Operational Momentum in Numerosity Production Judgments of Multi-Digit Number Problems
Abstract
The current study demonstrates a numerosity production task and investigates approximate mental calculations with two-digit numbers. Participants were required to produce random dot patterns to indicate the size of two-digit numbers and the results of addition and subtraction problems. The stimuli in the calculation task consisted of problems requiring a carry operation (e.g., 24 + 18) or no-carry problems (e.g., 24 + 53) or zero problems (e.g., 24 + 0). Our analysis revealed that the outcomes of additions were estimated to be larger than the outcomes of subtractions. Interestingly, this judgment bias was present for no-carry and zero problems but not for carry problems. Taken together, the presented data provide empirical support for the presence of an operational momentum effect (OM effect) in multi-digit number arithmetic. These findings and the dissociation of the OM effect for carry and no-carry problems are discussed in the context of recent models on multi-digit number processing.
References
(1991). Occupancy model of perceived numerosity. Perception and Psychophysics, 49, 303–314.
(1998). Stimulus-response compatibility in representational space. Neuropsychologia, 36, 731–735.
(2001). Variability signatures distinguish verbal from nonverbal counting for both large and small numbers. Psychonomic Bulletin and Review, 8, 698–707.
(1997). The number sense. Oxford, UK: Oxford University Press.
(2009). Origins of mathematical intuitions: The case of arithmetic. Annals of the New York Academy of Sciences, 1156, 232–259.
(2005). The addition of two-digit numbers: Exploring carry versus no-carry problems. Psychological Science, 47, 74–83.
(2004). The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 16, 353–386.
(1995). Texture Density Adaptation and the Perceived Numerosity and Distribution of Texture. Journal of Experimental Psychology: Human Perception and Performance, 21, 149–169.
(2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 9, 175–191.
(2006). The future for SNARC could be stark. Cortex, 42, 1066–1068.
(1984). Representational momentum. Journal of Experimental Psychology, 10, 126–132.
(2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435–448.
(2007). The role of working memory in the carry operation of mental arithmetic: Number and value of the carry. Quarterly Journal of Experimental Psychology, 60, 708–731.
(2008). Calibrating the mental number line. Cognition, 106, 1221–1247.
(2007). Working memory demands of exact and approximate addition. European Journal of Cognitive Psychology, 18, 187–212.
(2009). Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect. Attention, Perception and Psychophysics, 71, 803–21.
(2007). Getting a grip on numbers: Numerical magnitude priming in object grasping. Journal of Experimental Psychology: Human Perception and Performance, 33, 1400–1409.
(2008). Coding strategies in number space: Memory requirements influence spatial-numerical associations. Quarterly Journal of Experimental Psychology, 61, 515–524.
(1990). Regression analyses of repeated measures data in cognitive research. Journal of Experimental Psychology: Learning, Memory, and Cognition, 16, 149–157.
(2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Perception & Psychophysics, 69, 1324–1333.
(2011). Extending the mental number line: A review of multi-digit number processing. Zeitschrift für Psychologie / Journal of Psychology, 219, 3–22.
(2005). On the magnitude representations of two-digit numbers. Psychology Science, 47, 52–72.
(2008). Mental movements without magnitude? A study of spatial biases in symbolic arithmetic. Cognition, 109, 408–415.
(1973). Absolute error: The devil in disguise. Journal of Motor Behavior, 5, 141–153.
(2003). Nonlinear regression. New York, NY: Wiley.
(2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–243.
(1999). Nonverbal counting in Humans: The psychophysics of number representation. Psychological Science, 10, 130–137.
(2005). Linkages between number concepts, spatial thinking, and directionality of writing: The SNARC effect and the REVERSE SNARC effect in English and Arabic monoliterates, biliterates, and illiterate Arabic speakers. Journal of Cognition and Culture, 5, 165–190.
(1995). A representational analysis of numeration systems. Cognition, 57, 271–295.
