Symbolic representations and cardinal knowledge in 3- and 4-year-old children

Baillargeon, 2012, Core cognition and beyond: The acquisition of physical and numerical knowledge, 33 Barner, 2010, Inference and exact numerical representation in early language development, Cognitive Psychology, 60, 40, 10.1016/j.cogpsych.2009.06.002 Bialystok, 1996, Developing representations of quantity, Canadian Journal of Behavioural Science, 28, 281, 10.1037/0008-400X.28.4.281 Condry, 2008, The development of language and abstract concepts: The case of natural number, Journal of Experimental Psychology, 137, 22, 10.1037/0096-3445.137.1.22 Cragg, 2014, Skills underlying mathematics: The role of executive function in the development of mathematics proficiency, Trends in Neuroscience and Education, 3, 63, 10.1016/j.tine.2013.12.001 Cragg, 2017, Direct and indirect influences of executive functions on mathematics achievement, Cognition, 162, 12, 10.1016/j.cognition.2017.01.014 DeLoache, 1987, Rapid change in the symbolic functioning of very young children, Science, 238, 1556, 10.1126/science.2446392 DeLoache, 1991, Symbolic functioning in very young children: Understanding of pictures and models, Child Development, 62, 736, 10.2307/1131174 DeLoache, 1995, Early understanding and use of symbols: The model model, Current Directions in Psychological Science, 4, 109, 10.1111/1467-8721.ep10772408 DeLoache, 2002, Symbolic artefacts: Understanding and use, 206 Fuson, 1988 Gelman, 1978 Gelman, 2005, Mother-child conversations about pictures and objects: Referring to categories and individuals, Child Development, 76, 1129, 10.1111/j.1467-8624.2005.00876.x-i1 Gibson, 1979 Huang, 2010, When is four far more than three? Children’s generalization of newly-acquired number words, Psychological Science, 21, 600, 10.1177/0956797610363552 Hurst, 2017, Mapping among number words, numerals, and nonsymbolic quantities in pre-schoolers, Journal of Cognition and Development, 18, 41, 10.1080/15248372.2016.1228653 Huttenlocher, 1994, Assessing early arithmetic abilities: Effects of verbal and nonverbal response types on the calculation performance of middle-and low-income children, Learning and Individual Differences, 6, 413, 10.1016/1041-6080(94)90003-5 Ittelson, 1996, Visual perception of markings, Psychonomic Bulletin & Review, 3, 171, 10.3758/BF03212416 Le Corre, 2007, One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles, Cognition, 105, 395, 10.1016/j.cognition.2006.10.005 Martí, 2003 Martí, 2015, Semiotic systems, culture an early mathematical knowledge, Studies in Psychology, 36, 1, 10.1080/02109395.2014.1000008 Marzolf, 1994, Transfer in young children’s understanding of spatial representations, Child Development, 65, 1, 10.2307/1131361 McNeil, 2009, Should you show me the money? Concrete objects both hurt and help performance on mathematics problems, Learning and Instruction, 19, 171, 10.1016/j.learninstruc.2008.03.005 Mix, 2008, Children’s equivalence judgments: Crossmapping effects, Cognitive Development, 23, 191, 10.1016/j.cogdev.2007.03.001 Mix, 2002 Mix, 2011, One-to-one play promotes numerical equivalence concepts, Journal of Cognition and Development, 12, 463, 10.1080/15248372.2011.554928 Nicoladis, 2010, Are number gestures easier than number words for preschoolers?, Cognitive Development, 25, 247, 10.1016/j.cogdev.2010.04.001 Petersen, 2012, Effects of perceptually rich manipulatives on preschoolers’ counting performance: Established knowledge counts, Child Development, 84, 1020, 10.1111/cdev.12028 Petersen, 2014, Counting practice with pictures, but not objects, improves children’s understanding of cardinality, Proceedings of the Thirty-Sixth Annual Conference of the Cognitive Science Society Piaget, 1941 Salsa, 2015, Objects, pictures and words. Effects of representational format on four-year-olds’ quantity knowledge, Studies in Psychology, 36, 71, 10.1080/02109395.2014.1000031 Sarnecka, 2015, Learning to represent exact numbers, Synthese, 1 Sarnecka, 2008, How counting represents number: What children must learn and when they learn it, Cognition, 108, 662, 10.1016/j.cognition.2008.05.007 Sarnecka, 2009, Levels of number knowledge during early childhood, Journal of Experimental Child Psychology, 103, 325, 10.1016/j.jecp.2009.02.007 Sfard, 2000, Symbolizing mathematical reality into being: How mathematical discourse and mathematical objects create each other, 37 Sfard, 2005, Why cannot children see as the same what grown-ups cannot see as different? Early numerical thinking revisited, Cognition and Instruction, 23, 237, 10.1207/s1532690xci2302_3 Tolchinsky, 2003 Uttal, 2013, It works both ways: Transfer difficulties between manipulatives and written subtractions solutions, Child Development Research, 1, 10.1155/2013/216367 Wagner, 2011, An association between understanding cardinality and analog magnitude representations in pre-schoolers, Cognition, 119, 10, 10.1016/j.cognition.2010.11.014 Walkerdine, 1988 Wiese, 2003, Iconic and non-iconic stages in number development: The role of language, Trends in Cognitive Sciences, 7, 385, 10.1016/S1364-6613(03)00192-X Wynn, 1990, Children’s understanding of counting, Cognition, 36, 155, 10.1016/0010-0277(90)90003-3 Wynn, 1992, Children’s acquisition of the number words and the counting system, Cognitive Psychology, 24, 220, 10.1016/0010-0285(92)90008-P