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

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Getting Ready for Math Constructed Response Questions Accountability Conference February 2009Greensboro, NC
  • Mike Gallagher
  • Math Test and Measurement Consultant
  • Accountability Services, NCDPI
purposes today
Purposes Today
  • Summative Assessment Use of Constructed Response (CR) questions: Understand NC’s direction and goals.
  • 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
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
constructed response and r2f4c p 20
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
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
Role of CR questions
  • “Participating states stressed that …. [CR questions] … require students to demonstrate critical thinking and problem solving.” from American Diploma Project AlgebraII End-of-Course Exam: 2008 Annual Report, August 2008. (Available on-line)
  • CR questions had about 1/3 of the total point value on the test.
it s testing time grade 8 question from naep
It’s Testing Time! Grade 8Question* 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
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
Related Materials from NAEP
  • After you work the grade 8 problem, check over the:
  • Scoring Guide
  • Sample Responses
  • Student Results
  • CR questions, compared with multiple choice, present a scoring challenge and an instructional opportunity.
what is formative assessment
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
Instructional Opportunity – Descriptive Feedback
  • Constructed response questions provide an excellent resource for formative assessment … i.e.,
  • Assessment for Learning
  • What feedback could be given to students who generated the sample responses for the NAEP question?
problem solving strategy copy attached
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 Solving
  • 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 item
What feedback to give?(for responses to the NAEP item)
  • For “satisfactory” answer?
  • --------------------------------------------------
  • For “partial” answer?
  • --------------------------------------------------
  • For ‘minimal” answer?
  • --------------------------------------------------
follow the yellow brick road
“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
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
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 characteristics.
yb road 1 start up
YB Road – 1: Start Up
  • Get students acquainted with Polya’s 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 year.
yb road 2 regular classroom assessments design
YB Road – 2: Regular Classroom Assessments –Design
  • Be sure to include some “juicy” questions. Such items get at problem solving more than procedures.
  • 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 design20
YB Road – 2: Regular Classroom Assessments –Design
  • For some of the questions require students to explain:
  • Student’s reasoning guides feedback.
  • Students writing an explanation deepens understanding.
yb road 3 regular classroom assessments feedback
YB Road – 3: Regular Classroom Assessments -- Feedback
  • 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 don’t need to do more grading. Guide students to more peer and self assessment.
yb road 3 regular classroom assessments feedback22
YB Road – 3: Regular Classroom Assessments -- Feedback
  • 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 grading.
yb road 3
YB Road - 3
  • Use descriptive feedback that generalizes past this particular problem to the problem solving heuristic.
  • 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
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 don’t go into the grade book.
  • However, the assessments are corrected and feedback is given.
there is much to learn
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
2 Books of Note
  • G. Polya ... How to Solve It, the book is from the 1950s, but it’s 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
NC Math Formative Assess.
  • Menu Page
  • Good Strategies Missing
  • Adaptation of Polya’s Problem Solving Strategy.
  • Key Classroom Activities
  • Feedback Sheet
  • Problem Sources
  • Scroll down to Formative Assessments for Problem Solving
a message from the president
A Message from the President! *
  • “NCTM’s 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 …” (continued)
  • *Francis (Skip) Fennell, President of the National Council of Mathematics Teachers (NCTM)
president s message cont
President’s Message (cont)
  • “Formative assessment involves using classroom-based assessments to collect feedback that can be used to improve teaching and learning.”
  • From NCTM News Bulletin (December 2006) Complete message on the web at … Go to the “President’s Corner” -- Just one page and well worth reading!
a balanced math assessment diet






Assessment for Learning

Assessment of Learning

A BalancedMath Assessment Diet
feedback becomes key for higher level 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 users
Assessment for Learning inverts the pyramid of users
  • Classroom Formative Assessment is Assessment for Learning
  • 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 thinking
Try it! Formative Assessment for Higher-Level Thinking
  • “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
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:
  • Constructed response questions help with both summative and formative assessment.
  • In balanced assessment, students assess more.