Georgia Performance Standards

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Georgia Performance Standards

• Dr. Tom Ottinger
• Dr. Lynn Stallings
• Habersham County
• 7/11/05

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The previous Georgia curriculumQuality Core
Curriculum (QCCs)

• 1986 Quality Basic Education (QBE) Act of 1986
  led to the establishment of the Quality Core
  Curriculum (QCC).
• 1995 A major revision of the QCCs was undertaken.
• 2001 The Georgia State Board of Education
  requested an audit of Georgias Quality Core
  Curriculum. Phi Delta Kappa conducted the audit
  and found that in several areas the curriculum
  lacked rigor and was inadequate to guide teaching
  and to ensure common expectations for all
  students.

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Why new standards?

• In 2002, an external (Phi Delta Kappa) audit
  concluded that the QCCs were lacking
• too many topics
• too little depth
• did not meet national standards
• could not be covered in a reasonable amount of
  time (would take twenty-three yearsnot twelveto
  cover the topics in any depth)

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GDOE was charged with addressing the following
concerns

• The curriculum needs to be rigorousmore than an
  inch deep.
• The curriculum needs to be more focusedless than
  a mile wide.
• The curriculum needs to be clearer and more
  specific about what students are expected to know
  and be able to do.
• Instruction need to be student-centered rather
  than teacher-centered so that educators can focus
  on what students are learning.

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Why an integrated approach in high school?

• Integrated approaches are used in most other
  parts of the world.
• Separation is artificial and doesnt start until
  Algebra I.
• Integration encourages connections between
  mathematical ideas.
• All of Algebra I and part of Geometry are
  finished by Grade 8, so traditional courses
  wouldnt work.

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Georgia Performance Standards

• Heres the official Georgia Department of
  Education introduction
• Introductory Video

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Comparison of the Old/New Curriculum
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Just the numbers . . .
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Comparing GPS to the QCCs

• GPS often requires
• higher level in Blooms Taxonomy (knowledge,
  comprehension, application, analysis, synthesis,
  evaluation)
• or requires conceptual AND procedural knowledge
  (Hiebert).
• GPS are clearer or more specific about what is
  expected.
• Difference between laddered and spiral curriculum
  is evident.
• Important content (for example, in 6th grade
  nets, sketches of solid figures) is added.
• Data analysis and probability strand is
  strengthened.

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Social Studies Example

• QCC, Grade 8
• 14   Topic Influential People
• Standard Identifies well-known and influential
  Georgians from the colonial era (men, women and
  minorities).
• GPS, Grade 8
• SS8H2 The student will analyze the colonial
  period of
• Georgias history
• explain the importance of James Oglethorpe, the
  Charter of 1732, reasons for settlement (charity,
  economics, and defense) Tomochichi, Mary
  Musgrove, and the city of Savannah
• evaluate the Trustee Period of Georgias colonial
  history emphasizing the role of the Salzburgers,
  Highland Scots, malcontents, and the Spanish
  threat from Florida
• explain the development of Georgia as a royal
  colony with regard to land ownership, slavery,
  government and the impact of the royal governors

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Example 17th Grade Integers Computation

• QCC
• Topic Integers
• Standard Computes with integers using models,
  manipulatives, and/or rules.
• Topic Whole Numbers, Fractions, Decimals,
  Computation, Problem Solving
• Standard Uses addition, subtraction,
  multiplication, and division (interpreting
  remainders in context of problem) in computation
  and problem solving with whole numbers,
  fractions, and decimals.
• GPS
• M7N1. Students will understand the meaning of
  positive and negative numbers including rational
  numbers and will compute with them.
• a. Find the absolute value of a number and
  understand it as the distance from the origin on
  a number line.
• b. Compare and order rational numbers including
  repeating decimals.
• c. Add, subtract, multiply and divide positive
  and negative rational numbers.
• d. Solve problems using rational numbers.
• Note the level of thinking required in each. Note
  the emphasis on conceptual understanding. Note
  how the organization helps you identify connected
  concepts. Note the differences in specificity.

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Example 2Relations Functions

• QCC Algebra I Topic Connections, Patterns, and
  Functions
• 5   Standard Connects patterns to the concept of
  function and uses patterns, relations, and
  functions to solve problems.
• 6   Topic Patterns and Functions Standard
  Distinguishes between relations and functions,
  and identifies the domain and range.
• Has these two objectives under this topic, along
  with two on solving equations and nine on linear
  equations in two variables. All are in a list of
  37.
• M8A3. Students will understand relations and
  linear functions.
• a. Recognize a relation as a correspondence
  between varying quantities.
• b. Recognize a function as a correspondence
  between inputs and outputs where the output for
  each input must be unique.
• c. Distinguish between relations that are
  functions and those that are not functions.
• d. Recognize functions in a variety of
  representations and a variety of contexts.
• e. Use tables to describe sequences recursively
  and with a formula in closed form.
• f. Understand and recognize arithmetic sequences
  as linear functions with whole number input
  values.
• Note the level of thinking required in each. Note
  how the organization helps you identify connected
  concepts. Note the differences in specificity.

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Example 3 Data Analysis
QCC Algebra I, Topic Probability 36
Identifies possible outcomes of simple
experiments and predicts or describes the
probability of a given event expressed as a
rational number from 0 through 1. 37 Conducts
and interprets a compound probability experiment.
GPS 8th Math M8D2. Students will determine the
number of outcomes related to a given event. a.
Use tree diagrams to find the number of
outcomes. b. Apply the addition and
multiplication principles of counting. M8D3.
Students will use the basic laws of
probability. a. Find the probability of simple
independent events. b. Find the probability of
compound independent events. Note the level of
thinking required in each. Note how the
organization helps you identify connected
concepts. Note the differences in specificity.
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Example 4 Conic Sections
QCC Algebra II, Topic Analytical
Geometry Standard Recognizes and sketches the
graphs of and the relationships among conic
sections.
GPS Math III MMIIIG2. Students will recognize,
analyze, and graph the equations of the conic
sections (parabolas, circles, ellipses, and
hyperbolas). a. Convert equations of conics by
completing the square. b. Graph conic sections,
identifying fundamental characteristics. c. Write
equations of conic sections given appropriate
information. Note the level of thinking required
in each. Note how the organization helps you
identify connected concepts. Note the differences
in specificity.
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Comparing GPS to the QCCs

• GPS often requires
• higher level in Blooms Taxonomy (knowledge,
  comprehension, application, analysis, synthesis,
  evaluation)
• or requires conceptual AND procedural knowledge
  (Hiebert).
• GPS are clearer or more specific about what is
  expected.
• Difference between laddered and spiral curriculum
  is evident.
• Important content (for example, in 6th grade
  nets, sketches of solid figures) is added.
• Data analysis and probability strand is
  strengthened.

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Process of Developing GPS

• Two years ago, teacher teams were enlisted to
  write GPS.
• Writing teams drew on strengths of Japanese
  curriculum and North Carolina standards.
• Teachers produced a draft, which was made public
  for feedback.
• K-8 GPS approved in May 2004.

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Process of Developing GPS

• Because the new integrated high school curriculum
  was so different from the QCC, a group was formed
  to review it.
• High School Mathematics Advisory Committee
  included teacher writing team members, curriculum
  supervisors, and higher education faculty
  (mathematics, mathematics education, and
  statistics).
• The group met five times during 2004-2005.
• The 9-12 GPS was approved by the BOE in May 2005.

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Tasks for Georgia Performance Standards
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From the Executive Summary

• A performance standard has four components
• a content standard,
• illustrative tasks,
• examples of student work, and
• a commentary for teachers.
• Together, these components will be the teachers
  guide as to what to teach, how thoroughly to
  treat a topic, and what some instances of student
  work that meet the content standard might look
  like.

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What are tasks?

• A mathematical problem or series of problems that
  provide an opportunity for students to
  demonstrate their conceptual knowledge.
• Tasks may take minutes or days.
• Tasks may be used for a variety of purposes
  including classwork or assessment.

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Purpose of Tasks?

• Fewer topics, together with sample tasks, student
  work, and commentary,
• provide clear expectations for student
  performance,
• guide instruction, and
• allow for a careful alignment of instruction and
  assessment.

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Whats in the Teacher Commentary?

• Documentation of which parts of the problem
  assess which standards
• Analysis of student work
• May also include
• Extensions
• Notes to the teacher
• Suggestions about technology or manipulative use.

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Process

• Committees are working on drafts of the sets of
  tasks for each grade level or course.
• Committees include teachers, mathematicians,
  mathematics teacher educators, curriculum
  specialists, and system office mathematics
  specialists.

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The challenge?

• To pose tasks that give students opportunities to
  demonstrate their deep understanding.
• To provide tasks for instruction or assessment.
• Tasks may begin with procedural knowledge, but
  push towards conceptual or higher levels of
  Blooms taxonomy.
• Tasks emphasize connections across mathematics
  topics.
• Tasks encourage use of process standards.

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An Example

• Here are two of the 6th GPS
• a. Apply factors and multiples.
• c. Determine the greatest common factor (GCF) and
  the least common multiple (LCM) for a set of
  numbers.
• Imagine the typical textbook question.
• Take a minute to imagine a question that will
  help you learn more about the depth of that
  students understanding. Share it with a
  colleague.

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Here are two questions from the related 6th Grade
Task

• Find the prime factorization of 24. The factors
  of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Find their
  prime factorizations and compare them to the
  prime factorization of 24. What do you notice?
• The number 5 and another number less than 40 have
  a least common multiple of 40. What could the
  other number be? Could there be other answers? If
  so, list as many as you can.

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Where are we now?

• 6th grade tasks are on the web listed at the end
  of the standards.
• Committees are working on tasks at other grade
  levels. During the next school year, the emphasis
  will be on getting sample student work and
  writing commentaries about them.
• At Rock Eagle, check for sessions on tasks for
  your grade level or courses.

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Sources of similar problems

• New York City Standards
• NAEP items
• TIMSS problems
• FCAT (Florida) problems
• More on Performance Assessment Tasks
• http//www.aea267.k12.ia.us/cia/
• framework/tasks/writing/index.html

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GPS MATHEMATICS Implementation Plan
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Textbooks

• For grades 6-8, our current textbooks cover most
  of the GPS, although some supplementing of the
  textbooks will be necessary.
• For grades 9-12, publishers are already
  expressing interest in preparing textbooks for
  Georgias integrated curriculum.

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