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Conversions are especially challenging because they require understanding two representations and navigating how information changes across systems. The study uses wasan geometry as a thought provoker to analyze pre-service mathematics teachers’ written solutions, applying qualitative content analysis to classify treatments, conversions, counts, and relationships to correct or partially correct answers.",{"@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/treatments-and-conversions-in-student-written-solutions-to-wasan-geometry-problems/588176/",{"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/treatments-and-conversions-in-student-written-solutions-to-wasan-geometry-problems/588176.png","ImageObject",300,407,{"name":92,"@type":93},"Aditya","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-05","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why are conversions more difficult than treatments in this study?","Question",{"text":112,"@type":113},"Conversions require understanding two representations and how meaning changes between different representational registers, making them cognitively demanding compared with treatments within a single register.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How did the study analyze treatments and conversions?",{"text":117,"@type":113},"Treatments and conversions were analyzed using qualitative research content analysis of students’ written solutions to three wasan geometry problems.",{"name":119,"@type":110,"acceptedAnswer":120},"What relationship did the study find between conversion usage and success?",{"text":121,"@type":113},"Using more conversions was not related to success, and it did not lead to fewer treatments; direction of conversion could still be misleading.","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},588176,1792172819,{"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":24,"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":36,"preview_page_count":4},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","TREATMENTS AND CONVERSIONS IN STUDENT WRITTEN SOLUTIONS TO WASAN GEOMETRY PROBLEMS  \nÖzlem ÇEZİKTÜRK, Ahmet Şükrü ÖZDEMİR  \nAbstract: Cognitive difficulty arises from two types of cognitive processes: treatments; within the same, conversions; between different types of representational registers. Conversions are difficult since they ask for understanding of two representations. Direction and the choice of first register could be a threshold for the student. Wasan geometry is used as a thought provoker and pre service mathematics teachers’ written solutions to those problems for usage of cognitive processes:  \ntreatments and conversions are analyzed by content analysis method of qualitative research.  \nDescriptive data regarding number of conversions and treatments are given. As much as correct / partially correct answers, the relation between cognitive processes and answers were analyzed.  \nStudents’ written answers to three Wasan geometry problems on tangent circles are qualitatively analyzed for specific examples of treatment processes and conversion processes. Neither problem type nor correct answer is a reason for the choice of representational registers. One treatment maybe worth many conversions. More usage is related to students’ conformity. Direction of the conversion may be misleading. None of the students stays in mono-functional registers. Top and lowest grade students use more treatments and conversions. Usage of more conversions is not related to success and result in less number of treatments.  \nKey words: Wasan geometry, Representations, Cognitive processes, Treatments, Conversions  \n1. Introduction  \nWasan geometry flourished in the Edo seclusion period of Japan by the hang Wooden blocks from the roofs of temples as challenging mathematical problems. These did not consist any solutions. Monks, samurais, house-wives or even students would solve them (Hidetoshi & Rothman, 2008; Rubin, undated) . Although most of these problems were in geometry, some were in algebra. Due to its systematic structure, Wasan geometry was chosen to promote mathematical thinking in this study.  \nFoundations of concepts, thinking and the abilities as much as problem solving strategies and the way that mathematics is part of daily life are important constituents of mathematical learning (MEB 2013) . Same list includes different representational registers and using them to demonstrate concepts. Mathematical thinking includes thinking procedures with mathematical concepts and structures such as guessing, thinking via shapes or without shapes, induction, deduction, generalization, giving examples, thinking with concepts and lines of mathematical thinking, proving, approaching by patterns, data gathering, etc. (Schoenfeld, 1992; Wares, 2016; Alkan & Bukova-Güzel, 2005; Kahramaner & Kahramaner, 2002; & Yıldırım, 2004; Stacey, 2006) . Thinking becomes easier with the representational registers. Choice of the mode of representation depends not only to the problem but also to the concepts, thinking procedures and with respect to ease of use. Mathematical thinking asks for an artifact, some uses graphics, diagrams, and some use only verbs. These all end up with the representational choices, which build the structure of the solution. Stacey (2006) gives Fermat and his last theory as an example to this.“To prove asks for passing through many dark rooms to enter into a lighted one” as in his words. To think like a mathematician is the aim and by solving problems, by inquiring mathematical projects, by modeling, and by relating, it is possible to be a part of this intellectual promenade (Stacey, 2006; Devlin, 2012) .  \n2. Representations  \nRepresentations are physical realities that ideas, concepts, and processes can be changed by learners (Lesh, Post & Behr, 1987, as cited in Akkuş & Çakıroğlu, 2006) . Multiple representations can be used as tools for understanding mathematics and developers of new mathematics that students ask but prefer one repres","cbCaigF9AK7htfyT","https://ap.wps.com/l/cbCaigF9AK7htfyT","pdf",633624,16,"English","# 1. Introduction\n# 2. Representations\n## 2.1. Misconceptions due to representations","[{\"question\":\"Why are conversions more difficult than treatments in this study?\",\"answer\":\"Conversions require understanding two representations and how meaning changes between different representational registers, making them cognitively demanding compared with treatments within a single register.\"},{\"question\":\"How did the study analyze treatments and conversions?\",\"answer\":\"Treatments and conversions were analyzed using qualitative research content analysis of students’ written solutions to three wasan geometry problems.\"},{\"question\":\"What relationship did the study find between conversion usage and success?\",\"answer\":\"Using more conversions was not related to success, and it did not lead to fewer treatments; direction of conversion could still be misleading.\"}]","TREATMENTS AND CONVERSIONS IN STUDENT WRITTEN SOLUTIONS TO WASAN GEOMETRY PROBLEMS | PDF",1792064694]