{"id":"https://openalex.org/W2291228008","doi":null,"title":"From Recursive Pattern to Correspondence Rule: Developing Students' Abilities to Engage in Functional Thinking","display_name":"From Recursive Pattern to Correspondence Rule: Developing Students' Abilities to Engage in Functional Thinking","publication_year":2012,"publication_date":"2012-11-01","ids":{"openalex":"https://openalex.org/W2291228008","mag":"2291228008"},"language":"en","primary_location":{"id":"pmh:oai:https://open.metu.edu.tr:11511/72449","doi":null,"is_oa":false,"landing_page_url":"https://hdl.handle.net/11511/72449","pdf_url":null,"source":{"id":"https://openalex.org/S4306402495","display_name":"OpenMETU (Middle East Technical University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I201799495","host_organization_name":"Middle East Technical University","host_organization_lineage":["https://openalex.org/I201799495"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Thirty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (1 - 4 Kas\u0131m 2012)","raw_type":"Conference Paper"},"volume":null,"type":"conference-paper","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/A5076404275","display_name":"Ana C. Stephens","orcid":"https://orcid.org/0000-0002-1609-2021","observed_orcids":["https://orcid.org/0000-0002-1609-2021"]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ana C. Stephens","raw_affiliation_strings":["University of Wisconsin-Madison, #TAB#"],"raw_orcid":"https://orcid.org/0000-0002-1609-2021","affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison, #TAB#","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079272187","display_name":"I\u015f\u0131l I\u015fler","orcid":"https://orcid.org/0000-0002-2779-9241","observed_orcids":["https://orcid.org/0000-0002-2779-9241"]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"I\u015f\u0131l I\u015fler","raw_affiliation_strings":["University of Wisconsin-Madison, #TAB#"],"raw_orcid":"https://orcid.org/0000-0002-2779-9241","affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison, #TAB#","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048773156","display_name":"Tim Marum","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Timothy Marum","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048757232","display_name":"MARIA L. BLANTON","orcid":"https://orcid.org/0000-0003-0895-8478","observed_orcids":["https://orcid.org/0000-0003-0895-8478"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maria Blanton","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0895-8478","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064787956","display_name":"Eric Knuth","orcid":"https://orcid.org/0000-0003-3661-1789","observed_orcids":["https://orcid.org/0000-0003-3661-1789"]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric Knuth","raw_affiliation_strings":["University of Wisconsin-Madison, #TAB#"],"raw_orcid":"https://orcid.org/0000-0003-3661-1789","affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison, #TAB#","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077990502","display_name":"Angela Murphy Gardiner","orcid":"https://orcid.org/0000-0002-3241-2769","observed_orcids":["https://orcid.org/0000-0002-3241-2769"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Angela Murphy Gardiner","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3241-2769","affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3984,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.9240951,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":95},"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":0.9003999829292297,"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":0.9003999829292297,"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/T12522","display_name":"Mathematics Education and Pedagogy","score":0.02280000038444996,"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/T11875","display_name":"Statistics Education and Methodologies","score":0.016699999570846558,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/functional-thinking","display_name":"functional thinking","score":0.8510000109672546},{"id":"https://openalex.org/keywords/early-algebra","display_name":"early algebra","score":0.9110000133514404},{"id":"https://openalex.org/keywords/linear-functions","display_name":"linear functions","score":0.5950000286102295},{"id":"https://openalex.org/keywords/recursive-patterns","display_name":"recursive patterns","score":0.7250000238418579},{"id":"https://openalex.org/keywords/correspondence-rules","display_name":"correspondence rules","score":0.9879999756813049},{"id":"https://openalex.org/keywords/algebraic-representation","display_name":"algebraic representation","score":0.7850000262260437},{"id":"https://openalex.org/keywords/elementary-school-students","display_name":"elementary school students","score":0.5730000138282776}],"concepts":[{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.6698996424674988},{"id":"https://openalex.org/C2780665704","wikidata":"https://www.wikidata.org/wiki/Q959298","display_name":"Intervention (counseling)","level":2,"score":0.5342492461204529},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44755131006240845},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.43405503034591675},{"id":"https://openalex.org/C43971567","wikidata":"https://www.wikidata.org/wiki/Q3142865","display_name":"Logical reasoning","level":2,"score":0.4209459125995636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30637890100479126},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11198994517326355},{"id":"https://openalex.org/C118552586","wikidata":"https://www.wikidata.org/wiki/Q7867","display_name":"Psychiatry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:https://open.metu.edu.tr:11511/72449","doi":null,"is_oa":false,"landing_page_url":"https://hdl.handle.net/11511/72449","pdf_url":null,"source":{"id":"https://openalex.org/S4306402495","display_name":"OpenMETU (Middle East Technical University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I201799495","host_organization_name":"Middle East Technical University","host_organization_lineage":["https://openalex.org/I201799495"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Thirty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (1 - 4 Kas\u0131m 2012)","raw_type":"Conference Paper"},{"id":"mag:2291228008","doi":null,"is_oa":false,"landing_page_url":"http://algebra.wceruw.org/documents/PMENA_2012.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2764749937","display_name":"Proceedings of the ... PME Conference","issn_l":"0771-100X","issn":["0771-100X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4365922604","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/P4365922604"],"host_organization_lineage_names":["Utrecht University"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the ... PME Conference","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality education","score":0.975600004196167}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W140407908","https://openalex.org/W356089036","https://openalex.org/W2025677013","https://openalex.org/W2066546689","https://openalex.org/W2138040274","https://openalex.org/W2145672648","https://openalex.org/W2899573755","https://openalex.org/W4240904236"],"related_works":["https://openalex.org/W2725646256","https://openalex.org/W7000851777","https://openalex.org/W1983082366","https://openalex.org/W4404064900","https://openalex.org/W7221228101","https://openalex.org/W3164696756","https://openalex.org/W2145672648","https://openalex.org/W4288615120","https://openalex.org/W2975816473","https://openalex.org/W2995369338"],"abstract_inverted_index":{"Third-":[0],"through":[1],"fifth-grade":[2],"students":[3,41],"participating":[4],"in":[5,29,43,61],"a":[6,36],"classroom":[7],"teaching":[8],"experiment":[9],"investigating":[10],"the":[11],"impact":[12],"of":[13],"an":[14],"Early":[15],"Algebra":[16],"Learning":[17],"Progression":[18],"completed":[19],"pre-":[20],"and":[21,56,64],"post-assessment":[22],"items":[23],"addressing":[24],"their":[25,44],"abilities":[26,45],"to":[27,46,50,57],"engage":[28],"functional":[30],"thinking.":[31],"We":[32],"found":[33],"that":[34],"after":[35],"sustained":[37],"early":[38],"algebra":[39],"intervention,":[40],"grew":[42],"shift":[47],"from":[48],"recursive":[49],"covariational":[51],"thinking":[52],"about":[53],"linear":[54],"functions":[55],"represent":[58],"correspondence":[59],"rules":[60],"both":[62],"words":[63],"variables.":[65]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
