1. UCLA Graduate School of Education & Information Studies National Center for Research on Evaluation, Standards, and Student Testing David Niemi August 10, 2006 If you choose to use this title slide, simply delete the previous slide (the one-line title version). This will be slide 1 of your presentation. The Power of Formative Assessment of Big Ideas

2. 2/85 Three problems Students don’t understand what they’ve “learned” in elementary math. Too hard to memorize a lot of stuff that doesn’t mean anything--the “mile wide, inch deep” curriculum problem. No foundation for math advanced math. Teachers aren’t sure how to help students who are falling behind. Many students never master algebra.

3. 3/85 Our answer is: POWERSOURCE Strengthen formative assessment to support student learning through: Major intervention study in middle school mathematics (POWERSOURCE) Associated research studies Based on learning research Focus on organizing principles (big ideas)

4. 4/85 Effective formative assessment requires: Assessments that provide information that teachers can act on, and that are validated for this purpose Instructional strategies and resources linked to the information provided by the assessments Professional development to insure that teachers have the knowledge to put all this together

5. 5/85 Focus on big ideas Identify the “big ideas” of algebra, then find their precursors in elementary math Get this information from mathematicians and mathematics educators and researchers Build effective formative assessment system around those precursors

6. 6/85 Research base: the architecture of expert knowledge Expert knowledge is interconnected, organized around big ideas, and generalizable. Novices have piecemeal, context-bound knowledge. When pasting text from another document, do the following: 1.Highlight the text you want to replace 2.Go to the EDIT menu and select PASTE SPECIAL 3.Select “Paste as: UNFORMATTED TEXT”

7. 7/85 Big ideas are the landmarks in the cognitive landscape In a survey reported on the BBC news web site: UK adults were shown images of 12 well-known British landscapes with a key landmark missing to see if they recognised the landscape. Only 41% recognized the South Bank when shown images without the London Eye, a large ferris wheel. Two-thirds of Britons would not know where they were without landmarks such as Blackpool Tower or the Liver Building. 88% of Birmingham residents surveyed were unable to identify their city without the Regency Hyatt Hotel.

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9. 9/85 What is it like to see the big picture? Insert 3D graphic When pasting text from another document, do the following: 1.Highlight the text you want to replace 2.Go to the EDIT menu and select PASTE SPECIAL 3.Select “Paste as: UNFORMATTED TEXT”

10. 10/85 Big ideas drive problem solving When pasting text from another document, do the following: 1.Highlight the text you want to replace 2.Go to the EDIT menu and select PASTE SPECIAL 3.Select “Paste as: UNFORMATTED TEXT” --from Chi, Feltovich, & Glaser, 1991

11. 11/85 Examples of big ideas Rational number equivalence: You can generate equivalent rational number representations by multiplying any fraction by a/a (i. e., applying the multiplicative identity) The distributive property: a(b+c) = ab +bc When pasting text from another document, do the following: 1.Highlight the text you want to replace 2.Go to the EDIT menu and select PASTE SPECIAL 3.Select “Paste as: UNFORMATTED TEXT”

12. 12/85 Use this slide for any quotes or citations. When pasting text from another document, do the following: 1.Highlight the text you want to replace 2.Go to the EDIT menu and select PASTE SPECIAL 3.Select “Paste as: UNFORMATTED TEXT” Explaining rational number equivalence Multiplicative identity: If you multiply any number by one, you get the same number. 178 x 1 = 178 Any number divided by itself, or written over itself in a fraction, is 1 (except you can’t divide by 0). If you multiply any number by a/a, you get the same number (maybe in different form). 37 = 1 = 37 1212 x 74

13. 13/85 Explaining the distributive property When pasting text from another document, do the following: 1.Highlight the text you want to replace 2.Go to the EDIT menu and select PASTE SPECIAL 3.Select “Paste as: UNFORMATTED TEXT” 5 3 2 5(3 + 2) = 5 x 3 + 5 x 2

14. 14/85 How to demonstrate understanding of big ideas Recognize or give examples of problems that exemplify the big idea Solve the problems Use the big idea to justify the problem solution Explain the big idea When pasting text from another document, do the following: 1.Highlight the text you want to replace 2.Go to the EDIT menu and select PASTE SPECIAL 3.Select “Paste as: UNFORMATTED TEXT”

15. 15/85 Types of assessments Symbolic representation, computation Worked examples, with and without explanations Word problems Other complex problems Explanation When pasting text from another document, do the following: 1.Highlight the text you want to replace 2.Go to the EDIT menu and select PASTE SPECIAL 3.Select “Paste as: UNFORMATTED TEXT”

16. 16/85 Computation To adjust the slide numbering, do the following: 1.Go to the VIEW menu, MASTER, and select SLIDE MASTER 2.In the lower right, change the number 28 to your number of slides 3.Do not change the character. It generates the auto-numbers. Fill in the missing number:

17. 17/85 Worked Example With Explanation To adjust the slide numbering, do the following: 1.Go to the VIEW menu, MASTER, and select SLIDE MASTER 2.In the lower right, change the number 28 to your number of slides 3.Do not change the character. It generates the auto-numbers.

18. 18/85 Worked examples Partially worked problems assessing the distributive property To resize an image correctly, click on it once so that its “handles” appear. While holding down SHIFT, drag one of the corner handles. This will keep the image from being distorted while resizing. Task 1Task 2

19. 19/85 Explanation To adjust the slide numbering, do the following: 1.Go to the VIEW menu, MASTER, and select SLIDE MASTER 2.In the lower right, change the number 28 to your number of slides 3.Do not change the character. It generates the auto-numbers.

20. 20/85 POWERSOURCE Study Design Several States: California, Hawaii, Nevada, Arizona Large scale, multi-year experimental study: 80 middle schools (grades 6-8) 40 randomly assigned to POWERSOURCE intervention 40 control schools (assessment and instructions as usual) Start with 6th grade in first year, then phase in 7th and 8th grades When pasting text from another document, do the following: 1.Highlight the text you want to replace 2.Go to the EDIT menu and select PASTE SPECIAL 3.Select “Paste as: UNFORMATTED TEXT”

21. 21/85 next presentation