Mathematics

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Mathematics Item Specifications The School
District of Palm Beach County High School
Leadership Academy Presented by Michelle R.
White Mathematics Manager
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Presentation Requests

• Silence cell phones
• Participate and share
• Listen with an open mind
• Ask questions
• Work toward solutions
• Use time effectively

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Part I Item Specifications

• Test Structure and Item Format
• Blooms Taxonomy vs. Norman Webbs Depth of
  Knowledge
• Item Specifications
• Teaching Requirements
• FCAT Item Specifications Learning Objectives
• Identify the FCAT Item Assessment Formats
• List the Cognitive Complexity Levels addressed on
  the FCAT
• List the Strands assessed on the FCAT
• Identify the primary Target Audience for the FCAT
  Item Specifications
• Identify the percentage breakdown for the FCAT
  assessed strands in each grade level
• Recognize the need to utilize the FCAT Item
  Specifications in the Lesson Planning Process
• FCAT Test Taking Strategies
• Multiple Choice
• Gridded Responses
• Short and Extended Response Questions

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Part II What Leaders need to know about the
Mathematics Classroom

• The Mathematics Classroom
• Environment
• Materials
• The Mathematics Lesson
• Higher Order Questioning and Thinking
• Instruction Effectively Engages Students
• Small Group, Differentiated Instruction is
  Utilized to Address Students Instructional Needs
• Reading and Writing Activities are Evident
• Data is used to Redirect Instructional Focus and
  Students Instructional Needs
• School and District Leadership and Coaching is
  Evident

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Part III What Leaders need to know about the
Coaches Role

• Expectations of the Coach
• Professional Development
• Coaching Calendar
• Coaches Log

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Test Structure and Item Format
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Blooms Taxonomy vs. Norman Webbs Depth of
Knowledge 2004 Changes

• Blooms Taxonomy
• Students Ability
• Difficult to Use
• Requires Inference of Students
• Skill
• Knowledge
• Background

• Norman Webbs
• Question
• Thinking based on the Item QUESTION not on the
  ability of the student
• Focuses on what the item will require the student
  to do
• Recall
• Understand
• Analyze

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Bloom vs. Webb

Kris Lyon October 12, 2005
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Norman L. Webbs Depths of Knowledge (DOK)

• DOK Level 1 Recall and Reproduction
• Includes the recall of information such as a
  fact, definition, term, or a simple procedure, as
  well as performing a simple algorithm or applying
  a formula.
• DOK Level 2 Skills and Concepts/Basic Reasoning
• Includes the engagement of some mental
  processing beyond a habitual response. A Level 2
  assessment item requires students to make some
  decisions as to how to approach the problem or
  activity, whereas Level 1 requires students to
  demonstrate a rote response, perform a well-known
  algorithm, follow a set procedure (like a
  recipe), or perform a clearly defined series of
  steps.

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DEPTH OF KNOWLEDGE LEVEL 1 Low
Recall and Reproduction Depth of Knowledge
(DOK) Level 1 Some examples that represent but
do not constitute all of Level 1 performance are
Identify a diagonal in a geometric figure.
Multiply two numbers. Find the area of a
rectangle. Convert scientific notation to
decimal form. Measure an angle.
Kentucky Department of Education
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DEPTH OF KNOWLEDGE LEVEL 2 Moderate
Skills and Concepts/Basic Reasoning Depth of
Knowledge (DOK) Level 2 Some examples that
represent but do not constitute all of Level 2
performance are Classify quadrilaterals.
Compare two sets of data using the mean, median,
and mode of each set. Determine a strategy to
estimate the number of jellybeans in a jar.
Extend a geometric pattern. Organize a set of
data and construct an appropriate display.
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Norman L. Webbs Depths of Knowledge (DOK)

• DOK Level 3 Strategic Thinking/Complex Reasoning
  
• Requires reasoning, planning, using evidence,
  and a higher level of thinking than the previous
  two levels. The cognitive demands at Level 3 are
  complex and abstract and requires more demanding
  reasoning.
• DOK Level 4 Extended Thinking/Reasoning (Not
  Tested)
• Requires complex reasoning, planning,
  developing, and thinking most likely over an
  extended period of time.

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DEPTH OF KNOWLEDGE LEVEL 3 High
Strategic Thinking/Complex Reasoning Depth of
Knowledge (DOK) Level 3 Some examples that
represent but do not constitute all of Level 3
performance are Write a mathematical rule
for a non-routine pattern. Explain how
changes in the dimensions affect the area and
perimeter/circumference of geometric figures.
Determine the equations and solve and interpret a
system of equations for a given problem.
Provide a mathematical justification when a
situation has more than one possible outcome.
Interpret information from a series of data
displays.
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DEPTH OF KNOWLEDGE LEVEL 4 Extended Thinking
Extended Thinking/Reasoning Depth of Knowledge
(DOK) Level 4 Some examples that represent but
do not constitute all of Level 4 performance are
Collect data over time taking into
consideration a number of variables and analyze
the results. Model a social studies situation
with many alternatives and select one approach to
solve with a mathematical model. Develop a
rule for a complex pattern and find a phenomenon
that exhibits that behavior.
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FCAT Cognitive Levels of Complexity

• Low Solve a one step problem
• Recall and recognize
• Moderate Requires multiple steps
• Flexible thinking, informal reasoning or problem
  solving
• High Requires analysis and abstract reasoning
• Abstract reasoning, planning, analysis, judgment
  and creative thought.

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Percentage of Points by Cognitive Complexity
Level for FCAT Mathematics
These tests include performance tasks, typically
moderate to high complexity items.
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Expectations of Low Complexity Items

• Low Complexity Items
• Identify, recognize, retrieve, calculate
• Types of Questions
• MC and GR

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Expectations of Moderate Complexity Items

• Moderate Complexity Items
• Apply, infer, predict, compare contrast,
  formula
• Types of Questions
• MC, GR, SR, ER

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Expectations of High Complexity Items

• High Complexity Items
• Construct a model, draw conclusions, design,
  explain, justify, interpret
• Types of Questions
• MC, GR,SR and ER

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Not Tested on FCAT..Should be taught in class
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Not Tested on FCAT..Should be taught in class
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Depth Of Knowledge Classification Activity

• Using the High School Sample Assessments and the
  worksheet provided work in groups to classify
  the problems as DOK-1, DOK-2 or DOK-3. Please be
  prepared to discuss your classifications.
• Allotted Time 20min For Classification
• 5min Discussions

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Item Specifications

• Mathematics

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Fldoe.org
FCAT
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Educators
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FCAT Item Specifications
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FCAT Mathematics Assessed Content

• Strands (5 total)
• A Number Sense
• B Measurement
• C Geometry Spatial Sense
• D Algebraic Thinking
• E Data Analysis Probability

• Annually Assessed Benchmarks
• Grades 3 - 5
• 24-25 Benchmarks
• 77-89 GLES/Content Focus
• Grades 6 - 8
• 24-25 Benchmarks
• 78 -93 GLEs/Content Focus
• Grades 9-10
• 23 Benchmarks

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Item Specification Sections

• Strand Refers to the broad content areas in the
  Sunshine State Standards (8 total for Science) (5
  total for Mathematics)
• Standards Are general statements of expected
  student achievement within each strand. They are
  the same for all grade levels.
• Benchmark Are specific statements of expected
  student achievement.
• They are different for the different grade levels
  assessed.
• In some cases two or more related benchmarks are
  grouped and assessed as one benchmark.
• Item Type(s) Assess the benchmark or group of
  benchmarks.
• MC, GR, SR, ER

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Item Specification Sections (Continuation)

• Benchmark Clarification Explains how the
  student will demonstrate the achievement of the
  benchmark and what the student will do when
  responding to the question types.
• Content Limits Define the range of content
  knowledge and degree of difficulty that should
  and should not be assessed in the questions for
  the benchmark.
• Stimulus Attributes Types of stimulus materials
  that should be used in the items, including
  articles, graphic materials, and item context or
  content.

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Item Specification Sections (Continuation)

• Response Attributes Are included in those
  benchmarks where specific directions are
  necessary regarding the types of allowable
  responses
• Sample Items Are provided for each type of
  question assessed by a particular benchmark.

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Mathematics Benchmark Numeration System
MA. B. 2.3.2
Benchmark The student solves problems
involving units of measure and converts answers
to a larger or smaller unit within either the
metric or customary system.
Subject Area Mathematics
Strand Measurement
Level Grades 6-8
Standard The student compares, contrasts, and
converts within systems of measurement (both
standard/nonstandard and metric/customary),
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Strand
Standard
Benchmark
Item Type
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Mathematics Performance Task Benchmarks by Grade
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Bodies Of Knowledge 9-12
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Item Specifications Activity

• Work in groups to review current FCAT content
  limits and vertically align the Benchmark
  Clarification Content Limits by determining
  what new topics are assessed at each grade
  level. Please be prepared to share-out.

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FCAT
Test Taking Strategies
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Multiple Choice Questions

• Read the question first
• Underline key words within the question
• Read the answer choices

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MA.B.1.4.2
12) A truck left Charlotte, North Carolina, at
500 A.M. on day 1 to deliver cargo in the
Florida cities of Jacksonville, Miami, and Key
West. The driver stopped for breaks a total of 12
hours. His deliveries took an additional 4 hours.
He completed his deliveries in Key West at 300
P.M. on day 2. If the driver averaged 55 miles
per hour while driving, how many miles did the
truck travel during the trip?
uses concrete and graphic models to derive
formulas for finding rate, distance, time, angle
measures, and arc lengths. (Also assesses
B.1.2.2) MC, GR
10th Grade
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Short and Extended Responses

• Read the question first
• Underline key words within the question
• Read the background information given and
  underline the parts that support the question
• Interpret the diagrams

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11) When measured along the inside edge of lane
1, the distance around the jogging track below is
one-quarter mile. The inside edge of the track is
a 330.3-foot by 210-foot rectangle with
semicircles on each end. The distance between the
inside edge and the outside edge of the track is
a constant 40 feet (ft). The track has 10 running
lanes of equal width, as shown in the lane detail
diagram below.
MA.B.1.4.1
uses concrete and graphic models to derive
formulas for finding perimeter, area, surface
area, circumference, and volume of two- and
three-dimensional shapes, including rectangular
solids, cylinders, cones, and pyramids. (Also
assesses B.1.2.2 and B.1.4.2) Grade 9 MC,
GR Grade 10 MC, GR, SR
10th Grade
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MA.B.1.4.1
Part A Write an expression that can be used to
find the distance around the track when measured
along the inside edge of lane 10.
uses concrete and graphic models to derive
formulas for finding perimeter, area, surface
area, circumference, and volume of two- and
three-dimensional shapes, including rectangular
solids, cylinders, cones, and pyramids. (Also
assesses B.1.2.2 and B.1.4.2) Grade 9 MC,
GR Grade 10 MC, GR, SR
Part B What is the distance, in feet, around the
track when measured along the inside edge of lane
10? Show your work or provide an explanation to
justify your answer.
10th Grade
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MA.B.1.4.1
uses concrete and graphic models to derive
formulas for finding perimeter, area, surface
area, circumference, and volume of two- and
three-dimensional shapes, including rectangular
solids, cylinders, cones, and pyramids. (Also
assesses B.1.2.2 and B.1.4.2) Grade 9 MC,
GR Grade 10 MC, GR, SR
10th Grade
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MA.C.2.4.1
21) A surveyor wants to determine the distance,
x, across a lake, but she is not able to make the
measurement directly. She will use ADE and ACB,
shown with measurements in yards (yd) below, to
help determine the distance across the lake.
understands geometric concepts such as
perpendicularity, parallelism, tangency, congruenc
y, similarity, reflections, symmetry, and
transformations including flips (reflections),
slides (translations), turns (rotations),enlargeme
nts , rotations, and fractals. (Also assesses
B.1.4.3, C.1.4.1, andC.3.4.1) Grade 9 MC,
GR Grade 10 MC, GR, ER
10th Grade
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Part A Explain in geometric terms why ADE is
similar to ACB. Part B Write a proportion that
can be used to find the distance x. Part C
Solve the proportion to determine the distance,
in yards, across the lake. Show work or provide
an explanation to support your answer.
MA.C.2.4.1
understands geometric concepts such as
perpendicularity, parallelism, tangency, congruenc
y, similarity, reflections, symmetry, and
transformations including flips (reflections),
slides (translations), turns (rotations),enlargeme
nts , rotations, and fractals. (Also assesses
B.1.4.3, C.1.4.1, andC.3.4.1) Grade 9 MC,
GR Grade 10 MC, GR, ER
10th Grade
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MA.C.2.4.1
understands geometric concepts such as
perpendicularity, parallelism, tangency, congruenc
y, similarity, reflections, symmetry, and
transformations including flips (reflections),
slides (translations), turns (rotations),enlargeme
nts , rotations, and fractals. (Also assesses
B.1.4.3, C.1.4.1, andC.3.4.1) Grade 9 MC,
GR Grade 10 MC, GR, ER
10th Grade
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Part II What Leaders need to know about the
Mathematics Classroom

• The Mathematics Classroom
• Environment
• Materials
• The Mathematics Lesson
• Higher Order Questioning and Thinking
• Instruction Effectively Engages Students
• Small Group, Differentiated Instruction is
  Utilized to Address Students Instructional Needs
• Reading and Writing Activities are Evident
• Data is used to Redirect Instructional Focus and
  Students Instructional Needs
• School and District Leadership and Coaching is
  Evident

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Part II The Mathematics Classroom

• Classroom Environment is Conducive to Teaching
  and Learning
• Instructional goals are clearly posted, defined,
  and understood by the students.
• The classroom is inviting to students and
  promotes learning through the display of
  instructionally based resources (i.e. item
  specifications, student work, word walls, sight
  words, classroom libraries etc.) and is clear of
  clutter.
• Students are on-task, classroom activities are
  orderly, transitions between activities are
  smooth, expectations for behavior are clear, and
  instruction is bell-to-bell.
• The classroom environment is task oriented while
  the social and emotional needs of students are
  met through mutual respect and rapport.

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The Mathematics Classroom (Continuation)

• Materials Support a High Level of Teaching and
• Learning
• Adequate materials that support student learning
  are readily available and easily accessible by
  all students (i.e. calculators, rulers,
  textbooks, computers, lab materials, etc.).
• Culturally and developmentally appropriate
  materials are utilized to support student
  learning.
• Materials are available in a variety of formats,
  are research-based, and are aligned with the
  Sunshine State Standards.

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Part II The Mathematics Lesson

• Higher Order Questioning and Thinking is Evident
• Students fully participate in the learning
  process they are encouraged to ask and answer
  questions, attempt new approaches, make mistakes,
  and ask for assistance.
• Questioning strategies are designed to promote
  critical, independent, and creative thinking.
• Questioning techniques require students to
  compare, classify, analyze different
  perspectives, induce, investigate, problem solve,
  inquire, research, and to make decisions.
• The teacher models higher order thinking skills
  when presenting information and answering
  questions.
• Scaffolding, pacing, prompting, and probing
  techniques are used when asking questions.
• Students questions are answered and wait time
  is used.
• Teachers give students plenty of opportunities to
  contribute and elaborate their own ideas.

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The Mathematics Lesson (Continuation)

• Instruction Effectively Engages Students
• Students are engaged in rigorous work and are on
  task.
• Instructional delivery employs a variety of
  learning strategies that engages students in
  active participation, addresses multiple learning
  styles and cultural experiences, and stimulates
  students intellectual interest.
• Lessons are well planned, organized, and
  appropriately paced and allow for questioning and
  follow-up with adjustments to instruction as
  appropriate. Content mastery is evident.
• The re-teaching of previously taught material is
  seamlessly integrated and students are provided
  opportunities to apply prior knowledge to new
  content/concepts and to real word context.
• Activities are aligned with instructional
  objectives and the Sunshine State Standards are
  explicitly taught.
• Students interact with other students and
  teachers concerning their work and the standards.

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The Mathematics Lesson (Continuation)

• Reading and Writing Activities are Evident Across
  the Curriculum
• Multiple techniques and strategies are utilized
  to teach reading and writing across the
  curriculum (i.e. writing prompts and authentic
  writing practice, infusing reading benchmarks
  across the curriculum, etc.).
• Opportunities that involve reading and writing
  strategies are present in other curriculum areas.
  
• Teachers of other core-content areas are
  knowledgeable about appropriate reading and
  writing techniques and instructional strategies.

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The Mathematics Lesson (Continuation)

• Data Analysis is Used to Redirect Instructional
  Focus and Students Instructional Needs
• A variety of assessments are used to evaluate
  student achievement on the Sunshine State
  Standards.
• Student data are used in instructional calendars
  and lesson plans.
• Frequent progress checks are conducted to monitor
  student levels of mastery and to make adjustments
  during instruction.
• Teachers use formative assessments to determine
  whole class and small group instruction.

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The Mathematics Lesson (Continuation)

• School and District Leadership and Coaching is
  Evident
• School and district leadership monitors
  instruction and provides coaching and modeling
  designed to improve instruction.
• Members of the school and district leadership
  teams are visible in the classroom and serve as
  instructional leaders by offering and
  coordinating professional development to address
  instructional needs/concerns through data
  analysis and instructional walkthroughs.
• Coaching responsibilities are clearly delineated
  from other administrative activities.

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Part III What Leaders need to know about the
Coaches Role

• Expectations of the Coach
• Professional Development
• Coaching Calendar
• Coaches Log

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Coaching Expectations

• Works with teachers to plan, implement, and to
  reflect on mathematics instruction using the
  Florida Continuous Improvement Model (FCIM)
• Models best practices in mathematics instruction
  with teachers as active participants
• Plans and implements mathematical professional
  development sessions
• Works with the Managers/Instructional Specialist
  to promote the districts mathematics initiatives
  found in the K-12 Comprehensive Mathematics

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Coaching Expectations

• Attends weekly, full-day training sessions
  (Fridays) and other district-mandated trainings
  to aid in increasing knowledge in best practice
  strategies for mathematics
• Analyzes data and assists the administrative team
  in developing corrective action plans
• Facilitates the review, evaluation, and
  integration of mathematics resources
• Assists teachers in interpreting diagnostic tests

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Coaching Expectations

• Keeps an electronic log of their work and
  develops a weekly coaching calendar
• Provides daily coaching and mentoring support to
  teachers
• Meets regularly with leadership team
• Collaborates with Reading Coaches, Science
  Coaches and LTFs
• Keeps a Coach Binder documenting all support
  services

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Coaches are Not Expected To

• Be assigned as a regular classroom teacher
• Perform administrative functions that would
  confuse his/her role for teachers
• Spend a large portion of time administering or
  coordinating assessments
• Model in a class where the classroom teacher is
  not present

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A WEEK AT-A-GLANCE

• Monday Pre-Conference/Coach observes the
  teacher
• Tuesday Coach models the entire instructional
  block using required components
• Wednesday Coach and teacher co-teach
• Thursday Coach observes the teacher
  again/Debriefing
• Friday Coach attends District Coaches Training

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Coaches Tool Weekly Calendar
REFLECTION What did the teacher learn that
will make a difference in his/her teaching? What
did I learn? Did the teacher accomplish his/her
goal? Did I accomplish my goal?
Attach Lessons Plan and Support Documents
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Coaches Professional Development Guidelines

• Get permission from your principal.
• Reserve a room/area.
• Develop an agenda with the location, date(s) and
  time of the in-service. Please be sure to file a
  copy of the agenda in your support service
  binder.
• Conduct the in-service and have participants
  sign-in, upon conclusion have participants
  complete the in-service evaluation form. Give a
  copy of the sign-in sheet and PD evaluation form
  to your principal (if requested) and file a copy
  in your support service binder.

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Coaches Logs

• Each coach is required to complete an electronic
  bi-weekly coaching log that includes the
  following components
• Professional Development
• Planning
• Coaching Model
• Student Assessments and Data Analysis
• Pre/Post Conferences
• Meetings
• Knowledge Building
• Managing and evaluating materials
• Other
• List successes that have occurred in the last
  reporting period
• Once your principal has signed your log,
  make two copies one for your principal and one
  to be filed in your Coaches Binder.

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Coaches RecommendedTime Allocation Percent
DistributionWhat portion of the coaches time
will be spent in each of these roles?
Approximate Coaching Time Percentages
REFLECTION What percent of your time is spent
within each of the categories on the Coaching
Continuum?
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Thank You!
michelle.white_at_palmbeach.k12.fl.us