No problem can stand the assault of sustained thinking. ~Voltaire

1. No problem can stand the assault of sustained thinking. ~Voltaire

3. Welcome and Introductions Introduce yourselves to others at your table. What are your learning goals for the KoPS professional development?

5. KoPS Learning Outcomes • To implement research-based strategies for problem solving in Math • To integrate technology based resources and manipulatives in problem solving; • To make instructional decisions to plan and teach problem solving more effectively.

6. KoPS Instructional Strategies KoPS provides professional development for math and ESE teachers by: • Using Next Generation Sunshine State Standards in problem solving in mathematics • Infusing researched metacognitive strategies (mnemonic devices, self-monitoring skills, graphic organizers, etc.), • Including differentiated instruction and technology to meet the needs of all learners. • Including assessment and evaluation targeted to varying levels/types of instruction.

7. KoPS Professional Development • Developed by a cadre of math and special educators from school districts, educational agencies, universities and FDOE • Aligned with state standards (Next Generation) and national math standards (NCTM).

8. Advance Organizer: Day 1 • Introduction/Rationale • Assessment • The Problem Solving Process-overview

9. Advance Organizer: Day 2 • Review Day 1 • Problem Solving Process • Differentiated Instruction • Technology • Follow Up

10. KoPS Rationale Solving problems is not only a goal of learning mathematics but also a major means of doing so. It is an integral part of mathematics, not an isolated piece of the mathematics program. ~NCTM (2000)

11. Rationale for Change Daily, mathematics is used throughout our lives. The ability to compute, problem solve, and apply concepts and skills in mathematics influences decisions and life choices. From personal, professional, and societal perspectives, the mastery of mathematical skills of number sense and problem solving are necessary. This is especially evident in technology-rich societies, where number sense and problem solving skills have increasing importance, as technology enhances both the opportunities for, yet the demands of, advanced levels of proficiency in mathematics. ~Witzel & Little, 2009

12. KoPS Rationale But, what about our students? In the 2007 Programme for International Student Assessment (PISA), U.S. 15-year olds ranked 25th among 30 developed nations in math literacy and problem solving. ~Baldi, Jin, Shemer, Green, Hergert, & Xie (2007).

13. How many acronyms can you identify?

14. Bureau of Exceptional Education and Student Services: State Performance Plan (2005-2010) • 1-Increase percent of SWDs graduating with a regular diploma • 2-Improve percent of SWDs who complete school (decrease drop outs) • 3-Increase the participation and performance of SWDs on state assessments • (See rest of SPP for additional Indicators, Activities, Timelines, and Resources. (http://www.fldoe.org/ese/)

16. Rationale: It is about student learning! • US fourth graders showed no measurable gains in mathematics (NCES, 2004). • Only 2% of US students attained advanced levels by grade 12 in mathematics (NCES, 2006) • About 50% of the FCAT requires higher order thinking, which is the ability to solve complex problems. • 32% of eighth graders and 23% of fourth graders score below “basic” level (NCES, 2006). • The ranking of US students compared to 14 other countries was lower in 2003 than in 1995 (NAEP, 2005)

17. What is the Data Telling Us?

18. Trends Rationale: From The Nation’s Report Card ~http://nces.ed.gov/nationsreportcard/pdf/stt2005/2006454IA4.pdf

19. Student Achievement Achievement Gap 29 %

20. Student Achievement

21. In 2009, 67% of students in grades 3-10 are demonstrating mathematics skills at or above grade level.

22. Student Achievement by District http://nces.ed.gov/nationsreportcard/mathematics/

23. Overview of DA Model The new DA Bill has passed- ALL schools in the following categories will now be affected:

24. Overview of DA Model-con’t New DA Legislation just passed….ALL schools which have not met AYP for 2 consecutive years will be under the DA Model. They will looking at the last 7 years of data. • Further info: http://www.flbsi.org/assistplus/assistplusinfo.htm -Differentiated Accountability Implementation guide -List of Differentiated Accountability Schools -Differentiated Accountability FAQ’s

25. DA Check

26. AYP and Math Proficiency 62% scoring at or above grade level 2007-2008 school year 4 districts reflected Math Proficiency in the subgroup of “Students With Disabilities (SWD)” • Dixie County • Glades County • Lafayette County • Sumter County 2008-2009 school year 1 district reflected Math Proficiency in the subgroup of “Students With Disabilities (SWD)” • Union County

27. Our Goal, as Math Leaders in Florida….. To continue to plan, build understanding, and make or adjust implementation decisions regarding curriculum, instruction, and assessment of the Next Generation Sunshine State Standards in Mathematics and RtI. So, how do we meet these challenging and changing goals?

28. BenchmarkMA.3.A.2.2Describe how the size of the fractional part is related to the number of equal sized pieces in the whole. A rectangle is constructed using squares. The squares are colored teal, black, pink, and white. Half of the squares are teal and one-third of the squares are pink. Create the rectangle.

30. There are infinite solutions to this question. The minimum number of squares will be 12. Proof: Let x equal the number of squares needed The 1’s represent the minimum number of squares that are black and white While many students will want to use graph paper, using concrete items such as centimeter cubes, sticky notes, or cut out squares, students can easily manipulate the rectangle. For example, it is easy to justify that half of the rectangle is teal and that one-third of the rectangle is pink. What do you need to know to answer the question? • Understanding of ½ and 1/3 • Multiplication is an array

31. “For people to participate fully in society, they must know basic mathematics. Citizens who cannot reason mathematically are cut off from whole realms of human endeavor.” ~NRC, 2001 “The mathematics students need to learn today is not the same mathematics that their parents and grandparents needed to learn. When today’s student become adults, they will face new demands for mathematical proficiency that school mathematics should attempt to anticipate.” ~NRC, 2001

32. Research Findings: “Adding It Up” (2001) The National Research Council (2001) published major findings related to mathematics knowledge and research from last several years.

33. Problem Solving as aProcess Standard (NCTM)

35. The Next Generation There are NO benchmarks specific to problem solving in the old Sunshine State Standards… However, in the Next Generation Sunshine State Standards, there are deliberate efforts to emphasize problem solving in real-world applications.

36. New Standards Grade-level specific Measurable Leveled appropriately vertically to move students through CRA Mastery expected each grade level Less topics more time for greater depth

37. Revised Standards • Estimation • Mental calculation • Communication • Use of math tools • Arithmetic manipulation • Algebraic manipulation • Handling data

38. Taken from: Florida Department of Education, Next Generation Sunshine State Standards (2007).

39. Math Journal: Reflection Describe how your students are ready to face the increasing mathematical demands?

40. References • Baldi, S., Jin, Y., Skemer, M., Green, P.J., and Herget, D. (2007). Highlights from PISA • 2006: Performance of U.S. 15-year-old students in science and mathematics literacy • in an international context (NCES 2008-016). • Florida Department of Education. FCAT Mathematics Sunshine State Standards Test Book, Released: Fall 2007. Located at: http://fcat.fldoe.org/pdf/releasepdf/07/FL07_G5M_TB-Rel_WT_C002.pdf • Florida Department of Education. (2007). Next Generation Sunshine State Standards. Located at: http://www.floridastandards.org/downloads.aspx. • Jaywalking. The Tonight Show with Jay Leno. Located at: • http://www.nbc.com/The_Tonight_Show_with_Jay_Leno/video/ • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn • mathematics. Center for Education, National Academies Press: Washington, D.C.

41. References National Center for Educational Statistics. (2004). The condition of education 2004 in brief. Located at: http://nces.ed.gov/pubs2004/2004076.pdf National Center for Educational Statistics. (2005). The Nation’s Report Card: State Mathematics 2005. http://nces.ed.gov/nationsreportcard/pdf/stt2005/2006454IA4.pdf National Council of Teachers of Mathematics. (2008). Located at: http://www.nctm.org/ National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. President’s Commission on Excellence in Special Education. (2001). A New Era: Revitalizing Special Education for Children and Their Families. Located at: http://www.ed.gov/inits/commissionsboards/whspecialeducation/reports/index.html.

42. References Problem Solving and Response to Intervention. (2008). About problem Solving/Rti. Located at: http://floridarti.usf.edu/. Schmidt, W. H., C. C. McKnight, and S. A. Raizen. (1997). A Splintered Vision: An investigation of U.S. science and mathematics education. Boston: Kluwer Academic Publishers. U.S. Department of Education. Washington, DC: National Center for Education Statistics. Bureau of Exceptional Education and Student Services: Performance Plan (2005-2010). Located at: http://www.fldoe.org/ese/