[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-592902-105":59,"doc-detail-592902-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","cognitive-and-metacognitive-skills-performed-by-math-teachers-in-the-proving-process-of-number-theory","Cognitive and Metacognitive Skills Performed by Math Teachers in the Proving Process of Number Theory","","Evaluating teachers’ proof-related competencies supports the development of students’ meaningful understanding in mathematics, particularly in contexts where simple number theory proofs clarify multipliers and factors, as well as greatest common divisor and least common multiple concepts. This qualitative case study investigates cognitive and metacognitive skills used by elementary and secondary mathematics teachers during proof processes. Data from think-aloud task interviews, documents, and observation forms were analyzed via content analysis.",{"@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/cognitive-and-metacognitive-skills-performed-by-math-teachers-in-the-proving-process-of-number-theory/592902/",{"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/cognitive-and-metacognitive-skills-performed-by-math-teachers-in-the-proving-process-of-number-theory/592902.png","ImageObject",300,407,{"name":92,"@type":93},"Marglet","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the goal of evaluating math teachers’ proving processes in this study?","Question",{"text":112,"@type":113},"To examine the cognitive and metacognitive skills math teachers use during proof work, supporting the development of proof skills and students’ meaningful learning.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How was the study conducted and what data were collected?",{"text":117,"@type":113},"Using a qualitative case study design with 14 teachers. Data came from task-based interviews (think-aloud protocol), documents, and observation forms.",{"name":119,"@type":110,"acceptedAnswer":120},"What difference in skills did the results highlight between elementary and secondary teachers?",{"text":121,"@type":113},"Elementary math teachers generally used cognitive skills, while secondary mathematics teachers performed metacognitive skills.","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},592902,1792192385,{"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":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":56,"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":144,"preview_page_count":4},2336477982702,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Cognitive and Metacognitive Skills Performed by Math Teachers in the Proving Process of Number  \nTheory  \nBy Mesut Ozturk􀀍  \nEvaluating the proving process of mathematics teachers is important for the development of their proof skills. Developing the proof skills of teachers can contribute to their students’ meaningful learning of mathematics. For example, teachers showing simple proofs about number theory can make it easier for students to understand the concepts of multipliers and factors and the concepts of the greatest common divisor and the least common multiple. Within this context, this study was conducted in order to examine the cognitive and metacognitive skills performed by math teachers in the proving process.  \nThe study was conducted as a case study using qualitative research design. A total of 14 teachers participated in the study, six of which were elementary math teachers and eight were secondary math teachers. The data were collected through task-based interviews (think-aloud protocol), documents and observation forms. The collected data were analysed using the content analysis method. The results of the study showed that, based on the operational definition of cognition and metacognitive skills made in this study, elementary math teachers generally used cognitive skills, while secondary mathematics teachers performed metacognitive skills.  \nKeywords: proof, math teachers, number theory, elementary, secondary  \nIntroduction  \nStudies in the literature emphasize that proof is important for mathematics education as proof requires a high level of mathematical thinking and systematic work. However, many students and teachers think that proof is difficult to both write and understand (Öztürk& Kaplan, 2019) . Thus, they do not tend to lean towards the proof process (Knuth, 2002; Raman, 2003). The knowledge and thoughts students have regarding proof are related to the knowledge and thoughts their teachers have on the subject. Therefore, it is important to examine the knowledge and thoughts math teachers have regarding proof. Math teachers with advanced proof skills are able to work systematically and perform high level mathematical thinking skills. The math learning process of the students of such teachers can be positively affected as mathematical proof requires advanced cognitive skills and awareness. The awareness of cognition is generally defined asa metacognitive skill (Öztürk & Kaplan, 2019). Mathematical proof is extremely important for math teachers, however the math curriculum applied in schools in Turkey does not contain enough proof related subjects. The Trends in International Mathematics and Science Study (TIMSS) and the Programme for International Student Assessment (PISA) have both reported that Turkish students have low mathematics skills. The negative results obtained from the TIMSS and PISA led to the conducting of this study, which aimed to compare the cognitive and  \n􀀍Assistant Professor, Bayburt University, Turkey.  \n[https://doi.org/10.30958/aje.8-1-4](https://doi.org/10.30958/aje.8-1-4) doi=10.30958/aje.8-1-4  \nmetacognitive skills performed by elementary and secondary math teachers in the proving process.  \nProof in Mathematics Education and Mathematical Proof  \nMathematical proof is the process of determining whether a claim is correct or not by using mathematical symbols and formulas. The aim of proof in mathematics education is to convince the students of the accuracy or inaccuracy of mathematical propositions (Aydoğdu-İskenderoğlu, 2016, p. 66) . These definitions show that there are small but significant differences in the concept of proof in math and math education. The main point of distinction is that there is a multiple type of proof in mathematics education while there is only one type in mathematics. Therefore, the purpose of the proof is different in both disciplines. In mathematics, the first demonstration of a theorem's accuracy is proof, and all subsequent representations of acc","cbCaitB0ICpqojek","https://ap.wps.com/l/cbCaitB0ICpqojek","pdf",676373,"English","# Introduction\n# Proof in Mathematics Education and Mathematical Proof\n## Mathematical proof and its purposes\n## Validity and development of metacognitive skills\n# Cognition and Metacognition\n## Definitions and relationship to proof","[{\"question\":\"What is the goal of evaluating math teachers’ proving processes in this study?\",\"answer\":\"To examine the cognitive and metacognitive skills math teachers use during proof work, supporting the development of proof skills and students’ meaningful learning.\"},{\"question\":\"How was the study conducted and what data were collected?\",\"answer\":\"Using a qualitative case study design with 14 teachers. Data came from task-based interviews (think-aloud protocol), documents, and observation forms.\"},{\"question\":\"What difference in skills did the results highlight between elementary and secondary teachers?\",\"answer\":\"Elementary math teachers generally used cognitive skills, while secondary mathematics teachers performed metacognitive skills.\"}]","Cognitive and Metacognitive Skills Performed by Math Teachers in the Proving Process of Number Theory | PDF",1792076154,48]