Transcript Document 7131129

Student-Focused Coaching in
Mathematics
Coaching Model in the Silicon Valley Mathematics
Initiative, California
David Foster
Director of the SVMI
Robert Noyce Foundation
www.noycefdn.org/math/
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No Child
Left Behind
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High Stakes Accountability System
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- Albert Einstein
"Everything that
can be counted
does not
necessarily count;
everything that
counts can not
necessarily be
counted."
Goals for the Workshop
• To develop a well articulated vision of a mentor/coaching
program.
• To develop skills in working one-on-one with teachers to
improve their instructional practice and content knowledge.
• To use student thinking and work to inform instruction and
improve student learning.
• To explore, discuss and develop strategies for facing logistical
challenges and other coaching related issues.
• To further strengthen a professional community of leaders
whose goal is to support ongoing teacher development that
encourages capacity building and reflective practice.
Myth 1:
Teachers are fully knowledgeable in
content and pedagogy coming out of
schools of education
We train teachers in universities far removed
from practice, credential 21-year-olds to take
their place in classrooms, and then provide them
with hardly a fraction of the assistance or support
that is given to young professionals in industry.
Elliot Eisner
Myth 2:
The longer you teach,
the better you get.
Do we really believe, as our behavior seems to
indicate, that more years in the classroom are
directly correlated with better teaching? I think
not. Yet the regular provision of genuinely useful
feedback to teacher about their teaching is not a
normal part of our school structure.
Elliot Eisner
Good Teaching is What Counts
“The greater part of the failure of
mathematics is due to poor teaching. Good
teachers have in the past succeeded, and will
continue to succeed, in achieving highly
satisfactory results with the traditional
material; poor teachers will not succeed even
with the newer and better materials.”
This conclusion was made in 1923 by a national
commission on how to teach mathematics in school.
Good Teaching is What Counts
Through multiple waves of math reform, through
dramatic changes in technology, culture and schools
themselves, what was true in 1923 is true in 2007:
Teachers matter!
Horizon Research analyzed more than 300 math and
science classes in 31 school districts across the
United States. Using trained observers, it rated 59%
of classroom sessions as low in quality, 27% as
medium-quality and 15%as high quality.
http://www.horizon-research.com/reports/2003/insidetheclassroom/looking.php
Teaching Matters
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The greatest school related factor to learning
Good Instruction Makes A Difference
Good teaching can make a
significant difference in
student achievement, equal
to one effect size (a
standard deviation), which
is also equivalent to the
affect that demographic
classifications can have on
achievement.
Paraphrase Dr. Heather Hill, University of Michigan
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Our research indicates
that there is a 15%
variability difference in
student achievement
between teachers within
the same schools.
Deborah Loewenberg Ball
Documenting Uneven Instruction
“What Matters Very Much is Which Classroom”
If a student is in one of the
most effective classrooms he or
she will will learn in 6 months
what those in an average
classroom will take a year to
learn. And if a student is in one
of the least effective classrooms
in that school, the same amount
of learning take 2 years.
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Most effective classes learn 4 times the speed of least effective.
Dylan Wiliams, University of London
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We were led to teacher professional
development as the fundamental
lever for improving student
learning by a growing research base
on the influences on student
learning, which shows that teacher
quality trumps virtually all other
influences on student achievement.
(e.g., Darling-Hammond, 1999; Hamre and Pianta,
2005; Hanushek, Kain, O'Brien and Rivken, 2005;
Wright, Horn and Sanders, 1997)
Teaching for Mathematical Proficiency
Teacher
Students
Mathematics
Students
Adding It Up: helping children learn
mathematics, Kilpatrick, et. al 2001
“The effectiveness of mathematics
teaching and learning is a function
of teachers’ knowledge and use of
mathematical content, of teachers’
attention to and work with
students, and of students’
engagement in the use of
mathematical tasks. Effectiveness
depends on enactment, on the
mutual and interdependent
interactions of the three elements - mathematical content, teacher,
and student--as instruction
unfolds”
Teaching for Meaning
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Adding It Up: Helping Children Learn Mathematics, NRC, 2001
D ep th of Kn ow le dg e
Le v e l 1 : Rec a llin g a nd Rec o g n iz in g:
St u d e n t is a ble t o r e c al l r o u t in e f a ct s of k n o w led g e a nd ca n
r ec o gn iz e s h a p e, sym b ols , a t t r ib u t e s or o t h e r q u a li t ie s.
Le v e l 2 : Usi n g Pro c ed u re s :
St u d e n t uses o r a pp lie s pr o ce d u r es an d t e c h niq ues t o a r r iv e a t
so lu t io n s o r a n s w e r s.
Le v e l 3 : Ex pl a ini n g a nd Con c lu d in g:
St u d e n t re a so n s a nd d e r iv es c o n c lu sio n s . St u d e n t e xpl a in s r e a so n in g
a nd p r oc e sses . St u d e n t c ommu n ic a t es p ro c e d u r es a nd fi nd in gs.
Le v e l 4 : Ma kin g Con ne c t io n s, Ex te n d in g a nd Jus t ify in g:
St u d e n t mak e s c o n n e c t io n s b e t w ee n d iff e re nt co nc ep t s a n d s t r a n d s
of m a t h em a t ics . St u d en t e xt e n d s a n d b u il d s o n k n o w le d ge t o a
s itu a t io n t o a r r iv e a t a c o n clus io n . S t u d e n ts u se r eas o n an d log ic t o
p r o v e a n d ju st ify c on c lu si o ns .
Ada pt e d f r om th e w o r k of No r ma n L. We b b
Silicon Valley Mathematics Initiative
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Math Coaching Model
1996 - 2007
Optimism
"Optimism is an essential ingredient for
innovation. How else can the individual
welcome change over security, adventure
over staying in safe places? A significant
innovation has effects that reach much
further than can be imagined at the time,
and creates its own uses. It will not be held
back by those who lack the imagination to
exploit its use, but will be swept along by
the creative members of our society for the
good of all. Innovation cannot be mandated
any more than a baseball coach can
demand that the next batter hit a home run.
He can, however, assemble a good team,
encourage his players, and play the odds."
Robert N. Noyce
Thirteen Years of Supporting Schools to Improve
Teaching and Learning of Mathematics
From 1996 to 2009
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Supporting more than 40 school districts 2,100 teachers and 80,000 students
annually in Santa Clara, San Mateo, Alameda, Santa Cruz, Monterey, Contra
Costa, Marin, and San Francisco Counties.
Theory of Action
Teacher
Knowledge
Instruction
Student
Learning
Student
Achievement
Comprehensive professional development supports
teacher’s in improving:
Math content knowledge
Pedagogical content knowledge
Instructional strategies
A coherent curriculum to support higher level thinking
skills
Acquiring New Skills/Behaviors
Training v. Impact
Concept Understanding
Skill Attainment
Application
Presentation
85%
15%
10%
Modeling
85%
18%
15%
Practice
85%
80%
15%
Coaching
90%
90%
80%
Joyce and Showers, 1982
Silicon Valley Mathematics Initiative’s
Pedagogical Content Coaching
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Pedagogical Content Coaching
Coach
Teacher
Teachers
Students
Mathematics
Teachers
Students
Adapted from LCMPD Mumme, Carroll
The Silicon Valley Math Initiative aims to improve
teaching and learning of math through classroom coaching
During the 2007-08 school
year there are 63 f.t.e. math
coaches working in 36 SVMI
member districts. A total of
756 teachers were supported
with classroom coaching
reaching 33,516 students.
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Math Coaches are supported with ongoing professional
development including an annual Leadership Institute, Math
Coaching Institute and monthly Math Network meetings.
The Best Receive Coaching
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Tiger Woods has a coach
Pavarotti had a voice coach
Tom Brady has several coaches
Personal trainers are coaches
Psychologists are coaches
CEO of Fortune 500 companies often have a coach
Trustees of the Noyce Foundation have served as coaches
for company executives
Therefore, why shouldn’t Teachers be Coached?
Fundamental Requirements for
Successful Coaching
• A trusting, honest, respectful relationship between
coach and teacher.
• Time for preparation and reflection
• Clearly defined roles, responsibilities and
expectations
• Effective listening skills
• Strategic questions that promote thinking
• Data collection (teacher/student behavior) and
thoughtful feedback
Coaching Discussions
Aspect
Traditional
Coaching
Tellin g Instructions
Content
Coaching
Asking Questions
Types of questions
Critical, coachfocused
Yes/No
Nonjudgemental,
learner focused
Open-ended
Motivation
Extrinsic
Instrinsic
Focus
On teacher/teaching
On learner/learning
Negative “self talk”
Likely to increase
Likely to decrease
Purpose
To ge t the task done
and share coach’s
wisdom
To develop the
learner’s ability and
to access the
learner’s wisdom
Communication
Feedback
Adapted from“Partnership Coaching”, Cory and Bivens-Bradley
The key to success is to tie all
ideas back to student thinking!
The coach-teacher
relationship is
centered on
students’ thinking,
understandings and
misconceptions.
The conversations
are about student
work --what they
know and are able
to do. The focus of
coaching therefore
is centered squarely
on student learning.
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The goal of coaching is to build capacity and trust.
The work done by coaches all relates back directly to
student thinking and understanding – work they have
seen done by students. Student work is also the tool
for evaluating the effectiveness of changes in
curriculum and pedagogy.
Collectively score and analyze student work
Administer quality
assessment tasks
TOOTHPICK SHAPES
Tom uses toothpicks to make the shapes in the
diagram below.
shape 1
6 toothpicks
shape 2
9 toothpicks
shape 3
shape 4
1. How many toothpicks make shape 3?_________________
2. Draw shape 4 next to shape 3 in the diagram
above.
5. Tom says, “I need 36 toothp icks to make shape 12.”
Tom is not correct. Explain why he is not correct.
How many toothpicks are needed to make shape 12?
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Leads to improved teaching
and learning in the classroom
Cycle of Formative
Assessment to Inform
and Improve Learning
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Drives the professional development
experiences of the teachers.
Document student
thinking to inform
instruction.
Classification of Coaching Styles
Coach as Collaborator:
Coach see him/herself as a
resource to the teacher. In
partnership with the teacher, this
type of coach provides materials,
information, and encouragement.
Works collaboratively with the
teacher in planning lessons.
Coach give little direct feedback to the teacher about his/her
pedagogy or presentation of the math of the lesson. Rather,
discussion focuses more on what the students seem to
understand and teachers are free to interpret that information.
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Joanne Rossi Becker, 2001
Classification of Coaching Styles
Coach as Model:
Coach uses a long-range plan
of working with teachers by
modeling instruction. The
instruction actively involves
children in high level tasks as
well as modeling the
coaching process itself with
the coach as the teacher. The
coach may provide follow-up
lessons for the teacher to use
after the model lesson.
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Joanne Rossi Becker, 2001
Classification of Coaching Styles
Coach as Leader:
Coach is a guide to the
teacher. The direct
guidance is effective and
accepted on content issues
and pedagogy because of
the way it is approached.
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The comments are grounded in what the teacher did and
what the students seem to understand. The coach and
teacher become collaborative problem solvers in
designing next steps in instruction.
Joanne Rossi Becker, 2001
Pre-Conference
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Coaching: the pre-conference
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What did the coach focus on?
What did the teacher focus on?
What important information was learned?
What would you as a coach like to ask that
wasn’t asked by this coach?
• What do you anticipate in the lesson?
• What will you (as a coach) focus on in the
lesson?
The lesson
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• Second grade class.
• 3rd day of 3 day lesson on
addition and comparison
subtraction of 2 digit numbers.
• Determine the value in dollars
of your name if A is $1, B is
$2, …, Z is $26
• Compare your name with
another student and find the
difference between the two
amounts.
What is the difference between the names Melissa and Stephanie?
What is the difference between the
names Melissa and Stephanie?
A1
B2
C3
D4
E5
F6
G7
H8
I9
O 15
U 21
J 10
P 16
V 22
K 11
Q 17
W 23
L 12
R 18
X 24
M 13
S 19
Y 25
N 14
T 20
Z 26
Preparing to Observe the Lesson
What will you focus on as a coach?
What evidence will you be looking to collect?
What role will you play as a coach?
The Lesson
Brian’s Strategy
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Discuss the class lesson
• What are your thoughts as an observer of these
classroom segments?
• What is the mathematics being taught?
• How do the students think alike and how are they
different?
• Discuss Stevie’s or Brian’s Strategy. What do they
seem to understand? What might you notice as a
coach?
Prepare for a post-conference
• What would you say/do in a post-conference with
this teacher?
• What evidence did you collect to share with the
teacher?
• What did you notice about student thinking,
understandings or struggles?
• What did you notice about the students
relationships with each other and the
mathematics?
The Post-Conference
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Coaching: the post-conference
• What did the coach focus on during this
segment of the conference?
• What role did student thinking play in the
discussion?
• How was content knowledge addressed?
• What other issues were raised?
• What are the benefits/limitations of
focusing on student work?
Silicon Valley Mathematics Initiative
Providing Year-Around
Professional Development
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Leadership Institute (coaches)
Coaching Institute (teachers & coaches)
School Year P.D.(teachers with coaches)
Math Network (support for coaches)
PIL Meetings (principals with coaches)
Lesson Study (teacher teams with coaches)
Algebra for All (algebra teachers & coaches)
MAC Scoring Training (scoring leaders)
SVMI General Meetings (Admin)
Thoughts on Coaching by Teachers Who Has Been Coached
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Case Studies of the
Silicon Valley Mathematics Initiative
1996 - 2007
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An Initiative of the Noyce Foundation
Case Study II: A Middle School
Demographics
California
Santa Clara County
Comparable School
Target School
% Qualifying for NSLP
43%
25%
28%
28%
English Learners
19%
20%
18%
33%
Coaching Improves Teaching and
Student Achievement
100% of the seventh grade teachers were coached in the Target School
Comparison Study of Achievement
SVMI versus non-SVMI
San Mateo County was chosen to study, because the member
district population has remained fairly constant for the past
three years. Of the nineteen districts in the study, ten are
member districts of SVMI and nine are not. The analysis
involves data from 21,188 students whose teachers are not
members of SVMI and 14,615 students whose teachers are
involved in SVMI programs. The SVMI students as a group
are generally poorer than the comparison group. Thirty-seven
percent of the SVMI students qualify for the National School
Lunch Program (NSLP) compared to 30% of the non-SVMI
students. The percents of English Learners are the same in
both groups, 26%.
Comparison Study of Achievement
SVMI versus non-SVMI
Percent of Student Meeting Standard
Comparison of Achievement on CST 2005
80%
70%
60%
50%
non-SVMI Districts (30% NSLP)
40%
SVMI Districts (37% NSLP)
30%
20%
10%
0%
2nd
3rd
4th
5th
Grade Level
6th
7th
Case Study
Relationship between Teaching
and Student Achievement Over Time
• Four years of coaching and professional development for a
participating group of teachers in grades 4 - 7.
• A representative sample of seventh grade students (n=152) in
one district.
• Analysis of student scores on performance exam in the
students’ fourth year (7th grade).
• Comparison of the number of years in either participating
teachers’(n=21) or non-participating teachers’(n=52)
classrooms.
Students in participating classrooms were
significantly more successful
on the MARS exam.
"Don't be encumbered by
history-- go off and do
something wonderful."
Dr. Robert N. Noyce
Inventor of the Silicon Chip
Co-founder of Intel
Pedagogical Content Coaching
in Mathematics
Case Study of the Silicon Valley Mathematics Initiative
David Foster, Program Director:Mathematics
The Robert Noyce Foundation
www.noycefdn.org