{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T18:11:21Z","timestamp":1774030281121,"version":"3.50.1"},"reference-count":84,"publisher":"Wiley","issue":"9","license":[{"start":{"date-parts":[[2024,9,25]],"date-time":"2024-09-25T00:00:00Z","timestamp":1727222400000},"content-version":"am","delay-in-days":390,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#am"},{"start":{"date-parts":[[2023,9,25]],"date-time":"2023-09-25T00:00:00Z","timestamp":1695600000000},"content-version":"vor","delay-in-days":24,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100000181","name":"AF Office of Scientific Research","doi-asserted-by":"publisher","award":["F4FGA07074G001"],"award-info":[{"award-number":["F4FGA07074G001"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N0001416WX00762"],"award-info":[{"award-number":["N0001416WX00762"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Cognitive Science"],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The common view of the transition between subitizing and numerosity estimation regimes is that there is a hard bound on the subitizing range, and beyond this range, people estimate. However, this view does not adequately address the behavioral signatures of enumeration under conditions of attentional load or in the immediate post\u2010subitizing range. The possibility that there might exist a numerosity range where both processes of subitizing and estimation operate in conjunction has so far been ignored. Here, we investigate this new proposal, that people strategically combine the processes of subitizing and estimation to maximize accuracy and precision, given time or attentional constraints. We present a process\u2010level account of how subitizing and estimation can be combined through strategic deployment of attention to maximize the precision of perceived numerosity given time constraints. We then describe a computational model of this account and apply it in two experimental simulations to demonstrate how it can explain key findings in prior enumeration research. While recent modeling work has argued that the behavioral signatures of enumeration can best be explained through a single numerosity system with a single form of representation, we argue that our model demonstrates how the traditional two\u2010systems view of numerical representation accounts for behavioral data through coordination with a unified attentional mechanism, rather than a unified\u00a0representation.<\/jats:p>","DOI":"10.1111\/cogs.13337","type":"journal-article","created":{"date-parts":[[2023,9,25]],"date-time":"2023-09-25T18:03:52Z","timestamp":1695665032000},"update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Attentional Strategies and the Transition From Subitizing to Estimation in Numerosity Perception"],"prefix":"10.1111","volume":"47","author":[{"given":"Gordon","family":"Briggs","sequence":"first","affiliation":[{"name":"Navy Center for Applied Research in Artificial Intelligence U.S. Naval Research Laboratory"}]},{"given":"Andrew","family":"Lovett","sequence":"additional","affiliation":[{"name":"Navy Center for Applied Research in Artificial Intelligence U.S. Naval Research Laboratory"}]},{"given":"Will","family":"Bridewell","sequence":"additional","affiliation":[{"name":"Navy Center for Applied Research in Artificial Intelligence U.S. Naval Research Laboratory"}]},{"given":"Paul F.","family":"Bello","sequence":"additional","affiliation":[{"name":"Navy Center for Applied Research in Artificial Intelligence U.S. Naval Research Laboratory"}]}],"member":"311","published-online":{"date-parts":[[2023,9,25]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cub.2004.01.029"},{"key":"e_1_2_11_3_1","volume-title":"Task switching, stimulus\u2010response bindings, and negative priming","author":"Allport A.","year":"2000"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1037\/dev0000448"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-020-68111-1"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1177\/0956797613501520"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1177\/0301006615602599"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1167\/15.5.4"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tics.2012.06.010"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00426-019-01265-4"},{"key":"e_1_2_11_11_1","first-page":"1","volume-title":"Proceedings of the 4th Annual Conference on Advances in Cognitive Systems","author":"Bridewell W.","year":"2016"},{"key":"e_1_2_11_12_1","first-page":"1672","volume-title":"Proceedings of the 39th Annual Meeting of the Cognitive Science Society","author":"Briggs G.","year":"2017"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13414-019-01969-0"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1167\/10.6.20"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cognition.2020.104195"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1819956116"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41562-020-00946-0"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1002\/wcs.136"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tine.2013.12.001"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.3758\/PP.70.5.789"},{"key":"e_1_2_11_21_1","volume-title":"The number sense: How the mind creates mathematics","author":"Dehaene S. (2011)"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cogdev.2005.09.004"},{"key":"e_1_2_11_23_1","doi-asserted-by":"publisher","DOI":"10.1080\/13506280801937939"},{"key":"e_1_2_11_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tics.2004.05.002"},{"key":"e_1_2_11_25_1","doi-asserted-by":"publisher","DOI":"10.1080\/13506280500193545"},{"key":"e_1_2_11_26_1","doi-asserted-by":"publisher","DOI":"10.1037\/0096-1523.18.4.1030"},{"key":"e_1_2_11_27_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.neuro.051508.135603"},{"key":"e_1_2_11_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.actpsy.2016.09.003"},{"key":"e_1_2_11_29_1","doi-asserted-by":"publisher","DOI":"10.4159\/9780674037533"},{"key":"e_1_2_11_30_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-7687.2011.01050.x"},{"key":"e_1_2_11_31_1","doi-asserted-by":"publisher","DOI":"10.1037\/a0012682"},{"key":"e_1_2_11_32_1","doi-asserted-by":"publisher","DOI":"10.1162\/jocn.2010.21581"},{"key":"e_1_2_11_33_1","doi-asserted-by":"publisher","DOI":"10.1038\/003281a0"},{"key":"e_1_2_11_34_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-07515-0_17"},{"key":"e_1_2_11_35_1","doi-asserted-by":"publisher","DOI":"10.1167\/17.13.11"},{"key":"e_1_2_11_36_1","doi-asserted-by":"publisher","DOI":"10.2307\/1418556"},{"key":"e_1_2_11_37_1","doi-asserted-by":"publisher","DOI":"10.1038\/334430a0"},{"key":"e_1_2_11_38_1","doi-asserted-by":"publisher","DOI":"10.1177\/0734282908330586"},{"key":"e_1_2_11_39_1","doi-asserted-by":"publisher","DOI":"10.3758\/BF03206218"},{"key":"e_1_2_11_40_1","doi-asserted-by":"publisher","DOI":"10.1037\/cep0000070"},{"key":"e_1_2_11_41_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13414-017-1409-3"},{"key":"e_1_2_11_42_1","doi-asserted-by":"publisher","DOI":"10.1037\/xlm0000347"},{"key":"e_1_2_11_43_1","doi-asserted-by":"publisher","DOI":"10.1167\/19.14.23"},{"key":"e_1_2_11_44_1","doi-asserted-by":"publisher","DOI":"10.1038\/36846"},{"key":"e_1_2_11_45_1","doi-asserted-by":"publisher","DOI":"10.1037\/0096-3445.111.1.1"},{"key":"e_1_2_11_46_1","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/9780262514620.001.0001"},{"key":"e_1_2_11_47_1","doi-asserted-by":"publisher","DOI":"10.3389\/fnhum.2015.00162"},{"key":"e_1_2_11_48_1","doi-asserted-by":"publisher","DOI":"10.1162\/jocn_a_00349"},{"key":"e_1_2_11_49_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13414-020-02137-5"},{"key":"e_1_2_11_50_1","doi-asserted-by":"publisher","DOI":"10.1002\/9781118920497.ch2"},{"key":"e_1_2_11_51_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cub.2008.04.021"},{"key":"e_1_2_11_52_1","doi-asserted-by":"publisher","DOI":"10.1037\/a0029472"},{"key":"e_1_2_11_53_1","doi-asserted-by":"publisher","DOI":"10.1080\/13506280701825861"},{"key":"e_1_2_11_54_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuropsychologia.2018.05.006"},{"key":"e_1_2_11_55_1","doi-asserted-by":"publisher","DOI":"10.3758\/BF03200760"},{"key":"e_1_2_11_56_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jecp.2018.01.019"},{"key":"e_1_2_11_57_1","doi-asserted-by":"publisher","DOI":"10.1207\/s15516709cog2401_3"},{"key":"e_1_2_11_58_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cognition.2011.05.007"},{"key":"e_1_2_11_59_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13414-019-01831-3"},{"key":"e_1_2_11_60_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13414-019-01804-6"},{"key":"e_1_2_11_61_1","doi-asserted-by":"publisher","DOI":"10.1038\/nn1989"},{"key":"e_1_2_11_62_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cognition.2007.08.004"},{"key":"e_1_2_11_63_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9280.1997.tb00427.x"},{"key":"e_1_2_11_64_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9280.2008.02130.x"},{"issue":"2","key":"e_1_2_11_65_1","first-page":"193","article-title":"Enumeration processes of children with mathematical difficulties: An explorative eye\u2010tracking study on subitizing, groupitizing, counting, and pattern recognition","volume":"18","author":"Schindler M.","year":"2020","journal-title":"Learning Disabilities\u2013A Contemporary Journal"},{"key":"e_1_2_11_66_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13414-016-1221-5"},{"key":"e_1_2_11_67_1","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-385948-8.00018-9"},{"key":"e_1_2_11_68_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jecp.2014.03.006"},{"key":"e_1_2_11_69_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00426-011-0323-x"},{"key":"e_1_2_11_70_1","doi-asserted-by":"publisher","DOI":"10.3758\/BF03212078"},{"key":"e_1_2_11_71_1","doi-asserted-by":"publisher","DOI":"10.3758\/APP.71.6.1241"},{"key":"e_1_2_11_72_1","doi-asserted-by":"publisher","DOI":"10.1016\/0010-0285(80)90005-5"},{"key":"e_1_2_11_73_1","doi-asserted-by":"publisher","DOI":"10.1037\/0033-295X.101.1.80"},{"key":"e_1_2_11_74_1","doi-asserted-by":"publisher","DOI":"10.3758\/BF03213349"},{"key":"e_1_2_11_75_1","doi-asserted-by":"publisher","DOI":"10.1111\/desc.12495"},{"key":"e_1_2_11_76_1","doi-asserted-by":"publisher","DOI":"10.1037\/a0029333"},{"key":"e_1_2_11_77_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13423-021-02015-7"},{"key":"e_1_2_11_78_1","doi-asserted-by":"publisher","DOI":"10.1007\/s004260000021"},{"key":"e_1_2_11_79_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tics.2011.02.005"},{"key":"e_1_2_11_80_1","doi-asserted-by":"publisher","DOI":"10.3758\/BF03200774"},{"key":"e_1_2_11_81_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13423-020-01859-9"},{"key":"e_1_2_11_82_1","doi-asserted-by":"publisher","DOI":"10.3758\/BF03211924"},{"key":"e_1_2_11_83_1","doi-asserted-by":"publisher","DOI":"10.1016\/0010-0277(90)90003-3"},{"key":"e_1_2_11_84_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neulet.2008.05.063"},{"key":"e_1_2_11_85_1","doi-asserted-by":"publisher","DOI":"10.1037\/0096-1523.23.1.244"}],"container-title":["Cognitive Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/am-pdf\/10.1111\/cogs.13337","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/cogs.13337","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T17:55:11Z","timestamp":1695750911000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/10.1111\/cogs.13337"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9]]},"references-count":84,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2023,9]]}},"alternative-id":["10.1111\/cogs.13337"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1111\/cogs.13337","archive":["Portico"],"relation":{},"ISSN":["0364-0213","1551-6709"],"issn-type":[{"value":"0364-0213","type":"print"},{"value":"1551-6709","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9]]},"assertion":[{"value":"2021-11-05","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-08-23","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-09-25","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e13337"}}