No problem can stand the assault of sustained thinking. ~Voltaire
Jan 15, 2016
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/