The representation of fraction magnitudes and the whole number bias reconsidered
Tài liệu tham khảo
Bonato, 2007, The mental representation of numerical fractions: real or integer?, Journal of Experimental Psychology: Human Perception and Performance, 33, 1410
Christou, 2012, What kinds of numbers do students assign to literal symbols? Aspects of the transition from arithmetic to algebra, Mathematical Thinking and Learning, 14, 1, 10.1080/10986065.2012.625074
Dehaene, 1998, Abstract representations of numbers in the animal and human brain, Trends in Neurosciences, 21, 355, 10.1016/S0166-2236(98)01263-6
Dehaene, 1990, Is numerical comparison digital? Analog and symbolic effects in two-digit number comparison, Journal of Experimental Psychology: Human Perception and Performance, 16, 626
Desmet, 2010, Developmental changes in the comparison of decimal fractions, Learning and Instruction, 20, 521, 10.1016/j.learninstruc.2009.07.004
DeWolf, 2014, Magnitude comparison with different types of rational numbers, Journal of Experimental Psychology: Human Perception and Performance, 40, 71
DeWolf, 2011, The whole number bias in fraction magnitude comparisons in adults, 1751
Dunbar, 2007, Do naïve theories ever go away?, 193
Evans, 2013, Dual-process theories of higher cognition: advancing the debate, Perspectives on Psychological Science, 8, 223, 10.1177/1745691612460685
Fazio, L. K., DeWolf, M., & Siegler, R. S. Strategy use and strategy choice in fraction magnitude comparison (submitted for publication).
Fazio, 2011, Teaching fractions, Vol. 22, 1
Fischbein, 1985, The role of implicit models in solving verbal problems in multiplication and division, Journal for Research in Mathematics Education, 16, 3, 10.2307/748969
Gallistel, 2000, Nonverbal numerical cognition: from reals to integers, Trends in Cognitive Sciences, 4, 59, 10.1016/S1364-6613(99)01424-2
Gillard, 2009, Dual processes in the psychology of mathematics education and cognitive psychology, Human Development, 52, 95, 10.1159/000202728
Hartnett, 1998, Early understandings of numbers: paths or barriers to the construction of new understanding?, Learning and Instruction, 8, 341, 10.1016/S0959-4752(97)00026-1
Holyoak, 1978, Comparative judgments with numerical reference points, Cognitive Psychology, 10, 203, 10.1016/0010-0285(78)90014-2
Inagaki, 2008, Conceptual change in naïve biology, 240
Kallai, 2009, A generalized fraction: an entity smaller than one on the mental number line, Journal of Experimental Psychology: Human Perception and Performance, 35, 1845
Kallai, 2012, When meaningful components interrupt the processing of the whole: the case of fractions, Acta Psychologica, 139, 358, 10.1016/j.actpsy.2011.11.009
Mack, 1995, Confounding whole-number and fraction concepts when building on informal knowledge, Journal for Research in Mathematics Education, 26, 422, 10.2307/749431
Martin, 2007
Meert, 2009, Rational numbers: componential vs. holistic representation of fractions in a magnitude comparison task, Quarterly Journal of Experimental Psychology, 62, 1598, 10.1080/17470210802511162
Meert, 2010, Comparing 5/7 and 2/9: adults can do it by accessing the magnitude of the whole fractions, Acta Psychologica, 135, 284, 10.1016/j.actpsy.2010.07.014
Moyer, 1967, 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
Obersteiner, 2013, The natural number bias and magnitude representation in fraction comparison by expert mathematicians, Learning and Instruction, 28, 64, 10.1016/j.learninstruc.2013.05.003
Peled, 2009, Journey to the past: verifying and modifying the conceptual sources of decimal fraction knowledge, Canadian Journal of Science, Mathematics and Technology Education, 9, 73, 10.1080/14926150902908776
Resnick, 1989, Conceptual bases of arithmetic errors: the case of decimal fractions, Journal for Research in Mathematics Education, 20, 8, 10.2307/749095
Schneider, 2010, Representations of the magnitudes of fractions, Journal of Experimental Psychology: Human Perception and Performance, 36, 1227
Shtulman, 2012, Scientific knowledge suppresses but does not supplant earlier intuitions, Cognition, 124, 209, 10.1016/j.cognition.2012.04.005
Siegler, 2013, Fractions: the new frontier for theories of numerical development, Trends in Cognitive Sciences, 17, 13, 10.1016/j.tics.2012.11.004
Siegler, 2011, An integrated theory of whole number and fractions development, Cognitive Psychology, 62, 273, 10.1016/j.cogpsych.2011.03.001
Smith, 2005, Never getting to zero: elementary school students' understanding of the infinite divisibility of number and matter, Cognitive Psychology, 51, 101, 10.1016/j.cogpsych.2005.03.001
Sprute, 2010, Representations of fractions: evidence for accessing the whole magnitude in adults, Mind, Brain, and Education, 5, 42, 10.1111/j.1751-228X.2011.01109.x
Stacey, 2001, Preservice teachers' knowledge of difficulties in decimal numeration, Journal of Mathematics Teacher Education, 4, 205, 10.1023/A:1011463205491
Stacey, 1998, Refining the classification of students' interpretations of decimal notation, Hiroshima Journal of Mathematics Education, 6, 49
Stafylidou, 2004, The development of students' understanding of numerical value of fractions, Learning and Instruction, 14, 503, 10.1016/j.learninstruc.2004.06.015
Steinle, 1998, The incidence of misconceptions of decimal notation amongst students in Grades 5 to 10, 548
Vamvakoussi, 2012, Naturally biased? In search for reaction time evidence for a natural number bias in adults, The Journal of Mathematical Behavior, 31, 344, 10.1016/j.jmathb.2012.02.001
Vamvakoussi, 2010, How many decimals are there between two fractions? Aspects of secondary school students' understanding of rational numbers and their notation, Cognition and Instruction, 28, 181, 10.1080/07370001003676603
Van Hoof, 2013, Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks, Research in Mathematics Education, 15, 154, 10.1080/14794802.2013.797747
Vosniadou, 2013, Conceptual change in learning and instruction: the framework theory approach, 11
Vosniadou, 2013
Vosniadou, 2013, Conceptual change from the framework theory side of the fence, Science & Education, 1
Vosniadou, 2008, The framework theory approach to the problem of conceptual change
Vosniadou, 2004, Extending the conceptual change approach to mathematics learning and teaching, Learning and Instruction, 14, 445, 10.1016/j.learninstruc.2004.06.014