No problem can stand the assault of sustained thinking.

~Voltaire

Introduce yourselves to others at your table.

What are your learning goals for the KoPS professional development?

Welcome and Introductions

KoPS Learning OutcomesKoPS 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.

KoPS Instructional Strategies

KoPS provides professional development for math and ESE teachers by:Using Next Generation Sunshine State

Standards in problem solving in mathematicsInfusing 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.

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).

Advance Organizer: Day 1

•Introduction/Rationale

•Assessment

•The Problem Solving Process-overview

Advance Organizer: Day 2

•Review Day 1

•Problem Solving Process

•Differentiated Instruction

•Technology

•Follow Up

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)

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

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).

KoPS Rationale

How many acronyms can you identify?

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/)

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)

What is the Data Telling Us?

TrendsRationale: From The Nation’s Report Card

~http://nces.ed.gov/nationsreportcard/pdf/stt2005/2006454IA4.pdf

Student Achievement

Achievement

Gap 29 %

Student Achievement

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

Student Achievement by District

http://nces.ed.gov/nationsreportcard/mathematics/

Overview of DA Model The new DA Bill has passed- ALL schools in the

following categories will now be affected:

PREVENT I – 270 Schools PREVENT II – 147 Schools

• SINIs 1, 2, and 3; and are

• A, B, C, or Ungraded schools; and

• Meet at least 80% of AYP criteria.

• SINIs 1, 2, and 3;

• That meet less than 80% of AYP criteria; and

• All Title I D and F schools; and

• All non-Title I D schools.

CORRECT I – 377 Schools CORRECT II – 274 Schools

• SINIs 4 or 5+, schools planning for or implementing Restructuring; and are

• A, B, C, or Ungraded schools; and

• Meet at least 80% of AYP criteria.

• SINIs 4 or 5+, schools planning for or implementing Restructuring;

• That meet less than 80% of AYP criteria; and

• All Title I D and F schools; and

• All non-Title I Repeating F and F schools.

  INTERVENE – 13 Schools

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

DA Check

AYP and Math Proficiency

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

62% scoring at or above grade level

2008-2009 school year

1 district reflected Math Proficiency in the subgroup of “Students With Disabilities (SWD)”

Union County

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?

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.

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

“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

Research Findings: “Adding It Up” (2001)

The National Research Council (2001) published major findings related to mathematics knowledge and research from last several years.

Problem Solving as aProcess Standard (NCTM)

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.

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

Revised StandardsRevised Standards

Estimation

Mental calculation

Communication

Use of math tools

Arithmetic manipulation

Algebraic manipulation

Handling data

Estimation

Mental calculation

Communication

Use of math tools

Arithmetic manipulation

Algebraic manipulation

Handling data

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

Math Journal: Reflection

Describe how your students are ready to face the increasing mathematical demands?

ReferencesBaldi, 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.

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.

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/