Project PROMISE A Jacob K. Javits Grant Virginia Department of Education 2004-2008.
Todd Clark, Office of Math and Science FL Department of Education February 19, 2008 © 2008, Florida...
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Transcript of Todd Clark, Office of Math and Science FL Department of Education February 19, 2008 © 2008, Florida...
Todd Clark, Office of Math and Science
FL Department of Education
February 19, 2008
© 2008, Florida Department of Education
Florida’s Office of Math & Science
Established by Governor Crist in February 2007
Responsible for implementing K-12 mathematics and science standards and education policies that improve student achievement and prepare students for success
Website: www.fldoestem.org
An Era of Standards
NCTM publishes standards in 1989 (content), 1991 (teaching), 1995 (assessment), and 2000 (revision)
Florida adopts first set of Sunshine State Standards for Math in 1996
Grade Level Expectations written in 1999
Revision Process
September 2006 – Framers conveneOctober 2006 through January 2007 – Writers draft K-8 standards and secondary content standards with comment and review from framersFebruary through March 2007 – Individual, Public, and Committees review draftsApril through June 2007 – Revisions of drafts based on public reviewJune 2007 – Evaluation of cognitive complexity of BenchmarksAugust 2007 – Present new standards to the State Board of EducationSeptember 2007 – Standards are approved by the State Board of Education
Modeled From the World’s Leading Mathematics Curriculum –
World-Class Curriculum Standards
Singapore – top on the TIMSS
Finland – top on the PISA
Massachusetts, California, Indiana – standards that were graded “A”
National Council Teachers of Mathematics Curriculum Focal Points
What the Researchers said about Our Mathematics Standards
“A Mile Wide, An Inch Deep”
For Florida’s Grades 1-7, the average number of mathematics grade level expectations (GLEs) = 83.3
Singapore, the highest performing nation as measured by Trends in International Math and Science Study (TIMSS), has 15 GLEs per grade level
College Board
Define grade-level expectations for grade 9-12Increase rigor of middle through high school standardsIncrease specificity of standards, showing a progressive development across grade levelsIncrease the depth of knowledge required as grades progress
Recommendations From International and National Experts
“Increase rigor and specificity all the way around”
K-8 - By grade level up to Algebra 1Let NCTM’s Focal Points be a guideReduce number of GLEs, focused in-depth instruction
Secondary - By Bodies of KnowledgeAlgebra, Geometry, Probability, Statistics, Trigonometry, Discrete Math, Calculus, Financial Literacy“Upper level” mathematics courses will use standards set by AP, IB, College Board, Dual Enrollment course guidelines/standards
Terms in the 1996 and 2007 Standards
1996
Standards
Grade Band
Strand
Benchmark
Grade Level Expectation
2007
Standards
Body of Knowledge
Supporting Idea
Big Idea
Access Points
Benchmark
Coding Scheme
MA. 5. A. 1. 1Subject Grade-Level Body of
KnowledgeBig Idea/
Supporting Idea
Benchmark
MA. 912. G. 1. 1Subject Grade-Level Body of
KnowledgeStandard Benchmark
Secondary
Kindergarten through Grade 8
Standard 2
Standard 4
Standard 5Standard 3
Sunshine State Mathematics Standards
Standard 1
Benchmark
MA.912.T.1.1 Benchmark
MA.912.T.1.3
Benchmark
MA.912.T.1.4
Benchmark
MA.912.T.1.6 Benchmark
MA.912.T.1.7
Benchmark
MA.912.T.1.8
Benchmark
MA.912.T.1.5
Benchmark
MA.912.T.1.2
Trigonometry Body of Knowledge
Benchmark
MA.912.T.5.3
Benchmark
MA.912.T.3.1
Benchmark
MA.912.T.3.2
Benchmark
MA.912.T.3.3
Benchmark
MA.912.T.3.4
Benchmark
MA.912.T.2.3 Benchmark
MA.912.T.2.4
Benchmark
MA.912.T.2.1
Benchmark
MA.912.T.2.2
Benchmark
MA.912.T.4.1
Benchmark
MA.912.T.4.4 Benchmark
MA.912.T.4.3
Benchmark
MA.912.T.4.2
Benchmark
MA.912.T.5.2
Benchmark
MA.912.T.5.1
6
4
and
TRIGONOMETRY BODY OF KNOWLEDGEStandard 1: Trigonometric FunctionsStudents extend the definitions of the trigonometric functions beyond right triangles using the unit circle and they measure angles in radians as well as degrees. They draw and analyze graphs of trigonometric functions (including finding period, amplitude, and phase shift) and use them to solve word problems. They define and graph inverse trigonometric functions and determine values of both trigonometric and inverse trigonometric functions.
Benchmark Code Benchmark
MA.912.T.1.1 Convert between degree and radian measures.
MA.912.T.1.2 Define and determine sine and cosine using the unit circle.
MA.912.T.1.3 State and use exact values of trigonometric functions for special angles, i.e. multiples of
MA.912.T.1.4 Find approximate values of trigonometric and inverse trigonometric functions using appropriate technology.
MA.912.T.1.5 Make connections between right triangle ratios, trigonometric functions, and circular functions.
MA.912.T.1.6 Define and graph trigonometric functions using domain, range, intercepts, period, amplitude, phase shift, vertical shift, and asymptotes with and without the use of graphing technology.
MA.912.T.1.7 Define and graph inverse trigonometric relations and functions.
MA.912.T.1.8 Solve real-world problems involving applications of trigonometric functions using graphing technology when appropriate.
(degree and radian measures)
Grade 6Algebra
Body of KnowledgeBig Idea 1
Benchmark
MA.6.A.1.3
Benchmark
MA.6.A.1.2
Benchmark
MA.6.A.1.1
Big Idea 3Algebra
Body of Knowledge
Benchmark
MA.6.A.3.3
Benchmark
MA.6.A.3.5Benchmark
MA.6.A.3.4
Benchmark
MA.6.A.3.2
Benchmark
MA.6.A.3.1
Benchmark
MA.6.A.3.6
Big Idea 2 Algebra
Body of Knowledge
Benchmark
MA.6.A.2.2
Benchmark
MA.6.A.2.1
Supporting IdeaBenchmark
MA.6.G.5.2
Benchmark
MA.6.G.5.2
Benchmark
MA.6.G.5.1
Geometry
Body of Knowledge
Supporting Idea
Benchmark
MA.6.A.6.1
Benchmark
MA.6.A.6.2
Benchmark
MA.6.A.6.3
Algebra
Body of Knowledge
Supporting IdeaBenchmark
MA.6.A.6.1
Benchmark
MA.6.A.1.3
Statistics
Body of Knowledge
Sunshine State Mathematics Standards
Grade 6 Big Idea 1BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals.
BENCHMARK CODE
BENCHMARK
MA.6.A.1.1 Explain and justify procedures for multiplying and dividing fractions and decimals.
MA.6.A.1.2 Multiply and divide fractions and decimals efficiently.
MA.6.A.1.3 Solve real-world problems involving multiplication and division of fractions and decimals.
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 critical grade-level appropriate math concepts that are not included in the Big Ideas
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
Access Points Coding Scheme
MA. 5. A. 1. ln.aSubject Grade Level Body of
KnowledgeBig Idea/
Supporting Idea
Access Point
MA. 912. A. 1. ln.aSubject Grade-Level Body of
KnowledgeStandard Access
Point
Kindergarten through Grade 8
Secondary
Comparing the StandardsGrade Level Number of Old
GLE’sNumber of New
Benchmarks
K 67 11
1st 78 14
2nd 84 21
3rd 88 17
4th 89 21
5th 77 23
6th 78 19
7th 89 22
8th 93 19
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
Bodies Of Knowledge 9-12Old 9-12 Benchmarks
(Same for all 9-12)
New Body of Knowledge Benchmarks
12 Benchmarks in Number Sense, Concepts, and Operations
8 Benchmarks in Measurement
4 Benchmarks in Algebraic Thinking
5 Benchmarks in Geometry and Spatial Sense
7 Benchmarks in Data Analysis and Probability
84 Benchmarks for Algebra
52 Benchmarks for Calculus
41 Benchmarks for Discrete Math
41 Benchmarks for Financial Literacy
47 Benchmarks for Geometry
9 Benchmarks for Probability
28 Benchmarks for Statistics
24 Benchmarks for Trigonometry
ALGEBRA
DISCRETE MATH
GEOMETRY
Course Description Example:
ALGEBRA I
MA.912.A.4.2 Add, subtract, and multiply polynomials.
MA.912.G.1.4 Use coordinate geometry to find slopes, parallel lines, perpendicular
lines, and equations of lines.
MA.912.D.7.2 Use Venn diagrams to explore relationships and
patterns, and to make arguments about relationships between sets.
Benchmark MA.912.A.4.3:Factor polynomial expressions.
_______________________________
ex: Let a, b > 0, a > b, a,b Є
Factor the following expression:
a2 – b2
Solution:a2 – b2 = (a – b)(a + b)
Can this be done Geometrically with manipulatives?