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CTD was delivered via flashcards, supported initially by skip counting and later paired with math racetrack activities. Visual analysis, PEM-T and Tau-U effect sizes, and hierarchical piecewise regression showed immediate and substantial gains, with high social validity and perceived effectiveness.",{"@graph":14,"@context":63},[15,34,54],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/healthcare/","Healthcare",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/using-constant-time-delay-to-teach-multiplication-facts-to-two-fourth-grade-boys-with-learn-ing-difficulties/579838/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":48,"encodingFormat":47,"isAccessibleForFree":49,"interactionStatistic":50},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/using-constant-time-delay-to-teach-multiplication-facts-to-two-fourth-grade-boys-with-learn-ing-difficulties/579838.png","ImageObject",300,407,{"name":42,"@type":43},"Asher","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-15",true,{"@type":51,"interactionType":52,"userInteractionCount":4},"InteractionCounter",{"@type":53},"ViewAction",{"@type":55,"mainEntity":56},"FAQPage",[57],{"name":58,"@type":59,"acceptedAnswer":60},"What outcomes did the study report for multiplication fluency?","Question",{"text":61,"@type":62},"Both students showed immediate and substantial gains in multiplication fluency, supported by visual analysis, effect size indices (PEM-T, Tau-U), hierarchical piecewise regression, and high social validity ratings.","Answer","https://schema.org",{"og:url":32,"og:type":65,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":67,"canonical":32},"index,follow",{"doc_id":69,"site_id":7},579838,1792036444,{"code":4,"msg":72,"data":73},"success",[74,78,82,86,91,96,100,105,110,113,117],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":75,"show_sort_weight":76,"slug":77},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":79,"show_sort_weight":80,"slug":81},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":83,"show_sort_weight":84,"slug":85},"Exam",70,"exam",{"id":87,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},5,"Comic",60,"comic",{"id":92,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},6,"Technology",50,"technology",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":98,"slug":99},7,40,"healthcare",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},8,"Research & Report",30,"research-report",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},9,"Religion & Spirituality",20,"religion-spirituality",{"id":108,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":108,"slug":112},"World Cup","world-cup",{"id":114,"doc_module":4,"doc_module_name":25,"category_name":115,"show_sort_weight":114,"slug":116},10,"Lifestyle","lifestyle",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":119,"show_sort_weight":87,"slug":120},19,"General","general",{"code":4,"msg":72,"data":122},{"doc_id":69,"user_id":123,"nickname":42,"user_avatar":124,"doc_module":4,"category_id":97,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":125,"file_id":126,"file_url":127,"file_type":128,"file_size":129,"view_count":4,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":130,"language":131,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":132,"faqs":133,"seo_title":134,"seo_description":12,"update_tm":70,"read_time":98},687197207639,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Learning Disabilities: A Contemporary Journal 23(2), 201-216, 2025 Copyright @ by LDW 2025  \nUsing Constant Time Delay to Teach Multiplication Facts to Two Fourth-Grade Boys with Learn  \ning Difficulties  \nLinda Bell*  \nLVR Enst Jandl School Bornheim  \nMatthias Grünke  \nAnne Barwasser  \nSusanne Hoff  \nDepartment of Special Education and Rehabilitation, University of Cologne  \nConstant Time Delay (CTD) is a structured, error-reducing teaching strategy with promising applications for students with mathematical learning difficulties (MLD) . In this study, we systematically replicated CTD in a German inclusive classroom to evaluate its effects on multiplication fact fluency. Two fourth-grade boys with persistent multiplication difficulties but adequate addition skills participated in parallel singlecase experiments using two multiple-baseline designs across the 6-, 7-, and 8-times tables. CTD was implemented through flashcard practice, initially supported by skip counting and later complemented with math racetrack activities for motivation. Results demonstrated immediate and substantial gains in multiplication fluency for both students, confirmed through visual analysis, effect size indices (PEM-T, Tau-U), and hierarchical piecewise regression. Social validity ratings indicated high acceptance and perceived effectiveness. Limitations include the short intervention period and the combined use of supplemental strategies, findings provide preliminary evidence that CTD is a feasible and effective method for strengthening arithmetic fact retrieval in students with MLD. Future research should pursue larger-scale replications, long-term followup, and systematic isolation of CTD components to establish a stronger evidence base.  \nKeywords: constant time delay, multiplication fluency, mathematical learning difficulties, arithmetic fact retrieval, single-case design  \nIntroductIon  \nThe Importance of Multiplication and Challenges in Learning  \nMathematical processes are deeply embedded in everyday life. They appear constantly – whether shopping, cooking, planning, or budgeting. People routinely use mathematics to compare prices, manage household finances, or calculate time schedules. Among the basic operations, multiplication plays a particularly crucial role (Haigh, 2019) . While addition, subtraction, or division are often needed in specific situations, multiplication is involved wherever quantities occur regularly, uniformly, or in structured units (such as price per item, time per task, amount per person, or portions per meal) . Moreover, foundational multiplication skills are strong predic-  \n*Please send correspondence to: to Linda Bell, LVR-Ernst-Jandl-Schule, Wallrafstr. 4, 53332 Bornheim, Germany, Email: [lindabell@gmx.de](lindabell@gmx.de).  \nLearning Disabilities: A Contemporary Journal 23(2), 201-216, 2025  \ntors of higher-order mathematical competence, making their mastery essential not only for daily functioning but also for long-term academic success (Fullerton, 2020) .  \nTo apply multiplication efficiently and accurately in everyday situations, individuals require a solid foundation of factual knowledge in this area. While understanding the principle of multiplication is necessary, it is not sufficient; secure factual knowledge is also essential. Simple and frequently recurring problems (such as 3 × 4) should not require fresh computation each time but should instead be retrieved directly from memory. Such knowledge enables rapid and error-free calculations, thereby conserving cognitive resources for more complex problem-solving tasks (Geary et al., 2012). Automating basic arithmetic substantially reduces cognitive load, freeing working memory for higher-level reasoning (Fuchs et al., 2005; Menon, 2016; Swanson & Sachse-Lee, 2001) .  \nStudents who struggle with mathematics in general—and multiplication in particular—often face significant challenges in their academic development, which can limit their educational opportuniti","cbCaif4FoaazOBBi","https://ap.wps.com/l/cbCaif4FoaazOBBi","pdf",217913,16,"English","# IntroductIon\n## The Importance of Multiplication and Challenges in Learning\n## Principles of Effective Instruction in Mathematics\n## Constant Time Delay (CTD) as a Targeted Intervention","[{\"question\":\"What outcomes did the study report for multiplication fluency?\",\"answer\":\"Both students showed immediate and substantial gains in multiplication fluency, supported by visual analysis, effect size indices (PEM-T, Tau-U), hierarchical piecewise regression, and high social validity ratings.\"}]","Using Constant Time Delay to Teach Multiplication Facts to Two Fourth-Grade Boys with Learn ing Difficulties | PDF"]