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Northwest Georgia RESA Mathematics Academy

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Math Specialist at W.L. Swain Elementary School in Gordon County ... Lucy Calkins. Northwest Georgia RESA Mathematics Academy. Questions, Comments, and Concerns ... – PowerPoint PPT presentation

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Title: Northwest Georgia RESA Mathematics Academy


1
Northwest Georgia RESA Mathematics Academy
2
  • Northwest Georgia RESA Mathematics Academy
  • North Paulding High School
  • Dallas, Georgia
  • April 2, 2009
  • Dexter Mills, Executive Director
  • Karen Faircloth, Director of School
  • Improvement Professional
  • Learning

3
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) thaney_at_nwgaresa.com
Northwest Georgia RESA Mathematics Academy
4
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.
Northwest Georgia RESA Mathematics Academy
5
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
Northwest Georgia RESA Mathematics Academy
6
Content Topic Geometry Pedagogy Topic
Assessment
Northwest Georgia RESA Mathematics Academy
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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?

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

Northwest Georgia RESA Mathematics Academy
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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

Northwest Georgia RESA Mathematics Academy
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  • Inside the Black Box Raising Standards Through
    Classroom Assessment
  • Paul Black and Dylan Wiliam

Northwest Georgia RESA Mathematics Academy
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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.

Northwest Georgia RESA Mathematics Academy
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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

Northwest Georgia RESA Mathematics Academy
13
Building the Geometry Curriculum Ladder
  •  
  •  

We will build the Geometry Curriculum Ladder to
show the scope of topics addressed in grades
K-10. Your handout contains a list of
statements taken directly from the Geometry
strand of the Georgia Performance Standards at
each grade level. The statements are listed in
random order. Cut the statements apart and
reorder them as they would be addressed in the
K-12 curriculum. You will have about 15 minutes
to complete this process in your small
groups. Be prepared to share your thoughts on
the process.
Northwest Georgia RESA Mathematics Academy
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Building the Geometry Curriculum Ladder
  • K Students will correctly name simple 2-D and
    3-D figures and recognize them in their
    environment, including triangles, rectangles,
    squares, circles, spheres, and cubes. They will
    understand basic spatial relationships and will
    indentify, create, extend, and transfer patterns
    from one representation to another.
  •  
  • 1 Students will study and create various 2-D and
    3-D figures and identify basic figures within
    them. They will compare, contrast, and classify
    geometric shapes by their attributes. Students
    will also arrange and describe objects in space
    by proximity, position, and direction.
  • 2 Students will describe and classify plane
    figures according to the number of edges and
    vertices and the sizes of angles. They will also
    describe and classify solid geometric figures
    according to edges, vertices, faces, and
  • angles. Students will also describe changes as
    2-D and 3-D figures
  • are cut and rearranged.
  •  
  •  

Northwest Georgia RESA Mathematics Academy
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Building the Geometry Curriculum Ladder
  • 3 Students will further develop their
    understanding of geometric shapes by drawing them
    and stating and explaining their properties.
    This will include classifying previously learned
    figures and examining and comparing angles of
    fundamental geometric figures.
  • 4 Students will define and identify the
    characteristics of geometric figures through
    examination and construction, including angles,
    triangles, parallel and perpendicular lines in
    geometric figures, and classifying
    quadrilaterals. Students will understand
    fundamental solid figures, including the cube,
    prism, and cylinder. Students will also use the
    first quadrant of the coordinate system.
  •  
  • 5 Students will understand congruence of
    geometric figures and the correspondence of their
    vertices, sides, and angles. They will also
    understand that the relationship of the
    circumference of a circle to its diameter is pi.
  •  

Northwest Georgia RESA Mathematics Academy
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Building the Geometry Curriculum Ladder
  • 6 Students will further develop their
    understanding of plane figures, including lines
    of symmetry, rotational symmetry, use of ratio,
    proportion, and scale factor, and solving
    problems with scale drawings. They will also
    further develop an understanding of solid figures
    including comparing and contrasting right prisms,
    pyramids, cones, and cylinders. They will
    interpret and sketch different views of solids
    and construct their nets.
  • 7 Students will construct plane figures that
    meet given conditions using compass,
    straightedge, and appropriate technology.
    Students will demonstrate understanding of
    transformations, including translations,
    dilations, and rotations. They will also
    determine coordinates of various transformations.
    Students will also apply properties of
    similarity to geometric figures and will further
    develop their understanding of 3-D figures. This
    includes sketching, modeling, and describing
    cross sections of cones, cylinders, pyramids, and
    prisms.
  •  
  •  

Northwest Georgia RESA Mathematics Academy
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Building the Geometry Curriculum Ladder
  • 8 Students will understand and apply the
    properties of parallel and perpendicular lines
    and understand the meaning of congruence. This
    includes applying properties of angles formed by
    parallel lines and a transversal. Students will
    also understand and use the Pythagorean Theorem.
  • Math I Students will investigate properties of
    geometric figures in the coordinate plane,
    including use of distance between two points,
    distance between a point and a line, and the
    midpoint of a segment. They will use the
    language of mathematical argument including
    conjecture, inductive and deductive reasoning,
    counterexample, and indirect proof. Students
    will understand and use converse, inverse, and
    contrapositive of a statement. Students will
    also discover, prove, and apply properties of
    triangles, including an understanding of SSS,
    SAS, ASA, AAS, and HL.
  •  
  •  

Northwest Georgia RESA Mathematics Academy
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Building the Geometry Curriculum Ladder
  • Math II Students will identify and use special
    right triangles including 30-60-90 and 45-45-90.
    Students will define and apply sine, cosine, and
    tangent ratios to right triangles. They will
    solve problems using trigonometric ratios.
    Students will understand the properties of
    circles, including and understanding of chords,
    tangents, secants, central and inscribed angles,
    arc length and area of a sector. They will also
    find and compare measures of spheres, applying
    surface area and volume and determining the
    effect on surface area and volume when the radius
    or diameter is changed.

Northwest Georgia RESA Mathematics Academy
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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

Northwest Georgia RESA Mathematics Academy
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Sample Pre-Assessment for 6th grade unit on
Geometry and Measurement Surface Area and
Volume
Northwest Georgia RESA Mathematics Academy
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We are about to begin a unit on Geometry and
Measurement Surface Area and Volume. Tell
me everything you know about surface area and
volume. (You may write your answer in paragraph
form or you may make a list of ideas or
facts.) Give definitions of any vocabulary
terms, examples of formulas, and/or real-life
examples of surface area and volume. Include
labeled drawings or diagrams that would help to
demonstrate what you know. Write your answers in
complete sentences.
Northwest Georgia RESA Mathematics Academy
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Discuss What are the pros and cons of this type
of pre-assessment? What alternative
pre-assessment formats might be considered for
this unit?
Northwest Georgia RESA Mathematics Academy
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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

Northwest Georgia RESA Mathematics Academy
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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
Northwest Georgia RESA Mathematics Academy
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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
Northwest Georgia RESA Mathematics Academy
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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
Northwest Georgia RESA Mathematics Academy
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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
Northwest Georgia RESA Mathematics Academy
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Time on tasks
Northwest Georgia RESA Mathematics Academy
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Carnegie Candy Company
Northwest Georgia RESA Mathematics Academy
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Opening Answer the following questions in
complete sentences. You have 5 minutes. When
you have finished, compare answers with your
group and be prepared to share with the
class. What is the main goal of a candy
company? What are the major costs that a candy
company would have to pay? In what ways do you
think geometry and measurement would be used in a
candy company?
Northwest Georgia RESA Mathematics Academy
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Opening Read Problem 1 aloud. What is the
pattern in the table? How can you find the
answer to Part B? How would the question change
if they used a rectangular box? Could they use a
pyramid? Why or why not? Should the company
consider using bags? Why or why not?
Northwest Georgia RESA Mathematics Academy
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Work Period Begin working on the next portion
of the Carnegie Candy Company task. Make sure
that you give the most complete answers that you
possibly can. Be prepared to share some of
your work during the closing.
Northwest Georgia RESA Mathematics Academy
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Closing Student Presentations
Northwest Georgia RESA Mathematics Academy
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Closing Ticket out the Door What is
volume? What is surface area? How do you find
the volume and surface area of a rectangular
prism? of a triangular prism?
Northwest Georgia RESA Mathematics Academy
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Homework Suppose that you are designing a new
candy for the Carnegie Candy Company. What would
it be? What kind of packaging would you use?
How would you want it displayed? Describe the
candy and its packaging, including its exact
dimensions, volume, and surface area. Include a
diagram.
Northwest Georgia RESA Mathematics Academy
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Discuss What kinds of formative assessment were
used within this lesson? What other types of
formative assessment might be used with this task?
Northwest Georgia RESA Mathematics Academy
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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

Northwest Georgia RESA Mathematics Academy
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Sample Summative Assessment
  • Choose a set of dimensions for a rectangular
    prism and sketch a diagram (inches of cm may be
    used).
  • Make all possible calculations for length, area,
    and volume using your dimensions. Show how you
    arrive at each of your calculations.

Northwest Georgia RESA Mathematics Academy
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Sample Summative Assessment
  • Choose one of each measurement you made (length,
    area, or volume) and convert it to another type
    of unit (ex. convert cm to in).
  • Remember to include information (definitions,
    explanations, diagrams, etc.) about faces, edges,
    vertices, girth, diagonals, surface area, and
    volume.
  • Your work should be well organized with
    explanations written in complete
  • sentences.

Northwest Georgia RESA Mathematics Academy
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Student Sample
Northwest Georgia RESA Mathematics Academy
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Discuss Share your thoughts about this type of
summative assessment. How might you have changed
this assessment? What other types of summative
assessment might be used for a unit of surface
area and volume?
Northwest Georgia RESA Mathematics Academy
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Formative Assessment Presentation Vermont
Department of Education
Northwest Georgia RESA Mathematics Academy
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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

Northwest Georgia RESA Mathematics Academy
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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

Northwest Georgia RESA Mathematics Academy
45
  • 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.

Northwest Georgia RESA Mathematics Academy
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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

Northwest Georgia RESA Mathematics Academy
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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

Northwest Georgia RESA Mathematics Academy
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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

Northwest Georgia RESA Mathematics Academy
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Collecting Assessment Data
  • Status of the Class

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  • Connecting Assessment
  • to the
  • GAPSS Classroom Observation Instrument

Northwest Georgia RESA Mathematics Academy
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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

Northwest Georgia RESA Mathematics Academy
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Questions, Comments, and Concerns

Northwest Georgia RESA Mathematics Academy
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  • I hope you feel more empowered with the
    information youve gained from the Math Academy!
  • Remember
  • With great power comes great responsibility!

Northwest Georgia RESA Mathematics Academy
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Now go and be a hero

or a heroine!
Northwest Georgia RESA Mathematics Academy
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