{"id":"https://openalex.org/W73040759","doi":null,"title":"Cognitive Units, Connections and Mathematical Proof","display_name":"Cognitive Units, Connections and Mathematical Proof","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W73040759","mag":"73040759"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.377.4875","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.4875","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1997d-barnard-cog-units.pdf","raw_type":"text"},"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/A5029115720","display_name":"Tony Barnard","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tony Barnard","raw_affiliation_strings":["King \u2018s College London"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"King \u2018s College London","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057983489","display_name":"David O. Tall","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"David Tall","raw_affiliation_strings":["University of Warwick"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warwick","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":17.6858,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.98783438,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"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/T12522","display_name":"Mathematics Education and Pedagogy","score":0.5038999915122986,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12522","display_name":"Mathematics Education and Pedagogy","score":0.5038999915122986,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.29269999265670776,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.06469999998807907,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"mathematical proof","score":0.9330000281333923},{"id":"https://openalex.org/keywords/cognitive-units","display_name":"cognitive units","score":0.9919999837875366},{"id":"https://openalex.org/keywords/cognitive-structure","display_name":"cognitive structure","score":0.7910000085830688},{"id":"https://openalex.org/keywords/attention","display_name":"attention","score":0.6460000276565552},{"id":"https://openalex.org/keywords/deductive-reasoning","display_name":"deductive reasoning","score":0.8320000171661377},{"id":"https://openalex.org/keywords/decision-making","display_name":"decision-making","score":0.675000011920929},{"id":"https://openalex.org/keywords/cognitive-psychology-of-mathematics","display_name":"cognitive psychology of mathematics","score":0.42100000381469727}],"concepts":[{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5935899615287781},{"id":"https://openalex.org/C169900460","wikidata":"https://www.wikidata.org/wiki/Q2200417","display_name":"Cognition","level":2,"score":0.5748029351234436},{"id":"https://openalex.org/C2777019708","wikidata":"https://www.wikidata.org/wiki/Q1412340","display_name":"Irrationality","level":3,"score":0.5403251051902771},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5167735815048218},{"id":"https://openalex.org/C128394911","wikidata":"https://www.wikidata.org/wiki/Q1987578","display_name":"Unit interval","level":2,"score":0.47073400020599365},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4465548098087311},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42725670337677},{"id":"https://openalex.org/C188147891","wikidata":"https://www.wikidata.org/wiki/Q147638","display_name":"Cognitive science","level":1,"score":0.36294275522232056},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3495962619781494},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.18949410319328308},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.15909209847450256},{"id":"https://openalex.org/C201717286","wikidata":"https://www.wikidata.org/wiki/Q938185","display_name":"Rationality","level":2,"score":0.12776389718055725},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.12042132019996643},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.377.4875","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.4875","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1997d-barnard-cog-units.pdf","raw_type":"text"},{"id":"mag:73040759","doi":null,"is_oa":false,"landing_page_url":"https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1997d-barnard-cog-units.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"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":4,"referenced_works":["https://openalex.org/W82428586","https://openalex.org/W2049926613","https://openalex.org/W2072267223","https://openalex.org/W2146640773"],"related_works":["https://openalex.org/W7098420017","https://openalex.org/W2096302832","https://openalex.org/W1528055171","https://openalex.org/W173301169","https://openalex.org/W7095863790","https://openalex.org/W2404896623","https://openalex.org/W3021520900","https://openalex.org/W2976262706","https://openalex.org/W1535630130","https://openalex.org/W2182562172"],"abstract_inverted_index":{"Mathematical":[0],"proof":[1,43,60,82,103],"seems":[2],"attractive":[3],"to":[4,8,44,70,91,122],"some,":[5],"yet":[6],"impenetrable":[7],"others.":[9],"In":[10],"this":[11],"paper":[12],"a":[13,30,63,72,115,156,162,164,172,185,187],"theory":[14,75],"is":[15,76,104,120,170,183],"suggested":[16],"involving":[17],"\u201ccognitive":[18],"units":[19,97],"\u201d":[20],"which":[21],"can":[22,141],"be":[23,45,142,154,161],"the":[24,36,58,80,84,92,107,111,145],"conscious":[25],"focus":[26,146],"of":[27,67,83,86,94,102,110,137,147,179],"attention":[28,131,148],"at":[29,150],"given":[31],"time":[32,152],"and":[33,65,88,98,129],"connections":[34,99],"in":[35,144,189],"individual\u2019s":[37],"cognitive":[38,138,157],"structure":[39,109,139],"that":[40,140],"allow":[41],"deductive":[42],"formulated.":[46],"Whilst":[47],"elementary":[48],"mathematics":[49],"often":[50],"involves":[51],"sequential":[52],"algorithms":[53],"where":[54],"each":[55],"step":[56,188],"cues":[57],"next,":[59],"also":[61],"requires":[62],"selection":[64],"synthesis":[66],"alternative":[68],"paths":[69],"make":[71],"deduction.":[73],"The":[74,100],"illustrated":[77],"by":[78,106,125],"considering":[79],"standard":[81],"irrationality":[85,93],"\u221a2":[87],"its":[89],"generalisation":[90],"\u221a3.":[95],"Cognitive":[96],"logic":[101],"handled":[105],"biological":[108],"human":[112],"brain.":[113],"As":[114],"multiprocessing":[116],"system,":[117],"complex":[118],"decision-making":[119],"reduced":[121],"manageable":[123],"levels":[124],"suppressing":[126],"inessential":[127],"detail":[128],"focusing":[130],"on":[132],"important":[133],"information.":[134],"A":[135],"piece":[136],"held":[143],"all":[149],"one":[151],"will":[153],"called":[155],"unit.":[158],"This":[159],"might":[160],"symbol,":[163],"specific":[165],"fact":[166,174],"such":[167,175],"as":[168,176],"\u201c3+4":[169],"7\u201d,":[171],"general":[173],"\u201cthe":[177],"sum":[178],"two":[180],"even":[181],"numbers":[182],"even\u201d,":[184],"relationship,":[186],"an":[190]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2016-06-24T00:00:00"}