Florida K-8 Florida K-8 Mathematics Mathematics StandardsStandards

April 25, 2008April 25, 2008

Grade KGrade K

A student said this…A student said this…

When asked to compare 4/5 and 2/3, When asked to compare 4/5 and 2/3, a student said, “I know that 4/5 is a student said, “I know that 4/5 is greater than 2/3.”greater than 2/3.”

How would you respond?How would you respond?

Hopefully you would ask the Hopefully you would ask the student how he or she knew.student how he or she knew.

Perspective…Perspective…

The student said…The student said…

I made both fractions using manipulatives. I I made both fractions using manipulatives. I knew that 4/5 was bigger because 4/5 has 4 knew that 4/5 was bigger because 4/5 has 4 pieces and 2/3 only has 2 pieces and since 4 pieces and 2/3 only has 2 pieces and since 4 is greater than 2 then 4/5 is greater than 2/3.is greater than 2 then 4/5 is greater than 2/3.

What would this response tell you?What would this response tell you?

Perspective…Perspective…

Would you ask this student to Would you ask this student to compare 22/23 and 26/27?compare 22/23 and 26/27?

According to the intent of the new According to the intent of the new standards, the answer should be yes. standards, the answer should be yes. This problem is appropriate for a This problem is appropriate for a student in grade 3. Are our teachers student in grade 3. Are our teachers prepared to address this?prepared to address this?

Perspective…Perspective…

Developing the Developing the StandardsStandards The new Florida K-8 Mathematics Standards

are framed by the recently released NCTM Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics and informed by the Singapore Standards, the SSS Grade Level Expectations, and standards from other states that received high grades for rigor, focus, specificity and clear progression of content.

There are clear differences between the new

standards and the 1996 K-8 mathematics SSS.

Developing the Developing the StandardsStandards The “framers,” a group that

represented K-12 teachers, K-12 mathematics supervisors, mathematicians, and mathematics educators, were convened to address issues related to the current standards and to establish a framework for the design of the new standards. The framers recommended that the Curriculum Focal Points be used as the foundation for the new K-8 standards.

Developing the Developing the StandardsStandards The “writers,” a group that

represented the same set of stakeholders, were convened to generate the revised standards. The writers of the K-8 standards had the task of actualizing the intent of the Curriculum Focal Points within a set of grade-level specific standards.

Developing the Developing the StandardsStandards

September 2006: Framers met with “experts” to learn about task and conceptualize new standards.

October 2006 - January 2007: Writers wrote draft of standards.

February - March 2007: New standards posted for public review period.

April - May 2007: Standards revised by writers and representation from framers based on comments received during review

September 2007: Standards approved by State Board of Education.

Who were the Who were the “experts”?“experts”?

Dr. Barbara Reys: Center for the Study of Mathematics Curriculum (CSMC); shared a review of 42 state’s mathematics standards.

Dr. Jane Schielack: Chaired NCTM committee that wrote the Curriculum Focal Points.

Dr. Kaye Forgione: Senior Associate of Mathematics Benchmarking Initiative with Achieve, Inc.

Dr. Alan Ginsburg: US Dept. of Education, What the United States can Learn from Singapore’s World-class Mathematics System.

Dr. R. James Milgram: Wrote the California Mathematics Standards.

Describing the Describing the StandardsStandards Big Ideas---Standards which are aligned with

the Curriculum Focal Points. – They should be the primary focus of mathematics

instruction for each grade level, K - 8. – There are three Big Ideas for each grade. – The Big Ideas are not the same for each grade. – The order of the Big Idea does not determine the

order of instruction nor does it indicate that one idea requires greater instructional emphasis.

– Instructional time may not be evenly divided among the three Big Ideas.

Describing the Describing the StandardsStandards Supporting Ideas---standards that serve one or more of the

following purposes: – Establishing connections to and between the strands of

mathematics as defined by NCTM;

– Preparing students for future mathematics teaching and learning; and

– Addressing gaps in instruction that are important to the understanding, fluency, and application of mathematics ideas to problem solving.

The Supporting Ideas are not less important than the Big Ideas, but are key components to a structurally sound mathematics education.

Describing the Describing the StandardsStandards Access Points

– Written for students with significant cognitive disabilities Written for students with significant cognitive disabilities to access the general education curriculumto access the general education curriculum

– Reflect the core intent of the standards with reduced Reflect the core intent of the standards with reduced levels of complexitylevels of complexity

– Include three levels of complexity: participatory, Include three levels of complexity: participatory, supported, and independent with the participatory level supported, and independent with the participatory level being the least complexbeing the least complex

The Access points were not written by the Mathematics Standards Writing Committee and are not intended for mainstream students.

Describing the Describing the StandardsStandards Coding Scheme for Kindergarten through

Grade 8

MA.MA. 5.5. A.A. 1.1. 11

SubjectSubject Grade-Grade-LevelLevel

Body of Body of KnowledgKnowledg

ee

Big Idea/ Big Idea/ SupportinSupportin

g Ideag Idea

BenchmarBenchmarkk

Describing the Describing the StandardsStandards

Body of Knowledge Key:A - AlgebraC - CalculusD - Discrete MathematicsF - Financial LiteracyG - GeometryP - ProbabilityS - StatisticsT - Trigonometry

Describing the Describing the StandardsStandardsGrade LevelGrade Level Number of Number of OldOld

GLE’sGLE’sNumber of Number of NewNew

BenchmarksBenchmarks

KK 6767

11stst 7878

22ndnd 8484

33rdrd 8888

44thth 8989

55thth 7777

66thth 7878

77thth 8989

88thth 9393

Describing the Describing the StandardsStandardsGrade LevelGrade Level Number of Number of OldOld

GLE’sGLE’sNumber of Number of NewNew

BenchmarksBenchmarks

KK 6767 1111

11stst 7878 1414

22ndnd 8484 2121

33rdrd 8888 1717

44thth 8989 2121

55thth 7777 2323

66thth 7878 1919

77thth 8989 2222

88thth 9393 1919

Describing the Describing the StandardsStandards Old Standards had an average of 83.3

Grade Level Expectations (GLEs) per grade.

The new Standards have an average of 19 benchmarks per grade.

Intent of the Intent of the StandardsStandards What is the importance of having

fewer expectations per grade????

Intent of the Intent of the StandardsStandards A member of the Florida Department

of Education shared a reaction by a teacher during an open forum regarding the new Florida standards. The teacher looked at the short list of curricular topics in a grade and said,

“I can teach this in 20 days, what do

I do the rest of the year?”

Intent of the Intent of the StandardsStandards How do we help teachers with similar

views come to understand what is meant by facilitating “deep understanding, mathematical fluency, and an ability to generalize” (NCTM, 2006, p. 5)?

Describing the Describing the StandardsStandards To enable the development and

mastery of a few key concepts in each grade level it was necessary to make decisions about the placement of topics. As a result, some topics are not introduced until later grades. This does not necessarily mean that students are incapable of learning at an earlier grade. Instead, it is an attempt to streamline the focus of content at each grade level.

For Example…For Example…

Old Standards New Standards

Fractions are introduced in kindergarten

Money was introduced in kindergarten

For Example…For Example…

Old Standards New Standards

Fractions are introduced in kindergarten

Fractions are introduced in grade 2

Money is introduced in kindergarten

In Grade 2, money is introduced as: Identify, combine, and compare values of money in cents up to $1 and in dollars up to $100, working with a single unit of currency.

Kindergarten Big Kindergarten Big Ideas:Ideas: 1: Represent, compare, and 1: Represent, compare, and

order order

whole numbers and join and whole numbers and join and separate sets.separate sets.

2: Describes shapes and space.2: Describes shapes and space. 3: Orders objects by measurable 3: Orders objects by measurable

attributesattributes

Kindergarten Kindergarten Supporting IdeasSupporting Ideas

Algebra:Algebra: Identify and duplicate Identify and duplicate simple number and non-numeric simple number and non-numeric repeating and growing patterns. repeating and growing patterns.

Geometry & Measurement:Geometry & Measurement: Demonstrate an understanding of Demonstrate an understanding of the concept of time using the concept of time using identifiers such as morning, identifiers such as morning, afternoon, day, week, month, year, afternoon, day, week, month, year, before/after, and shorter/longer. before/after, and shorter/longer.

Describing the Describing the StandardsStandards Mathematics instruction at each

subsequent grade will continue to use concepts and understandings learned in earlier grades as needed.

When asked at a recent Florida Council When asked at a recent Florida Council of Teachers of Mathematics meeting, a of Teachers of Mathematics meeting, a representative from FCAT said, representative from FCAT said, “students would still need to know “students would still need to know concepts from previous grades. They concepts from previous grades. They just won’t be tested in isolation.” just won’t be tested in isolation.”

Describing the Describing the StandardsStandards Some prerequisite knowledge and

skills, not specifically identified in the standards, may need to be added to the curriculum to meet the standards.

Describing the Describing the StandardsStandards Students who move to Florida from

other states may need exposure to topics not addressed at their grade of entry.

Real-World ProblemsReal-World Problems

To the extent possible, it is expected that the relevance of mathematics would be made clear to students by illustrating how mathematics is used in the real world. To this end, the curriculum should include real-world contexts in addition to mathematical contexts. The overall goal is to help students relate mathematics to the real world and their experiences.

Remarks are provided to:Remarks are provided to:

Clarify what is described in the standards.

Provide context to be addressed as part of

the standards.

Provide examples of the types of problems

that the standards address.

Provide content limits when deemed

appropriate.

RemarksRemarks

Remarks were not included with the

standards presented to the State

Board of Education.

Remarks are currently included in

course descriptions.

Next steps should Next steps should include:include:

Statewide communication regarding new standards

(ongoing). A comprehensive crosswalk between the new and

existing standards (currently available in draft form).

District-by-district plans for transitioning to the new standards (work together!).

Professional development for teachers in order to provide tools and knowledge necessary to implement new standards with success (ongoing but more needed).