1. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 1 Formative Feedback for Math Problem Solving Accountability Conference February 2008 Mike Gallagher Math Test and Measurement Consultant Accountability Services, NCDPI mgallagher@dpi.state.nc.us

2. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 2 Opening Activity SAT Question of the Day – 2008. What thinking do SAT math questions tap? www.collegeboard.com Achieve, Incs report Aligned Expectations, April 2007. SATs math emphasis is heavily on understanding and problem solving, beyond routine procedural. www.achieve.org

3. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 3 Purposes Today Emphasize the importance of problem solving for students now and later. Highlight the potential of formative assessment feedback for problem solving growth. Discuss tools and strategies for professional development.

4. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 4 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.

5. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 5 NC Curriculum (Math 2003SCS) emphasizes problem solving 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 students mathematics education.

6. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 6 Web Pages Menu Page Good Strategies Missing Adaptation of Polyas Problem Solving Strategy. Key Classroom Activities Feedback Sheet Problem Sources www.ncpublicschools.org/accountability/testing/eog/math/ Scroll down to Formative Assessments for Problem Solving

7. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 7 Basics – 1: Start Up Get students acquainted with Polyas heuristic, using the web sheet. Set the target for students: become better math problem solvers. Explain that they will be getting feedback on problem solving throughout the school year.

8. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 8 Basics – 2: Assessing Be sure to include juicy items in each of your regular assessments or tests. Such items get at problem solving more than procedures. When reviewing how students did on each assessment or test, give descriptive feedback on problem solving.

9. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 9 Basics – 3: Feedback X & O Feedback when students have a plan ……… Which steps in the strategy sheet pertain? Mark with an X for executing. Feedback when students dont have a plan …….. Which strategy steps pertain? Mark with an O for a magnifying glass to hunt for how.

10. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 10 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 … (continued) * Francis (Skip) Fennell, President of the National Council of Mathematics Teachers (NCTM)

11. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 11 Presidents 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 http://www.nctm.org/ … just one page and well worth reading!

12. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 12 Motivation and Testing Over-use of summative assessment can impair motivation for many students: Some students who frequently get low grades take away a lesson we dont want to give, that they are unable to learn. Formative assessment, with emphasis on feedback rather than grades, can help low performers connect hard work with achievement.

13. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 13 Beyond Basics -> Planning to teach students to MAKE A PLAN Students need to spend some time on each Polya approach to finding a plan. (These are the Os on Slide 9) For example, what are some problems for which Make a Table will help? Work on those problems for a week or two.

14. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 14 Examples of make a table problems See attached sheet from Patricia Caseys Teacher to Teacher handout. To get Caseys slides and handout, Go to www.free.ed.gov/ Type problem solving in the search window. Then select 4. Teacher Workshops Scroll down and select: We Can Teach Problem Solving

15. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 15 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, 3 rd Edition. Richard J. Stiggins, 2001, Prentice-Hall.

16. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 16 Control ClassroomLarge-Scale UseForm- ative Summ- ative Geography: Where are we in assessment land? The test/assessment landscape & Examples

17. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 17 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.

18. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 18 NC maths great progress NAEP results from 1992 to 2005 Compared with the U.S. average and with other states, North Carolina went from back of the pack to ahead of the pack. NC was somewhat sluggish 2003 to 2005. For the NAEP data in the following slides, go to: http://nces.ed.gov/nationsreportcard/mathematics/

19. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 19 Fourth Grade NAEP Math Achievement in North Carolina – (National Assessment of Educational Progress)

20. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 20 Eighth Grade NAEP Math Achievement in North Carolina

21. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 21 NAEP Scale Score Averages – A Decade of Great Progress Grade 8 Grade 4 North Carolina U.S. Average North Carolina U.S. Average

22. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 22 NC Math SAT Results Mean Scores, North Carolina and U.S. North Carolina 1992 ……486 2006 …………….……….....…513 United States 1992 ……………………….508 2006 ………………………………518 Source: www.dpi.state.nc.us/accountability/reporting Scroll down to 2006 SAT Report

23. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 23 Are we there yet? Helping our students become better problem solvers is an important piece of NC making further progress. Please check and use our web materials: Formative Feedback for Math Problem Solving http://www.ncpublicschools.org/accountability/testing/eog/math/ … Follow the link under Test Resources

24. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 24 NAEP Scale for Grade 4 282 – Advanced 249 – Proficient 241 – North Carolina in 2005 237 – United States Average in 2005 219 – United States Average in 1992 214 – Basic 213 – North Carolina in 1992

25. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 25 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

26. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 26 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://www.assessmentinst.com/

27. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 27 Going Deep Paul Black & Dylan Wiliam, Assessment and Classroom Learning, Assessment in Education, Vol. 5, No.1, 1998, pp 7-71. This is a literature review. The teachers in these projects saw strong, positive effects, both in achievement and motivation, especially for students starting at lower levels.

28. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 28 Conclusion o Balance Assessment of Learning with Assessment for Learning. o Balance emphasis on algorithms with emphasis on heuristics.

29. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 29 Next Steps Use and share the Problem Solving Strategy sheet and the Key Classroom Activities sheet. Encourage formative assessment with feedback that transfers to problem solving strategies. At home: Students discuss & explain math problems and puzzles.