{"id":"https://openalex.org/W199837518","doi":null,"title":"Situated Intuitions, Concrete Manipulations and the Construction of the Integers: Comparing Two Experiments.","display_name":"Situated Intuitions, Concrete Manipulations and the Construction of the Integers: Comparing Two Experiments.","publication_year":1997,"publication_date":"1997-04-01","ids":{"openalex":"https://openalex.org/W199837518","mag":"199837518"},"language":"en","primary_location":{"id":"mag:199837518","doi":null,"is_oa":false,"landing_page_url":"https://files.eric.ed.gov/fulltext/ED412084.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/A5024835501","display_name":"Julian Scott Williams","orcid":"https://orcid.org/0000-0003-0161-0532","observed_orcids":["https://orcid.org/0000-0003-0161-0532","https://orcid.org/0000-0002-8366-7307"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Julian Williams","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0161-0532","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014946637","display_name":"Liora Linchevski","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liora Linchevski","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":2,"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":0.7803000211715698,"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":0.7803000211715698,"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":0.1995999962091446,"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":0.010499999858438969,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/integers","display_name":"integers","score":0.9350000023841858},{"id":"https://openalex.org/keywords/embeddings","display_name":"embeddings","score":0.5979999899864197},{"id":"https://openalex.org/keywords/ethnomathematics","display_name":"ethnomathematics","score":0.9279999732971191},{"id":"https://openalex.org/keywords/classroom-games","display_name":"classroom games","score":0.7480000257492065},{"id":"https://openalex.org/keywords/manipulatives","display_name":"manipulative materials","score":0.7940000295639038},{"id":"https://openalex.org/keywords/children-s-mathematical-development","display_name":"children's mathematical development","score":0.7850000262260437},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"mathematics education","score":0.36399999260902405}],"concepts":[{"id":"https://openalex.org/C132829578","wikidata":"https://www.wikidata.org/wiki/Q581151","display_name":"Situated","level":2,"score":0.7432811856269836},{"id":"https://openalex.org/C132010649","wikidata":"https://www.wikidata.org/wiki/Q189222","display_name":"Intuition","level":2,"score":0.7040303945541382},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49807167053222656},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.4666075110435486},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.4379725754261017},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4291859269142151},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4231593608856201},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3297432065010071},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2966082990169525},{"id":"https://openalex.org/C188147891","wikidata":"https://www.wikidata.org/wiki/Q147638","display_name":"Cognitive science","level":1,"score":0.2815225124359131},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.2028442621231079},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:199837518","doi":null,"is_oa":false,"landing_page_url":"https://files.eric.ed.gov/fulltext/ED412084.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":[{"id":"https://metadata.un.org/sdg/4","score":0.8278999924659729,"display_name":"Quality education"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W136818748","https://openalex.org/W186080570","https://openalex.org/W1483147224","https://openalex.org/W1544735704","https://openalex.org/W1597874749","https://openalex.org/W1982023621","https://openalex.org/W1996389296","https://openalex.org/W2049691627","https://openalex.org/W2049926613","https://openalex.org/W2050337565","https://openalex.org/W2054394753","https://openalex.org/W2116199508","https://openalex.org/W2164599981","https://openalex.org/W2726339047","https://openalex.org/W2993208980","https://openalex.org/W3021970622","https://openalex.org/W3185163171","https://openalex.org/W4213456552"],"related_works":["https://openalex.org/W1597089382","https://openalex.org/W22875182","https://openalex.org/W3161366522","https://openalex.org/W2144525438","https://openalex.org/W7024372094","https://openalex.org/W4408150993","https://openalex.org/W2736058977","https://openalex.org/W3217184907","https://openalex.org/W180538117","https://openalex.org/W2135700850"],"abstract_inverted_index":{"This":[0,84,231],"paper":[1],"further":[2],"develops":[3],"an":[4],"instructional":[5],"method":[6,157],"called":[7],"here":[8,88],"process-object":[9],"linking":[10],"and":[11,54,116,131,202,224,301],"embedding.":[12],"The":[13,134],"idea":[14],"is":[15,67,86,99,164],"to":[16,22,50,53,95,141,250],"link":[17,32,51],"the":[18,30,58,74,90,102,120,127,143,149,160,187,194,203,206,239,302,305],"familiar":[19,26],"mathematical":[20,34,38,82,108],"processes":[21,56],"objects":[23],"in":[24,57,80,89,119,147,158,170,260],"a":[25,70,156,167],"situation,":[27],"then":[28],"re-embed":[29],"new":[31],"through":[33],"symbols":[35],"into":[36,113,166],"their":[37],"construction.":[39],"It":[40,66,98],"makes":[41],"use":[42],"of":[43,72,76,92,129,136,205,221,255,304,312,317],"children's":[44,81],"extra-mathematical,":[45],"ethnomathematical,":[46],"or":[47,241,257,270],"everyday":[48],"knowledge":[49],"situations":[52],"unpack":[55],"mathematics":[59],"with":[60,126],"which":[61,148,159,171],"they":[62],"are":[63,173,186],"already":[64],"confident.":[65],"designed":[68],"as":[69,236],"means":[71],"overcoming":[73],"problem":[75],"intuitive":[77],"gaps":[78],"recurring":[79],"development.":[83],"process":[85],"illustrated":[87],"case":[91],"two":[93,308],"attempts":[94],"teach":[96],"integers.":[97],"based":[100],"on":[101],"principle":[103],"that":[104,189],"intuitions":[105,151],"arising":[106,118],"outside":[107],"experience":[109],"can":[110,123,190],"be":[111,124,191],"imported":[112],"mathematics:":[114],"strategies":[115],"concepts":[117],"extra-mathematical":[121],"situation":[122,146],"modeled":[125,174],"aid":[128],"tools":[130],"representational":[132],"devices.":[133],"design":[135],"appropriate":[137],"activity":[138],"does":[139],"need":[140],"address":[142],"whole":[144],"social":[145],"child's":[150],"arise.":[152],"Here":[153],"we":[154],"find":[155],"intuition":[161],"for":[162],"fairness":[163],"carried":[165],"classroom":[168],"game":[169],"integers":[172],"particularly":[175],"effectively.":[176],"Contains":[177],"41":[178],"references.":[179],"(PVD)":[180],"********************************************************************************":[181,197],"Reproductions":[182],"supplied":[183],"by":[184,211],"EDRS":[185],"best":[188],"made":[192,249],"from":[193,238],"original":[195],"document.":[196],"Situated":[198,297],"Intuitions,":[199,298],"Concrete":[200],"Manipulations":[201],"Construction":[204],"Integers:":[207],"Comparing":[208],"Two":[209],"Experiments":[210],"J.S.":[212],"Williams":[213],"L.":[214],"Linchevski":[215],"U.S.":[216],"DEPARTMENT":[217],"OF":[218],"EDUCATION":[219],"Office":[220],"Educational":[222],"Research":[223],"Improvement":[225],"EDUCATIONAL":[226,292],"RESOURCES":[227,293],"INFORMATION":[228,294],"CENTER":[229,295],"(ERIC)":[230,296],"document":[232,262],"has":[233],"been":[234,248],"reproduced":[235],"received":[237],"person":[240],"organization":[242],"originating":[243],"it.":[244],"Minor":[245],"changes":[246],"have":[247],"improve":[251],"reproduction":[252],"quality.":[253],"Points":[254],"view":[256],"opinions":[258],"stated":[259],"this":[261],"do":[263],"not":[264],"necessarily":[265],"represent":[266],"official":[267],"OERI":[268],"position":[269],"policy.":[271],"BEST":[272],"COPY":[273],"AVAILABLE":[274],"2":[275],"PERMISSION":[276],"TO":[277,290],"REPRODUCE":[278],"AND":[279],"DISSEMINATE":[280],"THIS":[281],"MATERIAL":[282],"HAS":[283],"BEEN":[284],"GRANTED":[285],"BY":[286],"clikaq":[287],"WIIA":[288],"kw-5":[289],"THE":[291],"concrete":[299],"manipulations":[300],"construction":[303],"integers:":[306],"comparing":[307],"experiments.":[309],"Williams,J.S.":[310],"(presenting),University":[311],"Manchester,":[313],"Linchevski,L.":[314],"Hebrew":[315],"University":[316],"Jerusalem.":[318]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}