2010 Alabama Course of Study: Mathematics College- and Career-Ready Standards

1. 2010 Alabama Course of Study: MathematicsCollege- and Career-Ready Standards Domains of Study/Conceptual Categories Learning Progressions/Trajectories

2. CHARACTERISTICS • Aligned with college and work expectations • Written in a clear, understandable, and consistent format • Designed to include rigorous content and application of knowledge through high-order skills • Formulated upon strengths and lessons of current state standards • Informed by high-performing mathematics curricula in other countries to ensure all students are prepared to succeed in our global economy and society • Grounded on sound evidence-based research

3. 2010 Alabama Course of Study: Mathematics • Coherent • Rigorous • Well-Articulated • Enables Students to Make Connections

4. Coherence • Articulated progressions of topics and performances that are developmental and connected to other progressions. • Conceptual understanding and procedural skills stressed equally. • Real-world/Situational application expected.

5. FOCUS • Key ideas, understandings, and skills are identified. • Deep learning stressed.

6. Mathematical Content Format Grade Domain Cluster Standard Course Conceptual Category Domain Cluster Standard K-8 9-12

7. What is the difference? • Domain • Cluster • Standards

8. What is the difference? Domain:Overarching “big ideas” that connect content across the grade levels. Cluster:Group of related standards below a domain. Standards:Define what a student should know (understand) and do at the conclusion of a course or grade.

9. K-8 Domains • Illustrate progression of increasing complexity from grade to grade. • Organize standards within each grade. Note: Domains typically span a few grades.

10. MathematicsDomains of Study by Grade

11. K-8 Clusters • May appear in multiple grades. • Illustrate progression of increasing complexity from grade to grade.

12. K – 8 Cluster

13. Content Standards • Content standards in this document contain minimum required content. • Each content standard completes the phrase “Students will.” • Reflect both mathematical understandings and skills, which are equally important.

14. How Many Skills? • Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. [4-NBT2] • 4.7.1.Read multi-digit whole numbers using base-ten numerals. • 4.7.2.Read multi-digit whole numbers using number names. • 4.7.3.Read multi-digit whole numbers using expanded form. • 4.7.4. Write multi-digit whole numbers using base-ten numerals. • 4.7.5. Write multi-digit whole numbers using number names. • 4.7.6. Write multi-digit whole numbers using expanded form • 4.7.7.Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

15. Grade Level Focus Grade Level Overview Grade Level Narrative Critical Area

16. CRITICAL AREASBRING FOCUS TO THE NEW STANDARDS

17. CRITICAL AREAS • Identify Two to Four Areas of Concentrated Study. • Bring Focus to the Standards. • Provide the Big Ideas for Building Curriculum and Guiding Instruction.

18. INVESTIGATING CRITICAL AREAS • In grade-level groups, analyze the critical areas for your grade. • Underline the key words and phrases that help summarize this area. • Design a poster that describes the focus of your grade level.

19. The Big Picture High School Functions, Statistics, Modeling and Proof K-2 Number and number sense. 3-5 Operations and Properties (Number and Geometry) Fractions 6-8 Algebraic and Geometric Thinking Data Analysis and using Properties

20. MathematicsDomains of Study by Grade

21. What Are Learning Trajectories? And What Are They Good For?—Save the Last Word for Me!!! Read the excerpt from Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction • Identify 3 ideas that you are willing to talk about with colleagues. • Highlight the location in the text where these ideas appear.

22. LearningProgressions/Trajectories Confrey (2007) “Developing sequenced obstacles and challenges for students…absent the insights about meaning that derive from careful study of learning, would be unfortunate and unwise.” CCSS, p. 4 “… the development of these Standards began with research-based learning progressions detailing what is known today about how students’ mathematical knowledge, skill, and understanding develop over time.”

23. Directions for Save the Last Word for Me • Designate a facilitator and timekeeper. • A volunteer begins by reading the sentence(s) from the text that embody one of his/her selected ideas. The speaker does not comment on the text at this point. • The individual to right of first speaker takes up to one minute to comment on the selected text. • The next two individuals also take up to one minute to comment on the initial speaker’s idea. • The individual selecting the idea has up to 1 minutes to react to colleagues’ ideas and to talk about why she or he thought this was important. • Another group member introduces one idea, and the group follows the same protocol. Continue until all members have shared or until time is called.

24. Learning Trajectories – sometimes called learning progressions – are sequences of learning experiences hypothesized and designed to build a deep and increasingly sophisticated understanding of core concepts and practices within various disciplines. The trajectories are based on empirical evidence of how students’ understanding actually develops in response to instruction and where it might break down. Daro, Mosher, & Corcoran, 2011

25. Learning Progression Framework Starting Point Starting Point Ending Point Ending Point

26. Investigating the Domains/Conceptual Categories Domains provide common learning progressions. Curriculum and teaching methods are not dictated. Standards are not presented in a specific instructional order. Standards should be presented in a manner that is consistent with local collaboration.

27. What Goes On The Chart Paper? • Summary and/or representation of how the concept of the use of numbers grows throughout your grade band. • Easy for others to interpret or understand. • Visual large enough for all to see. • More than just the letters and numbers of the standards – include key words or phrases.

28. Let’s Talk About It! • As a table group, consider your journey through the 2010 ACOS as you studied the concept of the use of numbers K-12. • What did you learn? • What surprised you? • What questions do you still have?

29. Learning Progressions

30. Value of Learning Progressions/Trajectories to Teachers • Know what to expect about students’ preparation. • More readily manage the range of preparation of students in your class. • Know what teachers in the next grade expect of your students. • Identify clusters of related concepts at grade level. • Clarity about the student thinking and discourse to focus on conceptual development. • Engage in rich uses of classroom assessment.

31. Review the Format

32. ?? Questions ??

33. Contact Information ALSDE Office of Student Learning Curriculum and Instruction Section Cindy Freeman, Mathematics Specialist Phone: 334.353.5321 E-mail: cfreeman@alsde.edu