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Reports results from a three-year study in which 78 teacher candidates used concrete and virtual manipulatives to learn fractions, integers, and non-decimal-based numbers, then compared formats by ease of use and helpfulness. Frames the need to bridge from concrete representations to abstract algorithms.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/virtual-vs-concrete-manipulatives-in-mathematics-teacher-education-is-one-type-more-effective-than-the-other-research-paper-on-a-three-year-study-comparing-virtual-and-concrete-manipulatives/599712/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/virtual-vs-concrete-manipulatives-in-mathematics-teacher-education-is-one-type-more-effective-than-the-other-research-paper-on-a-three-year-study-comparing-virtual-and-concrete-manipulatives/599712.png","ImageObject",300,407,{"name":92,"@type":93},"jayni","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main purpose of comparing virtual and concrete manipulatives?","Question",{"text":112,"@type":113},"To determine whether virtual manipulatives are as effective as concrete, hands-on manipulatives in building pre-service teachers’ conceptual understanding of number concepts and relationships.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How was conceptual understanding addressed in the study’s framework?",{"text":117,"@type":113},"Conceptual understanding is defined as knowledge rich in relationships, supported by visual, tactile, and kinesthetic experiences, reinforced through cooperative learning and reflective discussion.",{"name":119,"@type":110,"acceptedAnswer":120},"What research questions guide the comparison between the two manipulative formats?",{"text":121,"@type":113},"The study investigates teachers’ perceived advantages and disadvantages, differences in effectiveness for conceptual understanding, ease of use and availability, whether using both types provides benefits, and whether order affects transition to abstract algorithms.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},599712,1792208639,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144},3985747859343,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","CIMLE  \nCurrent Issues in Middle Level Education (2011) 16(2), 1-6  \nVirtual vs. Concrete Manipulatives in Mathematics Teacher Education:  \nIs One Type More Effective Than the Other?  \nDr. AnnitaW. Hunt, Ed.D.  \nDr. Kelli L. Nipper, Ph.D.  \nDr. Linda E. Nash, Ph.D.  \nClayton State University  \nAre virtual manipulativesas effective as concrete (hands-on) manipulativesin building conceptual understanding of number conceptsandrelationships in pre-service middle grades teachers? In the past, the use of concrete manipulativesin mathematics courses for Clayton State University’s pre-servicemiddle grades teachers has been effective in building conceptual understanding of a variety of mathematical topics. This paper presents the resultsof a three-year study in which 78 middle grades mathematics teacher candidates used various concrete and virtual manipulatives to study fractions, integers and nondecimal-based numbers. They then compared eachtypeof manipulativefor easeof use and helpfulness in understanding the conceptsaddressed.  \nSince the inception of Clayton State’s University’s Middle Level Teacher Education program in 1993, concrete manipulatives have been used successfully in the junior-level Number Concepts & Relationships course. In addition to a textbook, students were required to purchase a manipulative kit that included Cuisenaire Rods, Pattern Blocks, Fraction Circles, and Two-color Counters. Students worked collaboratively to build conceptual understanding of the arithmetic of fractions and integers, using those manipulatives. Students’ understanding was assessed by small group and whole class discussionsand by performance tests. Certain results occurred consistently, year after year, class after class. Invariably, students declared, “I wish I had been taught this way. This makes so much more sense.” And “I always hated (fill indifferent topics—fractions, negative integers, etc.) , but now I understand it.”  \nRationale  \nAlthough successful in the past, are concrete manipulatives the best resource for today’s students? The ubiquitous use of various forms of technology by today’s youth provides more incentive to investigate the usefulness of virtual manipulatives. Might they be more motivating to twenty-first century students than the more toy-like concrete manipulatives? Considering the meaning of “conceptual understanding” and the often omitted component of bridging from the concrete to the abstract, is there a difference between concrete and virtual manipulatives in the ease of that transition? Is there an advantage to using both types; and if so, does order matter? It is important for teacher educators to investigate these questions, and the teacher education classroom provides the ideal setting in which to conduct this research.  \nResearch Questions  \nWhat do teachers perceive asthe advantagesand disadvantages of each manipulative format? Specifically,  \n¾ What roles should each type play in mathematics teacher education?  \n¾ Is there a difference in the effectiveness of the two formats to build pre-service teachers’conceptual understanding?  \n¾ Is one type easier to use or more readily available than the other?  \n¾ Is there an advantage to incorporating both types of manipulatives, and  \n¾ If so, does the order in which they are used impact the development of conceptual understanding or students’ability to transition to the abstract algorithms?  \n¾ Does one format facilitate bridging to the abstract better than the other?  \nTo answer these questions, we began with areview of current research reports.  \nCurrent Research  \nConceptual Understanding  \nBecause weare concerned with the enhancement of conceptual understanding, it is imperative that we define the expression. Although definitions differ, we will adopt the statement from Hiebert and Lefevre (1986, pp. 3-4) that conceptual knowledge is “knowledge that is rich in relationships…Relationships pervade the individual factsand propositions so that all pieces of infor","cbCaidkJDTjD9TeO","https://ap.wps.com/l/cbCaidkJDTjD9TeO","pdf",58773,"English","# Introduction\n## Rationale\n## Research Questions\n## Current Research\n### Conceptual Understanding\n### Pedagogical Content Knowledge\n### Research Involving Concrete Manipulatives","[{\"question\":\"What is the main purpose of comparing virtual and concrete manipulatives?\",\"answer\":\"To determine whether virtual manipulatives are as effective as concrete, hands-on manipulatives in building pre-service teachers’ conceptual understanding of number concepts and relationships.\"},{\"question\":\"How was conceptual understanding addressed in the study’s framework?\",\"answer\":\"Conceptual understanding is defined as knowledge rich in relationships, supported by visual, tactile, and kinesthetic experiences, reinforced through cooperative learning and reflective discussion.\"},{\"question\":\"What research questions guide the comparison between the two manipulative formats?\",\"answer\":\"The study investigates teachers’ perceived advantages and disadvantages, differences in effectiveness for conceptual understanding, ease of use and availability, whether using both types provides benefits, and whether order affects transition to abstract algorithms.\"}]","Virtual vs. Concrete Manipulatives in Mathematics Teacher Education - Is One Type More Effective Than the Other? - Research paper on a three-year study comparing virtual and concrete manipulatives | PDF",1792089293,15]