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===Criticisms of Piaget's theoretical ideas=== Piaget's theories have not gone without scrutiny. A figure whose ideas contradicted Piaget's ideas was the Russian psychologist [[Lev Vygotsky]]. Vygotsky stressed the importance of a child's cultural background as an effect on the stages of development. Because different cultures stress different social interactions, this challenged Piaget's theory that the hierarchy of learning development had to develop in succession. Vygotsky introduced the term [[Zone of proximal development]] as an overall task a child would have to develop that would be too difficult to develop alone. Also, the so-called [[neo-Piagetian theories of cognitive development]] maintained that Piaget's theory does not do justice either to the underlying mechanisms of [[Information processing (psychology)|information processing]] that explain transition from stage to stage or [[individual differences]] in cognitive development. According to these theories, changes in information processing mechanisms, such as [[cognitive processing speed|speed of processing]] and [[working memory]], are responsible for ascension from stage to stage. Moreover, differences between individuals in these processes explain why some individuals develop faster than other individuals ([[Demetriou]], 1998). Over time, alternative theories of child development have been put forward, and empirical findings have done a lot to undermine Piaget's theories. For example, Esther Thelen and colleagues<ref>{{Cite journal | last1 = Spencer | first1 = J. P. | last2 = Clearfield | first2 = M. | last3 = Corbetta | first3 = D. | last4 = Ulrich | first4 = B. | last5 = Buchanan | first5 = P. | last6 = Schöner | first6 = G. | doi = 10.1111/j.1467-8624.2006.00955.x | title = Moving Toward a Grand Theory of Development: In Memory of Esther Thelen | journal = Child Development | volume = 77 | issue = 6 | pages = 1521–1538 | year = 2006 | pmid = 17107442| citeseerx = 10.1.1.531.5232 }}</ref> found that babies would not make the [[A-not-B error]] if they had small weights added to their arms during the first phase of the experiment that were then removed before the second phase of the experiment. This minor change should not impact babies' understanding of object permanence, so the difference that this makes to babies' performance on the A-not-B task cannot be explained by Piagetian theory. Thelen and colleagues also found that various other factors also influenced performance on the A-not-B task (including strength of memory trace, salience of targets, waiting time and stance), and proposed that this could be better explained using a [[dynamic systems theory]] approach than using Piagetian theory. [[Alison Gopnik]] and Betty Repacholi<ref>{{cite journal | title = Early reasoning about desires: Evidence from 14- and 18-month-olds | journal = Developmental Psychology | year = 1997 | first = Betty | last = Repacholi |author2=Alison Gopnik | volume = 3 | issue = 1 | pages = 12–21| doi=10.1037/0012-1649.33.1.12 | pmid = 9050386}}</ref> found that babies as young as 18 months old can understand that other people have desires, and that these desires could be very different from their own desires. This contradicts Piaget's view that children are very egocentric at this age. Modern cognitive science had undermined Piaget's view that young children are unable to comprehend numbers as they are not able to work with abstract concepts in the sensorimotor stage. This Piagetian view has led many educators to believe that it is not appropriate to teach simple arithmetic to young children as it will not lead to real understanding.<ref name="Dehaene 2011">{{cite book |last1=Dehaene |first1=Stanislas |title=The Number Sense: How the Mind Creates Mathematics |edition=2 |location=New York |publisher=Oxford University Press |year=2011 |isbn=978-0-19-975387-1 }}</ref> Experiments by Starkey et al. have shown that children have an understanding of abstract numbers from as young as 6 months old while more recent studies by Izard et al. have shown that even newborns can perceive abstract numbers.<ref name="StarkeySpelke1990">{{cite journal|last1=Starkey|first1=Prentice|last2=Spelke|first2=Elizabeth S.|last3=Gelman|first3=Rochel|title=Numerical abstraction by human infants|journal=Cognition|volume=36|issue=2|year=1990|pages=97–127|issn=0010-0277|doi=10.1016/0010-0277(90)90001-Z|pmid=2225757|s2cid=706365}}</ref><ref name="IzardSann2009">{{cite journal|last1=Izard|first1=V.|last2=Sann|first2=C.|last3=Spelke|first3=E.S.|last4=Streri|first4=A.|title=Newborn infants perceive abstract numbers|journal=Proceedings of the National Academy of Sciences|volume=106|issue=25|year=2009|pages=10382–10385|issn=0027-8424|doi=10.1073/pnas.0812142106|pmid=19520833|pmc=2700913|bibcode=2009PNAS..10610382I|doi-access=free}}</ref> For a full discussion of this, see [[Stanislas Dehaene|Stanislas Dehaene's]] ''The Number Sense: How the Mind Creates Mathematics''.<ref name="Dehaene 2011" /> Some supporters of Piaget counter that his critics' arguments depend on misreadings of Piaget's theory.<ref name="lm">{{Cite journal | doi = 10.1037/0033-295X.103.1.143 | last1 = Lourenço | first1 = O. | last2 = Machado | first2 = A. | year = 1996 | title = In defense of Piaget's theory: A reply to ten common criticisms | journal = Psychological Review | volume = 103 | issue = 1| pages = 143–164 | s2cid = 32390745 | url = http://pdfs.semanticscholar.org/2dec/e70e2b917d7e3f846db9285878811d1ddbe3.pdf | archive-url = https://web.archive.org/web/20200410214048/http://pdfs.semanticscholar.org/2dec/e70e2b917d7e3f846db9285878811d1ddbe3.pdf | archive-date = 2020-04-10 }}</ref> See also [[Brian Rotman]]'s ''Jean Piaget: Psychologist of the Real'', an exposition and critique of Piaget's ideas, and Jonathan Tudge and Barbara Rogoff's "Peer influences on cognitive development: Piagetian and Vygotskian perspectives".<ref>{{cite book |chapter-url=https://books.google.com/books?id=RnWym5-bm8kC&pg=PA32 |title=Lev Vygotsky: Critical Assessments, Volume 3 |first1=Jonathan |last1=Tudge |author2=Barbara Rogoff |editor1=Peter Lloyd |editor2=Charles Fernyhough |publisher=Routledge |year=1998 |chapter=Peer influences on cognitive development: Piagetian and Vygotskian perspectives |isbn=978-0-415-11154-6 }}</ref>
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