{"id":"https://openalex.org/W66185979","doi":null,"title":"Mental computation, computational estimation, and number fact knowledge for addition and substration in year four children","display_name":"Mental computation, computational estimation, and number fact knowledge for addition and substration in year four children","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W66185979","mag":"66185979"},"language":"en","primary_location":{"id":"mag:66185979","doi":null,"is_oa":false,"landing_page_url":"https://eprints.qut.edu.au/36516/","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},"volume":null,"type":"dissertation","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/A5013350506","display_name":"Ann M. Heirdsfield","orcid":"https://orcid.org/0000-0003-4271-0521","observed_orcids":["https://orcid.org/0000-0003-4271-0521"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ann M. Heirdsfield","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4271-0521","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5013350506"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":null,"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":0.9506999850273132,"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":0.9506999850273132,"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/T12522","display_name":"Mathematics Education and Pedagogy","score":0.04100000113248825,"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/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.007300000172108412,"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/mental-arithmetic","display_name":"mental arithmetic","score":0.9950000047683716},{"id":"https://openalex.org/keywords/computational-estimation","display_name":"computational estimation","score":0.9929999709129333},{"id":"https://openalex.org/keywords/addition-strategies","display_name":"addition strategies","score":0.7080000042915344},{"id":"https://openalex.org/keywords/subtraction-strategies","display_name":"subtraction strategies","score":1.0},{"id":"https://openalex.org/keywords/mathematical-ability","display_name":"mathematical ability","score":0.3889999985694885},{"id":"https://openalex.org/keywords/year-4-students","display_name":"Year 4 students","score":0.6769999861717224},{"id":"https://openalex.org/keywords/primary-school-mathematics","display_name":"primary school mathematics","score":0.39500001072883606}],"concepts":[{"id":"https://openalex.org/C68060419","wikidata":"https://www.wikidata.org/wiki/Q40754","display_name":"Subtraction","level":2,"score":0.6978015899658203},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.6370118260383606},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.6275132894515991},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5547486543655396},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.48717018961906433},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4720517098903656},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.46040213108062744},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.44598710536956787},{"id":"https://openalex.org/C2781316041","wikidata":"https://www.wikidata.org/wiki/Q1230584","display_name":"Diversity (politics)","level":2,"score":0.43612125515937805},{"id":"https://openalex.org/C2777267654","wikidata":"https://www.wikidata.org/wiki/Q3519023","display_name":"Test (biology)","level":2,"score":0.42246368527412415},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.40227264165878296},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3198856711387634},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3189026117324829},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28953176736831665},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21192193031311035},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20694756507873535},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10855862498283386},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:66185979","doi":null,"is_oa":false,"landing_page_url":"https://eprints.qut.edu.au/36516/","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":[{"score":0.75,"display_name":"Quality education","id":"https://metadata.un.org/sdg/4"}],"study_designs":[{"display_name":"Observational Study","id":"https://openalex.org/study-designs/observational-study"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W315417198","https://openalex.org/W1499307382","https://openalex.org/W1546025933","https://openalex.org/W1111864561","https://openalex.org/W145061345","https://openalex.org/W7100468175","https://openalex.org/W182544369","https://openalex.org/W1516730736","https://openalex.org/W3022546264","https://openalex.org/W2344726381"],"abstract_inverted_index":{"Educational":[0],"research":[1,34],"has":[2,35],"shown":[3],"when":[4],"students":[5,92,107,125,175,206,235,289,338,349,422],"are":[6,253,273],"actively":[7],"engaged":[8],"in":[9,30,78,250,370,381],"the":[10,23,28,56,64,87,111,167,201,219,245,286,299,316,371,382,388,436],"invention":[11],"of":[12,22,53,58,207,214,221,241,255,282,307,377,390,435,440],"alternative":[13],"mental":[14,54,66,94,120,215,262,271,379],"algorithms,":[15],"they":[16,113],"develop":[17],"an":[18],"understanding":[19,52,434],"and":[20,42,70,76,98,103,117,122,138,155,157,161,170,182,194,217,260,279,302,318,321,330,397,400,411,420,439],"appreciation":[21],"number\r\nsystem":[24],"as":[25,27,162,442],"well":[26],"flexibility":[29],"number":[31,43,71,99,183,283,331,398,437],"combinations.":[32],"Other":[33],"indicated":[36,247],"possible":[37],"links":[38],"with":[39,404],"computational":[40,68,96,180,277,346,368,395],"estimation":[41,181,278,329,355,369,396],"fact":[44,72,100,184,284,332],"knowledge.":[45],"With":[46],"a":[47,187,212,364,401,443],"focus":[48],"on":[49,110,142,315,323,367],"expanding":[50],"our":[51],"computation,":[55,67,95],"aim":[57],"this":[59,150,232,308],"study":[60,233],"was":[61,229],"to":[62,165,297,311,353,362,418,423,432],"investigate":[63],"relationship\r\nbetween":[65],"estimation,":[69,97,347],"knowledge":[73,185],"for":[74,93,115,128,136,145,179,199,226,345,394],"addition":[75,121,137],"subtraction":[77,222],"year":[79,105,251],"4":[80,106,252],"students.":[81],"Supporting":[82],"evidence":[83],"emanated":[84],"partially":[85],"from":[86,231],"identified":[88,374],"strategies":[89,112,135,216,223,239,333,344,393,428],"employed":[90,211],"by":[91],"knowledge.\r\n\r\nOne":[101],"hundred":[102],"seven":[104],"were":[108,126,176,197,334,350],"interviewed":[109,177],"used":[114,133,198,290],"2":[116],"3":[118],"digit":[119],"subtraction.":[123],"Thirty-two":[124],"selected":[127],"further":[129,178],"interviews,":[130],"16":[131,139],"who":[132,140,291],"multiple":[134],"relied":[141],"one":[143,294,305],"strategy":[144,151,287,295],"addition.":[146,227],"It\r\nwas":[147],"found":[148],"that":[149,205,218,225,234,248,268,288,409,429],"involved":[152],"separating":[153],"ones":[154,159],"tens":[156],"adding":[158],"first,":[160],"such":[163],"appeared":[164,296],"reflect":[166,298],"traditional":[168,300],"pen":[169,301,317],"paper":[171,303,319],"algorithm.":[172],"The":[173],"32":[174],"(including":[186],"written":[188],"test).":[189],"Both\r\nquantitative":[190],"(Spearman":[191],"rank":[192],"correlations)":[193],"qualitative":[195],"methods":[196],"analyzing":[200],"data.\r\n\r\nThe":[202],"results":[203,265],"showed":[204,267],"different":[208],"mathematical":[209],"abilities":[210],"variety":[213],"diversity":[220],"exceeded":[224],"It":[228,357,406],"evident":[230],"had":[236,339],"developed":[237,341],"these":[238,416],"independent":[240],"formal":[242],"classroom\r\ninstruction.":[243],"Further,":[244],"data":[246],"children":[249],"capable":[254],"inventing":[256],"their":[257,342,425],"own":[258,343,426],"valid":[259],"efficient":[261],"algorithms.":[263],"Tue":[264],"also":[266,274,335,340],"accurate":[269],"multi-strategy":[270,378],"computers":[272,380],"good":[275],"at":[276],"exhibit":[280],"mastery":[281],"recall.\r\n\r\nAs":[285],"only":[292],"exhibited":[293],"algorithm,":[304],"recommendation":[306],"thesis":[309,373],"is":[310,358,407],"place":[312],"less":[313],"emphasis":[314,366],"algorithm":[320],"more":[322,391],"developing":[324],"students'":[325],"legitimate,":[326],"spontaneous":[327],"strategies.\r\nComputational":[328],"identified.":[336],"Although":[337],"many":[348],"not":[351],"confident":[352],"employ":[354],"strategies.":[356],"felt":[359],"there":[360],"needs":[361],"be":[363],"greater":[365],"curriculum.\r\n\r\nThis":[372],"common":[375],"characteristics":[376],"middle":[383],"primary":[384],"years.":[385],"These":[386],"include":[387],"employment":[389],"advanced":[392],"facts,":[399],"superior":[402],"facility":[403],"number.":[405],"expected":[408],"teachers":[410],"curriculum":[412],"planners":[413],"will":[414,430],"utilize":[415],"findings":[417],"encourage":[419],"allow":[421],"invent":[424],"idiosyncratic":[427],"lead":[431],"better":[433],"system":[438],"mathematics":[441],"whole.":[444]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-09-26T08:19:03.415552","created_date":"2016-06-24T00:00:00"}
