Understanding decimal proportions: Discrete representations, parallel access, and privileged processing of zero

Baird, 1975, Psychophysical study of numbers: I. Generation of numerical responses, Psychology Research, 37, 281, 10.1007/BF00309723 Banks, 1976, Semantic congruity effects in comparative judgments of magnitudes of digits, Journal of Experimental Psychology: Human Perception and Performance, 2, 435, 10.1037/0096-1523.2.3.435 Bonato, 2007, The mental representation of numerical fractions: Real or integer?, Journal of Experimental Psychology: Human Perception and Performance, 33, 1410, 10.1037/0096-1523.33.6.1410 Butterworth, 2011, Dyscalculia: From brain to education, Science, 332, 1049, 10.1126/science.1201536 Cantlon, 2006, Functional imaging of numerical processing in adults and 4-y-old children, Public Library of Science Biology, 4, e125 Cohen, 2010, Evidence for direct retrieval of relative quantity information in a quantity judgment task: Decimals, integers, and the role of physical similarity, Journal of Experimental Psychology: Learning, Memory, and Cognition, 36, 1389, 10.1037/a0020212 De Smedt, 2009, The predictive value of numerical magnitude comparison for individual differences in mathematics achievement, Journal of Experimental Child Psychology, 103, 469, 10.1016/j.jecp.2009.01.010 Dehaene, 1993, The mental representation of parity and number magnitude, Journal of Experimental Psychology: General, 122, 371, 10.1037/0096-3445.122.3.371 Dehaene, 1990, Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison, Journal of Experimental Psychology: Human Perception and Performance, 16, 626, 10.1037/0096-1523.16.3.626 Dehaene, 1992, Cross-linguistic regularities in the frequency of number words, Cognition, 43, 1, 10.1016/0010-0277(92)90030-L Desmet, 2010, Developmental changes in the comparison of decimal fractions, Learning and Instruction, 20, 521, 10.1016/j.learninstruc.2009.07.004 DeWolf, 2011, The whole number bias in fraction magnitude comparison with adults, 1751 Eriksson, 2010, The grammar of approximating number pairs, Memory & Cognition, 38, 333, 10.3758/MC.38.3.333 Halberda, 2008, Individual differences in non-verbal number acuity correlate with maths achievement, Nature, 455, 665, 10.1038/nature07246 Henik, 1982, Is three greater than five: The relation between physical and semantic size in comparison tasks, Memory & Cognition, 10, 389, 10.3758/BF03202431 Hinrichs, 1982, Place information in multidigit number comparison, Memory & Cognition, 10, 487, 10.3758/BF03197652 Hinrichs, 1981, Two-digit number comparison: Use of place information, Journal of Experimental Psychology: Human Perception and Performance, 7, 890, 10.1037/0096-1523.7.4.890 Holyoak, 1978, Comparative judgments with numerical reference points, Cognitive Psychology, 10, 203, 10.1016/0010-0285(78)90014-2 Just, 1980, A theory of reading: From eye fixations to comprehension, Psychological Review, 87, 329, 10.1037/0033-295X.87.4.329 Korvorst, 2008, The differential influence of decades and units on multidigit number comparison, The Quarterly Journal of Experimental Psychology, 61, 1250, 10.1080/17470210701503286 Mazzocco, 2011, Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia), Child Development, 82, 1224, 10.1111/j.1467-8624.2011.01608.x McClelland, 1979, On the time relations of mental processes: An examination of systems of processes in cascade, Psychological Review, 86, 287, 10.1037/0033-295X.86.4.287 McCloskey, 1992, Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia, Cognition, 44, 107, 10.1016/0010-0277(92)90052-J Meert, 2009, Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task, The Quarterly Journal of Experimental Psychology, 62, 1598, 10.1080/17470210802511162 Moeller, 2009, Internal number magnitude representation is not holistic, either, European Journal of Cognitive Psychology, 21, 672, 10.1080/09541440802311899 Moyer, 1967, The time required for judgments of numerical inequality, Nature, 215, 1519, 10.1038/2151519a0 Ni, 2005, Teaching and learning fraction and rational numbers: The origins and implications of whole number bias, Educational Psychologist, 40, 27, 10.1207/s15326985ep4001_3 Nuerk, 2011, Extending the mental number line: A review of multi-digit number processing, Journal of Psychology, 219, 3, 10.1027/2151-2604/a000041 Nuerk, 2001, Decade breaks in the mental number line? Putting the tens and units back in different bins, Cognition, 82, B25, 10.1016/S0010-0277(01)00142-1 Nuerk, 2005, Language effects in magnitude comparison: Small, but not irrelevant, Brain and Language, 92, 262, 10.1016/j.bandl.2004.06.107 Parkman, 1971, Temporal aspects of digit and letter inequality judgments, Journal of Experimental Psychology, 91, 191, 10.1037/h0031854 Piazza, 2010, Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia, Cognition, 116, 33, 10.1016/j.cognition.2010.03.012 Pinel, 2001, Modulation of parietal activation by semantic distance in a number comparison task, NeuroImage, 14, 1013, 10.1006/nimg.2001.0913 Pollmann, 1996, The language user as an arithmetician, Cognition, 59, 219, 10.1016/0010-0277(95)00704-0 Poltrock, 1984, Comparative judgments of multidigit numbers, Journal of Experimental Psychology: Learning, Memory, and Cognition, 10, 32, 10.1037/0278-7393.10.1.32 Resnick, 1989, Conceptual bases of arithmetic errors: The case of decimal fractions, Journal for Research in Mathematics Education, 20, 8, 10.2307/749095 Sackur-Grisvar, 1985, Intermediate cognitive organizations in the process of learning a mathematical concept: The order of positive decimal numbers, Cognition and Instruction, 2, 157, 10.1207/s1532690xci0202_3 Schneider, 2010, Representations of the magnitudes of fractions, Journal of Experimental Psychology: Human Perception and Performance, 36, 1227, 10.1037/a0018170 Sekuler, 1977, Children’s judgments of numerical inequality, Child Development, 48, 630, 10.2307/1128664 Siegler, 2011, An integrated theory of whole number and fractions development, Cognitive Psychology, 62, 273, 10.1016/j.cogpsych.2011.03.001 Stafylidou, 2004, The development of students’ understanding of the numerical value of fractions, Learning and Instruction, 14, 503, 10.1016/j.learninstruc.2004.06.015 Van De Walle, 2004 Varma, 2011, The mental representation of integers: A symbolic to perceptual-magnitude shift, Cognition, 121, 363, 10.1016/j.cognition.2011.08.005 Verguts, 2005, Two-digit comparison: Decomposed, holistic, or hybrid?, Experimental Psychology, 52, 195, 10.1027/1618-3169.52.3.195 Wood, 2005, Deconstructing and reconstructing the base-10 structure of Arabic numbers, Psychology Science, 47, 84 Zhang, 2005, The effect of external representations on numeric tasks, The Quarterly Journal of Experimental Psychology, 58A, 817, 10.1080/02724980443000340 Zhou, 2008, Holistic or compositional representation of two-digit numbers? Evidence from the distance, magnitude, and SNARC effects of a number-matching task, Cognition, 106, 1525, 10.1016/j.cognition.2007.06.003