Florida K8 Mathematics Standards

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Florida K-8 Mathematics Standards

• Juli K. Dixon, Ph.D.
• University of Central Florida

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Agenda

• Writing process
• Intent of the document
• Organizational structure
• Work remaining
• Impact on assessment and
• Impact on required teacher content knowledge.

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Perspective
A student said this
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Perspective
A student said this
When asked to compare 4/5 and 2/3, a student
said, I know that 4/5 is greater than 2/3.
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Perspective
A student said this
When asked to compare 4/5 and 2/3, a student
said, I know that 4/5 is greater than 2/3.
How would you respond?
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Perspective
A student said this
When asked to compare 4/5 and 2/3, a student
said, I know that 4/5 is greater than 2/3.
How would you respond?
Hopefully you would ask the student how he or she
knew.
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Perspective
The student said
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Perspective
The student said
I made both fractions using manipulatives. I knew
that 4/5 was bigger because 4/5 has 4 pieces and
2/3 only has 2 pieces and since 4 is greater than
2 then 4/5 is greater than 2/3.
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Perspective
The student said
I made both fractions using manipulatives. I knew
that 4/5 was bigger because 4/5 has 4 pieces and
2/3 only has 2 pieces and since 4 is greater than
2 then 4/5 is greater than 2/3.
What would this response tell you?
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Perspective
Would you ask this student to compare 22/23 and
26/27?
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Perspective
Would you ask this student to compare 22/23 and
26/27?
According to the intent of the new standards, the
answer should be yes. This problem is appropriate
for a student in grade 3. Are our teachers
prepared to address this?
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Developing the Standards

• 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.

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Developing the Standards

• 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.

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Developing the Standards

• 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.

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Developing the Standards

• 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.

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Who were the experts?

• Dr. Barbara Reys Center for the Study of
  Mathematics Curriculum (CSMC) shared a review of
  42 states 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 Singapores
  World-class Mathematics System.
• Dr. R. James Milgram Wrote the California
  Mathematics Standards.

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Describing the Standards

• 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.

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Describing the Standards

• 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.

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Describing the Standards

• 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
• Include three levels of complexity
  participatory, supported, and independent with
  the participatory level being the least complex
• The Access points were not written by the
  Mathematics Standards Writing Committee and are
  not intended for mainstream students.

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Describing the Standards

• Coding Scheme for Kindergarten through Grade 8

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Describing the Standards
Body of Knowledge Key A - Algebra C - Calculus D
- Discrete Mathematics F - Financial Literacy G -
Geometry P - Probability S - Statistics T -
Trigonometry
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Describing the Standards
23
Describing the Standards
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Describing the Standards

• 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.

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Intent of the Standards

• What is the importance of having fewer
  expectations per grade????

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Intent of the Standards

• 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?

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Intent of the Standards

• 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)?

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Intent of the Standards

• How can a brief exploration of fractions help us
  to make sense of this depth of content
  knowledge? -- and why fractions?????

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• Virtually every time I ask teachers of algebra
  what they wish their incoming students knew,
  their response is fractions.
• Francis (Skip) Fennell, President of NCTM
• December 2007 NCTM News Bulletin, p. 3

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Focus Standard

• Grade 3Big Idea 2 Develop an understanding of
  fractions and fraction equivalence.
• MA.3.A.2.2 Describe how the size of the
  fractional part is related to the number if equal
  sized pieces in the whole
• MA.3.A.2.3 Compare and order fractions,
  including fractions greater than one, using
  models and strategies.

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Tell which Fraction is Larger

• 3/7 and 5/8
• 4/7 and 4/9
• 9/10 and 5/4
• 3/8 and 5/8
• 6/7 and 8/9

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Think about this

• Alex and Jessica are racing their bicycles. Alex
  is 3/7 of the way to the finish line and Jessica
  is 2/3 of the way to the finish line. Which racer
  is closer to the finish line? How do you know?

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Think about this

• Marc and Jake each bought the same type of energy
  bar. Marc has 1/8 of his energy bar left, Jake
  has 1/10 of his energy bar left. Who has more
  energy bar leftover? How do you know?

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Think about this

• Riley and Paige each bought a small pizza. Riley
  ate 2/3 of her pizza, and Paige ate 4/5 of her
  pizza. Who ate more pizza? How do you know?

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NOW Tell which Fraction is Larger

• 3/7 and 5/8
• 4/7 and 4/9
• 9/10 and 5/4
• 3/8 and 5/8
• 6/7 and 8/9

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A new perspective
Would you ask a student to compare 22/23 and
26/27?
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Describing the Standards

• 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.

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For Example
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Describing the Standards

• 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 of
  Teachers of Mathematics meeting, a representative
  from FCAT said, students would still need to
  know concepts from previous grades. They just
  wont be tested in isolation.

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For Example

• Generate equivalent fractions and simplify
  fractions is a benchmark for grade 4 and not
  grade 5. However, it will likely be used when
  adding and subtracting fractions in grade 5.

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Describing the Standards

• Some prerequisite knowledge and skills, not
  specifically identified in the standards, may
  need to be added to the curriculum to meet the
  standards.

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For Example

• Divisibility rules are not listed as specific
  requirements in the standards and may need to be
  addressed during exploration of prime
  factorization and simplifying fractions.

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Describing the Standards

• Students who move to Florida from other states
  may need exposure to topics not addressed at
  their grade of entry.

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For Example

• Surface area is addressed in grade 5. This is
  earlier than in the old standards and earlier
  than what is current common practice in many
  other states. Students entering in grade 7 are
  expected to work with surface area more formally.
  The expectation is that these students would have
  had informal experiences in grade 5.

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Real-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.

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Excerpts from Lynn Arthur Steen Educational
Leadership, November 2007, p. 9
Fractions and algebra represent the most subtle,
powerful, and mind-twisting elements of school
mathematics. But how can we teach them so
students understand? Few adults understand
fractions well enough to use them
fluently Even mathematics teachers have a hard
time imagining authentic problems that require
these exotic calculations (Ma, 1999)
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Focus Standard
Grade 6 Big Idea 1 Develop an understanding of
and fluency with multiplication and division of
fractions and decimals. MA.6.A.1.1 Explain and
justify procedures for multiplying and dividing
fractions and decimals. MA.6.A.1.3 Solve
real-world problems involving multiplication and
division of fractions and decimals.
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Make Sense of Fraction Division

• Write a word problem (story problem) to represent
  this
• 1 3/4 1/2

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Make Sense of Fraction Division

• Write a word problem (story problem) to represent
  this
• 1 3/4 1/2

So what does division of fractions actually mean?
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Make Sense of Fraction Division

• 1 3/4 1/2
• Joy has 1 3/4 gallons of iced tea. How many 1/2
  gallon containers can she make using all the tea
  she has?

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More examples

• Examples similar to the one just shared are
  provided with the remarks to the standards.

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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.

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Remarks

• Remarks were not included with the standards
  presented to the State Board of Education.
• Remarks are currently included in course
  descriptions.

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Next steps should include

• Establishment of content limits (expected
  completion February 2008 for grades 3 - 8).
• 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).

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Impact on Assessment

• FCAT Items will necessary change due to changes
  in the standards.
• Sample FCAT items were shared recently by
  representatives from FCAT at a meeting on this
  topic

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Sample Grade 4 Item

• Alex is 4 years more than twice as old as Sam.
  Which
• expression shows Alexs age, using s for Sams
  age?
• (4 2) x s C) 4s x 2
• (s 4) x 2 D) 2s 4

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Sample Grade 7 Item

• The records of a sporting goods company show that
  4 out
• of every 100 footballs manufactured have some
  defect.
• What is the probability that a football will NOT
  have a
• manufactured defect?
• 1/1 C) 1/25
• 1/4 D) 24/25

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Impact on Assessment

• FCAT item writers met for training and began
  writing items February 2008.
• New standards-based items will be field tested in
  2010.
• New standards-based FCAT will be administered in
  2011

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Impact on teacher content knowledge

• The impact on the required content knowledge for
  teaching standards-based mathematics is
  substantial.
• Teachers need a depth of content knowledge beyond
  what is expected with the new standards.
• The way teachers are prepared to teach
  mathematics may need to be revisited
• The way elementary mathematics instruction is
  delivered may need to be rethought.