{"id":"https://openalex.org/W2395465232","doi":null,"title":"Mathematical Model of Developmental Changes in Number Cognition.","display_name":"Mathematical Model of Developmental Changes in Number Cognition.","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2395465232","mag":"2395465232"},"language":"en","primary_location":{"id":"pmh:oai:escholarship.org:ark:/13030/qt5zv3m5kx","doi":null,"is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/5zv3m5kx","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the Annual Meeting of the Cognitive Science Society, vol 37, iss 0","raw_type":"article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010660024","display_name":"Richard Prather","orcid":"https://orcid.org/0000-0002-5538-3032","observed_orcids":["https://orcid.org/0000-0002-5538-3032"]},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Richard Prather","raw_affiliation_strings":["University of Maryland - College Park"],"raw_orcid":"https://orcid.org/0000-0002-5538-3032","affiliations":[{"raw_affiliation_string":"University of Maryland - College Park","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010660024"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11345","display_name":"Cognitive and developmental aspects of mathematical skills","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11345","display_name":"Cognitive and developmental aspects of mathematical skills","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10656","display_name":"Child and Animal Learning Development","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11577","display_name":"Cognitive Abilities and Testing","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/approximate-number-system","display_name":"approximate number system","score":0.953000009059906},{"id":"https://openalex.org/keywords/weber-fraction","display_name":"Weber fraction","score":0.6970000267028809},{"id":"https://openalex.org/keywords/numerical-discrimination","display_name":"number discrimination","score":0.7450000047683716},{"id":"https://openalex.org/keywords/ratio-effect","display_name":"ratio effect","score":0.7480000257492065},{"id":"https://openalex.org/keywords/children","display_name":"children","score":0.43700000643730164},{"id":"https://openalex.org/keywords/mathematical-ability","display_name":"mathematical ability","score":0.4699999988079071},{"id":"https://openalex.org/keywords/mathematics-achievement","display_name":"mathematics achievement","score":0.34200000762939453},{"id":"https://openalex.org/keywords/reaction-time","display_name":"reaction time","score":0.5019999742507935},{"id":"https://openalex.org/keywords/mathematics-anxiety","display_name":"mathematics anxiety","score":0.35600000619888306},{"id":"https://openalex.org/keywords/mathematics-self-concept","display_name":"mathematics self-concept","score":0.4429999887943268},{"id":"https://openalex.org/keywords/mathematics-self-efficacy","display_name":"mathematics self-efficacy","score":0.5479999780654907},{"id":"https://openalex.org/keywords/mathematics-teacher-beliefs","display_name":"teacher beliefs about mathematics","score":0.4050000011920929},{"id":"https://openalex.org/keywords/mathematical-knowledge-for-teaching","display_name":"mathematical knowledge for teaching","score":0.453000009059906},{"id":"https://openalex.org/keywords/mathematics-teacher-education-program","display_name":"mathematics teacher education program","score":0.3050000071525574}],"concepts":[{"id":"https://openalex.org/C163950791","wikidata":"https://www.wikidata.org/wiki/Q1301091","display_name":"Numerosity adaptation effect","level":3,"score":0.9490360021591187},{"id":"https://openalex.org/C45768438","wikidata":"https://www.wikidata.org/wiki/Q337432","display_name":"Numerical cognition","level":3,"score":0.8125547766685486},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.5697668790817261},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5141370892524719},{"id":"https://openalex.org/C26760741","wikidata":"https://www.wikidata.org/wiki/Q160402","display_name":"Perception","level":2,"score":0.48769912123680115},{"id":"https://openalex.org/C180747234","wikidata":"https://www.wikidata.org/wiki/Q23373","display_name":"Cognitive psychology","level":1,"score":0.45763683319091797},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.4451790153980255},{"id":"https://openalex.org/C169900460","wikidata":"https://www.wikidata.org/wiki/Q2200417","display_name":"Cognition","level":2,"score":0.43820568919181824},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.40172287821769714},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37508171796798706},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.09119352698326111},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:escholarship.org:ark:/13030/qt5zv3m5kx","doi":null,"is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/5zv3m5kx","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the Annual Meeting of the Cognitive Science Society, vol 37, iss 0","raw_type":"article"},{"id":"mag:2395465232","doi":null,"is_oa":false,"landing_page_url":"https://mindmodeling.org/cogsci2015/papers/0329/paper0329.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S78735424","display_name":"Cognitive Science","issn_l":"0364-0213","issn":["0364-0213","1551-6709"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-c","erih-plus","jufo-2","ki-jl-2","medline","norway-2","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Cognitive Science","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1528058320","https://openalex.org/W1966951272","https://openalex.org/W1970465408","https://openalex.org/W2011069740","https://openalex.org/W2014481741","https://openalex.org/W2057716394","https://openalex.org/W2059787294","https://openalex.org/W2089231967","https://openalex.org/W2094055797","https://openalex.org/W2097058229","https://openalex.org/W2102589218","https://openalex.org/W2106119216","https://openalex.org/W2107188560","https://openalex.org/W2121003285","https://openalex.org/W2144274054","https://openalex.org/W2144821625","https://openalex.org/W2162825757","https://openalex.org/W2171175639","https://openalex.org/W2504110702"],"related_works":["https://openalex.org/W2087456386","https://openalex.org/W639002133","https://openalex.org/W7096088051","https://openalex.org/W2095102375","https://openalex.org/W2613128663","https://openalex.org/W4241562944","https://openalex.org/W7135060285","https://openalex.org/W3109811306","https://openalex.org/W2097058229","https://openalex.org/W2071599215"],"abstract_inverted_index":{"The":[0,245,307,385],"acuity":[1,326,361],"of":[2,74,89,106,130,157,170,180,221,236,279,282,309,320,324,366,370],"individuals\u2019":[3],"approximate":[4],"number":[5,224],"system":[6],"(ANS)":[7],"is":[8,22,38,83,109,146,168,217,250,276,289,349,356,362,400],"measured":[9],"using":[10],"a":[11,178,331],"non-symbolic":[12,75,380],"numerical":[13,107,153,286,321,325,360,402,426,439],"discrimination":[14,154,287,381,403,427],"task":[15,37,68],"(e.g.,":[16,51,100,187,194,204],"Halberda":[17],"&":[18,30,58,62,102,190,198,206],"Feigenson,":[19],"2008)":[20],"which":[21,348,379],"encapsulated":[23],"by":[24],"the":[25,115,131,164,213,218,234,272,280,302,358,363,376,396,421,435],"Weber":[26],"Fraction":[27],"measure":[28,365],"(Piazza":[29],"Dehaene,":[31],"2004).":[32,208],"Children\u2019s":[33],"performance":[34,151,334,343],"on":[35,114,152,285,335,406],"this":[36,67],"linked":[39],"to":[40,111,269,318,329,333,378,394,424],"symbolic":[41],"arithmetic":[42],"skills,":[43],"standardized":[44],"test":[45],"scores":[46],"and":[47,77,138,143,159,167,182,201,239,262,300,337,391,416],"other":[48,92,122,338,383],"long-term":[49],"outcomes":[50],"Beddington":[52],"et":[53],"al.,":[54],"2008;":[55],"Libertus,":[56],"Odic,":[57],"Halberda,":[59],"2012;":[60],"Parsons":[61],"Bynner,":[63],"1997).":[64],"To":[65],"complete":[66],"individuals":[69],"must":[70],"perceive":[71],"relative":[72,80],"quantity":[73],"numerosity":[76],"indicate":[78],"their":[79],"values.":[81],"Numerosity":[82],"typically":[84,252,351],"presented":[85],"visually":[86],"as":[87,95,136],"sets":[88],"objects,":[90],"though":[91],"modalities":[93],"such":[94,135,292,310],"sound":[96],"have":[97],"been":[98,175],"used":[99,328],"Jordan":[101],"Brannon,":[103],"2006).":[104],"Discriminability":[105],"stimuli":[108],"thought":[110],"depend":[112],"solely":[113,404],"ratio-difference":[116],"between":[117,247,413],"values":[118,373],"being":[119],"compared":[120],"if":[121,291,301],"perceptual":[123],"factors":[124,422],"are":[125,140,267,315,327],"controlled":[126],"for.":[127],"Thus":[128,149],"comparison":[129,225],"same":[132],"ratio":[133,165,216,237,260,407,414],"difference,":[134],"20:25":[137],"40:50":[139],"equally":[141],"discriminable":[142],"absolute":[144,171,228,240,248,265,283,346,372,417],"value":[145,229,241,249,266,284],"not":[147,231,251,350],"relevant.":[148],"individual":[150],"in":[155,177,223,264,313],"terms":[156],"accuracy":[158],"reaction":[160],"time":[161],"varies":[162,304,344],"with":[163,185,210,258,298,430],"differences":[166,261],"independent":[169],"value.":[172],"This":[173],"has":[174],"shown":[176],"range":[179],"behavioral":[181,389,444],"neural":[183,436],"data":[184,255],"adults":[186,211],"Barth,":[188,195],"Kanwisher,":[189],"Spelke,":[191,199],"2003),":[192],"children":[193,314],"Mont,":[196],"Lipton,":[197],"2005)":[200],"non-human":[202],"primates":[203],"Nieder":[205],"Miller,":[207],"Research":[209],"contradicts":[212],"account":[214,441],"that":[215],"sole":[219],"predictor":[220],"discriminability":[222],"task.":[226],"Though":[227,274],"does":[230,242],"predict":[232],"discriminability,":[233],"interaction":[235,246,412],"difference":[238,408,415],"(Prather,":[243],"2014).":[244],"reported":[253,359],"because":[254],"including":[256],"comparisons":[257],"small":[259],"variations":[263],"needed":[268],"clearly":[270],"show":[271],"effect.":[273],"there":[275],"initial":[277],"evidence":[278],"effect":[281,294,303,312],"it":[288,355],"unclear":[290,357],"an":[293,311,411],"would":[295],"be":[296],"present":[297],"children,":[299],"across":[305,345],"development.":[306],"consequences":[308],"directly":[316],"relevant":[317],"measures":[319],"acuity.":[322],"Measures":[323],"evaluate":[330],"correlation":[332],"symbolic,":[336],"educational":[339],"outcomes.":[340,384],"If":[341],"children\u2019s":[342,401,425],"value,":[347,418],"accounted":[352],"for,":[353],"then":[354],"\u201ctrue\u201d":[364],"participants\u2019":[367],"accuracy.":[368],"Inclusion":[369],"varying":[371],"may":[374],"change":[375,429],"degree":[377],"predicts":[382],"current":[386],"study":[387],"employs":[388],"experimentation":[390],"computational":[392],"modeling":[393],"address":[395],"following":[397],"questions:":[398],"1)":[399],"dependent":[405],"or":[409],"also":[410],"2)":[419],"do":[420],"contributing":[423],"difficulty":[428],"development,":[431],"3)":[432],"how":[433],"might":[434],"coding":[437],"involved":[438],"perception":[440],"for":[442],"these":[443],"effects?":[445]},"counts_by_year":[],"updated_date":"2026-09-04T10:56:28.161419","created_date":"2016-06-24T00:00:00"}