[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-179805-105":59,"doc-detail-179805-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","public2farticles2fojs-arje-3052fg298","public%2Farticles%2Fojs-arje-305%2Fg298","","This document focuses on enhancing pupils' problem-solving skills through Cognitively Guided Instruction and the Concrete-Pictorial-Abstract (CPA) approach. It outlines the performance indicators for word problems, emphasizing comprehension, modeling techniques, solution strategies, and accuracy. The document details how to develop pupils' abilities to understand problems, model them using CPA, manipulate concrete and visual models, recognize relationships, use counting strategies, articulate solutions, and make sense of answers. The CPA approach is further explained as a progression from manipulating concrete materials to pictorial representations and finally to abstract notation. The document also addresses problem-solving skills, including conceptual understanding and procedural knowledge of fundamental operations, and presents various visualization models such as those with numerals, symbols, tallying, and number sentences, illustrating different levels of complexity in problem representation.",{"@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":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/public2farticles2fojs-arje-3052fg298/179805/",{"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/public2farticles2fojs-arje-3052fg298/179805.png","ImageObject",300,407,{"name":92,"@type":93},"Chumphorn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-02",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is Cognitively Guided Instruction?","Question",{"text":112,"@type":113},"Cognitively Guided Instruction is an approach aimed at developing pupils' abilities to understand, model, and solve word problems effectively, progressing from concrete representations to abstract concepts.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does the Concrete-Pictorial-Abstract (CPA) approach entail?",{"text":117,"@type":113},"The CPA approach involves three stages: first, the physical manipulation of concrete materials, second, creating pictorial representations from these manipulations, and third, problem-solving using abstract notation.",{"name":119,"@type":110,"acceptedAnswer":120},"What are the key elements of performance in word problems as manifested by Cognitively Guided Instruction?",{"text":121,"@type":113},"Performance is manifested through comprehension of the word problem, the modeling techniques used, the solution strategy employed, and the accuracy of the solution and answer.","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},179805,1790032106,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},2336475401981,"https://ap-avatar.wpscdn.com/avatar/22000c94efd8d5204d?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786935347598174694","| Models/Pictures | | |  |\n| --- | --- | --- | --- |\n| Models with Numerals | |  |  |\n| Models with Symbols | |  |  |\n| [https://myeduheart.com/publications/jour](https://myeduheart.com/publications/jour) |  |  | nals/ARJE |\n\n\n| Models with Counting/Tallying | |\n| --- | --- |\n| Models with Numerals and Symbols | |\n| Models with Numerals and Counting/Tallying | |\n| Models with Counting/Tallying and Number Sentence | |\n| Models with Numerals, Counting/Tallying, and Number Sentence | |\n\n\n| Models/Pictures | | |  |  |\n| --- | --- | --- | --- | --- |\n| Models with Numerals | |  |  |  |\n| Models with Symbols | |  | |  |\n| Models with Counting/Tallying | |  |  | |\n\n\n| Models with Numerals and Symbols | | |  |\n| --- | --- | --- | --- |\n| Models with Symbols and Counting/Tallying | |  |  |\n| Models with Numerals and Counting/Tallying | |  |  |\n| Models with Counting/Tallying and Number Sentence | |  |  |\n| Models with Numerals, Counting/Tallying, and Number Sentence | |  | |\n| Models with Numerals, Counting/Tallying, Number Sentence, and Skip Counting | \u003Cbr>|  |  |\n\n| Direct Modeling | |  | |  |\n| --- | --- | --- | --- | --- |\n| Invented Algorithm | | |  |  |\n| Direct Modeling with Counting | |  |  | |\n| Direct Modeling with Derived Facts or Recall | | |  |  |\n| Direct Modeling with Counting and an Invented Algorithm | |  |  |  |\n\n\n| Direct Modeling | |  |\n| --- | --- | --- |\n| Invented Algorithm | | |\n| Direct Modeling with Counting | |  |","cbCaic2D8onH4wjp","https://ap.wps.com/l/cbCaic2D8onH4wjp","pdf",1937545,18,"English","# Cognitively Guided Instruction\n## To develop pupils' ability to:\n### Understand the problem\n### Model the problem in various ways including CPA Approach\n### Manipulate the concrete model and/or visual model\n### Recognize the relationships of the elements of the model\n### Use counting strategies or algorithmic procedures\n### Articulate the solution verbally, in symbols or in a number sentence\n### Make sense of the solution and answers\n# Concrete-Pictorial-Abstract Approach\n## Physical manipulation of concrete materials\n## Pictorial representation from concrete manipulation\n## Problem solving using abstract notation (Witzel, 2005)\n# Problem Solving Skills of Pupils\n## Conceptual Understanding\n## Procedural Knowledge on the four fundamental operations\n# Models/Pictures","[{\"question\":\"What is Cognitively Guided Instruction?\",\"answer\":\"Cognitively Guided Instruction is an approach aimed at developing pupils' abilities to understand, model, and solve word problems effectively, progressing from concrete representations to abstract concepts.\"},{\"question\":\"What does the Concrete-Pictorial-Abstract (CPA) approach entail?\",\"answer\":\"The CPA approach involves three stages: first, the physical manipulation of concrete materials, second, creating pictorial representations from these manipulations, and third, problem-solving using abstract notation.\"},{\"question\":\"What are the key elements of performance in word problems as manifested by Cognitively Guided Instruction?\",\"answer\":\"Performance is manifested through comprehension of the word problem, the modeling techniques used, the solution strategy employed, and the accuracy of the solution and answer.\"}]","public%2Farticles%2Fojs-arje-305%2Fg298 | PDF",1788338297,45]