O que as pesquisas em educação matemática apontam sobre estimativas numéricas de crianças?

Referencias

Azevedo, M. M. D. O. (2016). A Aprendizagem da Estimação Matemática: um estudo no 2o ciclo. Dissertação de Mestrado. Lisboa: Universidade Nova de Lisboa. Barth, H. C. & Paladino, A. M. (2011). The Development of Numerical Estimation: evidence against a representational shift. Developmental Science, 14, 125- 135. Berch, D. B. (2005). Making Sense of Number Sense. Journal of Learning Disabilities, 38(4), 333-339. Berteletti, I. et al. (2010). Numerical Estimation in Preschoolers. Developmental Psychology, 46 (2), 545–551. Booth, J. L. & Siegler, R. S. (2006). Developmental and Individual Differences in Pure Numerical Estimation. Developmental Psychology, 41, 189–201. Booth, J. L. & Siegler, R. S. (2008). Numerical Magnitude Representations Influence Arithmetic Learning. Child Development, 79 (4), 1016 – 1031. Corso, L. V. & Dorneles, B. V. (2010). Senso Numérico e Dificuldades de Aprendizagem na Matemática. Revista Psicopedagogia, 27, 298-309. Crites, T. W. (1992). Skilled and Less Skilled Estimators’ Strategies for Estimating Discrete Quantities. Elementary School Journal, 5, 601–619. Dackermann, T. et al. (2015). An Integration of Competing Accounts on Children’s Number Line Estimation. Frontiers in Psychology, 6 (884). Dehaene, S. (1997). The Number Sense: How the mind creates mathematics. New York: Oxford University Press. Dehaene, S. et al. (2008). Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures. Stanislas Science, 320, 1217. Dorneles, B. V. et al. (2017). Number Estimation in Children: an assessment study with number line estimation and numerosity tasks. In Congress of the European Society for Research in Mathematics Education (CERME), 10., 2017, Dublin City University. Ebersbach, M. et al. (2008). The Relationship Between the Shape of the Mental Number Line and Familiarity with Numbers in 5- to 9-Year Old Children: Evidence for a segmented linear model. Journal of Experimental Child Psychology, 99, 1–17. Ebersbach, M., Luwel, K. & Verschaffel, L. (2015). The Relationship Between Children’s Familiarity with Numbers and Their Performance in Bounded and Unbounded Number Line Estimations. Mathematical Thinking and Learning, 17, 136-154. Feigenson, L., Libertus, M. E. & Halberda, J. (2013). Links Between the Intuitive Sense of Number and Formal Mathematics Ability. Child Development Perspectives, 7 (2), 74–79. Gandini, D., Ardiale, E.& Lemaire, P. (2010). Children’ Strategies in Approximate Quantification. Current Psychology Letters: Behaviour, Brain, & Cognition, 26, 1–14. Gandini, D., Lemaire, P. & Dufau, F. (2008). Older and Younger Adults’ Strategies in Approximate Quantification. Acta Psychologica, 129, 175–189. Gebuis, T. & Reynvoet, B. (2012). The Role of Visual Information in Numerosity Estimation. PLoS One, 7(5). Gibbon, J. & Church, R. M. (1981). Time Left: Linear Versus Logarithmic Subjective Time. Journal of Experimental Psychology: Animal Behavior Processes, 7(2), 87-108. Gilmore, C., Mccarthy, S. & Spelke, E. (2010). Non-symbolic Arithmetic Abilities and Achievement in the First Year of Formal Schooling in Mathematics. Cognition, 115(3), 394–406. Halberda, J. & Feigenson, L. (2008). Developmental Change in the Acuity of the “Number Sense": the approximate number system in 3, 4, 5, and 6-year-olds and adults. Developmental Psychology, 44, 1457-1465. Huntley-Fenner, G. (2001). Children's Understanding of Number is Similar to Adults' and Rats': numerical estimation by 5±7-year-olds. Cognition, 78, B27-B40. Jordan, N. C. et al. (2006). Number Sense Growth in Kindergarten: a longitudinal investigation of children at risk of mathematics difficulties. Child Development, 77, 153-175. Kovas, Y., Giampietro, V., Viding, E., Ng, V., Brammer, M., Barker, G. J., Happe, F. G. E. & Plomin, R. (2009). Brain Correlates of Non-Symbolic Numerosity Estimation in Low and High Mathematical Ability Children. PlosOne, 4(2). Laski, E. V. & Siegler, R. S. (2007). Is 27 a Big Number? Correlational and Causal Connections Among Numerical Categorization, Number Line Estimation, and Numerical Magnitude Comparison. Child Development, 78 (6), 1723 – 1743. Lefevre, J. et al. (2013). Charting the Role of the Number Line in Mathematical Development. Front. Psychol, 4. Lemaire, P. & Siegler, R. (1995). Four Aspects of Strategic Change: contributions to children’s learning of multiplication. Journal of Experimental Psychology: General, 124 (1), 83-97. Levine, D. R. (1982). Strategy Use and Estimation Ability of College Students. Journal for Research in Mathematics Education, 13, 350-359. Libertus, M., Feigenson, L. & Halberda, J. (2011). Preschool Acuity of the Approximate Number System Correlates with School Math Ability. Developmental Science, 14:6, 1292–1300. Link, T., Nuerk, H. & Moeller, K. (2014). On the Relation Between the Mental Number Line and Arithmetic Competencies. The Quarterly Journal of Experimental Psychology, 67:8, 1597-1613. Lipton, J. S. & Spelke, E. S. (2005). Preschool Children’s Mapping of Number Words to Nonsymbolic Numerosities. Child Development, 76:5, 978 – 988. Luwel, K. et al. (2001). Using Segmented Linear Regression Models with Unknown Change Points to Analyze Strategy Shifts in Cognitive Tasks. Behavior Research Methods, Instruments, & Computers, 33 (4), 470-478. Luwel, K. et al. (2009). Strengths and Weaknesses of the Choice/No-Choice Method in Research on Strategy Use. European Psychologist, 14(4), 351–362. Luwel, K. & Verschaffel, L. (2003). Adapting Strategy Choices to Situational Factors: the effect of time pressure on children’s numerosity judgement strategies. Psychologica Belgica, 43, 269-295. Luwel, K. & Verschaffel, L. (2008). Analyzing Strategy Use in Terms of the Four Parameters of Strategic Competence: contributions from a numerosity judgment task. Anales de Psicología, 24(2), 223-239. Luwel, K. et al. (2000). Children's Strategies for Numerosity Judgment in Square Grids of Different Sizes. Psychologica Belgica, 40 (3), 183-209. Matejko, A. A. & Ansari, D. (2016). Trajectories of Symbolic and Nonsymbolic Magnitude Processing in the First Year of Formal Schooling. PlosOne, 1-15. Menzies, V. et al. (2013). A Longitudinal Analysis of Estimation, Counting Skills, and Mathematical Ability Across the First School Year. Developmental Psychology, 49 (2), 250–257. Moeller, K. et al. (2009). Children’s Early Mental Number Line: Logarithmic or decomposed linear? Journal of Experimental Child Psychology, 103 (4), 503–515. Muldoon, K. et al. (2011). Cross-Cultural Comparisons of 5-Year-Olds’ Estimating and Mathematical Ability. Journal of Cross-Cultural Psychology, 42(4), 669–681. Nuerk, H. C. et al. (2004). On the Development of the Mental Number Line: More, Less, or Never Holistic with Increasing Age? Developmental Psychology, 40(6), 1199–1211. Obersteiner, A. et al. (2014). Do First Graders Make Efficient Use of External Number Representations? The Case of the Twenty-Frame. Cognition and Instruction, 32(4), 353–373. Opfer, J. & Siegler, R. (2007). Representational change and children’s numerical estimation. Cognitive Psychology, 55, 169–195. Park, J. & Brannon, E. M. (2013). Training the Approximate Number System Improves Math Proficiency. Psychol Sci, 24(10), 2013-9. Peeters, D., Verschaffel, L. & Luwel, K. (2016). Benchmark-Based Strategies in Whole Number Line Estimation. British Journal of Psychology. Revkin, S. K. et al. (2008). Does Subitizing Reflect Numerical Estimation? Psychological Science, 19(6), 607-614. Rousselle, L. & Noel, M. P. (2008). The Development of Automatic Numerosity Processing in Preschoolers: evidence for numerosity-perceptual interference. Developmental Psychology, 44(2), 544-560. Sasanguie, D. & Reynvoet, B. (2013). Number Comparison and Number Line Estimation Rely on Different Mechanisms. Psychologica Belgica, 53:4, 17-35. Sasanguie, D. et al. (2016). The Development of Symbolic and Non-Symbolic Number Line Estimations: three developmental accounts contrasted within cross-sectional and longitudinal data. Psychologica Belgica, 56(4), 382–405. Schillemans, V. et al. (2009). The Influence of Previous Strategy Use on Individuals’ Subsequent Strategy Choice: findings from a numerosity judgement task. Psychologica Belgica, 49(4), 191-205. Schillemans, V. et al. (2011). The Influence of the Previous Strategy on Individuals' Strategy Choices. Studia psychologica, 53(4), 339-350. Schneider, M., Grabner, R. H. & Paetsch, J. (2009). Mental Number Line, Number Line Estimation, and Mathematical Achievement: their interrelations in grades 5 and 6. Journal of Educational Psychology, 101, 359–372. Siegel, A. W., Goldsmith, T. H. & Madson, C. R. (1982). Skill in Estimation Problems of Extent and Numerosity. Journal for Research in Mathematics Education, 13, 211–232. Siegler, R. S. & Booth, J. L. (2004). Development of Numerical Estimation in Young Children. Child Development, 75, 428–444. Siegler, R. & Booth, J. L. (2005). Development of Numerical Estimation: a review. In Campbell, J. I. D. (2005). Handbook of Mathematical Cognition. Psychology Press: New York. Cap. 2, p. 197-212. Siegler, R. & Lemaire, P. (1997). Older and Younger Adult’s Strategy Choices in Multiplication: testing predictions of ASCM using the choice/no-choice method. Journal of Experimental Psychology: General, 126 (1), 71-92. Siegler, R. S. & Mu, Y. (2008). Chinese Children Excel on Novel Mathematics Problems Even Before Elementary School. Psychological Science, 19, 759-763. Siegler, R. S. & Opfer, J. E. (2003). The Development of Numerical Estimation: evidence for multiple representations of numerical quantity. Psychological Science, 14, 237-243. Starkey, P. & Cooper, R. G. (1980). Perception of Numbers by Human Infants. Science, 210, 1033–1035. Thompson, C. A. & Siegler, R. S. (2010). Linear Numerical-Magnitude Representations Aid Children’s Memory for Numbers. Psychological Science, 21(9), 1274–1281. Verschaffel, L. et al. (1998). The Acquisition and Use of an Adaptive Strategy for Estimating Numerosity. European Journal of Psychology of Educuation, 13, 347-370. White, S. L. J. & SzűC, D. (2012). Representational Change and Strategy Use in Children’s Number Line Estimation During the First Years of Primary School. Behavioral and Brain Functions, 8:1. Xu, X. et al. (2013). Development of Numerical Estimation in Chinese Preschool Children. Journal of Experimental Child Psychology, 116, 351–366.