Northwest Georgia RESA Summer Mathematics Institute

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Northwest Georgia RESA Summer Mathematics
Institute
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• Northwest Georgia RESA Mathematics Academy
• North Paulding High School
• Dallas, Georgia
• June 26, 2009
• Dexter Mills, Executive Director
• Karen Faircloth, Director of School
• Improvement Professional
• Learning

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Contact Information
Danny Lowrance, Math Specialist W.L. Swain
Elementary 2505 Rome Rd SW Plainville, GA
30733 706-629-0141 dlowrance_at_gcbe.org
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Facilitators for each Curriculum Band Claire
Pierce, Math I and II Independent Consultant
former DOE Math Program Manager Linda Segars,
Math I and II School Improvement Specialist for
Metro RESA Terry Haney, Grades 6-8 Math
Coordinator for Northwest Georgia RESA Danny
Lowrance, Grades 3-5 Math Specialist at W.L.
Swain Elementary School in Gordon County
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Purpose The purpose of the Northwest Georgia
RESA Summer Mathematics Institute 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  3-5, 6-8, and
Math I II.  Members of the teams may be
teachers and/or academic coaches, along with a
building-level and system-level
administrator.  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. 
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Perception vs. Reality
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Common Perceptions Openings, work periods, and
closings must meet exact time constraints.
While there are time suggestions for each
portion of the instructional framework, times
will vary depending on the type of lesson and
the content. Every concept must be completely
discovered by students. Discovery-based
lessons are highly encouraged as often as
possible however, time does not permit every
lesson to be completely based on discovery.
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Common Perceptions Skills lessons are never
appropriate. Skills are a crucial part of our
mathematics instruction. Skills lessons should
be embedded within tasks as often as possible.
When they are taught in isolation, skills should
be brought back into a context as soon as
possible. Direct instruction is never
appropriate. Some information will need to be
presented in the form of direct instruction,
with lecture and note taking. Think of this
time as a DIALOGUE as opposed to a
MONOLOGUE.
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Common Perceptions All work must be done in
pairs or in groups. The standards-based
classroom should incorporate a mix of group
work, partner work, and individual
accountability. Closings must always include
formal student presentations.
While student presentations are one of the most
effective methods of solidifying student
learning, not every lesson lends itself to this
type of closing. Sometimes a whole group
discussion with strategic questioning is just
as effective.
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Common Perceptions Every student must play a
major role in the closing every day. Our goal
should be to involve as many students as possible
each day (in meaningful ways). Using the status
of the class sheet allows teachers to make note
of students who either make formal presentations
or who contribute to the class discussions
through meaningful questions and comments. For
example, a closing may involve 1-4 students
giving formal presentations, with the remainder
of the class giving feedback and asking
questions.
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Common Perceptions Commentary should be
lengthy. Commentary can be of varying lengths,
depending on the purpose and the scope of the
work. The length also depends on the number of
standards being addressed. Commentary should
always be written for every student on a
particular task or assignment.
While our goal should be to have multiple pieces
of commentary for each student over the course
of the year to show growth, it is not
necessary to write commentary for each student
on every task!
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Common Perceptions All commentary should be
written by the teacher. The ultimate goal with
commentary is to give specific ways that students
have met or exceeded the standard, or next
steps to use in order to make the work better.
It should also be our goal to teach students how
to evaluate their own work. Consequently, we
should begin to train our students how to write
commentary for their work on the work of
others. Commentary is mainly used for student
work displays. It is important
that student work and commentary be displayed but
only if it is being used as a teaching tool.
Commentary may be public or private. Some
commentary may only be used by the teacher and
an individual student. Some of this commentary
may be verbal. Ultimately, it is a tool to
improve student achievement by giving students
a true understanding of how their work stacks
up with respect to the standards.
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Writing and Using Commentary

• Teacher Commentary should
• Use the language of the standards.
• Provide descriptive and specific comments related
  to the learning goals.
• Include honest and constructive guidance about
  steps to take or strategies to try next.
• Celebrate success and/or progress toward the
  learning goals.

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What Makes a Shape?

• Cut out the shapes on your paper.
• Sort the shapes into at least 3 groups.
• Glue the shapes onto a paper in groups.
• Label each group and identify the attribute(s)
  used for sorting.
• Write a few sentences that explain how you sorted
  the shapes.
• You may find it helpful to use the words all,
  some, or none to describe your groups.

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GEORGIA PERFORMANCE STANDARDS GEOMETRY Students
will further develop their understanding of
characteristics of previously studied geometric
figures. M3G1. Students will further develop
their understanding of geometric figures by
drawing them. They will also state and explain
their properties. a. Draw and classify
previously learned fundamental geometric figures
and scalene, isosceles, and equilateral
triangles. b. Identify and compare the
properties of fundamental geometric figures.
c. Examine and compare angles of fundamental
geometric figures. d. Identify the center,
diameter, and radius of a circle.
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Content Topic Numbers and Operations (Decimal
Fractions) Pedagogy Topic Assessment
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Essential Questions

• What should we assess?
• Why should we assess?
• How do we assess?
• How do I determine appropriate and acceptable
  evidence of learning?

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Discuss

• What are the differences between assessment and
  evaluation?
• Discuss with your group and prepare to share
  examples of each.

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Discuss

• When we assess, we are gathering information
  about student learning that informs our teaching
  and helps students learn more.
• When we evaluate, we decide whether or not
  students have learned what they needed to learn
  and how well they have learned it.
• Anne Davies
• Making Classroom Assessment Work

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• Inside the Black Box Raising Standards Through
  Classroom Assessment
• Paul Black and Dylan Wiliam

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• Table Talk
• In your small groups, discuss what you consider
  to be the 5 most compelling ideas from Inside the
  Black Box. Try to give specific focus to the
  topics over which the classroom teacher has
  significant control.
• List your ideas on the chart paper provided and
  be prepared to share.

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Who knows best??

• The student knows more than the teacher about
  what and how he has learnedeven if he knows less
  about what was taught.
• Peter Elbow
• Professor Emeritus at
• University of Massachusetts, Amherst

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What kinds of assessment should we be using?

• Pre-assessmentsThese assessments are used to
  indicate students readiness for content and
  skill development, and to guide instructional
  development.
• Rick Wormeli
• Fair Isnt Always Equal

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What kinds of assessment should we be using?

• Formative Assessments--en route checkpoints,
  done frequently. They provide ongoing and
  helpful feedback, informing instruction and
  reflecting subsets of the essential and enduring
  knowledge.
• Rick Wormeli
• Fair Isnt Always Equal

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Formative assessment is a planned process in
which assessment-elicited evidence of students
status is used by teachers to adjust their
ongoing instructional procedures or by students
to adjust their current learning
tactics. Transformative Assessment, W. James
Popham, ASCD, 2008, p.6
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FORMATIVE ASSESSMENT WHAT IT IS ???? A planned
process ???? Ongoing ???? Assessment-elicited
evidence ???? Teachers instructional
adjustments ???? Students learning tactics
adjustments Formative Assessment
Presentation Vermont Department of Education
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FORMATIVE ASSESSMENT WHAT IT ISNT ????
Unplanned ???? A one-time test ???? An interim
test (benchmark, periodic, etc.) ????
Instructional adjustments based on a
feeling or student cues ???? A quick magic
bullet Formative Assessment Presentation
Vermont Department of Education
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FORMATIVE ASSESSMENT WHAT IT DOES FOR
STUDENTS ???? Fosters motivation ???? Promotes
understanding of goals and criteria ????
Helps learners know how to improve ???? Develops
the capacity for self-
assessment ???? Recognizes all educational
achievement ???? Focuses on how students
learn Formative Assessment Presentation
Vermont Department of Education
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What kinds of assessment should we be using?

• Summative AssessmentsThese assessments are given
  to students at the end of the learning. They
  match objectives and experiences, and their
  formats are negotiable if the product is not the
  literal standard and would prevent students from
  revealing what they know about a topic. They
  reflect most, if not all, of the essential and
  enduring learning.
• Rick Wormeli
• Fair Isnt Always Equal

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Formative Assessment Presentation Vermont
Department of Education
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• a sculptor chips away at a block of marble for
  days and daysand a horse or a man emerges. But
  an ordinary person could chip away at the same
  block of marble for months and nothing at all
  might emerge. The difference is in the quality
  of attention. Its the intention
• The difference between assessment that is
  busywork and assessment that reflects the essence
  of our teaching is what we and our students make
  of what we collect.
• Lucy Calkins

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• Using a Problem-based (Task-based) Approach
• In a problem-based approach (or task-based
  approach), teachers often ask, How do I assess?
  The question stems from the realization and
  acceptance of the fact that the traditional
  skill-oriented testing fails to adequately tell
  what students know.
• the line between assessment and instruction
  should be blurred. Teaching with problems allows
  us to blur that line.
• Teaching Student-Centered Mathematics
• John A. Van de Walle

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• Using a Problem-based (Task-based) Approach
• Only using skill-based assessments tells students
  that getting the answer is the ONLY important
  aspect of mathematics. Curiosity and
  communication are soon stifled, and students only
  want to be shown how to get an answer.
• Teaching Student-Centered Mathematics
• John A. Van de Walle

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• Think
• How do we use problem-based (performance-based)
  tasks to assess student progress?
• What are the pros and cons of such assessments?
• Pair--Share
• Find a partner and share your ideas.
• Square
• Meet with another pair and share your ideas.
• Be prepared to share with the whole group.

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• The percentage of correct answers is a very
  incomplete picture of what a student knows.
  However, the potential data about your students
  can and should come daily as you listen in as
  many ways as possible to the methods that your
  students use to grapple with the tasks you give
  them.
• Teaching Student-Centered Mathematics
• John A. Van de Walle

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• Table Talk
• Collecting Assessment Data
• Finding ways to document assessment information
  is crucial for grades, parent conferences, etc.
• How might we do this effectively?
• Teaching Student-Centered Mathematics
• John A. Van de Walle

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• Collecting Assessment Data
• Make a habit or recording quick observational
  data. (status of the class form anecdotal
  comments on address labels)
• Focus on big ideas rather than small skills.
• You need not assess every child on every task.
  By focusing on big ideas, you will not feel
  required to check on every student on any given
  day. (conferencing schedule based on
  observation)
• Save or make copies of student work that
  indicates well the thinking of a child. (works
  in progress foldersstudent portfolios)
• Use traditional tests for skills that you feel
  are essential.
• Teaching Student-Centered Mathematics
• John A. Van de Walle

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Collecting Assessment Data

• Status of the Class

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• Connecting Assessment
• to the
• GAPSS Classroom Observation Instrument

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A closer look at decimals vertically

• K Use counting strategies to find out how many
  items are in two sets when they are combined,
  seperated, or compared. Use objects, pictures,
  numbers, or words to create, solve and explain
  story problems.
• 1 Exchange equivalent quantities of coins by
  making fair trades involving combinations of
  pennies, nickels, dimes, and quarters and count
  out a combination needed to purchase items less
  than a dollar.
• 2 Use money as a medium of exchange. Count back
  change and use a decimal notation and the dollar
  and cent symbols to represent a collection of
  coins and currency.

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A closer look at decimals vertically

• 3 Students will understand the meaning of
  decimal fractions in simple cases and apply them
  in problem-solving situations. Understand that a
  one place decimal fraction represents tenths,
  i.e., 0.3 3/10. Know and use decimal fractions
  to represent the size of parts created by equal
  divisions of a whole. Model addition and
  subtraction of decimal fractions. Solve problems
  involving decimal fractions.
• 4 Students will further develop their
  understanding of the meaning of decimal fractions
  and use them in computations. Understand the
  relative size of numbers and order two digit
  decimal fractions. Add and subtract both one and
  two digit decimal fractions. Model multiplication
  and division of decimal fractions by whole
  numbers. Multiply and divide both one and two
  digit decimal numbers by whole numbers.
•  

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A closer look at decimals vertically

• 5 Students will further develop their
  understanding of decimal fractions as part of the
  base-ten numbers system. They will further
  develop their understanding of the meaning of
  multiplication and division with decimal
  fractions and use them. Model and explain the
  process of multiplication and division, including
  situations which the multiplier and divisor are
  both whole numbers and decimal fractions.
• 6 Students will add and subtract fractions and
  mixed numbers with unlike denominators. They will
  multiply and divide fractions and mixed numbers.
  They will use fractions, decimals, and percents
  interchangeably. They will solve problems
  involving fractions, decimals and percents.
•  
•  
•  

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Time on tasks
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Decimal Fraction Unscramble

• Her menacing father the Math Magician is
  always incorporating math into her everyday life.
  He has changed the password to access the laptop
  with six decimal fractions that must be placed in
  order from least to greatest. Can you help
  Lindsey unscramble the decimal fractions so she
  can log into the computer?

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Relay For Life Money Bag Mystery

• Our school is having a competition
  between grade levels to see who can raise the
  most money for Relay for Life. A 4th grader,
  Owen Franzen, is in charge of collecting and
  summing the coins for the competition. Students
  have been bringing coins in all week long. Owen
  got in such a hurry this morning he was not able
  to record how much money was raised in each
  grade. He labeled each bag by grade. He needs
  your help.

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Questions, Comments, and Concerns

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Contact Information
Danny Lowrance, Math Specialist W.L. Swain
Elementary 2505 Rome Rd SW Plainville, GA
30733 706-629-0141 dlowrance_at_gcbe.org
Northwest Georgia RESA Summer Mathematics
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