Sunshine State Standards for Mathematics

1. Sunshine State Standards for Mathematics World Class Standards for our Students

2. What did the Researchers Report?(content available at flstandards.org) 1996 Sunshine State Standards for Math could be improved by: • More Coherence (i.e., better logical progression of topics and complexity) • Less Overlap of topics: More Depth at each topic • Increase in Cognitive Complexity • Improved Clarity of Expectations

3. Moving Forward with the Mathematics Standards • Revisions began September 2006 • Adoption anticipated in August of 2007 • 2007-2008 Transition year • New course descriptions • Standards cross walk • Text book alignment • 2008-2009 Implementation year • 2010-2011 Assessment

4. Structure of the Standards K-8 Grade Level -Big Ideas/Supporting Ideas -Benchmarks 9-12 Body of Knowledge -Standards -Benchmarks

5. Where does this structure come from? • National Council of Teachers of Mathematics (NCTM) Curriculum Focal Points for grades K-8 (NCTM, 2006). • State Standards that scored well in evaluation by external reviews (such as CA, IN) provided structure for the Secondary Bodies of Knowledge.

6. What is a Supporting Idea? • Supporting Ideas are not subordinate to Big Ideas • Supporting Ideas may serve to prepare students for concepts or topics that will arise in later grades • Supporting Ideas may contain grade-level appropriate math concepts that are not included in the Big Ideas

7. Coding Scheme Kindergarten through Grade 8 Secondary

8. Access Points Coding Scheme Kindergarten through Grade 8 Secondary

9. Comparing the Standards

10. How is this accomplished? • Fewer topics per grade due to less repetition from year to year. • Move from “covering” topics to teaching them in-depth for long term learning. • Individual teachers will need to know how to begin each topic at the concrete level, move to the abstract, and connect it to more complex topics.

11. Bodies Of Knowledge 9-12

12. What does this mean for teachers? • Teachers will now have content specific benchmarks to lead their instruction, no longer being dependent upon the text for the content of the course they are teaching • End-of-course exams and pre-tests can be built from the benchmarks listed in course descriptions • Teachers and Administrators will know exactly what benchmarks are to be taught in each course and at each grade level

13. Content Standards Mathematics Understanding, Ability, and Achievement How Do We Connect These? ?

14. The five process standards (NCTM, 2000): Problem Solving Reasoning and Proof Communication Connections Representations The five “strands” of mathematics proficiency (NRC, 2001): Conceptual Understanding – comprehension of mathematical concepts, operations, and relations Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately Strategic Competence – ability to formulate, represent, and solve mathematical problems Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy Mathematics Proficiency

15. Process Standards By National Council of Teachers of Mathematics, 2000.

16. Problem Solving • Engage students in challenging tasks • Build new mathematical knowledge • Deepen understanding of a mathematics concept • Involve multiple solution methods and different representations • Reflect on the problem solving process

17. Problem Solving • Example 1: Simplify • Example 2: Make a rectangle that is ½ blue and 1/3 red. What could the rectangle look like?

18. Problem Solving • Example 1: Simplify • Example 2: Make a rectangle that is ½ blue and 1/3 red. What could the rectangle look like?

19. Reasoning and Proof • Mathematical processes have reasons behind them • Students make, refine, and test conjectures • It should exist at all grade levels, with more abstract and complex forms in high school and later grades.

20. Communication • Students share ideas and clarify understanding • Students communicate mathematical ideas by speaking, listening, drawing, reading, and writing • By the end of the high school years, a student writes well-constructed mathematical arguments using formal vocabulary.

21. Connections • Mathematical ideas interconnect and build on one another to produce a coherent whole • Rich connections result in rich understanding • Connections involve relating mathematics to other disciplines

22. Representation • Supports students’ understanding and communication of mathematical ideas • Different representations may illuminate different aspects of concepts • Representations in mathematics include tables, graphs, diagrams, symbols, and words.

23. 4 3 MA.4.G.3.2 Justify the formula for the area of the rectangle “area = base x height.”

24. 4 3 Three times Four 3 x 4 = 4 x 3 = 12

25. Twelve times Twenty-three 23 12

26. 23 12 Twelve times Twenty-three 12 x23 6 30 40 +200 276 12 x23 36 +240 276 12 x 23 = (10+2)(20+3) = 10(20)+2(20)+10(3)+2(3) = 200+40+30+6 = 276 (a+b)(c+d)

27. Mathematical Proficiency National Research Council, 2001

28. Conceptual Understanding • Comprehension of mathematical concepts, operations, and relationships. • Example: Understanding why the multiplication algorithm works when multiplying whole numbers.

29. Procedural Fluency • Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. • Example: Being able to perform whole number multiplication fluently with different strategies, including the multiplication algorithm and mental processing.

30. Strategic Competence • Ability to formulate, represent, and solve mathematical problems • Related to problem solving and representation standards of NCTM (2000)

31. Adaptive Reasoning • Logical thought, reflection, explanation, and justification • Related to reasoning and proof process standard. • Inductive reasoning, deductive reasoning, informal justifications • Example: Students can justify “adding even numbers equals to an even number” by using manipulatives at earlier grade levels.

32. Productive Disposition • Seeing mathematics as sensible, useful, and worthwhile, coupled with a belief in one’s own efficacy

33. Thesefive strands are interwoven and interdependent.

34. Depth of Knowledge/Cognitive Complexity Based on Webb, N. L., 1999

35. Level 1: Low Complexity • Recall and recognition of previously learned concepts and principles. Examples: • solving a one-step problem • retrieving information from a graph, table, or figure • identifying appropriate units or tools for common measurements

36. Level 2: Moderate Complexity • Involve more flexible thinking and choice among alternatives. Examples: • solving a problem requiring multiple operations • selecting and/or using different representations, depending on situation and purpose • providing a justification for steps in a solution process

37. Level 3: High Complexity • Engage students in more abstract reasoning, planning, analysis, judgment, and creative thought. Examples: • solving a non-routine problem • providing a mathematical justification • formulating a mathematical model for a complex situation

38. What Role do the new Standards Play? • Define the content, knowledge, and abilities that a Florida K-12 mathematics student is expected to have and master at the end of each grade level or course. • Provide clear guidance to teachers for depth of knowledge and instructional goals. • Provide framework for textbooks and other instructional materials • Provide framework for assessment • Serve as a guide to improve student learning in mathematics!

39. What are Access Points? • Written for students with significant cognitive disabilities to access the general education curriculum • Reflect the core intent of the standards with reduced levels of complexity • Three levels of complexity include participatory, supported, and independent with the participatory level being the least complex

40. Where to Find the NGSSS for Math www.flstandards.org www.fldoestem.org