1. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 1 Squirrels: Problem Solvers?

2. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 2 A challenge!

3. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 3 Common Core State Standards for Mathematical Practice Numero Uno: Problem Solving Proficient 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

4. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 4 NCDigIns, Problem Solving and Squirrels ------------------- National Conference on Student Assessment June 2013 Mike Gallagher Math Test and Measurement Consultant North Carolina Deptartment of Public Instruction michael.gallagher@dpi.nc.gov

5. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 5 NCDigIns Data Focus Mostly Qualitative …. Trickle out one problem at a time. Guide the student to be the data user. What did I and my classmates do well? What could I do better? …. Pretty similar to post-game analysis done by sports teams!

6. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 6 The Givens and Our Niche Given: Teachers are becoming more versed in the principles of formative assessment. Given: Teachers are pretty busy. Niche: NCDigIns gives teachers math- specific tools and a template for formative assessment.

7. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 7 NCDigIns NCDigIns were created by NC teachers and test developers as a pilot project for grades 4, 7 and Algebra 1. Teachers deconstructed the North Carolina released test questions (based on the 2003 Standard Course of Study).

8. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 8 Data to Guide Descriptive Feedback for each problem Start with expert teachers’ view on likely sources of error and what to do next. Then focus on each student’s work. Where did the class go with the problem? Common errors/approaches

9. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 9 Template for NCDigIns 1.Question on a single page. (Not intended for use as a quiz.) 2.Feedback hints on common errors. 3.Feedback hints on Problem-Solving Strategies. 4.Concepts/Skills for Improvement 5.Where to go next (resources)

10. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 10 NCDigIns - - Example Grade 4 DigIn Number 11, Question 3 “Bowling Pins” 2003 SCS Objective 1.03 CCSSM 4.OA.3

11. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 11 Each Question One Page Willy went bowling with his family. The bowling pins were set up as shown. --GRAPHIC with 10 pins – If Willy knocked over 2/5 of the pins, how many pins were left standing? A 2 C 5 B 4 D 6

12. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 12 Feedback: Common Errors A The student may not have read the problem carefully or saw the numerator as the number of pins knocked over. B The student may have found the equivalent fraction correctly, but may not have read the problem carefully and picked 4 because it was the number of pins knocked down.

13. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 13 Common Errors …cont. C The student may not have a good understanding of fractions and just chose the denominator. D Correct answer.

14. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 14 Feedback: Problem Solving Strategies -> -> tied to 1 sheet! 1.Understand the problem. Can you make a sketch? 2.Make a Plan 3.Carry it out. 4.Check your answer. Is your answer reasonable?

15. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 15 Key concepts / skills Subtracting like fractions. Equivalent fractions. Understanding the relative size of fractions. For example, 2/5 is less than ½.

16. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 16 Resources Three links are provided to free sites with information and practice.

17. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 17 Build your own DigIns… Develop a classroom culture of peer and self descriptive feedback along the format of NCDigIns. This is a great way to find out the learning progressions of your students, which often do not match the logic of textbooks.

18. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 18 Using NCDigIns Teacher feedback is most effective for common errors … one to many Self and peer assessment expands feedback … many to many

19. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 19 Problem Solving “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.

20. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 20 There’s a Problem … … with Problem Solving Grade 4 Question from NAEP 2003 Estella wants to buy 2 notebooks that cost $2.79 each, including tax. If she has one- dollar bills and no coins, how many one- dollar bills does she need? A 3 B 4 C 5 C 6 Nationally, 31% of the students correctly selected D. And 41% chose A. nces.ed.gov/nationsreportcard/itmrls/

21. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 21 FA -> CCSSO Definition 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

22. PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION DEPARTMENT OF PUBLIC INSTRUCTION 22 FA -> Key User = Student! 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.