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Participants include in-service and prospective mathematics teachers, assessed through a qualitative case-research design using an interview form targeting student errors in rectangles, squares, and parallelograms. Results highlight gaps in prospective teachers’ understanding of students and in instructional strategy knowledge, alongside insufficient subject-matter command. To reduce misconceptions, teaching should emphasize concrete materials and real-life examples rather than introducing formulas first.",{"@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/mathematics-teachers-pedagogical-content-knowledge-involving-the-relationships-between-perimeter-and-area-research-findings-on-teaching-perimeter-area-concepts/593014/",{"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/mathematics-teachers-pedagogical-content-knowledge-involving-the-relationships-between-perimeter-and-area-research-findings-on-teaching-perimeter-area-concepts/593014.png","ImageObject",300,407,{"name":92,"@type":93},"Aran","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the study’s main purpose regarding perimeter and area?","Question",{"text":112,"@type":113},"To investigate and compare teachers’ pedagogical content knowledge about students’ understanding and instructional strategies related to perimeter-area relationships.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How was the data collected in the research?",{"text":117,"@type":113},"Using a qualitative case research approach and an interview form with four questions designed to reveal student errors related to perimeter and area.",{"name":119,"@type":110,"acceptedAnswer":120},"What misconceptions does the study report among prospective teachers?",{"text":121,"@type":113},"Prospective teachers show limited knowledge of students’ understanding and instructional strategies and are also found to be weak in necessary mathematical subject-matter knowledge, often relying on rules and formulas.","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},593014,1792105498,{"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":34,"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":26,"preview_page_count":4},137455076865,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Athens Journal of Education-Volume 8, Issue 4, November 2021 – Pages 361-384  \nMathematics Teachers’ Pedagogical Content Knowledge Involving the Relationships between Perimeter and Area  \nBy Demet Deniz Yilmaz * & BetülKüçükDemir±  \nThis study aims to investigate and compare mathematics teachers’ knowledge of pedagogical content, knowledge of students’ understanding and knowledge of instructional strategies, subcomponents of pedagogical content knowledge, student errors in the relationship between perimeter and areas in rectangles, squares, and parallelograms. 10 pre-secondary school in-service mathematics teachers and 10 prospective mathematics teachers participated in the study. The qualitative case research approach was used. To collect the data, an interview form consisting of four questions showing student errors related to perimeter and area was prepared. The participants were asked to comment on the questions given in the form, and their answers were recorded.  \nLater, they were asked to write down their answers to these questions. According to the outcomes, there is a lack of knowledge of students’ understanding and knowledge of instructional strategies, which are the subcomponents of the pedagogical content knowledge of prospective mathematics teachers. Moreover, prospective teachers are found to be incompetent as regards the necessary mathematical subject matter knowledge. To prevent difficulties, when the concepts of perimeter and area are taught, instead of giving formulae initially, concrete materials or real-life examples about these concepts should be provided.  \nKeywords: pedagogical content knowledge, perimeter, area, mathematics teachers, prospective mathematics teachers.  \nIntroduction  \nThe topics of perimeter and area are the basic subjects for the competence of elementary school teachers (Reinke, 1997). However, these are confusing topics as both involve measurement, their formulae are taught almost simultaneously to students, and memorizing these formulae may be confusing (Van de Walle, Karp,& Bay-Williams, 2014). This is confusing for both students and teachers. Some studies show that teachers often confuse the concepts of perimeter and area because they assume a constant relationship between area and perimeter (Baturo & Nason, 1996; De Sousa, Gusmão, Font, & Lando, 2020; Yeo, 2008). According to several studies, prospective teachers have also been found to be incompetent in comprehending concepts, their knowledge is based on rules and formulae, they have some difficulties in explaining what these formulae are for, and they focus on using formulae rather than activities designed to reinforce concepts (Baturo & Nason, 1996; Berenson et al., 1997; Livy, Muir, & Maher, 2012; Menon, 1998; Reinke, 1997; Runnalls & Hong, 2019) . According to Zacharos (2006), using formulae first while measuring area leads to misconceptions about area measurement and makes it difficult to interpret the physical meaning of the numerical representation of the area. According to Baturo and Nason (1996),  \n*  \nAssistant Professor, Faculty of Education, Mus Alparslan University, Turkey.±Assistant Professor, Faculty of Education Bayburt University, Turkey.  \n[https://doi.org/10.30958/aje.8-4-2](https://doi.org/10.30958/aje.8-4-2) doi=10.30958/aje.8-4-2  \nVol. 8, No. 4 Deniz Yilmaz & KüçükDemir: Mathematics Teachers’Pedagogical…  \nmany prospective teachers are devoid of concrete measurement experiences such as covering the surface area with measurement units, and they think of area as multiplication of width by length. This situation shows that the difficulties that prospective teachers face may stem from their learning experiences at school (Baturo & Nason, 1996) .  \nDifficulties regarding area and perimeter are usually related to conservation of area and perimeter and using inappropriate units while calculating them (not using square units while reporting area measurements) (Baturo & Nason, 1996; Guner & Akyuz, 2017; Ma, 1999; Murp","cbCaik5GHQyhpvOK","https://ap.wps.com/l/cbCaik5GHQyhpvOK","pdf",712346,24,"English","# Introduction\n## Perimeter and area as core elementary topics\n## Sources of teacher and prospective-teacher confusion\n## Role of misconceptions in students’ understanding\n## Pedagogical content knowledge (PCK) framework","[{\"question\":\"What is the study’s main purpose regarding perimeter and area?\",\"answer\":\"To investigate and compare teachers’ pedagogical content knowledge about students’ understanding and instructional strategies related to perimeter-area relationships.\"},{\"question\":\"How was the data collected in the research?\",\"answer\":\"Using a qualitative case research approach and an interview form with four questions designed to reveal student errors related to perimeter and area.\"},{\"question\":\"What misconceptions does the study report among prospective teachers?\",\"answer\":\"Prospective teachers show limited knowledge of students’ understanding and instructional strategies and are also found to be weak in necessary mathematical subject-matter knowledge, often relying on rules and formulas.\"}]","Mathematics Teachers’ Pedagogical Content Knowledge Involving the Relationships between Perimeter and Area - Research findings on teaching perimeter-area concepts | PDF",1792076398]