{"id":"https://openalex.org/W1589179847","doi":"https://doi.org/10.5948/upo9780883859841.006","title":"Adapting the Medieval \u201cRule of Double False Position\u201d to the Modern Classroom","display_name":"Adapting the Medieval \u201cRule of Double False Position\u201d to the Modern Classroom","publication_year":2011,"publication_date":"2011-05-13","ids":{"openalex":"https://openalex.org/W1589179847","doi":"https://doi.org/10.5948/upo9780883859841.006","mag":"1589179847"},"language":"en","primary_location":{"id":"doi:10.5948/upo9780883859841.006","doi":"https://doi.org/10.5948/upo9780883859841.006","is_oa":false,"landing_page_url":"https://doi.org/10.5948/upo9780883859841.006","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Time Capsules","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W611951358","display_name":"Mathematical Time Capsules"},"type":"book-chapter","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/A5025635197","display_name":"Randy K. Schwartz","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2801608483","display_name":"Schoolcraft College","ror":"https://ror.org/03j2znq68","country_code":"US","type":"education","lineage":["https://openalex.org/I2801608483"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Randy K. Schwartz","raw_affiliation_strings":["Schoolcraft College"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Schoolcraft College","institution_ids":["https://openalex.org/I2801608483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025635197"],"corresponding_institution_ids":["https://openalex.org/I2801608483"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11737288,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"29","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9824000000953674,"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"}},"topics":[{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9824000000953674,"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/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.009200000204145908,"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":0.002199999988079071,"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/history-of-mathematics","display_name":"history of mathematics","score":0.871999979019165},{"id":"https://openalex.org/keywords/medieval-mathematics","display_name":"medieval mathematics","score":0.6790000200271606},{"id":"https://openalex.org/keywords/interpolation","display_name":"interpolation","score":0.4309999942779541},{"id":"https://openalex.org/keywords/linear-equations","display_name":"linear equations","score":0.5460000038146973},{"id":"https://openalex.org/keywords/algebraic-problem-solving","display_name":"algebraic problem solving","score":0.5059999823570251},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"mathematics education","score":0.5479999780654907},{"id":"https://openalex.org/keywords/teaching-modules","display_name":"teaching modules","score":0.6539999842643738}],"concepts":[{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.879187285900116},{"id":"https://openalex.org/C148324565","wikidata":"https://www.wikidata.org/wiki/Q784221","display_name":"Rote learning","level":4,"score":0.6548843383789062},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.6282481551170349},{"id":"https://openalex.org/C47177190","wikidata":"https://www.wikidata.org/wiki/Q207137","display_name":"Curriculum","level":2,"score":0.5143619775772095},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.4963851571083069},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45894020795822144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4348345994949341},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4174797534942627},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4066951274871826},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3427526354789734},{"id":"https://openalex.org/C88610354","wikidata":"https://www.wikidata.org/wiki/Q1813494","display_name":"Teaching method","level":2,"score":0.2478748857975006},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19867169857025146},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.17707118391990662},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.13619887828826904},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.12457957863807678},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C51672120","wikidata":"https://www.wikidata.org/wiki/Q303446","display_name":"Cooperative learning","level":3,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5948/upo9780883859841.006","doi":"https://doi.org/10.5948/upo9780883859841.006","is_oa":false,"landing_page_url":"https://doi.org/10.5948/upo9780883859841.006","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Time Capsules","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8278999924659729,"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":0,"referenced_works":[],"related_works":["https://openalex.org/W1887283705","https://openalex.org/W59073229","https://openalex.org/W1999351169","https://openalex.org/W2397312707","https://openalex.org/W2940150797","https://openalex.org/W3119994320","https://openalex.org/W3108122802","https://openalex.org/W2347947920","https://openalex.org/W87432406","https://openalex.org/W2547895324"],"abstract_inverted_index":{"Introduction":[0],"The":[1,15,133],"rule":[2,128],"of":[3,55,95,126,129,160,187,244,247],"double":[4,130],"false":[5,131],"position":[6],"is":[7,25,41,69,135],"an":[8],"arithmetical":[9,114],"procedure":[10],"for":[11,83,119,173,200],"evaluating":[12],"linearly-related":[13],"quantities.":[14],"method":[16,170],"does":[17],"not":[18,89],"rely":[19],"on":[20,28,254],"variables":[21],"or":[22,31,36,140,202],"equations,":[23],"but":[24],"based":[26],"instead":[27],"interpolating":[29],"between,":[30],"extrapolating":[32],"from,":[33],"two":[34],"guesses,":[35],"suppositions.":[37],"Although":[38],"the":[39,65,78,100,127,169,177,212,215,242],"technique":[40,219],"seldom":[42],"mentioned":[43],"today":[44],"in":[45,53,72,144,171,211,225],"North":[46,59,123],"American":[47],"curricula,":[48],"it":[49,110,237],"was":[50,80],"routinely":[51],"used":[52],"much":[54],"Europe,":[56],"Asia,":[57],"and":[58,68,108,151,180,249],"Africa":[60],"from":[61,102,191],"medieval":[62],"times":[63],"to":[64,92,138,164,167,175,195,241],"19th":[66],"Century,":[67],"still":[70],"taught":[71],"many":[73],"classrooms":[74],"there":[75],"today.":[76],"Historically,":[77],"approach":[79],"especially":[81],"convenient":[82],"practical":[84],"tradesmen":[85],"whose":[86],"knowledge":[87],"did":[88],"normally":[90],"extend":[91],"a":[93,112,122,192,196,208,218,245],"mastery":[94],"algebra;":[96],"they":[97],"could":[98],"pull":[99],"algorithm":[101],"their":[103,232],"mathematical":[104],"toolkits":[105],"whenever":[106],"needed":[107],"deploy":[109],"as":[111],"rote":[113],"procedure.":[115],"I":[116,205],"have":[117],"adapted":[118],"instructional":[120,198],"use":[121],"African":[124],"version":[125],"position.":[132],"topic":[134],"well":[136],"suited":[137],"college":[139],"high":[141],"school":[142],"courses":[143],"College":[145],"Algebra,":[146],"Precalculus,":[147],"Calculus,":[148,150],"Applied":[149],"Linear":[152],"Algebra.":[153],"In":[154,235],"my":[155],"experience,":[156],"only":[157],"30\u201350":[158],"minutes":[159],"class":[161],"time":[162],"needs":[163],"be":[165],"devoted":[166],"teaching":[168],"order":[172],"students":[174,221],"grasp":[176],"mechanics,":[178],"justification,":[179],"various":[181,188],"applications.":[182],"Instruction":[183],"can":[184],"take":[185],"any":[186],"forms,":[189],"ranging":[190],"traditional":[193],"lecture":[194],"self-guided":[197],"module":[199,209],"individual":[201],"group":[203],"work.":[204],"describe":[206],"such":[207],"below,":[210],"section":[213],"\u201cIn":[214],"Classroom\u201d.":[216],"Covering":[217],"that":[220],"will":[222],"find":[223],"handy":[224],"solving":[226],"certain":[227],"problems":[228],"helps":[229,238],"round":[230],"out":[231],"technical":[233],"skills.":[234],"addition,":[236],"introduce":[239],"them":[240],"contributions":[243],"variety":[246],"cultures,":[248],"provides":[250],"some":[251],"historical":[252],"perspective":[253],"mathematics.":[255]},"counts_by_year":[],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2016-06-24T00:00:00"}
