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
• April 2, 2009
• 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) 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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Content Topic Geometry 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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Building the Geometry Curriculum Ladder

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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.
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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.
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• 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.
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•  

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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.
•  

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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.
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•  

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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.
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•  

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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.

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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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Sample Pre-Assessment for 6th grade unit on
Geometry and Measurement Surface Area and
Volume
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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.
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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?
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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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Time on tasks
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Carnegie Candy Company
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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?
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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?
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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.
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Closing Student Presentations
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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?
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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.
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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?
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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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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.

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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.

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Student Sample
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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?
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Formative Assessment Presentation Vermont
Department of Education
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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 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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Questions, Comments, and Concerns

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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!

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Now go and be a hero

or a heroine!
Northwest Georgia RESA Mathematics Academy