{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T18:07:37Z","timestamp":1789582057257,"version":"build-2803163510"},"reference-count":44,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2017,11,1]],"date-time":"2017-11-01T00:00:00Z","timestamp":1509494400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Research in Developmental Disabilities"],"published-print":{"date-parts":[[2017,11]]},"DOI":"10.1016\/j.ridd.2017.09.002","type":"journal-article","created":{"date-parts":[[2017,9,23]],"date-time":"2017-09-23T15:04:51Z","timestamp":1506179091000},"page":"163-174","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":40,"special_numbering":"C","title":["Using the virtual-abstract instructional sequence to teach addition of fractions"],"prefix":"10.1016","volume":"70","author":[{"given":"Emily C.","family":"Bouck","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiyoon","family":"Park","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jessica","family":"Sprick","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jordan","family":"Shurr","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laura","family":"Bassette","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abbie","family":"Whorley","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.ridd.2017.09.002_bib0005","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1111\/ldrp.12093","article-title":"Evidence-based practices: Applications of concrete representational abstract framework across math concepts for students with mathematics disabilities","volume":"31","author":"Agrawal","year":"2016","journal-title":"Learning Disabilities Research & Practice"},{"key":"10.1016\/j.ridd.2017.09.002_bib0010","series-title":"Acquisition of complex arithmetic skills and higher-order mathematics concepts","first-page":"295","article-title":"Evidence for cognitive science principles that impact learning in mathematics","author":"Booth","year":"2017"},{"key":"10.1016\/j.ridd.2017.09.002_bib0015","doi-asserted-by":"crossref","DOI":"10.1177\/0162643417727291","article-title":"Teaching equivalent fractions to secondary students with disabilities via the virtual-representational-abstract instructional sequence","author":"Bouck","year":"2017","journal-title":"Journal of Special Education Technology"},{"key":"10.1016\/j.ridd.2017.09.002_bib0020","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1177\/1053451209349530","article-title":"Virtual manipulatives: What are they and how teachers can use them?","volume":"45","author":"Bouck","year":"2010","journal-title":"Intervention in School and Clinic"},{"key":"10.1016\/j.ridd.2017.09.002_bib0025","unstructured":"Bouck, E. C., & Park, J. (in press). A systematic review of the literature on mathematics manipulatives to support students with disabilities. Education & Treatment of Children."},{"key":"10.1016\/j.ridd.2017.09.002_bib0030","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.ridd.2016.11.006","article-title":"Using the concrete-representational-abstract approach to support students with intellectual disability to solve change-making problems","volume":"60","author":"Bouck","year":"2017","journal-title":"Research in Developmental Disabilities"},{"key":"10.1016\/j.ridd.2017.09.002_bib0035","unstructured":"Bouck, E. C., Park, J., Shurr, J., Bassette, L., & Whorley, A. (under review). Using the virtual-representational-abstract approach to support students with intellectual disability in mathematics."},{"key":"10.1016\/j.ridd.2017.09.002_bib0040","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1007\/s10803-013-1863-2","article-title":"Virtual and concrete manipulatives: A comparison of approaches for solving mathematics problems for students with autism spectrum disorder","volume":"44","author":"Bouck","year":"2014","journal-title":"Journal of Autism and Developmental Disabilities"},{"key":"10.1016\/j.ridd.2017.09.002_bib0045","doi-asserted-by":"crossref","DOI":"10.1177\/0741932517721712","article-title":"The concrete-representational-abstract approach for students with learning disabilities","author":"Bouck","year":"2017","journal-title":"Remedial and Special Education"},{"key":"10.1016\/j.ridd.2017.09.002_bib0050","unstructured":"Bouck, E. C., Shurr, J., Bassette, L., Park, J., Kerr, J., & Whorley, A. (under review). Adding it up: Comparing concrete and app-based manipulatives to support students with disabilities with adding fractions."},{"key":"10.1016\/j.ridd.2017.09.002_bib0055","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1080\/1045988X.2011.603396","article-title":"Fix it with TAPE: Repurposing technology to be assistive technology for students with high incidence disabilities","volume":"56","author":"Bouck","year":"2012","journal-title":"Preventing School Failure"},{"key":"10.1016\/j.ridd.2017.09.002_bib0060","doi-asserted-by":"crossref","DOI":"10.1177\/1053451217702115","article-title":"Manipulative apps to support students with disabilities in mathematics","author":"Bouck","year":"2017","journal-title":"Intervention in School and Clinic"},{"key":"10.1016\/j.ridd.2017.09.002_bib0065","unstructured":"Brainingcamp (2017). Fraction Tiles. Retrieved from, https:\/\/itunes.apple.com\/us\/app\/fraction-tiles-manipulative\/id1111230448?mt=8."},{"key":"10.1016\/j.ridd.2017.09.002_bib0070","doi-asserted-by":"crossref","first-page":"308","DOI":"10.2511\/027494813805327205","article-title":"Early numeracy instruction for students with moderate and severe developmental disabilities","volume":"37","author":"Browder","year":"2012","journal-title":"Research & Practice for Persons with Severe Disabilities"},{"key":"10.1016\/j.ridd.2017.09.002_bib0075","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1111\/1540-5826.00066","article-title":"Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences","volume":"18","author":"Butler","year":"2003","journal-title":"Learning Disabilities Research & Practice"},{"key":"10.1016\/j.ridd.2017.09.002_bib0080","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1111\/1540-5826.00067","article-title":"Effects of manipulative instruction on solving area and perimeter problems by students with learning disabilities","volume":"18","author":"Cass","year":"2003","journal-title":"Learning Disabilities Research & Practice"},{"key":"10.1016\/j.ridd.2017.09.002_bib0085","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1177\/0741932514557271","article-title":"CEC\u2019s standards for classifying the evidence base of practices in special education","volume":"36","author":"Cook","year":"2014","journal-title":"Remedial and Special Education"},{"key":"10.1016\/j.ridd.2017.09.002_bib0090","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1177\/1053451212473151","article-title":"Explicit mathematics instruction: What teachers can do for teaching students with mathematics difficulties?","volume":"48","author":"Doabler","year":"2013","journal-title":"Intervention for School and Clinic"},{"key":"10.1016\/j.ridd.2017.09.002_bib0095","series-title":"Handbook of special education technology research and practice","first-page":"239","article-title":"Assistive technology and students with mild disabilities: From consideration to outcomes measurement","author":"Edyburn","year":"2005"},{"key":"10.1016\/j.ridd.2017.09.002_bib0100","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1177\/016264340602100408","article-title":"Cognitive prostheses for students with mild disabilities: Is this what assistive technology looks like?","volume":"21","author":"Edyburn","year":"2006","journal-title":"Journal of Special Education Technology"},{"key":"10.1016\/j.ridd.2017.09.002_bib0105","series-title":"Single case research methodology","author":"Gast","year":"2014"},{"key":"10.1016\/j.ridd.2017.09.002_bib0110","series-title":"Single subject research methodology in behavioral sciences","first-page":"176","article-title":"Visual analysis of graphic data","author":"Gast","year":"2014"},{"key":"10.1016\/j.ridd.2017.09.002_bib0115","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.3102\/0034654309334431","article-title":"Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components","volume":"79","author":"Gersten","year":"2009","journal-title":"Review of Educational Research"},{"key":"10.1016\/j.ridd.2017.09.002_bib0120","first-page":"7","article-title":"Eligibility under IDEA for other health impaired children","volume":"33","author":"Grice","year":"2002","journal-title":"School Law Bulletin"},{"key":"10.1016\/j.ridd.2017.09.002_bib0125","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1037\/a0019824","article-title":"Sources of group and individual differences in emerging fraction skills","volume":"102","author":"Hecht","year":"2010","journal-title":"Journal of Educational Psychology"},{"issue":"1","key":"10.1016\/j.ridd.2017.09.002_bib0130","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.jecp.2013.02.001","article-title":"Developmental predictors of fraction concepts and procedures","volume":"116","author":"Jordan","year":"2013","journal-title":"Journal of Experimental Child Psychology"},{"key":"10.1016\/j.ridd.2017.09.002_bib0135","first-page":"115","article-title":"The effects of concrete to semiconcrete to abstract instruction in the acquisition and retention of fraction concepts and skills","volume":"9","author":"Jordan","year":"1999","journal-title":"Learning Disabilities A Multidisciplinary Journal"},{"key":"10.1016\/j.ridd.2017.09.002_bib0140","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1177\/0741932512452794","article-title":"Single case intervention research design standards","volume":"34","author":"Kratochwill","year":"2013","journal-title":"Remedial and Special Education"},{"key":"10.1016\/j.ridd.2017.09.002_bib0145","doi-asserted-by":"crossref","first-page":"158","DOI":"10.5951\/teacchilmath.22.3.0158","article-title":"Unwrapping students\u2019 ideas about fractions","volume":"22","author":"Lewis","year":"2015","journal-title":"Teaching Children Mathematics"},{"key":"10.1016\/j.ridd.2017.09.002_bib0150","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1111\/j.1540-5826.2012.00363.x","article-title":"Using the concrete-representational-abstract sequence with integrated strategy instruction to teach subtraction with regrouping to students with learning disabilities","volume":"27","author":"Mancl","year":"2012","journal-title":"Learning Disabilities Research & Practice"},{"key":"10.1016\/j.ridd.2017.09.002_bib0155","first-page":"58","article-title":"The effects of using manipulatives in teaching math problem solving to students with learning disabilities","volume":"11","author":"Marsh","year":"1996","journal-title":"Learning Disabilities Research & Practice"},{"key":"10.1016\/j.ridd.2017.09.002_bib0160","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1111\/j.1540-5826.2011.00330.x","article-title":"A review of the literature: Fraction instruction for struggling learners in mathematics","volume":"26","author":"Misquitta","year":"2011","journal-title":"Learning Disabilities Research & Practice"},{"key":"10.1016\/j.ridd.2017.09.002_bib0165","series-title":"Foundations for success: The final report of the national mathematics advisory panel","author":"National Mathematics Advisory Panel","year":"2008"},{"key":"10.1016\/j.ridd.2017.09.002_bib0170","series-title":"Principles for designing intervention in mathematics","author":"National Center on Intensive Intervention","year":"2016"},{"key":"10.1016\/j.ridd.2017.09.002_bib0175","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.beth.2008.10.006","article-title":"An improved effect size for single case research: Nonoverlap of all pairs (NAP)","volume":"40","author":"Parker","year":"2009","journal-title":"Behavior Therapy"},{"key":"10.1016\/j.ridd.2017.09.002_bib0180","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1177\/0741932516643592","article-title":"Schema-based instruction with concrete and virtual manipulative to teach problem solving to students with autism","volume":"38","author":"Root","year":"2017","journal-title":"Remedial and Special Education"},{"key":"10.1016\/j.ridd.2017.09.002_bib0185","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1177\/0731948714550101","article-title":"Using virtual manipulative instruction to teach the concepts of area and perimeter to secondary students with learning disabilities","volume":"38","author":"Satsangi","year":"2015","journal-title":"Learning Disability Quarterly"},{"key":"10.1016\/j.ridd.2017.09.002_bib0190","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1177\/0731948716649754","article-title":"Comparing the effectiveness of virtual and concrete manipulatives to learn algebra for secondary students with learning disabilities","volume":"39","author":"Satsangi","year":"2016","journal-title":"Learning Disability Quarterly"},{"key":"10.1016\/j.ridd.2017.09.002_bib0195","doi-asserted-by":"crossref","DOI":"10.1080\/1045988X.2016.1275505","article-title":"The case for adopting virtual manipulatives in mathematics education for students with disabilities","author":"Satsangi","year":"2017","journal-title":"Preventing School Failure: Alternative Education for Children and Youth"},{"key":"10.1016\/j.ridd.2017.09.002_bib0200","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1177\/0741932515572910","article-title":"Fraction intervention for students struggling to learn mathematics: A research synthesis","volume":"36","author":"Shin","year":"2015","journal-title":"Remedial and Special Education"},{"key":"10.1016\/j.ridd.2017.09.002_bib0205","series-title":"Developing effective fractions instruction for kindergarten through 8th grade: A practice guide (NCEE 2010-4039)","author":"Siegler","year":"2010"},{"key":"10.1016\/j.ridd.2017.09.002_bib0210","first-page":"223","article-title":"An investigation of the effects of CRA instruction and students with autism spectrum disorder","volume":"50","author":"Stroizer","year":"2015","journal-title":"Education and Training in Autism and Developmental Disabilities"},{"key":"10.1016\/j.ridd.2017.09.002_bib0215","series-title":"Third graders\u2019 mathematics achievement and representation preference in using virtual and physical manipulative for adding fractions and balancing equations (Doctoral dissertation)","author":"Suh","year":"2005"},{"key":"10.1016\/j.ridd.2017.09.002_bib0220","series-title":"Wechsler Intelligence Scale for Children","author":"Wechsler","year":"2004"}],"container-title":["Research in Developmental Disabilities"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0891422217302251?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0891422217302251?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,8,27]],"date-time":"2018-08-27T05:24:14Z","timestamp":1535347454000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0891422217302251"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11]]},"references-count":44,"alternative-id":["S0891422217302251"],"URL":"https:\/\/doi.org\/10.1016\/j.ridd.2017.09.002","relation":{},"ISSN":["0891-4222"],"issn-type":[{"value":"0891-4222","type":"print"}],"subject":[],"published":{"date-parts":[[2017,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Using the virtual-abstract instructional sequence to teach addition of fractions","name":"articletitle","label":"Article Title"},{"value":"Research in Developmental Disabilities","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ridd.2017.09.002","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2017 Elsevier Ltd. All rights reserved.","name":"copyright","label":"Copyright"}]}}