@Article{Rips2006,
  author   = {Lance J Rips and Jennifer Asmuth and Amber Bloomfield},
  journal  = {Cognition},
  title    = {Giving the boot to the bootstrap: how not to learn the natural numbers.},
  year     = {2006},
  number   = {3},
  pages    = {B51-60},
  volume   = {101},
  abstract = {According to one theory about how children learn the concept of natural
	numbers, they first determine that "one", "two", and "three" denote
	the size of sets containing the relevant number of items. They then
	make the following inductive inference (the Bootstrap): The next
	number word in the counting series denotes the size of the sets you
	get by adding one more object to the sets denoted by the previous
	number word. For example, if "three" refers to the size of sets containing
	three items, then "four" (the next word after "three") must refer
	to the size of sets containing three plus one items. We argue, however,
	that the Bootstrap cannot pick out the natural number sequence from
	other nonequivalent sequences and thus cannot convey to children
	the concept of the natural numbers. This is not just a result of
	the usual difficulties with induction but is specific to the Bootstrap.
	In order to work properly, the Bootstrap must somehow restrict the
	concept of "next number" in a way that conforms to the structure
	of the natural numbers. But with these restrictions, the Bootstrap
	is unnecessary.},
  doi      = {10.1016/j.cognition.2005.12.001},
  keywords = {Humans, Learning, Mathematics, 16412414},
}

{"_id":"LH33o2GLu5dPvczkd","bibbaseid":"rips-asmuth-bloomfield-givingtheboottothebootstraphownottolearnthenaturalnumbers-2006","authorIDs":[],"author_short":["Rips, L. J","Asmuth, J.","Bloomfield, A."],"bibdata":{"bibtype":"article","type":"article","author":[{"firstnames":["Lance","J"],"propositions":[],"lastnames":["Rips"],"suffixes":[]},{"firstnames":["Jennifer"],"propositions":[],"lastnames":["Asmuth"],"suffixes":[]},{"firstnames":["Amber"],"propositions":[],"lastnames":["Bloomfield"],"suffixes":[]}],"journal":"Cognition","title":"Giving the boot to the bootstrap: how not to learn the natural numbers.","year":"2006","number":"3","pages":"B51-60","volume":"101","abstract":"According to one theory about how children learn the concept of natural numbers, they first determine that \"one\", \"two\", and \"three\" denote the size of sets containing the relevant number of items. They then make the following inductive inference (the Bootstrap): The next number word in the counting series denotes the size of the sets you get by adding one more object to the sets denoted by the previous number word. For example, if \"three\" refers to the size of sets containing three items, then \"four\" (the next word after \"three\") must refer to the size of sets containing three plus one items. We argue, however, that the Bootstrap cannot pick out the natural number sequence from other nonequivalent sequences and thus cannot convey to children the concept of the natural numbers. This is not just a result of the usual difficulties with induction but is specific to the Bootstrap. In order to work properly, the Bootstrap must somehow restrict the concept of \"next number\" in a way that conforms to the structure of the natural numbers. But with these restrictions, the Bootstrap is unnecessary.","doi":"10.1016/j.cognition.2005.12.001","keywords":"Humans, Learning, Mathematics, 16412414","bibtex":"@Article{Rips2006,\n author = {Lance J Rips and Jennifer Asmuth and Amber Bloomfield},\n journal = {Cognition},\n title = {Giving the boot to the bootstrap: how not to learn the natural numbers.},\n year = {2006},\n number = {3},\n pages = {B51-60},\n volume = {101},\n abstract = {According to one theory about how children learn the concept of natural\n\tnumbers, they first determine that \"one\", \"two\", and \"three\" denote\n\tthe size of sets containing the relevant number of items. They then\n\tmake the following inductive inference (the Bootstrap): The next\n\tnumber word in the counting series denotes the size of the sets you\n\tget by adding one more object to the sets denoted by the previous\n\tnumber word. For example, if \"three\" refers to the size of sets containing\n\tthree items, then \"four\" (the next word after \"three\") must refer\n\tto the size of sets containing three plus one items. We argue, however,\n\tthat the Bootstrap cannot pick out the natural number sequence from\n\tother nonequivalent sequences and thus cannot convey to children\n\tthe concept of the natural numbers. This is not just a result of\n\tthe usual difficulties with induction but is specific to the Bootstrap.\n\tIn order to work properly, the Bootstrap must somehow restrict the\n\tconcept of \"next number\" in a way that conforms to the structure\n\tof the natural numbers. But with these restrictions, the Bootstrap\n\tis unnecessary.},\n doi = {10.1016/j.cognition.2005.12.001},\n keywords = {Humans, Learning, Mathematics, 16412414},\n}\n\n","author_short":["Rips, L. J","Asmuth, J.","Bloomfield, A."],"key":"Rips2006","id":"Rips2006","bibbaseid":"rips-asmuth-bloomfield-givingtheboottothebootstraphownottolearnthenaturalnumbers-2006","role":"author","urls":{},"keyword":["Humans","Learning","Mathematics","16412414"],"metadata":{"authorlinks":{}},"downloads":0},"bibtype":"article","biburl":"http://endress.org/publications/ansgar.bib","creationDate":"2020-01-31T01:09:11.758Z","downloads":0,"keywords":["humans","learning","mathematics","16412414"],"search_terms":["giving","boot","bootstrap","learn","natural","numbers","rips","asmuth","bloomfield"],"title":"Giving the boot to the bootstrap: how not to learn the natural numbers.","year":2006,"dataSources":["SzgNB6yMASNi6tysA","xPGxHAeh3vZpx4yyE"]}