Northwest Georgia RESA Mathematics Academy

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Northwest Georgia RESA Mathematics Academy
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• Northwest Georgia RESA Mathematics Academy
• Heritage High School
• Ringgold, Georgia
• March 5, 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) 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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Content Topic Algebra Pedagogy Topic
Writing and Using Commentary Effectively
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Essential Questions Why should I post the
standards in my classroom? How do I effectively
integrate the Algebra standards into the
mathematics curriculum? How can teachers and
students write and use commentary effectively?
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A task
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SIXTH GRADE
GPS ALGEBRA M6A1. Students will understand the
concept of ratio and use it to represent
quantitative relationships. M6A2. Students
will consider relationships between varying
quantities. a. Analyze and describe
patterns arising from mathematical rules,
table, and graphs. b. Use
manipulatives or draw pictures to solve problems
involving proportional
relationships. c. Use proportions to
describe relationships and to solve
problems, including percents. d.
Describe proportional relationships
mathematically using y kx, where k
is the constant of proportionality.
e. Graph proportional relationships in the form y
kx and describe characteristics of
the graph. f. In a proportional
relationship expressed as y kx, solve for one
quantity given values of the other
two... Solve problems using the
relationship y kx. g.Use
proportional reasoning (a/b c/d and y kx) to
solve problems. M6A3. Students will evaluate
algebraic expressions, including those
with exponents, and solve simple one-step
equations using each of the four
basic operations.
Algebra Standards
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Opening

• Which class has more girls?
• Class A
  Class B
• 20 students 25
  students
• 10 girls
  12 girls
• How do you know?

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GEORGIA PERFORMANCE STANDARDS (PROCESS
STANDARDS) M7P1. Students will solve
problems. M7P2. Students will reason and
evaluate mathematical arguments. M7P3. Students
will communicate mathematically. M7P4. Students
will make connections among mathematical ideas
and to other disciplines. a. Recognize
and use connections among mathematical ideas.
b. Understand how mathematical ideas connect and
build on one another to produce a
coherent whole. c. Recognize and apply
mathematics in contexts outside of
mathematics. M7P5. Students will represent
mathematics in multiple ways. a. Create and
use representations to organize, record, and
communicate mathematical ideas. b.
Select, apply, and translate among mathematical
rep- resentations to solve problems.
c. Use representations to model and interpret
physical, social, and mathematical
phenomena.
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Work Period

• Redrawing Bucky the Blockhead
• 1. Get with a partner and redraw Bucky according
  to the directions on the page.
• 2. Complete the tables that show how each line
  segment changes.
• 3. Write an equation to represent each new
  drawing.
• 4. Graph the equation and discuss
  proportionality.

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Closing

• What is a ratio?
• What is a proportion?
• What does it mean to think proportionally?
• What does a proportional equation look like?
• What does a proportional graph look like?
• What is the constant of
• proportionality?

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SIXTH GRADE GPS ALGEBRA M6A1. Students will
understand the concept of ratio and use it to
represent quantitative relationships. M6A2.
Students will consider relationships between
varying quantities. a. Analyze and
describe patterns arising from mathematical
rules, table, and graphs. b.
Use manipulatives or draw pictures to solve
problems involving proportional
relationships. c. Use proportions to
describe relationships and to solve
problems, including percents. d. Describe
proportional relationships mathematically
using y kx, where k is the constant of
proportionality. e. Graph proportional
relationships in the form y kx and describe
characteristics of the graph. f.
In a proportional relationship expressed as y
kx, solve for one quantity given
values of the other two... Solve problems using
the relationship y kx. g.
Use proportional reasoning (a/b c/d and y kx)
to solve problems. M6A3. Students will evaluate
algebraic expressions, including those
with exponents, and solve simple one-step
equations using each of the four
basic operations.
Northwest Georgia RESA Mathematics Academy
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GEORGIA PERFORMANCE STANDARDS (PROCESS
STANDARDS) M7P1. Students will solve
problems. M7P2. Students will reason and
evaluate mathematical arguments. M7P3. Students
will communicate mathematically. M7P4. Students
will make connections among mathematical ideas
and to other disciplines. a. Recognize
and use connections among mathematical ideas.
b. Understand how mathematical ideas connect and
build on one another to produce a
coherent whole. c. Recognize and apply
mathematics in contexts outside of
mathematics. M7P5. Students will represent
mathematics in multiple ways. a. Create and
use representations to organize, record, and
communicate mathematical ideas. b.
Select, apply, and translate among mathematical
rep- resentations to solve problems.
c. Use representations to model and interpret
physical, social, and mathematical
phenomena.
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Writing and Using Commentary

• Poster of Proportionality
• Split your chart paper into 2 sections.
• 2. Use the drawings, tables, equations, and
  graphs from todays lesson to illustrate what
  proportionality is and what it is not.
• 3. Post your work on the wall in the classroom.
• 4. After discussing what it means to write
  commentary you will need to write a piece of
  commentary on one of the posters in the
  classroom.

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The parts of a performance standard

• STANDARDS AND ELEMENTS ADDRESSED
• THE TASK
• STUDENT WORK
• COMMENTARY
• Teacher-written
• Student-written

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A feedback system depends on
Vision
and
Reality.
Feedback exists between the two. Grant Wiggins
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Good commentary provides evidence that
shows the level of proficiency of the work as
measured against the standard, cites
specific strategies used, and uses the
language of the standards.
Why are these things important?
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Feedback is specific, and descriptive
information you can use.
Feedback is not advice, praise, or
blame. Grant Wiggins
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Time to Look at Student Work with Commentary
Take a look at the work and commentary provided.
Make notes about what you notice.
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What did you notice about the samples of
commentary?
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Time to Write
Using the standards and the student work sample
provided, write commentary you could use as a
teaching tool for your students.
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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 (Calkins, p. 325).
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Taking our temperature with respect to
establishing a standards-based
classroom
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Perception vs. Reality
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Common Perceptions Perception Openings, work
periods, and closings must meet exact time
constraints. Reality While there
are time suggestions for each portion of the
instructional framework, times will vary
depending on the type of lesson and the
content. Perception Every concept must be
completely discovered by students.
Reality 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 Perception Skills lessons
are never appropriate.
Reality 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. Perception Direct instruction is never
appropriate. Reality 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 Perception All work must be
done in pairs or in groups.
Reality The standards-based classroom should
incorporate a mix of group work, partner work,
and individual accountability. Perception Closi
ngs must always include formal student
presentations. Reality 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 Perception Every student
must play a major role in the closing every
day. Reality 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 Perception Commentary should
be lengthy. Reality 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. Perception Commentary should always
be written for every student on a particular task
or assignment. Reality 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 Perception All commentary
should be written by the teacher.
Reality 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. Perception
Commentary is mainly used for student work
displays. Reality 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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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