Creating the Mathematics Curriculum Guide to the Alabama Course of Study

1. Alabama Curriculum Guide 2011 Creating the Mathematics Curriculum Guide to the Alabama Course of Study

2. Reproductions of the slides and/or information from the slides in this PowerPoint related to Creating the Mathematics Curriculum Guide 2011 should be credited to: Alabama Department of Education, Special Education Services P.O. Box 302101 Montgomery, AL 36130 speced@alsde.edu 334.242.8114

3. What is a Course of Study? • A course of study (COS) is a curriculum document that specifies what students should know and be able to do in a particular subject area by the end of each grade level or course.

4. Characteristics of COS • Coherent • Rigorous • Well-Articulated • Enables Students to Make Connections

5. Characteristics of COS • 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; and • Grounded on sound evidence-based research.

6. Common Core State Standards College and Career Readiness Is every student graduating from high school ready for success in college or a well-paying career?

7. Common Core State Standards With few exceptions, the standards for mathematical content are: • Clear • Specific • Focused (Patricia F. Campbell: Presented at the Joint Mathematics Meetings, New Orleans, LA, January 6-9, 2011)

9. Organization • There are numbered and lettered standards that are grouped into domains and clusters. • Lettered items, are just as important as the numbered items and must be mastered. Often, they are specificity of the numbered items. • At the end of each standard is a content standard identifier that relates it to where that standard may be found in the CCSS document.

10. Organization • Additional Coding • ( ) Alabama Added Content • (+) STEM Standards • (*) Modeling Standards

11. Organization • 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.

12. Organization

13. Mathematical Content Format Grade Domain Cluster Standard K-8

14. Mathematical Content Format GRADE 4 Students will: Domain Cluster Content Standard Identifiers Content Standards

15. Mathematical Content Format Course Conceptual Category Domain Cluster Standard 9-12

16. Mathematical Content Format ALGEBRA II WITH TRIGONOMETRY Students will: FUNCTIONS Conceptual Category Domain ContentStandard Identifiers Cluster Content Standards

17. Domains of Study K-8

19. Trajectories & Progressions 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

20. Learning Progression Framework

21. Skills & Sub 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.

22. Standards for Mathematical Practice “The Standards for Mathematical practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.” (CCSS, 2010)

23. Standards for Mathematical Practice • Make sense of complex problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning. College and Career Readiness Standards for Mathematics

24. Assessment of the Common Core Assessment of the Common Core will begin in a few years. There are two consortia working on assessments. Smarter Balance www.k12.wa.us/SMARTER/default.aspx PARCC www.fldoe.org/parcc/

25. Nine Properties are the Most Important Preparation for Algebra • Just nine: foundation for arithmetic • Exact same properties work for whole numbers, fractions, negative numbers, rational numbers, letters, expressions. • Same properties in 3rd grade and in calculus • Not just learning them, but learning to use them Phil Daro (NCCTM, 2010)

26. Phil Daro (NCCTM, 2010)

27. Phil Daro (NCCTM, 2010)

28. Phil Daro (NCCTM, 2010)

29. What We Know… • Some students need additional instruction to work at grade level. Curriculum guides are developed to meet the needs of students who are working toward, but are not yet on, grade-level content standards.

30. Characteristics of Curriculum Guides • Provide instruction toward grade-level standards contained in courses of study • Beneficial for students working below grade level • Allow students to work at individual instructional levels • Skills continuum • Scaffolded support

31. Some Uses for Alabama Curriculum Guides • Lesson planning • BBSST • IEP development • Collaborative teaching • Tutorials • Planning for instructional grouping • Parent conferences • Development of curriculum-based assessments • Preparation for state assessments

32. Achieving Grade-Level Content Standards • All students must make progress toward grade-level content standards. • For students who are performing below grade level, the Alabama Curriculum Guides provide skills that lead to grade-level standards.

33. Curriculum Guides Curriculum guides are companion documents to the Alabama Courses of Study. They include all of the components of the Alabama Courses of Study and add objectives under each standard.

34. Purpose of Curriculum Guides • The Alabama Curriculum Guides list prerequisite skills and/or subsets of skills under each grade-level content standard. • The skills provide a trellis or scaffold to the standard.

35. Grade Clusters for Developing the Curriculum Guide • K-2 • 3-5 • 6-8 • 9-12

36. Contents of Curriculum Guide Documents • Introduction • Organization of Curriculum Guide • How Teachers Can Effectively Use This Document • Standards and Objectives • Appendices

37. Standards and Instructional Objectives • Standards • Contain minimum required content • Instructional objectives • Divide standards into smaller foundational and prerequisite skills that lead to the standard • Instructional objectives are listed in the order of most difficult prerequisites first and least difficult prerequisites last.

38. Organization of the Curriculum Guide Objective M. 2. 4. 1: (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends) Course Name Grade Level Standard # Objective #

39. Process for Developing Curriculum Guide Content • Read COS standard carefully • If more than one skill is included in the standard, break the smaller skills down so that each skill is listed separately. • Look back two grades in the COS standards to see which standards/skills are prerequisite to the skills in the selected standard. • Include the prerequisite skills under the selected standard if related—Note: Carefully consider the verb used in the standard and the verbs used in the objectives. As a general rule, the verbs in the objectives should be lower levels than the verb in the standard. • Target vocabulary that may be unfamiliar to the students—Note: some vocabulary will be listed as the first objective under the standard. Keep an ongoing list of vocabulary words for glossary.

40. Process for Developing Curriculum Guide Content • Examples for the objectives may be developed if examples are necessary to clarify CG objectives. • As a general rule, there should be a minimum of two objectives under each standard. • It will be necessary to develop some objectives. All prerequisites skills may not be found in backwards mapping. • After the prerequisite skills are complete, read the objectives carefully and ask, “If a student can do all of the skills listed here, is he/she ready to learn the knowledge and skills in the grade-level content standard?”