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Florida K8 Mathematics Standards

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Title: Florida K8 Mathematics Standards


1
Florida K-8 Mathematics Standards
  • Juli K. Dixon, Ph.D.
  • University of Central Florida

2
Agenda
  • Writing process
  • Intent of the document
  • Organizational structure
  • Work remaining
  • Impact on assessment and
  • Impact on required teacher content knowledge.

3
Perspective
A student said this
4
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.
5
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?
6
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.
7
Perspective
The student said
8
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.
9
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?
10
Perspective
Would you ask this student to compare 22/23 and
26/27?
11
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?
12
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.

13
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.

14
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.

15
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.

16
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.

17
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.

18
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.

19
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.

20
Describing the Standards
  • Coding Scheme for Kindergarten through Grade 8

21
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
22
Describing the Standards
23
Describing the Standards
24
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.

25
Intent of the Standards
  • What is the importance of having fewer
    expectations per grade????

26
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?

27
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)?

28
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?????

29
  • 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

30
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.

31
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

32
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?

33
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?

34
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?

35
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

36
A new perspective
Would you ask a student to compare 22/23 and
26/27?
37
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.

38
For Example
39
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.

40
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.

41
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.

42
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.

43
Describing the Standards
  • Students who move to Florida from other states
    may need exposure to topics not addressed at
    their grade of entry.

44
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.

45
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.

46
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)
47
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.
48
Make Sense of Fraction Division
  • Write a word problem (story problem) to represent
    this
  • 1 3/4 1/2

49
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?
50
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?

51
More examples
  • Examples similar to the one just shared are
    provided with the remarks to the standards.

52
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.

53
Remarks
  • Remarks were not included with the standards
    presented to the State Board of Education.
  • Remarks are currently included in course
    descriptions.

54
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).

55
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

56
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

57
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

58
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

59
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.
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