1. Math and the SBAC Claims
Elevating instruction for All students!
11:15
Cary Cermak-Rudolf
Roseburg Public Schools

2. Assumptions CCSS Math Shifts – Focus, Coherence, and Rigor
Standards for Mathematical Practice
Math Content Standards

3. Standards for Mathematical Practice
11:22

4. Smarter Balanced Reports
11:45
Concepts and Procedures 50% of the data

5. Four Claims Claim #1 Concepts & Procedures
“Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.”
Tammy

6. Outcome Assessments Claim 1 DOK 2 Domain NF
Domain NF – Numbers and Operations – Fractions
Claim 1
DOK 2
Domain NF

7. Four Claims Claim #2 Problem Solving
“Students can solve a range of complex well posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.”

8. Outcome Assessments
MD = Measurement and Data
Claim 2
DOK 2
Domain MD

9. Modeling and Data Analysis
Four Claims
Claim #4
Modeling and Data Analysis
“Students can analyze complex, real world scenarios and can construct and use mathematical models to interpret and solve problems.”

10. Outcome Assessment
Claim 4
DOK 3
Domain OA

11. Communicating Reasoning
Four Claims
Claim #3
Communicating Reasoning
“Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.”

12. What is different about Claim 3?
Importance of oral communication as well as connection to the ability to show a visual model of their understanding.
Claim 3
DOK 2
Domain G

13. Claim 2: Problem Solving Claim 4: Modeling and Data Analysis
What are the Claims?
Claim 1: Concepts
& Procedures
Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency
Claim 2: Problem Solving
Students can solve a range of complex well posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies
Claim 3: Communicating Reasoning
Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others
Claim 4: Modeling and Data Analysis
Students can analyze complex, real world scenarios and can construct and use mathematical models to interpret and solve problems
Cary -What do you notice about the claim language?

14. Why is CLAIM 3 so important?
“Communicating mathematical reasoning is not just a requirement of the Standards for Mathematical Practice – it is also a recurrent theme in the Standards for Mathematical Content.”
- Content Specification for the Summative Assessment July 2015

15. Accessibility Sped Ell Struggling learners
Read document (star and arrow)
Accessibility in Claim 3 (Student vs. Educator)
Cary
12:00

16. Supporting Instructionally
How can we support students’ struggle?
Explicitly Connecting Representations
Compression/Generalizations

17. Barriers for Struggling Students

18. How Students Learn Math
If teachers consistently and repeatedly engage all students in evidence-based learning experiences with the following features, students will learn mathematics with enduring understanding. 1)Cognitively demanding mathematical tasks 2) Adherence to mathematically productive classroom norms and relationships 3) Mathematical discourse that focuses on students’ mathematical reasoning, sense making, representations, justifications, and generalizations 4) Reflection and metacognition about their own and each other’s mathematical thinking 5) Productive disequilibrium about mathematical ideas and relationships
Page 9 Best Practices in Mathematics
Partner up – How do you see these being able to support students in critique the reasoning of others?

19. Compression
“The ability to file something away, recall it quickly and completely when you need it, and use it as just one step in some other mental process”. (Thurston, 1990)

20. Example of Compression
By building on experience, the child develops more sophisticated and more compressed methods of doing arithmetic – the more compressed, the more powerful the technique.
Later in the child’s development when asked what is 4 + 5, he or she may respond, “4 + 4 = 8 and since 5 is one more than 4, = 9.
When asked why, he or she says, “I just know it” or “I have it memorized.”
When a learner has this kind of “instantaneous” mathematical knowledge, we call that knowledge “derived facts.” What is interesting about derived facts is that they often represent multiple levels of compression.

21. What does compression look like?

22. Hierarchical learning

23. Opportunities to Learn – PISA report

24. Compression and Low Achievers
Math is a set of rules to be memorized
Labeled as low achieving
Placed in intervention supports that teach more rules
Rinse and Repeat
Jo Boaler, 2008
12:10

25. Sequencing Visual Representations
Concrete counting blocks
Representational tally marks
Abstract conceptual understanding what the number represents
Build Math Proficiency
2 + 3 = ?
2 + 3 = ?
II + III
Sequence of learning you take students through each time you work on mathematics.
2 + 3 = ?

26. If we don’t invest in all three areas we are robbing them of the opportunity to be mathematicians.
Some students may stay in the concrete longer than you expect.

29. 67 ÷ 4
11:40

30. Do the Math
56 ÷ 4
11:22 – 11:30

31. 11:32

33. One to do on Your Own
77 ÷ 5

34. Number Talks Do you agree or disagree and why?
Could you re-voice what your partner said?
How do these ideas connect?
What is the same or different about the two strategies that were shared?
How would you justify where you got the 16 from?

36. Go Back to the Math 5.NBT.6 In Claim 1, 2, 3 Compression
Leads to grade 6: Compute fluently with multi-digit numbers and find common factors and multiples.
Can’t see every problem as brand new. Deep connections between instruction, standards, claims, compression.

37. It will take a community.
It is not just about the mathematics

38. Action Plan
What supports do your teachers need in order to elevate claim 3 for ALL students?
How will you address professional learning needs to elevate instruction?
Record your next steps on the Action Plan form and be prepared to share.