[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-588781-105":59,"doc-detail-588781-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","8th-grade-students-understanding-of-the-definition-of-rectangle-1","8TH GRADE STUDENTS’ UNDERSTANDING OF THE DEFINITION OF RECTANGLE 1","","A descriptive study investigates how well 8th grade students define a rectangle and which aspects of the definition they can express. Ninety-three students completed a written open-ended test based on an adapted instrument. Researchers independently coded responses and derived final codes. Results show that students lacked sufficient and necessary conditions, frequently used terminology incorrectly, and mostly provided properties or visual examples rather than formal definitions, indicating understanding at Van Hiele Level 1.",{"@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/8th-grade-students-understanding-of-the-definition-of-rectangle-1/588781/",{"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/8th-grade-students-understanding-of-the-definition-of-rectangle-1/588781.png","ImageObject",300,407,{"name":92,"@type":93},"Chumphorn","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},"How was students’ understanding of the definition of a rectangle assessed?","Question",{"text":112,"@type":113},"The study used a written open-ended test asking students to define a rectangle, adapted from Ahuja (1996). Responses were coded independently by researchers and then consolidated into final codes.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What did the findings show about students’ ability to define a rectangle?",{"text":117,"@type":113},"None of the students provided sufficient and necessary conditions in their definitions. Most students used terminology incorrectly and mainly listed rectangle properties or gave visual examples, with only a few able to construct a definition.",{"name":119,"@type":110,"acceptedAnswer":120},"At what Van Hiele level were the students’ definitions evaluated?",{"text":121,"@type":113},"The students were concluded to be at Van Hiele Level 1, where learners perceive figures as whole shapes and rely on visual characteristics rather than logically constructed definitions.","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},588781,1792065921,{"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":34,"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":129,"read_time":144,"preview_page_count":4},2336475401981,"https://ap-avatar.wpscdn.com/avatar/22000c94efd8d5204d?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786935347598174694","8TH GRADE STUDENTS’UNDERSTANDING OF THE  \nDEFINITION OF RECTANGLE 1  \nEmine Gaye Çontay, Asuman Duatepe-Paksu  \nAbstract: This is a descriptive study which attempts to answer how well 8th grade students define a rectangle. The subjects for this study were 93 of 8th grade students. The students were administered a written open ended test on the definition of a rectangle which was adapted from Ahuja (1996) . Responses of the students were coded by each researcher independently and common expressions were grouped. Then, new codes were created and the final codes were generated by the researchers. Findings of the study revealed that none of the students could provide sufficient and necessary conditions for their descriptions and definitions. Besides, it was seen that the majority of the students used the terminology incorrectly. While trying to define the rectangle, most of the students listed the properties of the rectangle and only a few students were able to construct a definition. Students mostly gave visual examples. From these findings, it can be concluded that students were unsuccessful in defining the rectangle and they were at Van Hiele Level 1.  \nKey words: geometry, Van Hiele levels, definition, rectangle, 8th grade students  \n1. Introduction  \nThe definition of a concept is a form of words which specifies the concept (Tall and Vinner, 1981) . According to Herbst, Gonzales, and Macke (2005, 17)“Mathematical definitions can be described logically as the statement of the necessary and sufficient conditions that an object must meet to be labeled by a certain word or expression”. A student can learn a definition by rote or she/he can learn it more meaningfully by relating with the concept defined (Tall and Vinner, 1981) . As “definitions are the basic building blocks of mathematical thinking (Çakıroğlu, 2013, p. 1), they are fundamental in mathematics education and they improve at school years (Zavlavski and Shir 2005) . According to Alonso (2009), the correctness of the definitions promotes the development of science. Definitions show the intellectual progresses by making separations of different features and properties which corrects the transitions connecting with the other definitions and with reasoning which leads to mathematical proofs. Concepts should be defined precisely and clearly to express a mathematical system or idea. Defining concepts in many different ways can cause controversial situations; so some basic elements should be considered while making definitions such as considering the hierarchical concept structure, describing an existing phenomenon, equivalence of different definitions for the same concept, appropriateness with the axiomatic structure, providing sufficient and necessary conditions and being economical (Çakıroğlu, 2013) .  \nClassification is as important as definition in mathematics education (Fujita and Jones 2007) . Poincare, (1914, 452, in: Fujita and Jones, 2007, 3) says that: “The definition will not be understood until you have shown not only the object defined, but the neighboring objects from which it has to be distinguished, until you have made it possible to grasp the difference, and have added explicitly your reason for saying this or that in stating the definition”. Concepts in mathematics are built on each other  \n1 This study was presented in ECER 2012 which was held on 17-21 September, in Cadiz, Spain  \nand this leads to a hierarchical structure and this hierarchical structure is the nature of mathematics (Çakıroğlu, 2013) . De Villiers (1994, 12) says that “The classification of any set of concepts does not take place independently of the process of defining”. The hierarchy in definitions requires consideration of the hierarchical relationships between these concepts. Considering the definition of“A rectangle in which all angle measurements and side lengths are equal is called a square, the“rectangle” is more general concept class used in defining the square (Çakıroğlu, 2013) .","cbCaimaPhJYsOhbb","https://ap.wps.com/l/cbCaimaPhJYsOhbb","pdf",431627,14,"English","# Introduction\n## Concept definition and its role in mathematics education\n## Classification versus definition\n## Van Hiele theory and geometric development levels","[{\"question\":\"How was students’ understanding of the definition of a rectangle assessed?\",\"answer\":\"The study used a written open-ended test asking students to define a rectangle, adapted from Ahuja (1996). Responses were coded independently by researchers and then consolidated into final codes.\"},{\"question\":\"What did the findings show about students’ ability to define a rectangle?\",\"answer\":\"None of the students provided sufficient and necessary conditions in their definitions. Most students used terminology incorrectly and mainly listed rectangle properties or gave visual examples, with only a few able to construct a definition.\"},{\"question\":\"At what Van Hiele level were the students’ definitions evaluated?\",\"answer\":\"The students were concluded to be at Van Hiele Level 1, where learners perceive figures as whole shapes and rely on visual characteristics rather than logically constructed definitions.\"}]","8TH GRADE STUDENTS’ UNDERSTANDING OF THE DEFINITION OF RECTANGLE 1 | PDF",35]