Todd Clark, Office of Math and Science FL Department of Education February 19, 2008 © 2008, Florida Department of Education.

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?