[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-593531-105":59,"doc-detail-593531-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","second-year-pre-service-teachersresponses-to-proportional-reasoning-test-items-article-2","Second-Year Pre-Service Teachers’Responses to Proportional Reasoning Test Items - Article 2","","A study examines second-year Australian primary pre-service teachers’ mathematical content knowledge (MCK) for real-number items involving ratio, rate, proportion, and proportional reasoning. Proportional reasoning is treated as a challenging area previously identified as problematic for pre-service teachers. Using a method to analyze responses to five test items ranked by difficulty, the study reports strengths and weaknesses, including correct solution approaches and common incorrect responses, and highlights where multiplication and division are required.",{"@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/second-year-pre-service-teachersresponses-to-proportional-reasoning-test-items-article-2/593531/",{"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/second-year-pre-service-teachersresponses-to-proportional-reasoning-test-items-article-2/593531.png","ImageObject",300,407,{"name":92,"@type":93},"Jasmine","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"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 on pre-service teachers’ proportional reasoning?","Question",{"text":112,"@type":113},"The study aims to identify strengths and weaknesses in primary pre-service teachers’ mathematical content knowledge of ratio, rate, proportion, and proportional reasoning.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are test items analyzed and compared in the paper?",{"text":117,"@type":113},"Responses to five real-number ratio items are analyzed using a method that ranks items by three levels of difficulty.",{"name":119,"@type":110,"acceptedAnswer":120},"What do the results reveal about students’ understanding?",{"text":121,"@type":113},"The results show insights into correct solution methods and common incorrect responses, including identifying which difficulties occur where multiplication and division are needed.","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},593531,1792171315,{"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":29,"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},2336478487870,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Australian Journal of Teacher Education  \n\n| Volume 38 | Issue 11 | Article 2 |\n| --- | --- |\n| 2013\u003Cbr>Second-Year Pre-Service Teachers’Responses to Proportional Reasoning Test Items\u003Cbr>Sharyn Livy\u003Cbr>Deakin University, [s.livy@bigpond.net.au](s.livy@bigpond.net.au)\u003Cbr>Sandra Herbert\u003Cbr>Deakin University, [sandra.herbert@deakin.edu.au](sandra.herbert@deakin.edu.au) |  |\n\nRecommended Citation  \nLivy, S., & Herbert, S. (2013). Second-Year Pre-Service Teachers’ Responses to Proportional Reasoning Test Items. Australian Journal of Teacher Education, 38 (11).  \n[http://dx.doi.org/10.14221/ajte.2013v38n11.7](http://dx.doi.org/10.14221/ajte.2013v38n11.7)  \nThis Journal Article is posted at Research Online.  \n[http://ro.ecu.edu.au/ajte/vol38/iss11/2](http://ro.ecu.edu.au/ajte/vol38/iss11/2)  \nAustralian Journal of Teacher Education  \nSecond-Year Pre-Service Teachers’ Responses to Proportional Reasoning  \nTest Items  \nSharyn Livy  \nSandra Herbert  \nDeakin University  \nAbstract: A recent international study of pre-service teachers  \nidentified that proportional reasoning was problematic for pre-service teachers. Proportional reasoning is an important topic in the middle years of schooling and therefore it is critical that teachers understand  \nthis topic and can rely on their Mathematical Content Knowledge  \n(MCK) when teaching. The focus of this paper is second-year  \nAustralian primary pre-service teachers’ MCK of real number items  \nrelated to ratio, rate, proportion and proportional reasoning. This  \npaper reports on strengths and weakness of pre-service teachers’  \nMCK when responding to test items; including a method suitable for  \nanalysing responses to five items and ranked by three levels of  \ndifficulty. The results revealed insights into their correct methods of  \nsolutions and common incorrect responses, identifying difficulty,  \nwhere multiplication and division were required. The method of  \ncoding test items by difficulty ranking may assist with developing an appropriate learning trajectory, which will assist pre-service teachers  \ndevelop their MCK of this and other difficult topics  \nIntroduction  \n“[V]irtually the entire population is now deemed to be in need of significant mathematical power”(Kaput, 1992, p. 518) . Proportional reasoning is one aspect of the significant mathematical power to which Kaput refers. Expertise in analysing the mathematics of change, such as “the relations between varying quantities [proportion] and the accumulation of those quantities”(Kaput, 1995, p. 49) has become important for all (Roschelle, Kaput, & Stroup, 2000) . Hoyles, Wolf, Molyneux-Hodgson and Kent (2002), mentioned many important instances of proportional reasoning in their report to the United Kingdom’s Science, Technology and Mathematics Council of mathematical skills required in the workplace. Proportional reasoning is the thinking involved when working with ratios (Reys, Lindquist, Lambdin, Smith, et al., 2012) .  \nThe aim of this study is to identify strengths and weaknesses in primary pre-service teachers’ mathematical content knowledge of ratio, rate, proportion and proportional reasoning since this is an area which has been previously reported as problematic (Tatto, Schwillie, Senk, & Ingvarson, 2012). This paper interprets pre-service teachers’ correct and incorrect responses to Mathematical Content Knowledge (MCK) items hence reporting their strengths and weaknesses. The results will contribute to the literature and assist with identifying aspects of real number items that pre-service teachers find least difficult, difficult or most difficult.  \nTatto et al’s recent study, the Teacher Education and Development Study in Mathematics (TEDS-M), which was an international study of pre-service primary and secondary teachers from 17 countries, identified proportional reasoning as problematic for  \nVol 38, 11, November 2013 17  \nAustralian Journal of Teacher Education  \npre-service teachers. This study contributes to the disc","cbCaiqJUtqbigA61","https://ap.wps.com/l/cbCaiqJUtqbigA61","pdf",342187,17,"English","# Abstract\n# Introduction\n# Background\n# Methodology\n# Results\n## Responses to five ratio items\n## Common incorrect responses\n# Conclusion","[{\"question\":\"What is the aim of the study on pre-service teachers’ proportional reasoning?\",\"answer\":\"The study aims to identify strengths and weaknesses in primary pre-service teachers’ mathematical content knowledge of ratio, rate, proportion, and proportional reasoning.\"},{\"question\":\"How are test items analyzed and compared in the paper?\",\"answer\":\"Responses to five real-number ratio items are analyzed using a method that ranks items by three levels of difficulty.\"},{\"question\":\"What do the results reveal about students’ understanding?\",\"answer\":\"The results show insights into correct solution methods and common incorrect responses, including identifying which difficulties occur where multiplication and division are needed.\"}]","Second-Year Pre-Service Teachers’Responses to Proportional Reasoning Test Items - Article 2 | PDF",1792077426,43]