.
(1996). Cerebral activations during number multiplication and comparison: A PET study. Neuropsychologia, 34, 1097–1106.
(2006). Finger-digit compatibility in Arabic numeral processing. The Quarterly Journal of Experimental Psychology, 59, 1648–1663.
(2010). Absence of low-level visual difference between canonical and noncanonical finger-numeral configurations. Experimental Psychology, 57, 202–207.
(2008). Mind the gap between both hands: Evidence for internal finger-based number representations in children’s mental calculation. Cortex, 44, 359–367.
(2012). A common right fronto-parietal network for numerosity and duration processing: An fMRI study. Human Brain Mapping, 33, 1490–1501.
(2006). Numerosity-duration interference: A Stroop experiment. Acta Psychologica, 121, 109–124.
(1998). Footedness is a better predictor of language lateralization than handedness. Laterality, 3, 41–51.
(1998). Predicting arithmetical achievement from neuropsychological performance: A longitudinal study. Cognition, 68, 63–70.
(2010). Numerical performance increased by finger training: A fallacy due to regression toward the mean? Cortex, 46, 272–273.
(1982). An analysis of the counting-on solution procedure in addition. In , Addition and subtraction: A cognitive perspective (pp. 67–81). Hillsdale, NJ: Erlbaum.
(1988). Children’s counting and the concepts of number. New York, NY: Springer.
(1940). Syndrome of finger agnosia, disorientation for right and left, agraphia, acalculia. Archives of Neurology and Psychology, 44, 398–408.
(2008). Does finger training increase young children’s numerical performance? Cortex, 44, 544–560.
(1999). The role of gesture in children’s learning to count. Journal of Experimental Child Psychology, 74, 333–355.
(2005). Interactions between numbers and space in parietal cortex. Nature Reviews Neuroscience, 6, 435–448.
(2011). Passive hand movements disrupt adults’ counting strategies. Frontiers in Psychology, 2, 201. doi: 10.3389/fpsyg.2011.00201
(2011). The influence of implicit hand-based representations on mental arithmetic. Frontiers in Psychology, 2, 197. doi: 10.3389/fpsyg.2011.00197
(2009). Recruitment of an area involved in eye movements during mental arithmetic. Science, 324, 1583–1585.
(2002). Arithmetic operation and working memory: Differential suppression in dual tasks. Cognition, 83, B63–B68.
(1996). Multiple routes to solution of single-digit multiplication problems. Journal of Experimental Psychology: General, 125, 284–306.
(1994). Using confidence intervals in within-subject designs. Psychonomic Bulletin & Review, 1, 476–490.
(1999). A pure case of Gerstmann syndrome with a subangular lesion. Brain, 122, 1107–1120.
(1986). Do our mathematics textbooks reflect what we preach? School Science and Mathematics, 86, 591–596.
(2010). Let us redeploy attention to sensorimotor experience? Behavioral and Brain Sciences, 33, 283–284.
(2011). Representation of multiplication facts – evidence for partial verbal coding. Behavioral and Brain Functions, 7, 25. doi: 10.1186/1744-9081-7-25
(2005). Finger gnosia: A predictor of numerical abilities in children? Child Neuropsychology, 11, 413–430.
(1971). The assessment and analysis of handedness: The Edinburgh Inventory. Neuropsychologia, 9, 97–113.
(2008). An alternative view of the relation between finger gnosis and math ability: Redeployment of finger representations for the representation of number. In , Proceedings of the 30th Annual Meeting of the Cognitive Science Society (pp. 1647–1652). Austin, TX: Cognitive Science Society.
(2000). Neuroanatomical substrate of Arabic number processing, numerical comparison and simple addition: A PET study. Journal of Cognitive Neuroscience, 12, 461–479.
(2008). Mental movements without magnitude? A study of spatial biases in symbolic arithmetic. Cognition, 109, 408–415.
(2011). Five- to 7-year-olds’ finger gnosia and calculation abilities. Frontiers in Psychology, 2, 359. doi: 10.3389/fpsyg.2011.00359
(2009). A disconnection account of Gerstmann syndrome: Functional neuroanatomy evidence. Annals of Neurology, 66, 654–662.
(2007). Numbers within our hands: Modulation of corticospinal excitability of hand muscles during numerical judgment. Journal of Cognitive Neuroscience, 19, 684–693.
(2002). E-Prime user’s guide. Pittsburgh, PA: Psychology Software Tools.
(1987). The role of learning in children’s strategy choices. In , Development and learning: Conflict and congruence? (pp. 71–107). Hillsdale, NJ: Erlbaum.
(1984). Strategy choices in addition and subtraction: How do children know what to do? In , Origins of cognitive skills (pp. 229–293). Hillsdale, NJ: Erlbaum.
(2010). Body-specific representations of action verbs: Neural evidence from right- and left-handers. Psychological Science, 21, 67–74.
(2001). Neural correlates of simple and complex mental calculation. NeuroImage, 13, 314–327.
