{"id":"https://openalex.org/W2954465356","doi":null,"title":"The Importance of Representational Shift: An Investigation of the Cognitive Mechanisms and Individual Differences Underlying Math Performance","display_name":"The Importance of Representational Shift: An Investigation of the Cognitive Mechanisms and Individual Differences Underlying Math Performance","publication_year":2019,"publication_date":"2019-01-30","ids":{"openalex":"https://openalex.org/W2954465356","mag":"2954465356"},"language":"en","primary_location":{"id":"pmh:oai:d-scholarship.pitt.edu:35289","doi":null,"is_oa":true,"landing_page_url":"https://d-scholarship.pitt.edu/35289/1/Liu_Dissertation_Investigating%20Math%20Mechanisms_ETD_final_1.pdf","pdf_url":"http://d-scholarship.pitt.edu/35289/1/Liu_Dissertation_Investigating%20Math%20Mechanisms_ETD_final_1.pdf","source":{"id":"https://openalex.org/S4306402372","display_name":"D-Scholarship@Pitt (University of Pittsburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170201317","host_organization_name":"University of Pittsburgh","host_organization_lineage":["https://openalex.org/I170201317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://d-scholarship.pitt.edu/35289/1/Liu_Dissertation_Investigating%20Math%20Mechanisms_ETD_final_1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023044068","display_name":"Allison S. Liu","orcid":"https://orcid.org/0000-0003-1075-2575","observed_orcids":["https://orcid.org/0000-0003-1075-2575"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Allison S. Liu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-1075-2575","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5023044068"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"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/T11345","display_name":"Cognitive and developmental aspects of mathematical skills","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11345","display_name":"Cognitive and developmental aspects of mathematical skills","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12522","display_name":"Mathematics Education and Pedagogy","score":0.0,"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/T14079","display_name":"Mathematics Education and Programs","score":0.0,"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/mathematics-achievement","display_name":"mathematics achievement","score":0.7639999985694885},{"id":"https://openalex.org/keywords/individual-differences","display_name":"individual differences","score":0.6660000085830688},{"id":"https://openalex.org/keywords/symbolic-number-representation","display_name":"symbolic number representation","score":0.9980000257492065},{"id":"https://openalex.org/keywords/university-dropout","display_name":"university dropout","score":0.7009999752044678},{"id":"https://openalex.org/keywords/cognitive-mechanisms","display_name":"cognitive mechanisms","score":0.7260000109672546},{"id":"https://openalex.org/keywords/intervention-effectiveness","display_name":"intervention effectiveness","score":0.4390000104904175}],"concepts":[{"id":"https://openalex.org/C169900460","wikidata":"https://www.wikidata.org/wiki/Q2200417","display_name":"Cognition","level":2,"score":0.607803463935852},{"id":"https://openalex.org/C27415008","wikidata":"https://www.wikidata.org/wiki/Q7256382","display_name":"Psychological intervention","level":2,"score":0.44470348954200745},{"id":"https://openalex.org/C180747234","wikidata":"https://www.wikidata.org/wiki/Q23373","display_name":"Cognitive psychology","level":1,"score":0.4152769446372986},{"id":"https://openalex.org/C2780665704","wikidata":"https://www.wikidata.org/wiki/Q959298","display_name":"Intervention (counseling)","level":2,"score":0.41444772481918335},{"id":"https://openalex.org/C165637930","wikidata":"https://www.wikidata.org/wiki/Q845527","display_name":"Mathematical anxiety","level":3,"score":0.4104449450969696},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.38879910111427307},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.37831711769104004},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.0},{"id":"https://openalex.org/C558461103","wikidata":"https://www.wikidata.org/wiki/Q154430","display_name":"Anxiety","level":2,"score":0.0},{"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:d-scholarship.pitt.edu:35289","doi":null,"is_oa":true,"landing_page_url":"https://d-scholarship.pitt.edu/35289/1/Liu_Dissertation_Investigating%20Math%20Mechanisms_ETD_final_1.pdf","pdf_url":"http://d-scholarship.pitt.edu/35289/1/Liu_Dissertation_Investigating%20Math%20Mechanisms_ETD_final_1.pdf","source":{"id":"https://openalex.org/S4306402372","display_name":"D-Scholarship@Pitt (University of Pittsburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170201317","host_organization_name":"University of Pittsburgh","host_organization_lineage":["https://openalex.org/I170201317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"mag:2954465356","doi":null,"is_oa":false,"landing_page_url":"http://d-scholarship.pitt.edu/35289/","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":{"id":"pmh:oai:d-scholarship.pitt.edu:35289","doi":null,"is_oa":true,"landing_page_url":"https://d-scholarship.pitt.edu/35289/1/Liu_Dissertation_Investigating%20Math%20Mechanisms_ETD_final_1.pdf","pdf_url":"http://d-scholarship.pitt.edu/35289/1/Liu_Dissertation_Investigating%20Math%20Mechanisms_ETD_final_1.pdf","source":{"id":"https://openalex.org/S4306402372","display_name":"D-Scholarship@Pitt (University of Pittsburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170201317","host_organization_name":"University of Pittsburgh","host_organization_lineage":["https://openalex.org/I170201317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},"sustainable_development_goals":[{"score":0.8278999924659729,"display_name":"Quality education","id":"https://metadata.un.org/sdg/4"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2954465356.pdf","grobid_xml":"https://content.openalex.org/works/W2954465356.grobid-xml"},"referenced_works_count":108,"referenced_works":["https://openalex.org/W209594168","https://openalex.org/W1015013738","https://openalex.org/W1493258968","https://openalex.org/W1669314434","https://openalex.org/W1799486215","https://openalex.org/W1963973994","https://openalex.org/W1965333862","https://openalex.org/W1967654316","https://openalex.org/W1969953200","https://openalex.org/W1980546639","https://openalex.org/W1981433596","https://openalex.org/W1981548213","https://openalex.org/W1985525819","https://openalex.org/W1985701917","https://openalex.org/W1989085009","https://openalex.org/W1990688007","https://openalex.org/W1997301264","https://openalex.org/W1998683120","https://openalex.org/W2006697556","https://openalex.org/W2007177889","https://openalex.org/W2012934300","https://openalex.org/W2013424363","https://openalex.org/W2014481741","https://openalex.org/W2015008170","https://openalex.org/W2015191501","https://openalex.org/W2020001059","https://openalex.org/W2027115852","https://openalex.org/W2035295062","https://openalex.org/W2036671961","https://openalex.org/W2037222790","https://openalex.org/W2037863475","https://openalex.org/W2038507018","https://openalex.org/W2040323638","https://openalex.org/W2041073898","https://openalex.org/W2042395498","https://openalex.org/W2043721471","https://openalex.org/W2044433368","https://openalex.org/W2047363189","https://openalex.org/W2050052198","https://openalex.org/W2051073825","https://openalex.org/W2055754709","https://openalex.org/W2058167172","https://openalex.org/W2062802998","https://openalex.org/W2064283772","https://openalex.org/W2065018473","https://openalex.org/W2068475187","https://openalex.org/W2068681777","https://openalex.org/W2075953930","https://openalex.org/W2083194920","https://openalex.org/W2085633407","https://openalex.org/W2087499131","https://openalex.org/W2088175925","https://openalex.org/W2090066738","https://openalex.org/W2090901636","https://openalex.org/W2094133148","https://openalex.org/W2099894028","https://openalex.org/W2100305841","https://openalex.org/W2100414621","https://openalex.org/W2103810998","https://openalex.org/W2103921488","https://openalex.org/W2107029160","https://openalex.org/W2110638291","https://openalex.org/W2114474640","https://openalex.org/W2115386976","https://openalex.org/W2120833953","https://openalex.org/W2121822954","https://openalex.org/W2123235791","https://openalex.org/W2126612724","https://openalex.org/W2127599416","https://openalex.org/W2134407639","https://openalex.org/W2136103657","https://openalex.org/W2136211634","https://openalex.org/W2137962211","https://openalex.org/W2141445112","https://openalex.org/W2142915129","https://openalex.org/W2143287810","https://openalex.org/W2147244822","https://openalex.org/W2149606986","https://openalex.org/W2159990821","https://openalex.org/W2160277448","https://openalex.org/W2160443699","https://openalex.org/W2163123484","https://openalex.org/W2167123834","https://openalex.org/W2167156572","https://openalex.org/W2170003707","https://openalex.org/W2238632339","https://openalex.org/W2281029169","https://openalex.org/W2286032394","https://openalex.org/W2345558807","https://openalex.org/W2400368494","https://openalex.org/W2411630809","https://openalex.org/W2462026930","https://openalex.org/W2498129876","https://openalex.org/W2504555135","https://openalex.org/W2508364723","https://openalex.org/W2511227844","https://openalex.org/W2531352963","https://openalex.org/W2536326322","https://openalex.org/W2586436514","https://openalex.org/W2613590599","https://openalex.org/W2724114227","https://openalex.org/W2766093218","https://openalex.org/W2789034346","https://openalex.org/W2795333070","https://openalex.org/W2801335932","https://openalex.org/W2802889977","https://openalex.org/W2803126412","https://openalex.org/W4240553276"],"related_works":["https://openalex.org/W2160443699","https://openalex.org/W4380142336","https://openalex.org/W7112690614","https://openalex.org/W2062168040","https://openalex.org/W2476110125","https://openalex.org/W4400652341","https://openalex.org/W798128891","https://openalex.org/W6991735444","https://openalex.org/W31963233","https://openalex.org/W2117161524"],"abstract_inverted_index":{"College":[0],"dropout":[1],"is":[2],"a":[3,88,172],"significant":[4],"issue":[5],"that":[6,22,31,112,123,132,175,196,207],"particularly":[7],"plagues":[8],"students":[9],"with":[10,140,161],"poor":[11],"math":[12,25,35,78,100,134,143,151,162,178,191,203],"preparation.":[13],"Many":[14],"studies":[15,39],"have":[16,40,64],"attempted":[17],"to":[18,24,47,57,72,77,119,146,159],"understand":[19],"the":[20,48,85,105,121,127,130,149],"factors":[21,122],"contribute":[23],"performance":[26,179],"and":[27,92,96,129,182],"create":[28],"training":[29,110],"interventions":[30],"can":[32],"effectively":[33],"improve":[34],"achievement.":[36],"However,":[37],"few":[38,63],"investigated":[41,84],"these":[42,116],"questions":[43],"within":[44],"populations":[45],"similar":[46],"lower":[49],"achieving":[50],"adults":[51,154],"who":[52,155],"are":[53,156],"most":[54,157],"at":[55,66,70],"risk":[56],"drop":[58],"out":[59],"from":[60],"college.":[61,164],"Further,":[62],"looked":[65],"many":[67],"potential":[68],"mechanisms":[69,118,131,195,206],"once":[71],"determine":[73,120],"how":[74],"each":[75],"contributes":[76],"performance.":[79,101],"In":[80],"this":[81],"dissertation,":[82],"we":[83,137,168],"relationships":[86],"between":[87],"number":[89,199,211],"of":[90,99,107,115,171],"cognitive":[91,117],"individual":[93],"difference":[94],"measures":[95],"different":[97],"types":[98],"We":[102],"also":[103],"evaluated":[104],"effectiveness":[106],"an":[108],"estimation-based":[109],"program":[111],"targeted":[113],"one":[114],"predict":[124],"progress":[125],"during":[126],"intervention":[128],"explain":[133],"improvements.":[135],"Importantly,":[136],"recruited":[138],"participants":[139],"relatively":[141],"low":[142],"skill":[144],"level":[145],"better":[147],"examine":[148],"underlying":[150],"foundations":[152],"in":[153,163,180,186],"likely":[158],"struggle":[160],"Across":[165],"both":[166],"studies,":[167],"find":[169],"evidence":[170],"representational":[173],"shift":[174],"supports":[176],"higher":[177,187],"procedural":[181,190],"complex":[183,202],"math;":[184],"specifically,":[185],"math-skilled":[188],"individuals,":[189],"relies":[192],"more":[193],"on":[194],"involve":[197,208],"non-symbolic":[198],"representations,":[200],"while":[201],"draws":[204],"upon":[205],"primarily":[209],"symbolic":[210],"representations.":[212]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2019-07-12T00:00:00"}
