[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-588179-105":59,"doc-detail-588179-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","authentic-investigation-activities-for-reasoning-ratio-concept","AUTHENTIC INVESTIGATION ACTIVITIES FOR REASONING - RATIO CONCEPT","","Research examining how authentic investigation activities influence students’ reasoning when learning the ratio concept, regarded as a key milestone in mathematics and science teaching. The qualitative study involved eight 7th-grade students from a public school in Turkey’s Central Anatolia Region, with heterogeneous mathematics success levels. Data were gathered through authentic investigation activities, researcher logs, and interviews, then analyzed descriptively. Results indicate that learning environments incorporating these activities positively support reasoning about ratio.",{"@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/authentic-investigation-activities-for-reasoning-ratio-concept/588179/",{"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/authentic-investigation-activities-for-reasoning-ratio-concept/588179.png","ImageObject",300,407,{"name":92,"@type":93},"Aditya","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","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 is the aim of the study about the ratio concept?","Question",{"text":112,"@type":113},"The study examines how authentic investigation activities affect students’ reasoning process related to the ratio concept.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How was the research conducted and what data were collected?",{"text":117,"@type":113},"The qualitative study involved eight 7th-grade students and used authentic investigation activities, researcher logs, and interviews for data collection, analyzed descriptively.",{"name":119,"@type":110,"acceptedAnswer":120},"What conclusion does the study reach regarding authentic investigation activities?",{"text":121,"@type":113},"Teaching environments that include authentic investigation activities have a positive effect on students’ reasoning about the ratio concept.","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},588179,1792192680,{"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":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,"preview_page_count":4},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","AUTHENTIC INVESTIGATION ACTIVITIES FOR REASONING  \nRATIO CONCEPT  \nPınar Anapa SABAN, Merve Koçyiğit GÜRBÜZ  \nAbstract: The aim of this research is to examine the effect of authentic investigation  \nactivities on the reasoning process of ratio concept which has been regarded as the  \nmilestone of mathematics and science teaching. In line with this purpose, the research  \nhas been carried out with eight 7th grade students attending a public school located in  \nCentral Anatolia Region in Turkey. The success levels of these students in  \nmathematics are in a heterogeneous structure ranging from higher and moderate to  \nlower levels. The data of this qualitative study has been collected through authentic  \ninvestigation activities, researcher logs, and interviews and has been analysed via  \ndescriptive techniques. At the end of the study, it has been concluded that the teaching  \nenvironment containing authentic investigation activities has a positive effect on the  \nreasoning process of students on ratio concept.  \nKey words: Ratio, Authentic Investigation Activities, Constructivist Approach,  \nConceptual Reasoning.  \n1. Introduction  \nIn today’s world, the concept of number is composed of natural, rational, real and complex number concepts although this has not always been the case. Euclid (330-270 BC) used to deal only with whole numbers while he made use of ratio and proportion instead of real numbers (fractions and irrational numbers) in his efforts to explain the numeric relationships between such geometric shapes as line segments, triangles, circles, and spheres. Even though we have all the number systems today, the ratio and proportion concepts are still useful in comparing quantities (Snow J.E & Porter M.K, 2009) . In addition, ratio is one of the fundamental concepts in mathematics used extensively in teaching such subjects as probability, slope ofa line, similarity and trigonometric ratios. These subjects provide a basis for important topics in science teaching such as calculation of chemical equations, use of ideal gas laws, identification of density, velocity, and acceleration, and analysis of electric circuits. In this regard, the concept of ratio is one of the most important subjects in the mathematics curriculum of secondary schools (Akar, 2009). However, the studies in the literature put emphasis on the fact that there are serious problems in reasoning and teaching of ratio (Post, Behr & Lesh, 1988) .  \nStudents is Turkey formally come across with the concept of ratio firstly in 6th grade and in higher grades, they are taught the similarities of geometric shapes, slope calculations, linear equations and inequalities, the subjects designed to improve their discernment. It will be wrong to expect from students having issues in making sense of ratio in 6th grade to effectively use their proportional discernment. Consequently, it is of very importance to carry out studies that aim to identify learning environments facilitating better understanding the ratio concept and activities and strategies to be used within these environments.  \nThis study has analysed the effect of authentic investigation activities developed by Ben-Chaim, Ilany & Keret (2012) on the process of reasoning of ratio concept.  \n1.1 The Concept of Ratio  \nRatio is the number that compares the two quantities or measurements in a multiplicative relationship (contrary to that in subtractive or additive relationship) in a given situation (Van de Walle, 2013) . Freudenthal (1983) has proposed three different methods for comparing the two quantities; with:  \n● The comparison of one whole with its own part: That is the comparison of one part with the whole that it exists in.  \n● The comparison of one part with another part with which it has a relationship: That is the comparison of parts of different wholes or different parts of a same whole.  \n● The comparison of one part with another part with which it has an indirect relationship: That is the comparison ","cbCainbZy7L9QMkb","https://ap.wps.com/l/cbCainbZy7L9QMkb","pdf",431210,17,"English","# 1. Introduction\n## 1.1 The Concept of Ratio\n# 2. Theoretical Framework\n## 2.1 Authentic Investigation Activities on Ratio","[{\"question\":\"What is the aim of the study about the ratio concept?\",\"answer\":\"The study examines how authentic investigation activities affect students’ reasoning process related to the ratio concept.\"},{\"question\":\"How was the research conducted and what data were collected?\",\"answer\":\"The qualitative study involved eight 7th-grade students and used authentic investigation activities, researcher logs, and interviews for data collection, analyzed descriptively.\"},{\"question\":\"What conclusion does the study reach regarding authentic investigation activities?\",\"answer\":\"Teaching environments that include authentic investigation activities have a positive effect on students’ reasoning about the ratio concept.\"}]","AUTHENTIC INVESTIGATION ACTIVITIES FOR REASONING - RATIO CONCEPT | PDF",1792064695,43]