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It presents four plane representation approaches—layered, orthogonal, coded orthogonal, and isometric—detailing their characteristics and educational implications. The analysis is grounded in a research experiment with primary school children in Grades 2, 4, 6, and 8, and offers practical guidance on when and how teachers should introduce each representation to support meaningful interpretation and information recovery.",{"@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/childrens-ability-for-using-different-plane-representations-of-space-figures/136887/",{"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/childrens-ability-for-using-different-plane-representations-of-space-figures/136887.png","ImageObject",300,407,{"name":92,"@type":93},"\tWilliam","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-17","2026-08-22",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},"Why are plane representations important in teaching Space Geometry?","Question",{"text":112,"@type":113},"Plane representations are crucial because any representation of a 3D solid in 2D loses some information, so learners must reconstruct missing meaning to interpret the figure accurately.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What four plane representation methods does the paper discuss?",{"text":117,"@type":113},"The paper presents four methods: layers, orthogonal, coded orthogonal, and isometric representations.",{"name":119,"@type":110,"acceptedAnswer":120},"How was the study conducted and with which students?",{"text":121,"@type":113},"The research experiment involved primary school children in Grades 2, 4, 6, and 8.","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},136887,1787394854,{"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":52,"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":129,"read_time":143},5909887254083,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","CHILDREN’S ABILITY FOR USING DIFFERENT PLANE  \n*  \nREPRESENTATIONS OF SPACE FIGURES  \nAngel Gutiérrez  \nDepartamento de Didáctica de la Matemática  \nUniversidad de Valencia  \nApartado 22045. 46071-Valencia (Spain)  \nAn important, but often neglected, aspect of the teaching and learning of Space Geometry is the use of plane representations of geometric solids (by ‘use’ I mean both draw and read). In this paper I present four ways of plane representation (by layers, orthogonal, coded orthogonal, and isometric ) that can be used at Schools: I describe the representations, I analyze their particularities, and I make some suggestions to teachers about the way and time for teaching each one of them. This is based on the results of a research experiment carried out with primary school children in Grades 2, 4, 6, and 8.  \nINTRODUCTION  \nIf we were thinking on an ideal school in the future, we could imagine classrooms with plenty of computers, many CDs lying on a shelf, and a big closet containing lots of apparatuses and manipulatives.  \nWhen the children in this classroom are starting the study of a new kind of geometric solid, the pyramid for instance, each pupil would be given by the teacher a pyramid and a CD for the computer. A few seconds later students shall have instant access to all the pyramids and other spatial objects they need for the lesson. First, the teacher asks them to spend some minutes handling their real pyramid, moving several pyramids on their computer’s screen and transforming them. Afterwards, with guidance by the teacher, the children would talk in group about their findings, make verbal descriptions of their pyramids, and put together the properties they have discovered.  \nThis may be a school of the 21st. Century, but today the textbooks are still the main source of information for school children, and likely it shall continue in this way for many years, at least in most countries in the world. In many schools, when children start to learn about pyramids (or cubes, prisms, cylinders, . . .), they only have available the description written in the book, accompanied by some colourful figures and by the teacher’s explanation. In many other schools, the previous work is complemented with physical models of pyramids, used by the teacher to show what a pyramid is, and by pupils to discover properties and elements of pyramids. So we have to pay attention to the way textbooks transmit to children information about Space Geometry, and tray to solve the limitations of this way of communication.  \nOur ordinary life provides plenty of interactions between plane and space, and most of them imply the dissemination of some kind of spatial information by means of plane data (drawings, schemas, pictures, figures, etc.) . And textbooks are still plane!! This issue is  \n* The research reported in this paper has been funded by the Universidad de Valencia in 1992-3.  \n34 GUTIERREZ  \nparticularly important for Space Geometry, since any kind of plane representation of spatial objects has some loss of information. Therefore, a person reading a plane representation of a solid has to recover as much of the lost information as possible. This phenomenon is called“restitution of meaning” by Parzysz (1988), and he points out the importance of having “a connivance between the author of the representation and its reader, it being possible only because of a common geometrical culture. This connivance is concerned in the first place with the nature of the objects represented (e.g., point, straight line, triangle, circle, plane, pyramid, cylinder,…)”. And this connivance is concerned in the second place with the typeof representation used (both author and reader have to agree in using the same type of plane representation) . For instance, the drawing in Figure 1-a can be interpreted in some different ways: We can think on the outer square as the front face of a cube (Figure 1-b) seen from very near, on the inner square as the front face of a ","cbCaidecfDkL5SYW","https://ap.wps.com/l/cbCaidecfDkL5SYW","pdf",39553,"English","# Introduction\n# The Types of Plane Representations\n# Children’s Plane Representations of Space Figures","[{\"question\":\"Why are plane representations important in teaching Space Geometry?\",\"answer\":\"Plane representations are crucial because any representation of a 3D solid in 2D loses some information, so learners must reconstruct missing meaning to interpret the figure accurately.\"},{\"question\":\"What four plane representation methods does the paper discuss?\",\"answer\":\"The paper presents four methods: layers, orthogonal, coded orthogonal, and isometric representations.\"},{\"question\":\"How was the study conducted and with which students?\",\"answer\":\"The research experiment involved primary school children in Grades 2, 4, 6, and 8.\"}]","Children’s Ability for Using Different Plane Representations of Space Figures | PDF",25]