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A persistent teacher-education challenge is supporting preservice teachers (PSTs) to develop these competencies. The memorandum describes “Mr. Lee’s Dilemma,” a practice-based instructional minicase grounded in assessment of PSTs’ engagement with student reasoning about comparing fractions. PSTs judge students’ mathematical explanations to further build MKT.",{"@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/mr-lees-dilemma-an-instructional-minicase-on-evaluating-student-approaches-to-comparing-fractions/583692/",{"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/mr-lees-dilemma-an-instructional-minicase-on-evaluating-student-approaches-to-comparing-fractions/583692.png","ImageObject",300,407,{"name":92,"@type":93},"Connor ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","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 does the memorandum mean by mathematical knowledge for teaching (MKT)?","Question",{"text":112,"@type":113},"MKT is the mathematical knowledge required to recognize, understand, and respond to the mathematical work of teaching. It is framed as knowledge needed to engage with students’ mathematical work.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does “Mr. Lee’s Dilemma” use the practice-based instructional minicase format?",{"text":117,"@type":113},"The minicase is based on an assessment scenario where preservice teachers attend to student reasoning about comparing fractions. PSTs then evaluate the mathematical validity of students’ explanations.",{"name":119,"@type":110,"acceptedAnswer":120},"Why are preservice teachers asked to judge students’ explanations in this minicase?",{"text":121,"@type":113},"Judging explanations is used to further develop preservice teachers’ MKT by requiring them to assess mathematical validity related to fraction comparison.","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},583692,1792189496,{"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":36,"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},687207022233,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Research Memorandum  \nETS RM–20-03  \nMr. Lee’s Dilemma: An Instructional Minicase on Evaluating Student Approaches to Comparing Fractions  \nLeslie Nabors Oláh Heather Howell Yvonne Lai  \nMaria DeLucia Eun Mi Kim  \nMay 2020  \nETS Research Memorandum Series  \nINTERIM EIGNOR EXECUTIVE EDITOR  \nJohn Mazzeo Distinguished Presidential Appointee  \nASSOCIATE EDITORS  \nMalcolm Bauer  \nSenior Research Scientist  \nBeata Beigman Klebanov Senior Research Scientist  \nBrent Bridgeman  \nDistinguished Presidential Appointee Heather Buzick  \nSenior Research Scientist  \nKeelan Evanini Research Director  \nMarna Golub-Smith  \nPrincipal Psychometrician  \nPriya Kannan  \nManaging Research Scientist  \nSooyeon Kim  \nPrincipal Psychometrician Anastassia Loukina Research Scientist  \nDonald Powers  \nPrincipal Research Scientist Gautam Puhan  \nPrincipal Psychometrician  \nJesse Sparks  \nResearch Scientist  \nElizabeth Stone Research Scientist  \nRebecca Zwick  \nDistinguished Presidential Appointee  \nPRODUCTION EDITORS  \nKim Fryer  \nManager, Editing Services  \nAriela Katz Proofreader  \nAyleen Gontz Senior Editor  \nSince its 1947 founding, ETS has conducted and disseminated scientific research to support its products and services, and to advance the measurement and education fields. In keeping with these goals, ETS is committed to making its research freely available to the professional community and to the general public. Published accounts of ETS research, including papers in the ETS Research Memorandum series, undergo a formal peer-review process by ETS staff to ensure that they meet established scientific and professional standards. All such ETS-conducted peer reviews are in addition to any reviews that outside organizations may provide as part of their own publication processes. Peer review notwithstanding, the positions expressed in the ETS Research Memorandum series and other published accounts of ETS research are those of the authors and not necessarily those of the Officers and Trustees of Educational Testing Service.  \nThe Daniel Eignor Editorship is named in honor of Dr. Daniel R. Eignor, who from 2001 until 2011 served the Research and Development division as Editor for the ETS Research Report series. The Eignor Editorship has been created to recognize the pivotal leadership role that Dr. Eignor played in the research publication process at ETS.  \nMr. Lee’s Dilemma:  \nAn Instructional Minicase on Evaluating Student Approaches to Comparing Fractions  \nLeslie Nabors Oláh and Heather Howell  \nEducational Testing Service, Princeton, New Jersey  \nYvonne Lai  \nUniversity of Nebraska  \nMaria DeLucia  \nMiddlesex County College  \nEun Mi Kim  \nEducational Testing Service, Princeton, New Jersey  \nMay 2020  \nCorresponding author: L. Nabors Oláh, E-mail: [lnaborsolah@ets.org](lnaborsolah@ets.org)  \nSuggested citation: Nabors Oláh, L., Howell, H.,Lai, Y., DeLucia, M., & Kim, E. M. (2020) . Mr. Lee’s dilemma: An instructional minicase on evaluating student approaches to comparing fractions (Research Memorandum No. RM-20-03). Educational Testing Service.  \nFind other ETS-published reports by searching the ETS ReSEARCHER database at [http://search.ets.org/researcher/](http://search.ets.org/researcher/)  \nTo obtain a copy of an ETS research report, please visit [http://www.ets.org/research/contact.html](http://www.ets.org/research/contact.html)  \nAction Editor: Heather Buzick  \nReviewers: Cara Laitusis and Eric Steinhauer  \nCopyright © 2020 by Educational Testing Service. All rights reserved.  \nETS and the ETS logo are registered trademarks of  \nEducational Testing Service (ETS). All other trademarks are the property of their respective owners.  \nAbstract  \nThere is a broad consensus that beginning teachers of mathematics need a strong foundation in mathematical knowledge for teaching (MKT), defined as the mathematical knowledge required to recognize, understand, and respond to the mathematical work of teaching one must engage in. One recurrent challenge in teacher e","cbCaiaPPzTVd8tc3","https://ap.wps.com/l/cbCaiaPPzTVd8tc3","pdf",1339421,"English","# Abstract\n# Keywords\n# Acknowledgments\n# Minicase purpose and rationale","[{\"question\":\"What does the memorandum mean by mathematical knowledge for teaching (MKT)?\",\"answer\":\"MKT is the mathematical knowledge required to recognize, understand, and respond to the mathematical work of teaching. It is framed as knowledge needed to engage with students’ mathematical work.\"},{\"question\":\"How does “Mr. Lee’s Dilemma” use the practice-based instructional minicase format?\",\"answer\":\"The minicase is based on an assessment scenario where preservice teachers attend to student reasoning about comparing fractions. PSTs then evaluate the mathematical validity of students’ explanations.\"},{\"question\":\"Why are preservice teachers asked to judge students’ explanations in this minicase?\",\"answer\":\"Judging explanations is used to further develop preservice teachers’ MKT by requiring them to assess mathematical validity related to fraction comparison.\"}]","Mr. Lee’s Dilemma - An Instructional Minicase on Evaluating Student Approaches to Comparing Fractions | PDF",1792048073,101]