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Getting Ready for Math Constructed Response Questions Accountability Conference February 2009 Greens


... American Diploma Project Algebra II End-of-Course Exam: 2008 ... Francis (Skip) Fennell, President of the National Council of Mathematics Teachers (NCTM) ... – PowerPoint PPT presentation

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Title: Getting Ready for Math Constructed Response Questions Accountability Conference February 2009 Greens

Getting Ready for Math Constructed Response
Questions Accountability Conference February
2009Greensboro, NC
  • Mike Gallagher
  • Math Test and Measurement Consultant
  • Accountability Services, NCDPI

Purposes Today
  • Summative Assessment Use of Constructed Response
    (CR) questions Understand NCs direction and
  • Formative Assessment Use of CR questions.
    Evaluate an approach to use CR questions
    instructionally to improve results on both
    multiple choice and CR math questions.

Framework for Change
  • The Response to the Framework for Change (R2F4C)
    calls for
  • Inclusion of constructed response (CR) questions
    in summative assessments
  • Use of formative assessment as part of a balanced
    assessment system.
  • See the Response on the DPI web site
  • http//

Constructed Response and R2F4C (p.20)
  • General Summative Assessment Recommendations
  • 1. Use constructed-response and performance task
    items when such items are appropriate based on
    developed criteria. Note Criteria are due to
    the SBE August 2009.

Math Timeline (from R2F4C)
  • June 2009 Essential standards to SBE
  • 2009-10 Item Development
  • 2010-11 Field Test
  • 2011-12 Operational Tests
  • Note that test specifications will be set after
    standard adoption. Test specs will detail number
    and type of items.

Role of CR questions
  • Participating states stressed that . CR
    questions require students to demonstrate
    critical thinking and problem solving. from
    American Diploma Project Algebra II End-of-Course
    Exam 2008 Annual Report, August 2008. (Available
  • CR questions had about 1/3 of the total point
    value on the test.

Example test design Ohio Graduation Test
Its Testing Time! Grade 8 Question from NAEP
  • How many boxes of tiles are needed?
  • (See pages attached.)
  • Since you may not have a ruler handy, the figure
    is 2 ½ inches by 4 inches.
  • Block 2005-8M3 No.18

Notes on the NAEP item
  • This is an example of a Constructed Response (CR)
    question of the Extended Response type
  • Students need practice with EXPLAIN and SHOW
    YOUR WORK. !!!

Related Materials from NAEP
  • After you work the grade 8 problem, check over
  • Scoring Guide
  • Sample Responses
  • Student Results
  • CR questions, compared with multiple choice,
    present a scoring challenge and an instructional

What is Formative Assessment?
  • Formative assessment is a process used by
    teachers and students during instruction that
    provides feedback to adjust ongoing teaching and
    learning to improve intended instructional
    outcomes (CCSSO FAST SCASS, 2006). Quoted in
    R2F4C, p. 14.

Instructional Opportunity Descriptive Feedback
  • Constructed response questions provide an
    excellent resource for formative assessment
  • Assessment for Learning
  • What feedback could be given to students who
    generated the sample responses for the NAEP

Problem Solving Strategy(Copy Attached)
  • The Strategy is a one-page sheet of bullet items
    on the DPI web site,
  • Scroll down to Formative Assessments for Problem
  • The strategy sheet can be used to guide Formative
    Assessment descriptive feedback for problem
    solving throughout the year.

What feedback to give?(for responses to the NAEP
  • For satisfactory answer?
  • --------------------------------------------------
  • For partial answer?
  • --------------------------------------------------
  • For minimal answer?
  • --------------------------------------------------

Follow the Yellow Brick Road
  • YB Road How to use math constructed response
    questions as part of ongoing formative assessment
    to help students improve their performance on
    current EOG/EOC math tests and on coming tests
    under essential standards.

The Yellow Brick Road (YB Road) is a different
sort of road.
  • Formative assessment does not have teachers doing
    more grading. Teachers guide students to more
    peer and self assessment.

YB Road 1. Getting Started
  • Use an initial quiz or test, which includes some
    problem solving questions.
  • Use a class discussion to get to characteristics
    of good problem solving.
  • At a later class, introduce the Polya strategy
    sheet and compare with the class developed

YB Road 1 Start Up
  • Get students acquainted with Polyas heuristic,
    using the Problem Solving Strategy sheet.
  • Set the target for students become strong math
    problem solvers.
  • Explain that they will be getting and giving
    feedback on problem solving throughout the school

YB Road 2 Regular Classroom Assessments
  • Be sure to include some juicy questions. Such
    items get at problem solving more than
  • Such questions would not need to be tied to the
    current chapter sample EOC/EOG questions, DPI
    indicators, NAEP released questions, .. etc.

YB Road 2 Regular Classroom Assessments
  • For some of the questions require students to
  • Students reasoning guides feedback.
  • Students writing an explanation deepens

YB Road 3 Regular Classroom Assessments --
  • When reviewing how students did on each
    assessment or test, give and model descriptive
    feedback on problem solving to the class.
  • Oh, and remember Teachers dont need to do more
    grading. Guide students to more peer and self

YB Road 3 Regular Classroom Assessments --
  • One to many. Teachers provide feedback to the
    class on common strengths and weaknesses.
  • Many to many. Students provide feedback to each
    other and themselves. For self and peer
    assessment, students are providing feedback, not

YB Road - 3
  • Use descriptive feedback that generalizes past
    this particular problem to the problem solving
  • Discussion example Released NAEP grade 8
    question about boxes of tile needed for a room.
    Block 2005-8M3, No. 18.

YB Road 4 Ungraded Classroom Assessments
  • Transition to more ungraded assessments as
    students develop with self and peer assessment.
  • Ungraded as used here means that the results
    dont go into the grade book.
  • However, the assessments are corrected and
    feedback is given.

There is much to learn .
  • Go to the NCDPI web site
  • Select for educators on the left.
  • Scroll way down and select Learn more about
    formative assessment on the left.
  • And PD modules are coming!!

2 Books of Note
  • G. Polya ... How to Solve It, the book is from
    the 1950s, but its stood the test of time.
  • R. Stiggins Student-Based Classroom Assessment,
    Very readable textbook. Stiggins has done a lot
    on focusing assessment feedback to the learner.

NC Math Formative Assess.
  • Menu Page
  • Good Strategies Missing
  • Adaptation of Polyas Problem Solving Strategy.
  • Key Classroom Activities
  • Feedback Sheet
  • Problem Sources
  • Scroll down to Formative Assessments for Problem

A Message from the President!
  • NCTMs Assessment Principle indicates that
    assessment should not be done to students
    rather, assessments are for students and should
    be used to guide and enhance their learning
  • Francis (Skip) Fennell, President of the
    National Council of Mathematics Teachers (NCTM)

Presidents Message (cont)
  • Formative assessment involves using
    classroom-based assessments to collect feedback
    that can be used to improve teaching and
  • From NCTM News Bulletin (December 2006) Complete
    message on the web at http// Go
    to the Presidents Corner -- Just one page and
    well worth reading!

A BalancedMath Assessment Diet
  • Type
  • Exercises
  • Problems
  • Puzzles
  • Projects
  • Goal
  • Assessment for Learning
  • Assessment of Learning

Feedback becomes key for higher-level learning
  • When it comes to learning, students are the key
    assessment users Am I succeeding? Am I
    improving over time? What should I do next to
    succeed? Does my teacher think I am capable of
    success? Do I think I am capable of success?
  • from Student-Involved Classroom Assessment, 3rd
    Edition. Richard J. Stiggins, 2001, Prentice-Hall.

Assessment for Learning inverts the pyramid of
  • Classroom Formative Assessment is Assessment for
  • For large scale, summative assessment, the key
    users are often national and state, moving down
    to teachers.
  • For classroom formative assessment, the key users
    should start with the student.

Try it! Formative Assessment for Higher-Level
  • Students who participate in the thoughtful
    analysis of quality work, so as to identify its
    critical elements or to internalize valued
    achievement targets, become better performers.
    When students learn to apply those standards so
    thoroughly that they can confidently and
    competently more

Higher-Level (cont)
  • evaluate their own and each others work, they
    are well down the road to becoming better
    performers in their own right (Stiggins, p. 25)
  • Good papers to read and other resources at
    Stiggins ATI website
  • http//

  • Constructed response questions help with both
    summative and formative assessment.
  • In balanced assessment, students assess more.