1. 1

2. An Overview of the Standards for School Mathematics? 2

3. 3 The Standards The ten Standards describe a connected body of mathematical understandings and competencies. It is a comprehensive foundation recommended for all students. Standards are descriptions of what mathematics instruction should enable students to know and do.

4. 4 The Standards The standards are in two sets. The content standards and the processing standards. For purposes of curriculum development and teaching the two sets are inseparable.

5. 5 The Content Standards Number and Operations These standards span all grade bands and describe the content that students should learn. Number and Operations Algebra Number and Operations Algebra Geometry Number and Operations Algebra Geometry Measurement Number and Operations Algebra Geometry Measurement Data Analysis and Probability

6. 6 The Processing Standards Problem Solving These standards span all grade bands and highlight ways of acquiring and using content knowledge. Problem Solving Reasoning and Proof Problem Solving Reasoning and Proof Communication Problem Solving Reasoning and Proof Communication Connections Problem Solving Reasoning and Proof Communication Connections Representation

7. 7 Emphasis Across the Grades Number Algebra Geometry Measurement Data Analysis and Probability Pre-K–23–56–89–12

8. 8 Each standard comprises a small number of goals that apply across all grades. Each of the content Standards offer an additional set of expectations specific to each grade band. The appendix contains a summary of the Standards.

9. 9 Although the ten Standards apply to all grades, emphasis will vary both within and between grade bands. Because mathematics as a discipline is highly interconnected, the standards overlap and are integrated. Those who design curriculum frameworks will need to make their own decisions about emphasis and order.

10. 10 Standards for Grades 6 – 8.

11. Middle-grades students are drawn toward mathematics if they find both challenge and support in the mathematics classroom. Grades 6–8

12. 12 Characteristics of Students Major physical, emotional and intellectual changes in adolescence. Grades 6–8 These factors make it especially important for teachers to create classroom environments in which clearly established norms support the learning of mathematics. continued

13. 13 Characteristics of Students Are drawn toward mathematics with challenge and support in the classroom Should see mathematics as an exciting, useful, and creative field Are drawn toward mathematics with challenge and support in the classroom. Should see mathematics as an exciting, useful, and creative field. Will benefit from rich and integrated mathematics instruction. Grades 6–8

14. 14 More and Better Mathematics More understanding and flexibility with rational numbers. More understanding and flexibility with rational numbers More algebra and geometry. More understanding and flexibility with rational numbers More algebra and geometry More integration across topics. Grades 6–8

15. 15 Stronger Basics rational numbers Increasing students’ ability to understand and use— rational numbers linear functions rational numbers linear functions proportionality

16. 16 Builds on and helps build “more and better mathematics” In Grades 6–8 Developing Flexible Problem Solvers Builds on and helps strengthen “stronger/bolder basics” Builds on and enhances flexible use of representations Builds on and helps strengthen “stronger/bolder basics” Builds on and enhances flexible use of representations Builds on and deepens UNDERSTANDING of mathematical ideas Builds on and helps strengthen “stronger/bolder basics” Builds on and enhances flexible use of representations Builds on and deepens UNDERSTANDING of mathematical ideas Develops through regular experience with interesting, challenging problems

17. 17 Middle school teachers need to know much more mathematics than is required in most elementary school teacher-certification program. Middle school teachers need to know much more about adolescent development, pedagogical alternatives, and interdisciplinary approaches than most secondary school teachers.

18. 18 Standards for Grades 9 – 12.

19. To ensure that students will have a wide range of career and educational choices, the secondary school mathematics program must be both broad and deep. Grades 9–12 19

20. 20 Characteristics of Students Face decisions that will determine the course of their lives Grades 9–12 Face decisions that will determine the course of their lives Are more autonomous, also more able to work with others Face decisions that will determine the course of their lives Are more autonomous, also more able to work with others Are more reflective

21. 21 More and Better Mathematics Should study mathematics all four years Should experience a common foundation of mathematics Can study mathematics beyond what is expected for all, via: –Increased depth within foundational courses –Supplementary courses –Options in the fourth year Grades 9–12

22. 22 More and Better Mathematics Use of algebra to model interesting situations Increased attention to data analysis Use of algebra to model interesting situations Increased attention to data analysis Connections between algebra, geometry, and data analysis Use of algebra to model interesting situations Increased attention to data analysis Connections between algebra, geometry, and data analysis Discrete mathematics Grades 9–12

23. 23 Stronger Basics Transforming algebraic expressions Families of functions Transforming algebraic expressions Families of functions Conjecture and proof Grades 9–12

24. 24 In Grades 9–12 Builds and deepens UNDERSTANDING of mathematical concepts Developing Flexible Problem Solvers— Builds and deepens UNDERSTANDING of mathematical concepts Builds and promotes “more and better mathematics” Builds and deepens UNDERSTANDING of mathematical concepts Builds and promotes “more and better mathematics” Builds and strengthens “stronger basics” Builds and deepens UNDERSTANDING of mathematical concepts Builds and promotes “more and better mathematics” Builds and strengthens “stronger basics” Builds and enhances flexible use of representations Builds and deepens UNDERSTANDING of mathematical concepts Builds and promotes “more and better mathematics” Builds and strengthens “stronger basics” Builds and enhances flexible use of representations Develops through regular experiences with interesting, challenging problems

25. 25 The content and curricula aligned with these Standards will require extensive and sustained professional development for teachers and a large degree of administrative support.

26. 26 Assignment Read: NCTM Principles and Standards p 41-43, 232-39, and 308-18.