Northwest Georgia RESA Mathematics Academy

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Northwest Georgia RESA Mathematics Academy
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• Northwest Georgia RESA Mathematics Academy
• North Paulding High School
• Dallas, Georgia
• November 13, 2008
• Dexter Mills, Executive Director
• Karen Faircloth, Director of School
• Improvement Professional
• Learning

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Contact Information
Terry Haney, Math Coordinator Northwest Georgia
RESA 3167 Cedartown Hwy., SE Rome, Georgia
30161 706-295-6189 (EXT. 20) 706-295-6098
(FAX) 256-630-8362 (CELL) thaney_at_nwgaresa.com
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Purpose The purpose of the Northwest Georgia
RESA Mathematics Academy is to provide ongoing
professional learning experiences for district
teams in mathematics.  Each team should consist
of at least one representative from each of the
following curriculum bands  3-4, 5-6, 7-8 and
Math I.  Members of the teams may be teachers
and/or academic coaches, along with a
building-level and system-level administrator. 
Each of the meetings will begin with a brief
whole group session.  Each representative will
then attend a session based on his or her
appropriate curriculum band.  During this
extended session, instructors for all curriculum
bands will address one specific content strand
(algebra, geometry, numbers and operations, data
analysis) by facilitating work on performance
tasks and pedagogy.    Other topics may include
data-driven teaching and learning,
characteristics of the standards-based
classroom,  and ACTION planning for mathematics. 
Each system-level team will reassemble at the
end of the day to analyze the progression of
content across the grade bands and to plan
methods of redelivery within their system.
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Facilitators for each Curriculum Band Claire
Pierce, Math I Independent Consultant former
DOE Math Program Manager Terry Haney, Grades
7-8 Math Coordinator for Northwest Georgia
RESA Jason Pelham, Grades 5-6 Assistant
Principal at Lakeview Middle School in Catoosa
County RESA Math Consultant Danny Lowrance,
Grades 3-4 Math Specialist at W.L. Swain
Elementary School in Gordon County
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• Questions, concerns, and comments from our
  previous session
• Building the Data Analysis Ladder
• GAISE Report
• Instructional Framework The Workshop Model
• Tasks The Mean as Fair Share
• Mean and Variance Level B
• Random Rectangles

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Creating and Managing a Student-Centered
Classroom with the Workshop Model
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Opening

• Teacher-centered
• The teacher is giving notes,
• explaining a process, modeling
• a process, etc.
• Students are involved
• -taking notes,
• -asking questions, and/or
• -sharing information
• NOT the longest portion of class
• Time will vary with the difficulty of
• subject matter and amount of time
• spent on content previously (approximately
• 20 minutes or less based on 90-minute block).

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Work Period

• Student-centered
• There are varying combinations of
• working alone, working in pairs, and
• working in small groups.
• There is a mix of
• authentic, real-world applications,
• multiple representations, showing
• work, explaining processes, inquiry,
• skills practice.
• Connections to standards are obvious to everyone
  .
• Teachers involved
• Constantly monitoring for engagement physically
  present in the work area, and/or holding
  individual or group conferences.

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Closing

• Student-centered
• Students take responsibility for teaching or
  sharing what
• they have learned. Students are speaking
  intelligently
• about work and standards, using the language of
  the
• standards and content terminology.
• Includes such activities as sharing work, sharing
  ideas, discussing what theyve learned,
  presenting solutions to problems, talking about
  how their work meets the standard.
• Teachers involved
• Choose students to share and let them prepare
  during the
• work period monitor and push discussion toward
  the standard.

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Managing the Workshop
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Managing the Workshop

• Rituals and Routines
• Establish requirements for constructive
  individual attempts before pair or group work
  begins.
• Use a timer.

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Managing the Workshop

• Rituals and Routines
• Create a systematic procedure
• for students to receive assistance
• SELF (notes, book, anchor charts, word wall,
  manipulatives, etc.)
• PARTNER OR GROUP MEMBERS
• TEACHER

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Managing the Workshop

• Rituals and Routines
• Teacher serves as facilitator during the work
  period and the closing.
• Monitor student progress using a status of the
  class form.
• Allow students to explain concepts and
  procedures
• to you.
• Respond to their questions with more probing
  questions.

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Managing the Workshop

• Status of the Class

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Planning the Workshop
Title_______________________________
Standard(s)________________________
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Content Topic Probability Pedagogy Topic
Questioning Strategies and Techniques
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Essential Questions How do I effectively
integrate the Probability standards into the
mathematics curriculum? How do the Probability
standards build across the curriculum bands? How
do I effectively implement high- impact
questioning strategies in the mathematics
classroom
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Examining the Probability StandardsA Card Sort

• You will be given a set of cards consisting of
• Assessment items
• Grade levels
• Standards
• Vocabulary
• You are to match cards from each of the last 3
  categories to the assessment items. You are also
  given 6 blank cards. On each of these cards you
  are to add an item from any one of the last three
  categories to each of your card sets.

•  

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The Probability Standards

• 6 M6D2. Students will use experimental and
  simple theoretical probability and understand the
  nature of sampling. They will also make
  predictions from investigations.
• a. Predict the probability of a given event
  through trials/simulations (experimental
  probability), and represent the probability as a
  ratio.
• b. Determine, and use a ratio to represent, the
  theoretical probability of a given event.
• c. Discover that experimental probability
  approaches theoretical probability when the
  number of trials is large.
•  
•  
•  

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The Probability Standards

• 8 M8D1. Students will apply basic concepts of
  set theory.
• a. Demonstrate relationships among sets through
  use of Venn diagrams.
• b. Determine subsets, complements, intersection,
  and union of sets.
• c. Use set notation to denote elements of a set.
  
• 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.
•  
•  

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The Probability Standards

• Math I MM1D1. Students will determine the
  number of outcomes related to a given event.
• a. Apply the addition and multiplication
  principles of counting.
• b. Calculate and use simple permutations and
  combinations.
• MM1D2. Students will use the basic laws of
  probability.
• a. Find the probabilities of mutually exclusive
  events.
• b. Find the probabilities of dependent events.
• c. Calculate conditional probabilities.
• d. Use expected value to predict outcomes.
•  
•  

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According to Wagner, seven survival skills are
imperative to our students success in the new
world of work. From Educational Leadership
October, 2008 Rigor Redefined by Tony Wagner
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• Critical Thinking and Problem Solving
• Collaboration and Leadership
• Agility and Adaptability
• Initiative and Entrepreneurialism
• Effective Oral and Written Communication
• Accessing and Analyzing Information
• Curiosity and Imagination
• From Educational Leadership October, 2008
  Rigor Redefined by Tony Wagner

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What do all of these skills have in common? They
can all be directly correlated to good
questioning.
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The heart of critical thinking and problem
solving is the ability to ask the right
questions. From Educational Leadership October,
2008 Rigor Redefined by Tony Wagner
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Read What role does teacher questioning play in
learning mathematics? In your small groups,
discuss specific ideas or strategies that your
have tried or ones that you feel will be most
important for you to implement in your classroom.
Make a list of these strategies on chart paper.
Be prepared for whole group discussion. From ED
Thoughts (2002) What We Know About Mathematics
Teaching and Learning J.S. Sutton and A. Krueger
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If you want to build a shipdont herd people
together to collect wood and dont assign them
tasks and work, but rather teach them to long for
the endless immensity of the sea. Antoine de
Saint-Exupéry
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Questioning

• Encourage and support questioning and discussion
  from the first day of class.

• Take multiple answers from students and allow
  them decide which one is correct.

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Questioning

• Stress the logic of mathematics and how
  mathematical definitions are very similar to
  meanings they already know.

• Require that students show all of their work.

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Questioning

• Require justification of true/false statements.

• Explain how to

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Questioning

• Write your own problem and solve it.

• Explain the mistakes in the given solution.

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Questioning

• What is this problem asking?

• Is this answer reasonable? Why or why not?

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Questioning

• Give an example when this strategy would not work.

• How can you make sure your answer is correct?

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Questioning

• Explain 3 ideas that you have learned in todays
  lesson.

• Describe a type of problem that is still unclear
  to you.

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Questioning

• What would happen if

• Tell me anything and everything you know about

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Multiple Representations
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Good questions should

• Monitor for meaning
• Activate prior knowledge
• Use sensory and emotional images
• Require students to make predictions and
  inferences
• Help determine importance
• Require students to synthesize information
• Adapted from 7 Metacognitive Strategies from
  Mosaic of Thought by Ellin Oliver Keene and Susan
  Zimmerman

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A Few SamplesPositive and Negative Numbers

• Tell me anything that you already know about
  positive and negative numbers. (activating prior
  knowledge)
• Imagine a thermometer at 15 degrees. What will
  the thermometer look like if the temperature
  falls 20 degrees? (visualizing)
• Find examples of positive and negative numbers in
  your text. Think of a time when you have worked
  with negative numbers or have seen them. Name 2
  situations in real life when you have seen
  positive and negative numbers. (making
  connections)

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A Few SamplesPositive and Negative Numbers

• What do you think will happen when you add,
  subtract, multiply, or divide positive and
  negative numbers? (make predictions--inferring)
• From the examples you have seen so far, what
  types of patterns are emerging? (inferring)

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A Few SamplesPositive and Negative Numbers

• What are integers? How are integers used?
  Demonstrate how to use a number line to make
  integer calculations. Do you think the patterns
  and rules that you have discovered will work with
  all numbers or only with integers. Say why.
  (explainingmaking predictions)
• Why do you think it is important to know about
  integers? Create 3 real-life situations in which
  a knowledge of integers would be required. Then
  solve the problems and show all of your work.
  (synthesizing)

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Designing Content-Specific Questions and Prompts

• Using specific topics from your current unit of
  study or an upcoming unit and strategies that we
  have discussed, design 5-10 questions and/or
  prompts. You may want to think about designing
  questions from simple to complex. You may also
  want to consider different ways to ask the same
  question as a means of differentiation.

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Task time
lets collaborate!
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Whats the Probability of a Hit?
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Shooting Free throws
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The Probability of Math I

• Be sure they know.
• Permutations
• Repeated elements
• Circular
• Combinations
• Probabilities requiring applications of the
  addition and multiplication principles involving
  combinations and permutations
• Probabilities of mutually exclusive events
• Probabilities of dependent events
• Conditional probabilities
• Binomial probability
• Expected value

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Great Resources

• Navigating through Probability in Grades 9-12
• www.NCTM.org
• Unit 4 Sample homework
• Unit 4 Websites

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Questions, Comments, and Concerns

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Contact Information
Terry Haney, Math Coordinator Northwest Georgia
RESA 3167 Cedartown Hwy., SE Rome, Georgia
30161 706-295-6189 (EXT. 20) 706-295-6098
(FAX) 256-630-8362 (CELL) thaney_at_nwgaresa.com
Northwest Georgia RESA Mathematics Academy