Transcript Mathematics Design Collaborative 2012 and Beyond

Mathematics Design
Collaborative
2012 and Beyond
GACIS 2012
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Last Year’s Presentation – In
Review
• The project is working to design and develop
well-engineered assessment tools to support US
schools in implementing the Common Core State
Standards for Mathematics (CCSS).
• Data shows long range retention
• The Big Idea of Formative Assessment
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Students and Teachers
Using evidence of learning
To adapt teaching and learning
To meet the immediate learning needs
Minute-to-minute and day-by-day
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Five Strategies
of Formative Assessment
• Clarifying and sharing learning intentions and
criteria for success
• Engineering effective discussion, questions,
activities, and tasks that elicit evidence of learning.
• Providing feedback that moves students forward
• Activating students as instructional resources for
one another
• Activating students as owners of their own learning
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
2011-2012
• School Level – Micah Hoyt, East Hall High
School, Hall County
– Lessons learned
– Collaboration is key
• District Level – Dr. Cassie Rape, Houston
County Mathematics Supervisor, 6-12
– Scaling district-wide
– Vertical and horizontal collaboration
– Analysis for Growth (and repair)
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
MDC Tools and Takeaways
• Student Engagement
• Depth of Understanding
• Collaboration and planning
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
The Changing Face of Student
Engagement
Before
• Students working quietly
• Students completing a task
with a high degree of
accuracy
• Students asking questions
of the teacher
• Students DOING
mathematics
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
After
• Students communicating
mathematically with each
other
• Students working together
to solve an authentic
problem
• Students activating each
other as learning resources
• Students
UNDERSTANDING
mathematics
Student Comments
 “I liked the class a lot better than I had been”.
(sic)
 “I loved the math class today. I actually had
fun interacting with everyone and solving the
problems.”
 “I think that it’s more fun and intriguing than a
regular math class because we didn’t just do
book work.”
 “It felt like I was in science class with the
polluted water.”
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Teaching for Conceptual
Understanding
• Phil Daro – “Against Answer Getting”
• Moving toward understanding and away
from steps.
• Stop making it easy!
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
What is Happening Now?
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Promoting MDC Strategies
Recruiting Teachers
Collaboration
Data Driven Instruction
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
A Vertical Look at Formative
Assessment Lessons
Why is this any different from
regular math “tasks” or “quizzes?”
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
We don’t learn passively.
• People are active participants in their own learning.
• We construct bridges between what we are learning now
and what we already know
• Misconceptions arise naturally as a result.
• FOR INSTANCE: A third grader constructs the following
“rule” for themselves based on their previous learning: I
will get larger number whenever I multiply two numbers
together.
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
There is a BIG difference
between a Mistake and a
Misconception.
MISTAKES
• Computational
Errors
• Lack of Attention
• Careless Errors
• Misreading Own
Handwriting
• Observed
Occasionally/
Infrequently
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
MISCONCEPTIONS
• Wrong applications
of Mathematical
Rules
• Incorrect
interpretation of
mathematical
concepts
• Observed
consistently
Why is the consideration of misconceptions important?
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Children construct meaning internally by accommodating
new concepts within their existing mental frameworks.
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Thus, unless there is intervention, there is likelihood that
the pupil’s conception may deviate from the intended one.
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Pupils are known to misapply algorithms and rules in
domains where they are inapplicable.
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A surprisingly large proportion of pupils share the same
misconceptions.
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Undiagnosed
Misconceptions Become
Owned and Embedded
Misconceptions
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Undiagnosed Misconceptions
Become Owned and
Embedded Misconceptions
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Formative Assessment is
Shown to be more successful
than direct instruction alone.
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Student does not understand
conceptually the relationship between
slope and speed
Student gets all parts of graph correct.
Student does not explain why the graph
is realistic
Student misinterprets scale (either
misplacing the x and y axis or interpreting
the units in the wrong increments).
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Does not know that speed is distance
(per) time
Student does not calculate speed
(incorrect descriptions of speed)
Student fails to mention specific distance
or specific time
Student interprets graph as speed vs.
time (acceleration)
Tricked by picture. Student interprets the
graph as a picture.
PRE-Test ERRORS ANALYSIS
PERCENTAGES
G
A(10%) B (25%) C (80%) D (95%) E (50%) F (5%) (90%+) H (5%) J (10%)
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
B (5%) C (30%) D (45%) E (5%) F (less than 5%) G (10%+) H (30%)
Student does not understand conceptually the
relationship between slope and speed
Student gets all parts of graph correct.
Student does not explain why the graph is
realistic
Student misinterprets scale (either misplacing
the x and y axis or interpreting the units in the
wrong increments).
Does not know that speed is distance (per) time
Student does not calculate speed (incorrect
descriptions of speed)
Student fails to mention specific distance or
specific time
A (5%)
Student interprets graph as speed vs. time
(acceleration)
Tricked by picture. Student interprets the graph
as a picture.
POST-Test ERRORS ANALYSIS
PERCENTAGES (approximates)
J (5%)
A SIDE-BY-SIDE
COMPARISON
PRE
• A(10%)
• B (25%)
• C (80%)
• D (95%)
• E (50%)
• F (5%)
• G (90%+)
• H (5%)
• J (10%)
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
POST
• A (5%)
• B (5%)
• C (30%)
• D (45%)
• E (5%)
• F (less than 5%)
• G (10%+)
• H (30%)
• J (5%)
A Horizontal Look at
Formative Assessment
Lessons
CONVINCING TEACHERS OF
FAL VALUE
ENSURING FIDELITY IN
SCALING ACROSS SYSTEM
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
The Beliefs of Educated
Educators…. A Cycle
No Personal
Proof of
Effectiveness
No Results
Generated
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Unwillingness
to Try
Because
Potentially
Ineffective
TRAINING FOR TEACHERS
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STRUCTURED FAL STUDY
TEACHERS START AS STUDENTS
DEMONSTRATE PROCESS
NO-PRESSURE OPPORTUNITIES
TO RUN TRIALS
• USE LESSONS PERTINENT TO
THEIR GRADE/SUBJECT
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
INSPECT WHAT YOU EXPECT
• Make the Expectation Clear:
“Non-Optional” Formative
Assessments
• Observe the Lessons
• Ask for Student Work Samples
• Ask to see Analysis of Student
Errors
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
PROVIDING for TEACHERS
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Lessons Provided by DOE
Matched lessons to units
Opportunities to Collaborate
Materials to Implement
Support for the Process
Time to Analyze Student Work
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
MOTIVATING TEACHERS
• THE GAME IS CHANGING: Math is
no longer an exercise in
choreography, but in true
understanding and application
– PARCC
– SHELL
– CCGPS
– Standards for Mathematical
Practice
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
OUR PLATES, as MATH TEACHERS
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
MAP(Shell Centre) Formative Assessment
Compared to Instructional Framework
PreAssessment
(NO HELP
from
teacher)!
Analysis of
Student Work
and
Understandin
gs
Creation of
Leading
/Probing/Gui
ding
Questions
Standard/Esse
ntial Question
Opening
Opening
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Collaborative
Session
(Utilize
Questioning)
MiniLesson
Student Work
Session
(Utilize
Questioning,
Create
“Experts”)
Student
Work
Session
Plenary
(Summarizin
g) Discussion
Closing
PostAssessment
(Students
can have
their Probing
Questions
and Pre-Test
to use during
PostAssessment)
Why does a FAL matter?
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Summary
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Cohort 1: 6 pilot systems, 2011-2012
Cohort 2: 44 additional systems
RESA involvement
2013-2014 and beyond; all training and
teacher support will be provided by RESA
• MDC provides the best practices strategies,
tools, formative assessments and lessons.
We enact, observe, collaborate, analyze
student work, adjust instruction, and have
student talking about mathematics.
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
So what is formative
assessment?
• It is the biopsy that we take to diagnose
current conditions; rather than the autopsy
at the end of the unit . . . when it is too late
to administer assistance.
• When the chef tastes the sauce, this is
formative assessment. When the
customer tastes the food, this is
summative.
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Challenges
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Less teaching
More questioning
Collaborative planning
Analysis of growth: pre to post
Next steps
Time
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org
Final Comments
Questions???
Share
[email protected]
Listen more, talk less
Students engaged – teacher
facilitates
Dr. John D. Barge, State School
Superintendent
“Making Education Work for All Georgians”
www.gadoe.org