The Journal of Mathematics Education at Teachers College is a publication of the Program in Mathematics and Education at Teachers College

Columbia University in the City of New York.

!"#$%&'()%*+&Ms. Heather Gould

'()%*+),-&.*,+(&Dr. Philip Smith Dr. Bruce Vogeli Dr. Erica Walker

/*++#$0*1()12&'()%*+&Ms. Krystle Hecker

3145)1#&'()%*+&Dr. Diane R. Murray

5,6*"%&Ms. Sonja Hubbert

78*%*&'()%*+&,1(&/*9#+&:#$)21&Dr. Mark Causapin

Dr. Elizabeth Hagan was discharged from the US Navy as a Lieutenant in 1946 and completed the PhD in Measurement and Evaluation at Teachers College in 1952. Her collaboration with Robert Thorndike resulted in many papers and books including the influential 1961 John Wiley publication, Measurement and Evaluation in Psychology and Education. Dr. Hagan concluded her career at Teachers College in 1976 as Acting Dean of Academic Affairs.

Dr. Stuart Weinberg was the Mathematics Department Chairman at Stuyvesant High School before joining the Teachers College faculty as Director of Student Teaching for the Program in Mathematics. Dr. Weinberg has applied his extensive classroom experience to the development of methods of assessing teachers’ classroom performance utilizing belief systems and attitudes.

;)<$&,1(&=>*0#&The JMETC is a re-creation of an earlier publication by the Teachers College Columbia University Program in Mathematics. As a peer-reviewed, semi-annual journal, it is intended to provide dissemination opportunities for writers of practice-based or research contributions to the general field of mathematics education. Each issue of the JMETC will focus upon an educational theme. The themes planned for the 2012 Fall-Winter and 2013 Spring-Summer issues are Equity and Leadership, respectively.

JMETC readers are educators from pre-K-12 through college and university levels, and from many different disciplines and job positions—teachers, principals, superintendents, professors of education, and other leaders in education. Articles to appear in the JMETC include research reports, commentaries on practice, historical analyses, and responses to issues and recommendations of professional interest.

?,1"$>+)0%&="@<)$$)*1&JMETC seeks conversational manuscripts (2,500-3,500 words in length) that are insightful and helpful to mathematics educators. Articles should contain fresh information, possibly research-based, that gives practical guidance readers can use to improve practice. Examples from classroom experience are encouraged. Articles must not have been accepted for publication elsewhere. To keep the submission and review process as efficient as possible, all manuscripts may be submitted electronically at www.tc.edu/jmetc.

Abstract and keywords. All manuscripts must include an abstract with keywords. Abstracts describing the essence of the manuscript should not exceed 150 words. Authors should select keywords from the menu on the manuscript submission system so that readers can search for the article after it is published. All inquiries and materials should be submitted to Ms. Krystle Hecker at P.O. Box 210, Teachers College Columbia University, 525 W. 120th St., New York, NY 10027 or at JMETC@tc.columbia.edu.

/*06+)28%$&,1(&7#+<)$$)*1$&Those who wish to reuse material copyrighted by the JMETC must secure written permission from the editors to reproduce a journal article in full or in texts of more than 500 words. The JMETC normally will grant permission contingent on permission of the author and inclusion of the JMETC copyright notice on the first page of reproduced material. Access services may use unedited abstracts without the permission of the JMETC or the author. Address requests for reprint permissions to: Ms. Krystle Hecker, P.O. Box 210, Teachers College Columbia University, 525 W. 120th St., New York, NY 10027.

5)@+,+6&*A&/*12+#$$&/,%,-*2)124)147"@-)>,%)*1&:,%,&Journal of mathematics education at Teachers College

p. cm. Includes bibliographical references. ISSN 2156-1397 EISSN 2156-1400 1. Mathematics—Study and teaching—United States—Periodicals QA11.A1 J963

More Information is available online: www.tc.edu/jmetc

Journal of Mathematics Education at Teachers College

/,--&A*+&7,0#+$&The “theme” of the fall issue of the Journal of Mathematics Education at Teachers College will be Equity. This “call for papers” is an invitation to mathematics education professionals, especially Teachers College students, alumni and friends, to submit articles of approximately 2500-3500 words describing research, experiments, projects, innovations, or practices related to equity in mathematics education. Articles should be submitted to Ms. Krystle Hecker at JMETC@tc.columbia.edu by September 1, 2012. The fall issue’s guest editor, Mr. Nathan N. Alexander, will send contributed articles to editorial panels for “blind review.” Reviews will be completed by October 1, 2012, and final manuscripts of selected papers are to be submitted by October 15, 2012. Publication is expected by November 15, 2012.

/,--&A*+&B*-"1%##+$&This Call for Volunteers is an invitation to mathematics educators with experience in reading/writing professional papers to join the editorial/review panels for the fall 2012 and subsequent issues of JMETC. Reviewers are expected to complete assigned reviews no later than 3 weeks from receipt of the manuscripts in order to expedite the publication process. Reviewers are responsible for editorial suggestions, fact and citations review, and identification of similar works that may be helpful to contributors whose submissions seem appropriate for publication. Neither authors’ nor reviewers’ names and affiliations will be shared; however, editors’/reviewers’ comments may be sent to contributors of manuscripts to guide further submissions without identifying the editor/reviewer.

If you wish to be considered for review assignments, please request a Reviewer Information Form. Return the completed form to Ms. Krystle Hecker at hecker@tc.edu or Teachers College Columbia University, 525 W 120th St., Box 210, New York, NY 10027.

5**C)12&;8#,(&Anticipated themes for future issues are:

Fall 2012 Equity Spring 2013 Leadership Fall 2013 Modeling Spring 2014 Teaching Aids

D3&3.D;EF&/37E'=&3G&!"#$%&To obtain additional copies of JMETC, please visit the Journal’s website www.tc.edu/jmetc. The cost per copy delivered nationally by first class mail is $5.00. Payment should be sent by check to JMETC, Teachers College Columbia University, 525 W 120th St., Box 210, New York, NY 10027.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear the full citation on the first page. Copyrights for components of this work owned by other than The Program in Mathematics and Education must be honored. Abstracting with credit is permitted. To copy, to republish, to post on servers for commercial use, or to redistribute to lists requires prior specific permission. Request permission from JMETC@tc.columbia.edu.

Journal of

Mathematics Education at Teachers College

Spring – Summer 2012

A CENTURY OF LEADERSHIP IN MATHEMATICS AND ITS TEACHING

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v Assessment, Evaluation, and Testing: Measurement at Various Levels Heather Gould

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6 Assessment for the Common Core Mathematics Standards Hung-Hsi Wu, University of California at Berkeley!

19 A Population of Assessment Tasks Phil Daro, University of Californic at Berkeley Hugh Burkhardt, Shell Centre, University of Nottingham University of California at Berkeley!

26 Assessing Students’ Mathematical Proficiencies on the Common Core Henry S. Kepner and DeAnn Huinker, University of Wisconsin – Milwaukee!

33 Assessment in a Common Core Era: Revolutionary or Evolutionary?!Allen M. Dimacali, College Board

40 Assessment in Finnish Schools Lasse Savola, Fashion Institute of Technology!

45 The Russian Uniform State Examination in Mathematics: The Latest Version Albina Marushina, Teachers College Columbia University!

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50 Will the CCSSM Have Staying Power? Matthew R. Larson, Lincoln Public Schools, Lincoln, NE!

53 Using Item Analysis Data as a Tool to Inform Instruction in the Mathematics Classroom: A Model of Data-Driven Instruction William Farber, Mercy College!

61 Assessment of Mathematical Modeling Ronny Kwan Eu Leong, Universiti Malaya, Kuala Lumpur, Malaysia!

66 The Mathematics Portfolio: An Alternative Tool to Evaluate Students’ Progress Marla A. Sole, Eugene Lang College of the New School for Liberal Arts!

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Use the chart below to answer question 4.

Input 3 4 5 6 Q!Q!Q! n!Output 10 13 16 19 Q!Q!Q! m!

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Comments:!Sometimes part of an item could be about high school mathematics according to the CCSSM, but if the rubrics indicate that answers using only eighth grade mathematics together with guess-and-check also get full credit, then that part of the item will be classified as K–8. A good example is Funsize Cans of the first test form and Strawberry Boxes of the second test form.

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