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Next Generation Math Assessments Getting Ready for the Next Gen (and This Gen) February 2010

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Mike Gallagher

Math Test and Measurement Consultant

Accountability Services, NCDPI

Readiness & The Beehive

- Present and Review Schedules for new generation math tests.
- Highlight what’s new and different.
- Suggest preparations, some of which pertain specifically to the new generation, others which apply across math generations.

- Encourage teachers and math specialists to take the on-line moodle class in item writing and review and participate in test development.
- http://www.dpi.state.nc.us/accountability/testing/
scroll down to:

Test Item Writer/Reviewer Online Training

- Things will be happening quickly!
- Be sure that most teachers are on the math curriculum listserv to get the regular, fun, and informative messages.
- Just send a request and indicate the level: elementary, middle, or high

1. Several step algebra problem.

2. A non-routine problem.

What are some starting strategies for the second question?

These are similar to SAT questions. Note that students need to be able to apply both procedures and strategies.

Check out the SAT question of the day:

http://sat.collegeboard.com/practice/sat-question-of-the-day

- This conference’s Global Positioning Students / 21st Century theme implies strong math problem solving. e.g., see next slide: Common Core Readiness Standard for Mathematical Practice.

Mathematical PracticeProficient students expect mathematics to make sense. They take an active stance in solving mathematical problems. When faced with a non-routine problem, they have the courage to plunge in and try something, and they have the procedural and conceptual tools to carry through. They are experimenters and inventors, and can adapt known strategies to new problems. They think strategically. See … www.corestandards.org

From … Common Core State Standards Initiative:College and Career Readiness Standards

- Essential Standard plan from Sept.09
- Sept. 2009, Standards adopted NCSBE
- Spring 2010, Item Tryouts (small sample)
- 2010-2011, Stand alone field test
- 2011-2012, 1st Operational year
See: http://www.ncpublicschools.org/acre/

- January 2010. North Carolina submitted a RttT application.
http://racetothetop.nc.gov/

- RttT involves state work in four areas, including standards and assessments.
http://www2.ed.gov/programs/racetothetop/

- February 2010. K-12 math draft standards posted for public comment
www.corestandards.org/

- April 2010. NC to release common core plus possible additional 15% for public comment.*
- July 2010. Standards to State Board*
*From NC RttT application, January 2010, p. 48.

- Alert the math people in your area to review, discuss, and comment on these common core standards, both in February and in April.

The Essential Standards and RttT call for a Comprehensive Assessment System, including:

- Formative Assessment
- Benchmark Assessment
- Summative Assessment
- Diagnostic Assessment

You cant win Song from The Wiz:

“You can’t win, chile,

you can’t break even,

and you can’t get out of the game.”

A fine book on motivation and attribution is Learned Optimism by Martin Seligman (check it on youtube also )

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.

[Diagnostic Assessment] requires treating assessment as an ongoing process of evaluating student knowledge and ability, not through the administration of more standardized tests but through meaningful analysis of student work. p.184.

- The Trouble with Black Boys…and other Reflections on Race, Equity and the Future of Public Educationby Pedro A. Noguera, Jossey-Bass, 2008.

Formative Diagnostic Assessment can be a BIG part of closing the gap.

- Attend the NC Falcon session at this conference on a great professional development tool for formative assessment (FA).
- Share the information so that teachers can become more proficient at FA

- Using Student-Involved Classroom Assessment to Close Achievement Gaps, Richard Stiggins and Jan Chappuis. Theory into Practice, 44, 1,11-18.
- A very short and readable article.
At www.assessmentinst.com

….(Point to “Resources” and click on “Papers.”)

- Go to a Quantiles® Session.
- Alert math people that students will receive a Quantile score on their ISR and that the Qtaxon map can help teachers understand skill progressions.
e.g., If a student does not have an understanding of slope, what comes prior? What resources are there?

- Math Level A and Level B/C
- Discrete math and graph theory in the standards for Level A and Level B/C.
- Constructed Response Questions – “Explain …” These are especially good for Formative Assessment.
- More tests with calculator inactive sections: Grade 8 & Levels A and B/C

- Target math understanding, math procedural skills, and problem solving.
- Regularity, e.g., biweekly
- Short size, e.g., 10 questions
- Mixture, e.g., 7 multiple choice and 3 constructed response.

- Content: start with previous grade questions and mix in current grade standards
- Source: Released and sample items.
- Scoring: Nope. Teacher usually gives one to many feedback, students grow in self and peer assessment. Use Polya’s problem solving strategy:
http://www.ncpublicschools.org/docs/accountability/testing/eog/ProblemSolvingStrategy.pdf

- Quantiles, Wed. at 2:15
- Math Formative – Wed. at 3:45
- Tryouts – Thurs. at 8:00
- Quantiles – Thurs. at 9:15
- ACRE – Thurs. at 10:45
- Next Generation - Thurs. at 2:15
- NC FALCON – Formative at 5:00

- The Strategy is a one-page sheet of bullet items on the DPI web site,
www.ncpublicschools.org/accountability/testing/eog/math/

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.

- PROBLEM SOLVING
G. Polya ... How to Solve It, the book is from the 1950s, but it’s stood the test of time.

- FORMATIVE ASSESSMENT
R. Stiggins … Student-Based Classroom Assessment, Very readable textbook.

“I’d unravel any riddle, for any individ’le

In trouble or in pain .. Oh, I would tell you why, The ocean’s near the shore. I could think of things I never thunk before …” If I only had a brain. Scarecrow in The Wizard of Oz.

“Problem solving and reasoning are stressed throughout the goals at each grade level and in every course. … Experiences in problem solving processes should permeate instruction. Problem solving should be integrated early and continuously into each student’s mathematics education.”

- Sketching a drawing and
- Making a table
are two problem solving tactics that are extremely useful.

Students need ongoing experience and assessment with these and other problem solving tactics.

Definition: “Formative assessment is a process used by teachers and students during instruction that provides feedback to adjust teaching and learning to improve students achievement of intended instructional outcomes.”

CCSSO 2008, adopted by N.C. Board of Education

Help students answer three questions:

- Where am I going? (Target)
- Where am I now?
- How do I get there?
Formative Assessment helps students take more responsibility for their 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.

“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)

“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 http://www.nctm.org/ … Go to the “President’s Corner” -- Just one page and well worth reading!

- Problem Solving is learnable.
- Formative Assessment is Effective for Complex Reasoning.
- Descriptive Feedback without grades is key to formative assessment.
- Formative assessment emphasizes self and peer assessment, not more teacher grading.

- Released test questions
- Problem Solving Strategy Sheet
- Math Problem Solving Worksheet.
- Other problem sources, NAEP, PISA, textbook, sample questions, etc.

- Choose a problem for class discussion. e.g., NAEP, Estela.
- Introduce Polya’s strategy sheet and connect to the problem in Step 1.
- Talk about problems as puzzles.

- Tell students what the target is: to become great math problem solvers!
- Have a class discussion on what great problem solving looks like. Use examples.
- Ask students to critique the quality of problem solving of some examples.

- Explain that these puzzles will provide feedback, not grades.
- BUT, similar problems will be graded on quizzes or tests.

Introduce “Problem Solving Sheet Worksheet”

- Work through a problem as a class, having students answer the questions on a sheet.
- Have students try on their own to solve a problem and provide the answers on the sheet.
- Students should not hurry through the problems. Stress understanding.

- Students will build a non-graded portfolio with their notes on some of the problems.
- Students will choose problems to include in the portfolio to keep track of their work, to help plan further action, and to communicate their progress to teacher and parents.

- What do I need to find?
- What is given?
- Make a sketch or table.
- What facts are needed?
- What procedures are needed?
- Stuck? What tactics did I try?

- Work the problem. Be sure to check each step.
- Did I get a reasonable answer?
- Is there another way to solve it?
- Are there any choices that are clearly wrong?
- How did I check my answer by solving the problem in a different way?

- What mistakes could cause errors in solving this problem?
- What can I learn to help with future problem solving?
- What will I work on next to become a better problem solver?

Select problems from the “grade below” released test which are cognitively complex. Call them “puzzles!”

Assign a puzzle regularly.

Discuss the next day. Use self assessment and peer assessment.

Mix in constructed response questions with the multiple choice.

Include one or more cognitively challenging problem on your regular quiz or test.

In discussing the quiz results, highlight common mistakes which are related to Polya’s strategies.

Have students self assess while you are going over the problem.

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.

- Have students explain to you their progress and difficulty in become better problem solvers.
- Have students explain at parent visits, how they are improving as problem solvers, using examples from their portfolios.
- Students grow in responsibility for their own learning, but not overnight!

Second semester – start using questions from the “on level” released test. The questions should be cognitively complex and use concepts and procedures you have already covered.

Help the students to use non-graded portfolios to track their growth. Efficacy: “Achievement results from effort.”

What does the student believe is the cause of his/her success (or failure) on a summative test?

- “I passed because I’m smart.” “I failed because I’m not smart.”
- “I passed because I worked hard.” “I failed because I didn’t work.”
Learned Optimism by Seligman

You cant win Song from The Wiz:

“You can’t win, chile,

you can’t break even,

and you can’t get out of the game.”

There are lots of wonderful techniques to learn in formative assessment.

Professional Development modules are being added to the web this fall at:

http://www.dpi.state.nc.us/accountability/educators/

Scroll way down and click on “Learn More about Formative Assessment.”

Cut for Proficient = 249

Cut for Basic = 214

Cut for Proficient = 299

Cut for Basic = 262

North Carolina’s rapid progress from the 1980s through the 1990s may have been due to better teaching of procedures.

To get off the plateau, we need to get better at problem solving.

- There are lots of choices and details to tie math problem solving and formative assessment into your classroom.
- Please let me know what you try and what works (or doesn’t) for you:
- Just put YB Road in the subject line

Type

Exercises

Problems

Puzzles

Projects

Goals

Assessment for Learning

Assessment of Learning

“Ever since I can remember, my father has given us little problems or puzzles. … These puzzles challenged us and encouraged our curiosity … they taught us how to reason and think for ourselves.” Sarah Flannery In Code – a Young Woman’s Mathematical Journey. Algonquin Books of Chapel Hill, 2002. Ms. Flannery’ high school project on cryptography won Ireland’s Young Scientist award in 1999.

“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

… 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://www.assessmentinst.com/

www.ncpublicschools.org/

accountability/testing/

- Details about EOGs and EOCs
- Sample questions
- Take the on-line writer/reviewer training
- Link to NAEP results

And More

- Balance Assessment of Learning with Assessment for Learning.
- Balance emphasis on algorithms with emphasis on heuristics.