{"id":"https://openalex.org/W319367492","doi":"https://doi.org/10.5951/mathteacher.107.2.0150","title":"Delving Deeper: Transforming Shapes Physically and Analytically","display_name":"Delving Deeper: Transforming Shapes Physically and Analytically","publication_year":2013,"publication_date":"2013-08-26","ids":{"openalex":"https://openalex.org/W319367492","doi":"https://doi.org/10.5951/mathteacher.107.2.0150","mag":"319367492"},"language":"en","primary_location":{"id":"doi:10.5951/mathteacher.107.2.0150","doi":"https://doi.org/10.5951/mathteacher.107.2.0150","is_oa":false,"landing_page_url":"https://doi.org/10.5951/mathteacher.107.2.0150","pdf_url":null,"source":{"id":"https://openalex.org/S2764739392","display_name":"Mathematics Teacher Learning and Teaching PK-12","issn_l":"0025-5769","issn":["0025-5769","2330-0582"],"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":"The Mathematics Teacher","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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":"https://openalex.org/A5114253457","display_name":"Margaret M. Rathouz","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Margaret Rathouz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108566130","display_name":"Christopher Novak","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christopher Novak","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065420918","display_name":"John Clifford","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John Clifford","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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":"107","issue":"2","first_page":"150","last_page":"155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.9970999956130981,"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":0.9970999956130981,"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":0.0017000000225380063,"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/T12504","display_name":"Mathematics and Applications","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/geometric-measurement","display_name":"geometric measurement","score":0.699999988079071},{"id":"https://openalex.org/keywords/area-formula","display_name":"area formula","score":0.847000002861023},{"id":"https://openalex.org/keywords/triangle-area","display_name":"triangle area","score":0.8999999761581421},{"id":"https://openalex.org/keywords/deductive-reasoning","display_name":"deductive reasoning","score":0.8529999852180481},{"id":"https://openalex.org/keywords/visual-models","display_name":"visual models","score":0.6600000262260437},{"id":"https://openalex.org/keywords/manipulative-models","display_name":"manipulative models","score":0.9660000205039978},{"id":"https://openalex.org/keywords/formula-derivation","display_name":"formula derivation","score":0.4699999988079071},{"id":"https://openalex.org/keywords/geometry-teaching","display_name":"geometry teaching","score":0.3050000071525574}],"concepts":[{"id":"https://openalex.org/C2781235140","wikidata":"https://www.wikidata.org/wiki/Q275131","display_name":"Scratch","level":2,"score":0.7376187443733215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4801061451435089},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38956719636917114},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37252527475357056},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33111870288848877},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09231001138687134}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5951/mathteacher.107.2.0150","doi":"https://doi.org/10.5951/mathteacher.107.2.0150","is_oa":false,"landing_page_url":"https://doi.org/10.5951/mathteacher.107.2.0150","pdf_url":null,"source":{"id":"https://openalex.org/S2764739392","display_name":"Mathematics Teacher Learning and Teaching PK-12","issn_l":"0025-5769","issn":["0025-5769","2330-0582"],"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":"The Mathematics Teacher","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6164000034332275,"id":"https://metadata.un.org/sdg/4","display_name":"Quality education"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W152615572","https://openalex.org/W288822704","https://openalex.org/W1510713464","https://openalex.org/W1569094758","https://openalex.org/W2024962498","https://openalex.org/W2726766044","https://openalex.org/W3164274164"],"related_works":["https://openalex.org/W2473838590","https://openalex.org/W4400948678","https://openalex.org/W3022694564","https://openalex.org/W7118610553","https://openalex.org/W50673032","https://openalex.org/W7144704161","https://openalex.org/W3009994337","https://openalex.org/W7016200559","https://openalex.org/W3159228920","https://openalex.org/W3111197372"],"abstract_inverted_index":{"Constructing":[0],"formulas":[1],"\u201cfrom":[2],"scratch\u201d":[3],"for":[4],"calculating":[5],"geometric":[6],"measurements":[7],"of":[8,13,50],"shapes\u2014for":[9],"example,":[10],"the":[11,41,51],"area":[12],"a":[14,35],"triangle\u2014involves":[15],"reasoning":[16],"deductively":[17],"and":[18,26,30,47,53],"drawing":[19],"connections":[20],"between":[21],"different":[22],"methods":[23],"(Usnick,":[24],"Lamphere,":[25],"Bright":[27],"1992).":[28],"Visual":[29],"manipulative":[31],"models":[32],"also":[33],"play":[34],"role":[36],"in":[37,45,55],"helping":[38],"students":[39],"understand":[40],"underlying":[42],"mathematics":[43],"implicit":[44],"measurement":[46],"make":[48],"sense":[49],"numbers":[52],"operations":[54],"formulas.":[56]},"counts_by_year":[],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2016-06-24T00:00:00"}