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International assessments such as TIMSS are cited as emphasizing mathematical language, problem solving, and reasoning. The research focuses specifically on pupils’ argumentation and the geometrical notions they use when explaining their steps, with Euclidean geometry presented as a suitable basis for learning justification.",{"@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/research-on-how-secondary-school-pupils-do-geometrical-constructions-volume-2-number-3-2009/588438/",{"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/research-on-how-secondary-school-pupils-do-geometrical-constructions-volume-2-number-3-2009/588438.png","ImageObject",300,407,{"name":92,"@type":93},"Putri","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-23","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What competencies does the research focus on for secondary school pupils?","Question",{"text":112,"@type":113},"The research focuses on solving problems, reasoning, and communicating in the mathematical language while performing geometrical constructions.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What constructions were assigned to the participating pupils?",{"text":117,"@type":113},"Pupils completed three tasks: constructing an equilateral triangle, constructing a segment’s multiple, and constructing a perpendicular bisector of a segment.",{"name":119,"@type":110,"acceptedAnswer":120},"How were pupils’ approaches to the equilateral triangle construction analyzed?",{"text":121,"@type":113},"The study identifies three approaches: visual construction, measurement-based construction, and mathematical construction, and then compares counts of correct and incorrect drawings for each method.","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},588438,1792209393,{"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":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"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":46,"preview_page_count":4},962085571259,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Volume 2, Number 3, 2009  \nRESEARCH ON HOW SECONDARY SCHOOL PUPILS DO GEOMETRICAL CONSTRUCTIONS  \nIuliana Marchis, Andrea Éva Molnár  \nAbstract. Communicating on the mathematical language, problem solving, and reasoning are competencies tested on international test. The aim of this research is to study how secondary school pupils do geometrical constructions, how they give mathematical argumentation and use geometrical notions in their explanations.  \nKey words: Mathematics Education, Mathematics problem, geometrical constructions  \n1. Introduction  \nTwo of the core competencies in Romanian secondary school curricula are [4]:  \no development of the capacity to communicate on the mathematical language;  \no development of the ability of problem solving.  \nThe TIMSS (Trends in International Mathematics and Science Study) international test also focuses on these competencies. Between the competencies evaluated in TIMSS 1995 and TIMSS-R 1999 we can find the following two [5]:  \no communicating in the language of Mathematics;  \no solving problems.  \nAt TIMSS 2003 using concepts, develop explanations, and solve problems are tested too [1] . At TIMSS 2007 solving problems and reasoning had an important place [2] .  \nThus our research focuses on the following three competencies: solving problems, reasoning, and communicating on the mathematical language. To study this we have chosen, as mathematical content, the geometrical constructions.  \nFor geometrical reasoning arguments based on mathematical properties are required. The axiomatic structure of the Euclidian geometry constitutes a favorable ground for learning reasoning and argumentation.  \nIn [3] the research focuses on how preservice teachers do geometrical constructions, wether they use elements or geometrical properties. The conclusion is that a large proportion of preservice teachers use visual elements and they are trying to use naïve empirical reasoning instead of geometrical one. The aim of this paper is to study how secondary school pupils do geometrical constructions, how they give mathematical argumentation and use geometrical notions in their explanations.  \n2. Geometrical constructions with compass and straightedge  \nWe gave the task to the pupils to conctruct an equaliteral triangle, a segment’s multiple, and a segment’s perpendicular bisector using only compass and straightedge. The straightedge is assumed tobe infinite in length, has no markings on it and only one edge. In this section we give the methods of making these three geometrical constructions.  \nReceived 7 September 2009, accepted 25 September 2009, published 30 September 2009  \n2.1. Construction of an equilateral triangle  \nThe construction has the following steps: construct a segment AB (this will be one of the triangle’s sides); draw a circle whose center is A and radius is AB; draw a circle whose center is B and the radius is AB; set C as one of the intersaction point of the two circles; draw the segments AC and BC (see Figure 1) .  \nFigure 1. Construction of an equilateral triangle  \n2.2. Construction of a segment’s multiple  \nThe essence of the construction is, that only with the help of a compass we can construct a segment's multiple. After we draw the segment AB, we take into the slot of the compass the segment's endpoints, then we distribute it so many times beside the segment as many times it is necessary (in our case two times) . So we obtain the requested segment AB’, which is three times longer than the original segment AB (Figure 2) .  \nFigure 2. Construction of a segment’s multiple (|AB’|=|AB|)  \n2.3. Construction of a perpendicular bisector of a segment  \nIn this construction method first we draw the segment AB, for which we want to construct its perpendicular bisector. Then with the help of a compass we draw two arcs with equal radius, whose centers are the segment’s endpoints. The line determined by the points of these arc’s intersection is the perpendicular bisector of the segment AB (Fi","cbCail8TawjlDz6g","https://ap.wps.com/l/cbCail8TawjlDz6g","pdf",226544,"English","# Introduction\n## Geometrical constructions with compass and straightedge\n## Construction methods\n## Research methodology\n## Analyzing the pupil’s work on the test","[{\"question\":\"What competencies does the research focus on for secondary school pupils?\",\"answer\":\"The research focuses on solving problems, reasoning, and communicating in the mathematical language while performing geometrical constructions.\"},{\"question\":\"What constructions were assigned to the participating pupils?\",\"answer\":\"Pupils completed three tasks: constructing an equilateral triangle, constructing a segment’s multiple, and constructing a perpendicular bisector of a segment.\"},{\"question\":\"How were pupils’ approaches to the equilateral triangle construction analyzed?\",\"answer\":\"The study identifies three approaches: visual construction, measurement-based construction, and mathematical construction, and then compares counts of correct and incorrect drawings for each method.\"}]","RESEARCH ON HOW SECONDARY SCHOOL PUPILS DO GEOMETRICAL CONSTRUCTIONS - Volume 2 - Number 3 - 2009 | PDF",1792065253]