Mr. Lee’s Dilemma - An Instructional Minicase on Evaluating Student Approaches to Comparing Fractions

Oct 15, 2026

Uploaded by Connor

A broad consensus holds that beginning mathematics teachers require strong mathematical knowledge for teaching (MKT) to recognize, understand, and respond to students’ mathematical work. 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.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages40

Reading Time1 h 41 min

AccessFree to download

Abstract

Keywords

Acknowledgments

Minicase purpose and rationale

Research Memorandum ETS RM–20-03 Mr. Lee’s Dilemma: An Instructional Minicase on Evaluating Student Approaches to Comparing Fractions Leslie Nabors Oláh Heather Howell Yvonne Lai Maria DeLucia Eun Mi Kim May 2020 ETS Research Memorandum Series INTERIM EIGNOR EXECUTIVE EDITOR John Mazzeo Distinguished Presidential Appointee ASSOCIATE EDITORS Malcolm Bauer Senior Research Scientist Beata Beigman Klebanov Senior Research Scientist Brent Bridgeman Distinguished Presidential Appointee Heather Buzick Senior Research Scientist Keelan Evanini Research Director Marna Golub-Smith Principal Psychometrician Priya Kannan Managing Research Scientist Sooyeon Kim Principal Psychometrician Anastassia Loukina Research Scientist Donald Powers Principal Research Scientist Gautam Puhan Principal Psychometrician Jesse Sparks Research Scientist Elizabeth Stone Research Scientist Rebecca Zwick Distinguished Presidential Appointee PRODUCTION EDITORS Kim Fryer Manager, Editing Services Ariela Katz Proofreader Ayleen Gontz Senior Editor Since 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. The 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. Mr. Lee’s Dilemma: An Instructional Minicase on Evaluating Student Approaches to Comparing Fractions Leslie Nabors Oláh and Heather Howell Educational Testing Service, Princeton, New Jersey Yvonne Lai University of Nebraska Maria DeLucia Middlesex County College Eun Mi Kim Educational Testing Service, Princeton, New Jersey May 2020 Corresponding author: L. Nabors Oláh, E-mail: [lnaborsolah@ets.org](lnaborsolah@ets.org) Suggested 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. Find other ETS-published reports by searching the ETS ReSEARCHER database at [http://search.ets.org/researcher/](http://search.ets.org/researcher/) To obtain a copy of an ETS research report, please visit [http://www.ets.org/research/contact.html](http://www.ets.org/research/contact.html) Action Editor: Heather Buzick Reviewers: Cara Laitusis and Eric Steinhauer Copyright © 2020 by Educational Testing Service. All rights reserved. ETS and the ETS logo are registered trademarks of Educational Testing Service (ETS). All other trademarks are the property of their respective owners. Abstract There 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

FAQs

What does the memorandum mean by mathematical knowledge for teaching (MKT)?

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.

How does “Mr. Lee’s Dilemma” use the practice-based instructional minicase format?

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.

Why are preservice teachers asked to judge students’ explanations in this minicase?

Judging explanations is used to further develop preservice teachers’ MKT by requiring them to assess mathematical validity related to fraction comparison.

Oct 15, 2026

Uploaded by Connor