{"id":"https://openalex.org/W2126745375","doi":"https://doi.org/10.5951/tcm.6.4.0232","title":"Early Childhood Corner: Children's Understanding of Equality: A Foundation for Algebra","display_name":"Early Childhood Corner: Children's Understanding of Equality: A Foundation for Algebra","publication_year":1999,"publication_date":"1999-12-01","ids":{"openalex":"https://openalex.org/W2126745375","doi":"https://doi.org/10.5951/tcm.6.4.0232","mag":"2126745375"},"language":"en","primary_location":{"id":"doi:10.5951/tcm.6.4.0232","doi":"https://doi.org/10.5951/tcm.6.4.0232","is_oa":false,"landing_page_url":"https://doi.org/10.5951/tcm.6.4.0232","pdf_url":null,"source":{"id":"https://openalex.org/S2764603942","display_name":"Teaching Children Mathematics","issn_l":"1073-5836","issn":["1073-5836","2327-0780"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310315778","host_organization_name":"National Council of Teachers of Mathematics","host_organization_lineage":["https://openalex.org/P4310315778"],"host_organization_lineage_names":["National Council of Teachers of Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Teaching Children Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Karen Falkner","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karen Falkner","raw_affiliation_strings":["1 Is a primary-grade teacher at Lapham Elementary School, Madison, WI 53703"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"1 Is a primary-grade teacher at Lapham Elementary School, Madison, WI 53703","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020305730","display_name":"Linda W. Levi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405271864","display_name":"Wisconsin Center for Education Research","ror":"https://ror.org/036ervr32","country_code":"US","type":"facility","lineage":["https://openalex.org/I4405271864"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Linda Levi","raw_affiliation_strings":["2 Affiliated with the Wisconsin Center for Educational Research, Madison, WI 53706"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"2 Affiliated with the Wisconsin Center for Educational Research, Madison, WI 53706","institution_ids":["https://openalex.org/I4405271864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102452593","display_name":"Thomas Carpenter","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405271864","display_name":"Wisconsin Center for Education Research","ror":"https://ror.org/036ervr32","country_code":"US","type":"facility","lineage":["https://openalex.org/I4405271864"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas Carpenter","raw_affiliation_strings":["2 Affiliated with the Wisconsin Center for Educational Research, Madison, WI 53706"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"2 Affiliated with the Wisconsin Center for Educational Research, Madison, WI 53706","institution_ids":["https://openalex.org/I4405271864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.0399,"has_fulltext":false,"cited_by_count":243,"citation_normalized_percentile":{"value":0.9703672,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"6","issue":"4","first_page":"232","last_page":"236"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.9634000062942505,"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":0.9634000062942505,"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/T11345","display_name":"Cognitive and developmental aspects of mathematical skills","score":0.014700000174343586,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12522","display_name":"Mathematics Education and Pedagogy","score":0.011099999770522118,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/equality","display_name":"equality","score":0.47699999809265137},{"id":"https://openalex.org/keywords/algebraic-thinking","display_name":"algebraic thinking","score":0.5720000267028809},{"id":"https://openalex.org/keywords/early-mathematics","display_name":"early childhood mathematics","score":0.843999981880188}],"concepts":[{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.6240203380584717},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5531483888626099},{"id":"https://openalex.org/C2777082460","wikidata":"https://www.wikidata.org/wiki/Q3377398","display_name":"Early childhood","level":2,"score":0.4902825653553009},{"id":"https://openalex.org/C2780966255","wikidata":"https://www.wikidata.org/wiki/Q5474306","display_name":"Foundation (evidence)","level":2,"score":0.477934867143631},{"id":"https://openalex.org/C178229462","wikidata":"https://www.wikidata.org/wiki/Q1472221","display_name":"Early childhood education","level":2,"score":0.4668259024620056},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29398036003112793},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.2755005955696106},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.26573455333709717},{"id":"https://openalex.org/C138496976","wikidata":"https://www.wikidata.org/wiki/Q175002","display_name":"Developmental psychology","level":1,"score":0.2325834333896637},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.09167554974555969},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07395303249359131},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5951/tcm.6.4.0232","doi":"https://doi.org/10.5951/tcm.6.4.0232","is_oa":false,"landing_page_url":"https://doi.org/10.5951/tcm.6.4.0232","pdf_url":null,"source":{"id":"https://openalex.org/S2764603942","display_name":"Teaching Children Mathematics","issn_l":"1073-5836","issn":["1073-5836","2327-0780"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310315778","host_organization_name":"National Council of Teachers of Mathematics","host_organization_lineage":["https://openalex.org/P4310315778"],"host_organization_lineage_names":["National Council of Teachers of Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Teaching Children Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.75,"display_name":"Quality education","id":"https://metadata.un.org/sdg/4"}],"sustainable_development_goals_aurora":[{"score":0.800000011920929,"display_name":"Quality education","id":"https://metadata.un.org/sdg/4"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W189126076","https://openalex.org/W223457013","https://openalex.org/W1992274553","https://openalex.org/W2795555060"],"related_works":["https://openalex.org/W2460043178","https://openalex.org/W2462352614","https://openalex.org/W7162055970","https://openalex.org/W2987506863","https://openalex.org/W4252308292","https://openalex.org/W7164666441","https://openalex.org/W2773457294","https://openalex.org/W2464701853","https://openalex.org/W115156861","https://openalex.org/W3176305546"],"abstract_inverted_index":{"Many":[0],"states":[1],"and":[2,9],"school":[3],"districts,":[4],"as":[5,7],"well":[6],"Principles":[8],"Standards":[10],"for":[11,48],"School":[12],"Mathematics:":[13],"Discussion":[14],"Draft":[15],"(NCTM":[16],"1998),":[17],"recommend":[18],"that":[19],"algebra":[20,47],"be":[21],"taught":[22],"in":[23],"the":[24,49],"early":[25,50],"childhood":[26,51],"years.":[27,52],"Although":[28],"young":[29],"children":[30],"often":[31],"understand":[32],"much":[33],"more":[34],"than":[35],"traditionally":[36],"thought,":[37],"adults":[38],"can":[39],"have":[40],"difficulty":[41],"conceptualizing":[42],"what":[43],"would":[44],"constitute":[45],"appropriate":[46]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":16}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2016-06-24T00:00:00"}