American Publishers School Division Summit on Mathematics and Science

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American Publishers School Division Summit on
Mathematics and Science October 4, 2007 Nancy
Kinard President, Florida Council of Teachers of
Mathematics
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Floridas New World-class Mathematics Sunshine
State Standards

• World Class Education Standards (WCES) are
  defined as standards by subject area that require
  critical thinking and problem-solving skills,
  foster creativity and innovation, and cultivate
  the acquisition of communication and information
  through the use of contextual and
  applied-learning strategies that promote global
  competitiveness.
• When implemented through quality instruction and
  content, these standards prepare all students to
  compete internationally at their highest levels.

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Why World-Class?Modeled From the Best of the Best

• Singapore top on the TIMMS international
  assessment
• Finland top on the PISA international
  assessment
• Massachusetts, California, Indiana standards
  that were graded A
• National Council Teachers of Mathematics
• K 8 Focal Points Big Ideas

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Mathematics Standards

• Revisions began September 2006
• Adoption in September of 2007
• Access points utilized for alternative assessment
  in 2008
• 2007-2008 Transition year
• New course descriptions
• Standards cross walk
• Textbook alignment
• 2008-2009 Implementation year
• 2010-2011 Assessment

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Of the People, By the People,

• 20 people on the framers committee
• 5 external experts
• 22 people on the writers committee
• 43,025 ratings of benchmarks through online
  review process
• 15 expert review panelists
• 7 reviewers from the business community
• 22 depth of knowledge raters

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Web-based Public Review

• 43,025 total ratings of 504 benchmarks
• Ratings from all school districts
• 503 of 504 benchmarks 50 or more rated agree
  or strongly agree
• Ratings included public comment

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Web-based Public Review 1,391 Raters Completed
the Visitor Profile

• How they Identified Themselves
• 50 as administrators
• 32 as district staff
• 37 as other interested persons
• 26 as parents
• 1,242 as teachers
• 4 no response

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What is the Role of the Standards?

• Define the content, knowledge, and abilities that
  a Florida K-12 mathematics student is expected to
  have and master at the end of each grade level or
  course
• Provide clear guidance to teachers for Depth of
  Knowledge and instructional goals
• Provide framework for textbooks and other
  instructional materials
• Provide framework for Assessment
• Serve as a guide to improve student learning in
  mathematics

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Big Ideas K-8
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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

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Why World-Class

• Old average of 83 grade level expectations per
  grade K-8
• New average of 18.5 benchmarks per grade K-8
• Singapore 15 standards per grade K-8

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Whats Different?Fewer but More Aligned Topics

• Old Geometry K 2, There is no specific
  benchmark for dividing shapes into parts for the
  purpose of building a foundation to understand
  the concept of fractions.
• New Benchmark Grade 2, MA.2.G.5.1
  Use geometric models to demonstrate the
  relationships between wholes and their parts as a
  foundation for fractions.
• Fractions are then introduced in grade 3.

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What does this mean?

• Fewer topics per grade, less repetition from year
  to year
• Move from covering topics to teaching them
  in-depth for long term learning and building
  connections
• Teachers will need to know how to introduce each
  new topic at the concrete level and move to the
  abstract and then connect it to other and more
  complex topics
• Students, build, draw, write and explain

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What does this look like?

• Grade 4 Example Lesson Day 1
• Provide each student with 30 cm2 tiles and
  several sheets of cm2 paper
• Reintroduce cm2 tiles and the concepts of squares
  and rectangles, request student volunteers build
  and share models of squares and rectangles and
  articulate the definitions for each
• Request students build as many rectangles and
  squares as possible using one up to all of the
  tiles and draw these models on their graph paper

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Day 2

• Ask students individually to identify for each
  number of tiles used, how many rectangles or
  squares can be built
• Pair up students and have them compare and
  discuss their findings
• Have student pairs share with the class their
  findings and communicate their defense for
  correctness
• When the correct total is agreed upon (58),
  provide students the opportunity to review their
  work to make any necessary improvements prior to
  the next step (teacher reviews for correctness)

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Day 3

• Have students list the numbers of tiles from
  which
• only one square or rectangle could be built
• a square could be built
• multiple rectangles and/or squares could be built
• Pair up students and have them compare and
  discuss their findings
• Have student pairs share with the class their
  findings and communicate their defense for
  correctness
• When the correct responses are agreed upon,
  provide students the opportunity to review their
  work to make any necessary improvements prior to
  the next step (teacher reviews for correctness)

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Here are the solutions

• 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 tiles only
  build one rectangle
• 1, 4, 9, 16, 25 tiles build squares
• 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22,
  24, 25, 26, 27, 28, 30 tiles build multiple
  rectangles and/or squares
• What mathematical concepts do these models
  represent?

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More and More and MoreThis example lesson should
take several more days to complete.

• Primes, composites, perfect squares
• Other concepts by continuing this lesson
• Number patterns
• Perimeter and addition facts
• Repeated addition (precursor to multiplication)
• Area and multiplication facts (precursor to
  factoring in algebra and use of algebra tiles)
• Prime factorization and factors

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Applying These Concepts

• Make these concepts relevant by applying them
• Using one sheet of your graph paper, design a
  floor plan for your first home that includes
  eight square and rectangular rooms. Your plan
  must include at least one perfect square and one
  rectangle with a prime area. Label all
  perimeters, areas, and room purposes.
  Write a defense for your plan.

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Related Benchmarks

• Grade 4 MA.4.A.1.1 Use and describe various
  models for multiplication in problem-solving
  situations and demonstrate recall of basic
  multiplication and related division facts with
  ease
• Grade 4 MA.4.G.3.2 Justify the formula for the
  area of the rectangle area base x height
• Grade 5 MA.5.A.2.4 Determine the prime
  factorization of numbers (a concept needed to add
  and subtract fractions with unlike denominators)

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Secondary Bodies of Knowledge
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Course Description Example ALGEBRA I
ALGEBRA
GEOMETRY
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.
STATISTICS
MA.912.S.5.8 Use a regression line equation to
make predictions.
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Business and Industry

• The mathematics standards revision process began
  with the research from the Achieve Mathematics
  Benchmarking Initiative presented to the
  Mathematics Framers group by Kaye Forgione.
• Achieve (online here  http//www.achieve.org/)
  is sponsored by the National Governors
  Association and has a board of directors composed
  of 3 state governors and 6 business CEOs (see
  http//www.achieve.org/node/337).
• The research accomplished by the Achieve group is
  based on input from the business community. Their
  academic benchmarks are based on input from
  front-line managers in a variety of industries
  such as health care, gaming, high-tech
  manufacturing, information technology, law,
  television, shipping and transportation, retail,
  and financial services.
• The following slide delineates the mathematics
  courses recommended for success by the 16
  nationally recognized career and technical
  education career clusters by Achieve.org.

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Recommended Math Courses for 16 CTE Career
Clusters
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Bodies Of Knowledge 9-12
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Why World-Class

• Finland
• Compulsory Courses
• Expressions and Equations
• Geometry
• Statistics and Probability
• Mathematical Analysis Derivative, Polynomial
  Functions
• Advanced Courses
• Vectors (covered in Discrete)
• Trigonometric Functions and Number Sequences
• The derivative Radical and logarithmic
  functions, Integral Calculus
• Specialization Courses
• Commercial Mathematics
• Mathematical Models

• Florida
• Algebra
• Geometry
• Trigonometry
• Probability
• Statistics
• Discrete
• Calculus
• Financial Literacy

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Whats Different?Benchmarks Specific to Content

• Old Data Analysis and Probability had seven
  benchmarks to guide instruction for a statistics
  course.
• New We now have 9 benchmarks for Probability and
  28 benchmarks for Statistics to guide instruction
  in Floridas four approved courses in this area
  as well as other courses where these benchmarks
  would be applicable.

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Whats Different?Benchmarks Specific to Content

• Old Measurement, we had eight benchmarks in
  measurement but no direction on where and when
  they should be taught.
• New We have no Measurement Body of Knowledge,
  our Bodies of Knowledge relate to math content
  areas, not topics within mathematics for
  example MA.912.G.6.4 Find and use measures of
  arcs and related angles (central inscribed, and
  intersections or secants and tangents).

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Whats Different?Benchmarks Specific to Content

• Old There were NO benchmarks to guide instruction
  in Financial Literacy, Trigonometry, Discrete
  Mathematics, and Calculus.
• New Now there ARE!

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What does this mean?

• Teachers will now have content specific
  benchmarks to lead their instruction no longer
  being dependent upon the text for the content of
  the course they are teaching.
• End-of-course exams and pre-tests can be built
  from the benchmarks listed in course
  descriptions.
• Administrators will know exactly what benchmarks
  are to be taught in each course.

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From Business Reviewers

• I and several of my Engineering and Physics
  peers enjoyed solving the questions in this
  section.  I especially loved the example in
  Standard Number MA.912.A.7.8 9. Thank you for
  allowing me to review your math standards
  document.  I had fun, and I am sincerely glad to
  be able to provide feedback and become a more
  active citizen in our childrens education.
• Kim Robinson,
• Senior Performance Engineer, Adaptec, Inc.

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Kims Input

• Standard Number MA.912.A.1.5 I am continuously
  surprised by the number of students that are not
  actually able to perform dimensional analysis.
   In my job, this is one of the most important
  things to be able to understand and perform.  Im
  glad to see this standard within the algebra
  section and think it should be reinforced in
  Chemistry, Physics and higher level mathematics
  courses.
• Standard Number MA.912.A.2.2 Again hooray for
  Florida for including graph representation for
  real world situations.  Being able to visual
  represent problems, something that girls tend to
  perform less optimally/frequently than boys,
  significantly aids in solving problems.  There is
  a certain realness to problems that can be
  displayed graphically.
• Standard Number MA.912.A.2.12 Never heard of
  joint variations, google couldnt even find it
  (sans the FL DOE website).
• Standard Number MA.912.A.4.3 Factoring
  polynomial expressions is the bane of most
  Algebra and pre-calculus students.  There are no
  perfect, guaranteed recipes for success for n
  degree (gt2) poly equations. I would encourage
  more emphasis on this distinct problem and more
  tools (i.e. completing the square, rational zero
  test, etc.)
• And a list of 24 concepts that she requested be
  included. We cited where 21 of these are already
  explicitly included and have place more emphasis
  on the other three in remarks and examples

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Others

• Adequacy Yes. the standards include the
  concepts for higher learning.   Depth of
  coverage While for most of the standards include
  important concepts in depth, some areas can be
  improved.
• Tim Madhanagopal, Engineer, Orange County
  Utilities 
• The Financial Literacy component is excellent
  kudos for adding this.Howard Ludwig, Senior
  Staff Engineer,
• SoftwareLockheed Martin Missiles and Fire
  Control
• Statistical SectionDo Florida's revised math
  standards include the math concepts/knowledge/skil
  ls that students should learn in grades 9 through
  12 to ultimately succeed in high-performance,
  high-growth jobs? Yes
• Floyd Freeman, Jr.,
• Technical Project Manager, Sprint

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World-class Policies

• Graduation requirements
• 2007-2008 9th grade students will be required to
  earn four credits in mathematics for graduation,
  including Algebra I or equivalent (2003 2006
  40 graduated with four credits).
• Eight other states already require credit in
  Algebra II, eight more require credit in
  Geometry.

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How Can You Help?Public Relations!

• Believe students need math and science
• Encourage teachers to learn more about their
  content
• Provide classrooms with hands-on learning tools
• Be aware of what good math and science
  instruction looks like and support it
• The students should be doing the work!

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Where to Find the 2007 Standards Document
www.flstandards.org
www.fldoestem.org