1. Assessment Workshop A Holistic Approach How Assessments Demonstrate Student Understanding and Inform Instruction November 4, 2008

2. The Structure of the Session Research on Assessment Research on Assessment Touch on: Assessing through discourse/student conversations Touch on: Assessing through discourse/student conversations Touch on: Looking at student Touch on: Looking at student self-assessment self-assessment Touch on: Student choice for assessment Touch on: Student choice for assessment Main Focus: Pre/Post Assessment- Assessing student work samples through error analysis- Dynamic Classroom Assessment Approach Main Focus: Pre/Post Assessment- Assessing student work samples through error analysis- Dynamic Classroom Assessment Approach

3. Assessment Discuss: Why is assessment so important? Why is assessment so important? What can you use to help you assess students? What can you use to help you assess students? Turn and Talk……….. Turn and Talk………..

4. Importance of Assessment To make instructional decisions that support student learning To make instructional decisions that support student learning Differentiation of content Differentiation of content Differentiation of format Differentiation of format Differentiation of materials Differentiation of materials Differentiation through choice Differentiation through choice To provide timely descriptive feedback To provide timely descriptive feedback To develop students ability to reflect and self- assess To develop students ability to reflect and self- assess

5. Triangulation-Sources of Assessment Observation of Process Observation of Process Work Samples Pre-Post tests Conversations Adapted from Dr. Anne Davis, 2007

6. Assessments: Based on Values Howard Gardner: Once we expand and reformulate our view of what counts as human intellect will we be able to devise more appropriate ways of assessing it and more effective ways of educating it. Howard Gardner: Once we expand and reformulate our view of what counts as human intellect will we be able to devise more appropriate ways of assessing it and more effective ways of educating it. Turn and Talk: Using your prior knowledge, discuss on which values math instruction should be based? Turn and Talk: Using your prior knowledge, discuss on which values math instruction should be based?

7. Research What’s Valued = What’s Assessed NCTM values the ability to problem solve, make connections across math strands and content areas, reason, and communicate thinking. NCTM values the ability to problem solve, make connections across math strands and content areas, reason, and communicate thinking. Dr. Deborah Ball- (Univ. of Michigan) research shows social value math- students share different perspectives; working collaboratively and cooperatively leads to a more democratic society. Dr. Deborah Ball- (Univ. of Michigan) research shows social value math- students share different perspectives; working collaboratively and cooperatively leads to a more democratic society. National Advisory Panel (2008) & National Research Council (2001 National Advisory Panel (2008) & National Research Council (2001) value the following abilities: 1) conceptual understanding, 2) procedural fluency, 3) use of strategies to solve problems, 4) reasoning, 5) student diligence, and 6) students’ view of math

8. Assess student understanding and misunderstanding Assess student understanding and misunderstanding Sometimes students understand relevant mathematics and are not able to communicate their correct understanding. Sometimes students understand relevant mathematics and are not able to communicate their correct understanding. Sometimes students misunderstand but can clearly communicate that misunderstanding. Sometimes students misunderstand but can clearly communicate that misunderstanding. As teachers we need to know the difference. As teachers we need to know the difference.

9. Conceptual and Procedural Understanding/Knowledge Conceptual knowledge demonstrates understanding of the big ideas. Conceptual knowledge demonstrates understanding of the big ideas. Procedural knowledge demonstrates understanding of ways to do things. Procedural knowledge demonstrates understanding of ways to do things.

10. Conceptual Knowledge Conceptual knowledge demonstrates understanding of the “big ideas.” the substance of an idea is the mental construct that is in the student’s head. the substance of an idea is the mental construct that is in the student’s head. (what a student knows) the presentation of the idea is the way the mental images get communicated. the presentation of the idea is the way the mental images get communicated. (what a student shows)

11. Procedural Knowledge Procedural knowledge demonstrates understanding of “ways to do things.” the substance of a procedure is an understanding of how the procedure works the substance of a procedure is an understanding of how the procedure works (what a student knows) (what a student knows) the presentation of a procedure is the way the procedure is represented the presentation of a procedure is the way the procedure is represented (what a student shows) (what a student shows)

12. Assessment Matrix Substance (what a student knows) Presentation (what a student shows) Conceptual (Big Ideas) Procedural (Ways to do things)

13. Grade 3 –Student A Addition Substance (what a student knows) Presentation (what a student shows) Conceptual (Big Ideas) Student knows that two numbers can be added together by breaking apart the tens and the ones. Student shows concept of addition by counting up by tens and ones. Procedural (Ways to do things) Student does not know algorithm for regrouping. Student does not show algorithm for regrouping.

14. Grade 3 –Student B Addition Substance (what a student knows) Presentation (what a student shows) Conceptual (Big Ideas) Student knows concept of addition by counting, not regrouping into tens and ones Student shows concept of addition by counting up by ones. Procedural (Ways to do things) Student does not know algorithm for regrouping Student does not show algorithm for regrouping

15. Grade 3 –Student C Addition Substance (what a student knows) Presentation (what a student shows) Conceptual (Big Ideas) Student knows concept of addition of tens and ones. Student shows concept of addition by adding 50 + 30, then 5 + 5 + 4. Procedural (Ways to do things) Student does not know algorithm for regrouping Student does not show algorithm for regrouping

16. Grade 3 –Student D Addition Substance (what a student knows) Presentation (what a student shows) Conceptual (Big Ideas) Student knows concept of addition with tens and ones. Student shows concept of addition by correctly adding the ones and the tens together to get a sum of 94. Procedural (Ways to do things) Student knows algorithm for regrouping. Student shows algorithm for regrouping. 56 + 38 = 94

17. Grade 3 –Student E Addition Substance (what a student knows) Presentation (what a student shows) Conceptual (Big Ideas) Student does not know concept of two digit addition. Student does not show concept of two digit addition. Procedural (Ways to do things) Student does not know algorithm for regrouping. Student does not show the algorithm for addition.

18. Ongoing Assessment- Student Discourse Five Productive Talk Moves Revoicing- Clearing confusion with the correct math language. Revoicing- Clearing confusion with the correct math language. ”So you’re saying you added 3 tens plus 4 tens and got 7 tens.” Restating -Asking students to restate someone else’s reasoning. Restating -Asking students to restate someone else’s reasoning. ”Can you repeat what he just said in your own words.” ”Can you repeat what he just said in your own words.” Corroborate- Asking students to apply their own reasoning to someone else’s reasoning. Corroborate- Asking students to apply their own reasoning to someone else’s reasoning. “Do you agree or disagree and why?” “Do you agree or disagree and why?” Expand - Prompting for further participation Expand - Prompting for further participation ”Would someone like to add on?” Reflect -Using wait time to encourage deeper thinking Reflect -Using wait time to encourage deeper thinking ”I will give everyone time to think about this question before sharing your thinking.” ”I will give everyone time to think about this question before sharing your thinking.” Classroom Discussions: Using Math Talk to Help Students Learn (2003) Classroom Discussions: Using Math Talk to Help Students Learn (2003) Classroom Discussion: Using Math Talk to help Children Learn, Chapin et al., Classroom Discussion: Using Math Talk to help Children Learn, Chapin et al.,

19. CHOICE When students make choices about what and how they learn they: Become more motivated to learn Become more motivated to learn Think harder and use more academic skills Think harder and use more academic skills Are more likely to behave in constructive ways and develop more friendships with a wider range of their classmates Are more likely to behave in constructive ways and develop more friendships with a wider range of their classmates