[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-600810-105":59,"doc-detail-600810-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","using-concrete-manipulatives-in-mathematical-instruction","Using Concrete Manipulatives in Mathematical Instruction","","Concrete manipulatives strengthen early childhood mathematics instruction by linking concrete ideas to abstract concepts and supporting a smoother transition across learning stages. CRA (Concrete, Representational, Abstract) instruction uses physical materials first, then moves to drawings and pictorial representations, and finally to numbers and symbols. Interactive, hands-on experiences increase engagement, accessibility, retention, and positive attitudes toward education, while enabling instruction that meets learners at their developmental level.",{"@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/using-concrete-manipulatives-in-mathematical-instruction/600810/",{"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/using-concrete-manipulatives-in-mathematical-instruction/600810.png","ImageObject",300,407,{"name":92,"@type":93},"dhado","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are concrete manipulatives, and why are they used in math instruction?","Question",{"text":112,"@type":113},"Concrete manipulatives are physical objects used as teaching tools for hands-on learning. They help learners connect concrete ideas to abstract ideas, improving understanding and retention.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does CRA instruction progress across learning stages?",{"text":117,"@type":113},"CRA starts with manipulation of concrete materials, moves to representational activities (such as drawings or tallies), and reaches the abstract stage where numbers and symbols express understanding without relying on pictures or objects.",{"name":119,"@type":110,"acceptedAnswer":120},"How do concrete manipulatives support student engagement and accessibility?",{"text":121,"@type":113},"Interactive experiences with manipulatives increase relevance and engagement. Learners can participate directly, and everyday objects make mathematical knowledge easier to access for different mathematical levels.","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},600810,1792208671,{"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":29,"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},5909893218464,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Using Concrete Manipulativesin Mathematical Instruction  \n“A little creativity and enthusiasm are as effective as cutting edge tools for teaching mathematics to young children. Physical mathematics teaching aids can engage children’s minds in valuable ways that result in high retention of the information.”  \nDr. Julie P. Jones Margaret Tiller  \nWith the ever-increasing shift in the accountability movement, teachers and parents are constantly in search of the “key” to high-quality mathematical instruction. Teachers and parents believe they must compete with lively television shows, faddish computer applications, and popular video games in order to capture student attention and interest; however, using concrete manipulatives in math instruction can generate student interest in mathematics (Moch, 2001; Moyer, 2001) . This truth applies whether instruction is being performed in a formal learning setting, such as a classroom, or an informal learning setting, such as a family’s kitchen.  \nManipulatives are “physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics”(TeacherVision, 2009, p. 1) . Manipulatives can be particularly effective in further developing conceptual understanding in mathematics (Witzeland Allsopp, 2007), because they help students relate concrete ideas to abstract ideas, as well as link informal approaches with formal approaches (Uribe-Flórez & Wilkins, 2010). Using hands-on, concrete manipulatives throughout math instruction can lead to higher retention rates and a more positive student attitude toward education in general. The early childhood years, from ages 0-8, are critical in terms of development (McGuire, Kinzie, & Berch, 2012), so it is important to explore instructional strategies that align with and cater to the young child’s growing understanding of the world. As Smith (2009) writes,“A good manipulative bridges the gap between informal math and formal math. To accomplish this objective, the manipulative must fit the developmental level of the child”(p. 20) .  \n18  Vol 45, No 1, 2017  \nConcrete, Representational, Abstract Instruction  \nConcrete, Representational, Abstract (CRA) instruction is a process for teaching and learning mathematical concepts. Starting with manipulation of concrete materials (counters, beans, Unifix cubes), the process moves students to the representational level (tallies, dots, stamps), and peaks at the abstract level, at which numbers and symbols are used to demonstrate understandings (Witzel, 2005) . With the purpose of giving students a thorough understanding of math concepts, CRA instruction allows students to make associations from one stage of the process to the next. When students are allowed to first develop a concrete understanding of the math concept/skill, they are much more likely to perform that math skill and truly understand math concepts at the abstract level. Specific information for the stages ofCRA can be found in Table 1 (next page) .  \nChildren understand math better when they can see and touch it  \nStudent Engagement and Accessibility using CRA Instruction  \nWitzel, Smith, & Brownell (2001) suggest that interactive experiences with concrete manipulatives can increase  \nDimensions of Early Childhood  \nUsing Concrete Manipulatives in Mathematical Instruction  \nTable 1: CRA instruction materials and practice.  \n\n| Stages | Key Elements | Sample Problem | Explanation |\n| --- | --- | --- | --- |\n| Concrete | Chips, Unifix cubes, base ten blocks | | Here, a ten frame with colored counters is used to show the equation 7 + 3 = 10. |\n| Transition to Representational | Use of concrete and representational materials together | | Once the concrete materials have been used, students begin to draw their own ten frames using the concrete model as a guide. |\n| Representational | Tallies, dots, circles, stamps | | At the representational level ofCRA, the student is comfortable using pictures to solve the problem. |\n| Transit","cbCaibMHpnckF2aN","https://ap.wps.com/l/cbCaibMHpnckF2aN","pdf",273936,"English","# Concrete, Representational, Abstract Instruction\n## Children understand math better when they can see and touch it\n## Student Engagement and Accessibility using CRA Instruction\n## Do-It-Yourself Math Manipulatives","[{\"question\":\"What are concrete manipulatives, and why are they used in math instruction?\",\"answer\":\"Concrete manipulatives are physical objects used as teaching tools for hands-on learning. They help learners connect concrete ideas to abstract ideas, improving understanding and retention.\"},{\"question\":\"How does CRA instruction progress across learning stages?\",\"answer\":\"CRA starts with manipulation of concrete materials, moves to representational activities (such as drawings or tallies), and reaches the abstract stage where numbers and symbols express understanding without relying on pictures or objects.\"},{\"question\":\"How do concrete manipulatives support student engagement and accessibility?\",\"answer\":\"Interactive experiences with manipulatives increase relevance and engagement. Learners can participate directly, and everyday objects make mathematical knowledge easier to access for different mathematical levels.\"}]","Using Concrete Manipulatives in Mathematical Instruction | PDF",1792091426,15]