{"id":"https://openalex.org/W285413896","doi":null,"title":"An Arithmetic Carol.","display_name":"An Arithmetic Carol.","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W285413896","mag":"285413896"},"language":"en","primary_location":{"id":"mag:285413896","doi":null,"is_oa":false,"landing_page_url":"https://files.eric.ed.gov/fulltext/ED445880.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},"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/A5048350517","display_name":"Cathy Kessel","orcid":"https://orcid.org/0000-0002-1553-7279","observed_orcids":["https://orcid.org/0000-0002-1553-7279"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cathy Kessel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5048350517"],"corresponding_institution_ids":[],"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/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.7529000043869019,"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/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.7529000043869019,"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":0.19359999895095825,"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/T12522","display_name":"Mathematics Education and Pedagogy","score":0.04089999943971634,"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/arithmetic","display_name":"arithmetic","score":0.6449999809265137},{"id":"https://openalex.org/keywords/algebra","display_name":"algebra","score":0.39899998903274536},{"id":"https://openalex.org/keywords/mathematical-rules","display_name":"mathematical rules","score":0.36899998784065247},{"id":"https://openalex.org/keywords/generalization","display_name":"generalization","score":0.7179999947547913},{"id":"https://openalex.org/keywords/symbolization","display_name":"symbolization","score":0.8600000143051147}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7648811340332031},{"id":"https://openalex.org/C2992503517","wikidata":"https://www.wikidata.org/wiki/Q620584","display_name":"Mental arithmetic","level":4,"score":0.5305421948432922},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.48063960671424866},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.4515955150127411},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4300723075866699},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42242342233657837},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41861218214035034},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.3382079601287842},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.23806115984916687},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13119518756866455},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C2777953023","wikidata":"https://www.wikidata.org/wiki/Q1073121","display_name":"Heart rate","level":3,"score":0.0},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C84393581","wikidata":"https://www.wikidata.org/wiki/Q82642","display_name":"Blood pressure","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:285413896","doi":null,"is_oa":false,"landing_page_url":"https://files.eric.ed.gov/fulltext/ED445880.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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W66143725","https://openalex.org/W185341291","https://openalex.org/W1533490605","https://openalex.org/W1573196333","https://openalex.org/W1579414271","https://openalex.org/W1582364809","https://openalex.org/W1605635802","https://openalex.org/W1760924282","https://openalex.org/W1807908125","https://openalex.org/W1979890010","https://openalex.org/W2040086733","https://openalex.org/W2093755430","https://openalex.org/W2323458370","https://openalex.org/W2612211396","https://openalex.org/W2897290720","https://openalex.org/W2990615699","https://openalex.org/W4245878728"],"related_works":["https://openalex.org/W3120205067","https://openalex.org/W1555369790","https://openalex.org/W145893347","https://openalex.org/W7223070937","https://openalex.org/W2258510480","https://openalex.org/W626527017","https://openalex.org/W3158532691","https://openalex.org/W1505819268","https://openalex.org/W1505827279","https://openalex.org/W1541192345"],"abstract_inverted_index":{"This":[0,16],"paper":[1],"illustrates":[2],"a":[3,36],"different":[4,22],"conception":[5],"of":[6,27,42,60,67],"arithmetic,":[7],"an":[8],"arithmetic":[9,17,68,130],"with":[10],"reasons":[11],"as":[12,14,29,31,54],"well":[13,30],"rules.":[15],"includes":[18],"making":[19,25],"connections":[20],"between":[21,77],"representations":[23],"and":[24,44,58,64],"sense":[26,48],"rules":[28],"using":[32],"them.":[33],"It":[34],"provides":[35],"foundation":[37],"for":[38],"Algebra":[39],"the":[40,47,55,75,96,103],"Web":[41],"Knowledge":[43],"Skill":[45],"in":[46,71],"that":[49,98],"algebra":[50],"can":[51,99],"be":[52,100],"seen":[53],"generalization,":[56],"formalization,":[57],"symbolization":[59],"this":[61],"arithmetic.":[62],"Past":[63],"recent":[65],"views":[66],"are":[69,95],"contrasted":[70],"order":[72],"to":[73,82],"make":[74],"differences":[76],"them":[78],"explicit..":[79],"Arithmetic":[80],"yet":[81],"come":[83],"is":[84],"also":[85],"considered.":[86],"(Contains":[87],"27":[88],"references.)":[89],"(ASK)":[90],"Reproductions":[91],"supplied":[92],"by":[93],"EDRS":[94],"best":[97],"made":[101],"from":[102],"original":[104],"document.":[105],"PERMISSION":[106],"TO":[107,121],"REPRODUCE":[108],"AND":[109],"DISSEMINATE":[110],"THIS":[111],"MATERIAL":[112],"HAS":[113],"BEEN":[114],"GRANTED":[115],"BY":[116],"00":[117,118],"kr)":[119],"'1":[120],"THE":[122],"EDUCATIONAL":[123],"RESOURCES":[124],"'1'":[125],"INFORMATION":[126],"CENTER":[127],"(ERIC)":[128],"An":[129],"carol":[131]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
