Intensive Immersion Institute

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Intensive Immersion Institute
Katherine Foulser, Chelsea Public Schools Donna
Chevaire, Lawrence Public Schools Linda
Simeone, North Middlesex Regional School District
Claire Abrams, Lowell Public Schools Paula
Giaquinto, Fitchburg Public Schools Laureen
Cipolla, Leominster Public Schools Andrew Chen,
EduTron
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Intensive Immersion Institute
Katherine Foulser, Chelsea Public Schools Donna
Chevaire, Lawrence Public Schools Linda
Simeone, North Middlesex Regional School District
Claire Abrams, Lowell Public Schools Paula
Giaquinto, Fitchburg Public Schools Laureen
Cipolla, Leominster Public Schools Andrew Chen,
EduTron
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Lessons Learned from an Intensive Immersion
Institute(2008 MA DESE PD Institute)
I3

• Kathy Foulser
• Chelsea Public Schools
• STEM Summit V, October 28, 2008

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Unlocking Linear Equationsand Exploring their
Fundamentals

• Presented by EduTron
• (Andrew Chen et al.)
• Chelsea Public Schools
• July, 2008

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Rationale

• Why Chelsea Public Schools sought this workshop
• Grades 5 and 6 in self-contained classrooms
• Dearth of licensed math teachers in middle
  schools
• Goal more math classes taught by teachers
  licensed in Math
• Encourage Team Teaching
• Hire Math Specialists
• Assist Chelsea teachers in Math licensure
• Enrollment in ALEKS
• Offering PD Focused on Linearity

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Revisions to Elementary Generalist Licensure

• New Beginning 2009
• Mathematics is an independently scoreable
  sub-test that also requires a passing score.
• Math problems are demanding.

• Old -- Still in Place!
• 70 required for passing
• 30 of questions are math

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Who Attended?

• 15 of 30 registrants were Chelsea teachers.
  Twenty three (23) showed up on day one.
• 11 of 22 who completed the course were Chelsea
  teachers
• 1 8th grade math teacher highly qualified but
  has not passed MTEL in Math
• 1 middle school math coach
• 1 8th grade Substantially Separate classroom
  teacher
• 1 Special Education Resource teacher
• 7 5th and 6th grade classroom teachers

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Elementary teachers got just as much out of the
program
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Doing the Math An Example

• Let n be an odd number. Prove n2 is odd.
• Gails approach Building on experience
• Square 1, 3, 5, 7, and 9. The result is always
  odd.
• Since every other odd number will have one of the
  same last digits, youll always get one of the
  same last digits when you square it.
• Evenness/oddness (parity) depends only on the
  last digit, so the square of an odd number will
  always be odd number. QED!

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Doing the Math An Example

• Let n be an odd number. Prove n2 is odd.
• Bobs approach Check the parity of the parts
• every odd number is just one more than an even
  number. Using O for odd and E for even, he wrote
  O2 (E1) 2
• (E1)2 (E1)(E1) E22E 1.
• E2 is even because an even number multiplied by
  an even number also is an even number. 2E is
  even because its a multiple of 2. So E2 2E
  1 is the sum of 2 even numbers plus a dangling
  1 which means it will make it odd.

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Doing the Math An Example

• Let n be an odd number. Prove n2 is odd.
• Karens model of the partial products
• if n is odd, then n-1 is even
• (n-1)2 is even if n-1 is even
• n-1 is even (and we even have 2 of them, so
  2(n-1) is definitely even)
• 1 is odd, so the sum is odd.

n-1
1
(n-1)2
n-1
n-1
n-1
1
1
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Doing the Math An Example

• Apply this model to Bobs idea.
• Everything but the dangling 1 is odd
• So the sum is odd.

Even
1
Even
Even
Even
Even
1
1
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Doing the Math An Example

• Let n be an odd number. Prove n2 is odd.
• Alicias approach
• Squaring means multiplying by the same number.
• Squaring an odd number means we are multiplying
  an odd number by an odd number.
• Multiplication is repeated Addition.
• Multiplying an odd by an odd means we are adding
  together an odd number of odd numbers. This will
  always make an odd sum.

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Doing the Math An Example

• Let n be an odd number. Prove n2 is odd.
• Kims approach
• An even number can be represented by 2n
• An odd number is just one more than an even
  number, or 2n1.
• Squaring 2n1 means
• (2n 1)(2n 1) 4n24n 1.
• 4n2 and the 4n parts are both even, so the sum is
  odd.

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Learning Pedagogy through Example

• Students do all the work
• Multiple approaches to every problem
• Keys to broadening understanding
• Persistence
• Asking questions
• Listening to others explanations
• Essential Qualities modeled by Edutron staff
  throughout workshop

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Excerpts from 50 WAYS TO SOLVE THE PROBLEMBy
Mary Anne Gauthier(Forgive me Paul Simon!)

• The problem is all inside your head, Andrew
  said to me.
• The answer is easy if you take it logically.
• Id like to help you in your struggle to see
• There must be fifty ways to solve this problem.

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Chorus!

• Try slope-intercept form, Norm.
• Graph it on a plane, Jane.
• An equation might do, Lou.
• Just listen and see.
• Make a chart, Bart.
• We have to discuss much!
• Dont forget the key, Lee,
• And use x, y, and z.

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The Ultimate Tribute!

• He said, Why doesnt someone come up and write?
• And I believe by the end well begin to see the
  light.
• And then he picked me and I realized he probably
  was right.
• There must be fifty ways to solve this problem!

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Intensive Immersion Institute
Katherine Foulser, Chelsea Public Schools Donna
Chevaire, Lawrence Public Schools Linda
Simeone, North Middlesex Regional School District
Claire Abrams, Lowell Public Schools Paula
Giaquinto, Fitchburg Public Schools Laureen
Cipolla, Leominster Public Schools Andrew Chen,
EduTron
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Teacher Math Academy in Lawrence August 4th -
August 8th 2008 An Intensive Immersion
Institute Donna L. Chevaire District
Mathematics Principal K-12 Lawrence Public
Schools Lawrence High School Campus 70-71 North
Parish Road Lawrence, MA 01843 dchevaire_at_lawrence.
k12.ma.us
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TMA Participants
Gr. 3/4 Gr. 5/6 Gr. 7/8 Gr. 9 Total /
Math 1 subject 2 7 7 0 16 /28
Math 2 subjects 5 1 0 6 /10
Math 3 subjects 7 0.5 1.5 0 9 /16
No math 2 4.5 8.5 2 17 /29
SPED 1 1 4 6 /10
Math/sci. coach 2 .5 .5 3 /5
Math Facilitator .5 .5 1 /2
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Math True or False
1. A number with 3 digits is always bigger than
one with two. T F
2. When you multiply two numbers together, the
answer is always bigger than both the original
numbers.
T F
3. The diagonal of a square is the same length as
the side. T F
4. To multiply by 10, just add a zero.
T F
5. The area of a rectangle is always larger than
the perimeter. T F
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Math True or False

• A number with 3 digits is always bigger than one
  with two. T F
• 2. When you multiply two numbers together, the
  answer is always bigger than both the original
  numbers.
  T F
• 3. The diagonal of a square is the same length as
  the side. T F
• 4. To multiply by 10, just add a zero.
  T F
• 5. The area of a rectangle is always larger than
  the perimeter. T F

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Investigation
Leslie has 48 identical cubes each with 3 cm.
edges. She glued them together to form a
rectangular solid. If the perimeter of the base
is 42 cm., find the surface area of the
rectangular solid (in sq. cm.).
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Conceptual Understanding
1 ¾ divided by ½ Solve. Devise a story or
model to explain the meaning of this division by
a fraction.
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According to Ma, Liping Knowing and Teaching
Elementary Mathematics A Volume in the Studies
in Mathematical Thinking and Learning Series,
55-83. Berkeley University of California,
1999 43 of US teachers could solve and
satisfactorily give an example of the meaning of
division of fractions. Lawrence teachers mirrored
these findings. 90 of Chinese teachers could
solve and satisfactorily give an example of the
meaning of division of fractions.
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• Three students present their methods for solving
  a multiplication problem (Adapted from Deborah
  Ball)
• A B C
• 35 35 35
• x 25 x 25 x 25
• 125 175 25
• 75 700 150
• 875 875 100
• 600
• 875
• Explain how each student solved the problem.
• 2. Describe or draw another representation of
  this problem that can be used to explain an
  operation or process students have employed.

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2008 Lawrence TMA Pedagogical Reflection
Have I made some observations on pedagogy that I
found impacted my learning and that were relevant
to my classroom? What do I want to try to
duplicate? Support observations with specific
examples experienced in the first four days.
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Sample responses
This week the instructors constantly questioned
the answers rather than answer the questions.
(6th grade science teacher)
We were asked to explore challenging problems
and discuss them with our group. (8th grade
math teacher)
They asked, Why do you think that? or Does
anyone have a different method? (4th grade
teacher)
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This course has answered so many of the why
questions students ask me. I now know that
telling students that Its the rule, is no
longer acceptable. (3rd/4th grade teacher)
I need to model using the appropriate math
vocabulary. (5th grade math teacher)
The instructors had us working at a level where
we forgot about lunch/breaks. There was heavy
engagement. (5th -8th grade technology teacher)
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Lets start with what we know. I want to bring
this idea to my classroom. (7th grade humanities
teacher)
You dont know how to do it yet. There was
always a positive attitude. (Unanimous during
sharing sessions)
We want more! (95 of participants!)
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Intensive Immersion Institute
Katherine Foulser, Chelsea Public Schools Donna
Chevaire, Lawrence Public Schools Linda
Simeone, North Middlesex Regional School District
Claire Abrams, Lowell Public Schools Paula
Giaquinto, Fitchburg Public Schools Laureen
Cipolla, Leominster Public Schools Andrew Chen,
EduTron
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MATH BOOT CAMP North Middlesex Regional School
District July 2008 Dr. Andrew Chen the Data
Divas Linda Simeone Department Chair High
School Karen Capizzi Middle School
Coordinator Jamie Monico Middle School
Coordinator Cathy McCulley - 3rd grade teacher
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NMRHS BOOT CAMP

• Participants
• Teachers grades K 12, math, science, special
  education, title one and a school librarian.
• Teaching experience 0 to 30 years
• Singapore experience 0 to 9 years
• Purpose
• We all need to strengthen our MATH skills
• Looking at data to improve instruction
• Creation of an ALGEBRA foundation for all grades
• Investigation into weak areas in our curriculum,
  instruction, and student understanding.
• Instruction based on the Singapore model and the
  power behind the model.

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Feedback from teachers about LEARNING
the thought process and frustration that
students go through when learning new concepts.
This was demonstrated very effectively when we
learned the base 4 system.
the value of allowing kids to struggle after
experiencing the struggle first hand.
always ask students to explain their reasoning
before offering your input.
being forced to explain my thinking, not just
plug in a value
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Feedback from teachers about MATH
I went home and showed off everything and I
taught my friend and he understood.
to realize I had something to offer the whole
class.
I can do the math in 4 land, so I can do MATH
I solved problems after 3 different tries and
then I had to teach everyone and I did it.
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What we learned from BOOT CAMP 1

• Key areas that need more focus on instruction
  fractions, algebra, variety of solution methods.
• Curriculum areas that need investigation use of
  Singapore books in some but not all classes.
• Connections between schools, teachers, levels and
  classrooms throughout the district.
• Teachers need support training in MATH.
• Students struggle with new ideas, let them try
  several times before jumping in.

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What worked!

• Math Professional Development that addressed
  grade level content as well as higher order
  thinking skills benefits all teachers.
• Creation of MATH Professional Learning
  Communities improves instruction.
• Utilizing different grade level teachers to
  present their methods/solutions from model
  drawing to graphing a hyperbola.

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Benchmarks Data
NMRHS Boot Camp participants created 2 benchmark
tests for each grade level (1-12). Benefits
discussion between teachers at grade level about
methodology pedagogy, instruction, curriculum,
and resources. DATA will show us Problems in
curriculum coverage Problems in delivery and
instruction of content Problems in students
understanding
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Results

• 42 teachers know more math content
• Teachers are working together at grade level
  across the district
• Parents have a toolkit to help with math
  homework problems
• Teachers are asking when is BOOT CAMP 2
• Benchmarks are due Oct 23rd and the data will
  tell a story

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Intensive Immersion Institute
Katherine Foulser, Chelsea Public Schools Donna
Chevaire, Lawrence Public Schools Linda
Simeone, North Middlesex Regional School District
Claire Abrams, Lowell Public Schools Paula
Giaquinto, Fitchburg Public Schools Laureen
Cipolla, Leominster Public Schools Andrew Chen,
EduTron
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Massachusetts MSP

• Intensive Immersion Institute I3
• Claire Abrams
• Lowell Public Schools and EduTron Corp.,
  Massachusetts
• Presented at the 2008 STEM Summit V

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In my experiences, teaching and learning have
typically been done at an individual level. The
collaborative approach to both teaching and
learning that takes place in these classes has
proven to be very beneficial to all involved. I
would (and do) recommend this course as well as
any others presented by these instructors to
anyone in the education profession. LPS
Participant in the Intensive Immersion Institute!
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Who Has Taken These Courses?

• Functioning as true instructional leaders,
  thirteen Principals and Assistant Principals
  along with the Math Coordinator and Math
  Specialists have taken at least one MMSP course.
• All in all 141 educators have taken part in the
  MMSP courses in the Lowell Public Schools.

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Improvement in Classroom Practice

• more confident
• listening to students more
• dare to push students harder
• become more empathetic towards students
  learning struggle
• life-changing experience

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Main Ingredients of Intensive Immersion
Institute (I3)

• Highly Optimized Courses Based on Detailed
  Pretest Analyses
• Intensive Immersion Work on World-class
  Problems (Rich, Challenging, Multi-tiered)
• High Intensity Collegial Interaction Model
  Standards-based Instruction
• Just-in-time Compact Lectures on Demand
• Depth Active Learning

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Assessments

• WIDE SPECTRUM OF PARTICIPANTS BACKGROUND
• OPEN RESPONSE
• DETAILED DIAGNOSTICS
• Example Monitors 72 Knowledge Atoms with 17
  Problems

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Sample Problem

• Problem 2. The vertices of a triangle are
  A(-5, 5), B(4, 4) and C(-6, -4).
• Find the slope of each side of the triangle.
• Is the triangle a right triangle?
• Find the area of the triangle.
• Show (prove) that the three perpendicular
  bisectors of this triangle meet at a common
  point.

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Pre and Post Test Results
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Pre and Post Test Results
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IMPROVEMENTS IN STUDENT PERFORMANCE
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Formation of Professional Learning Communities

• In addition to the measurable content gains, the
  chemistry, dynamics, and positive peer pressure
  fostered in the intensive immersion experience
  has triggered certain qualitative changes in
  individual teachers to such an extent that some
  of them have become catalysts to transform their
  local math community into a learning machine.
  These transformations are playing a pivotal role
  in sustaining peer-based learning beyond the
  project span.
• We are much further along as a community of
  learners and teachers due to the MMSP project!
•   -- MS Mathematics Specialist,
  Lowell Public Schools

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Teachers are saying

• Your classes are engaging and fun, and I try to
  bring that same attitude into my own classes.
  There is value in seeing multiple approaches to
  the same problem, so I try to let the students
  explain to each other. I can let this happen
  because I am not struggling with my own
  understanding.

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• I would describe this Institute as an opportunity
  to acquire a deeper understanding of the
  mathematical concepts and accompanying procedures
  that we are expected to teach. Regardless of your
  mathematical knowledge or ability, the content of
  the course will be sufficiently challenging.
• The problem sets are well developed, requiring
  problem solving skills as well as mathematical
  skills to complete. In addition to this, and
  almost as important, the opportunity to genuinely
  learn with and from our colleagues, as well as
  discuss issues concerning mathematics education,
  is not something that most of us have been
  accustomed to doing.

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• The quality of instruction is fantastic. The
  pedagogical strategies used in these classes
  allow participants of all levels of mathematical
  understanding and skill to be able to access the
  content and build their own knowledge from where
  it currently is.
• The classes are designed in a manner that is
  truly a model for differentiating instruction.
  Problems are designed to be accessible to all at
  some level, yet challenging enough for everyone
  to achieve some level of mathematical struggle or
  confusion to promote their own learning, as well
  as acquire a better understanding of what their
  own students are going through when attempting to
  learn mathematics, or any content for that matter.

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Intensive Immersion Institute
Katherine Foulser, Chelsea Public Schools Donna
Chevaire, Lawrence Public Schools Linda
Simeone, North Middlesex Regional School District
Claire Abrams, Lowell Public Schools Paula
Giaquinto, Fitchburg Public Schools Laureen
Cipolla, Leominster Public Schools Andrew Chen,
EduTron
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Middle School Mathematics in Fitchburg and
Leominster - A Tale of Two Cities

• Intensive Immersion Institutes and their role in
  a comprehensive mathematics improvement
  initiative
• Laureen Cipolla, Leominster Public Schools
• Paula Giaquinto, Fitchburg Public Schools

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Intensive Immersion Institutes

• Program Components
• Two 15 hour Math Content Institutes
• One 45 hour Math Content Institutes
• 30 teacher-participants from Fitchburg,
  Leominster and Gardner
• Building-level Coaching Support
• District and Partnership level adult learning
  support

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Professional Mathematics Learning Community

• Components
• Collaborative Coaching Model
• Modified Lesson Study
• Protocols for looking at student work
• Standards-based delivery model
• Power Standards
• Formative and Benchmark Assessments
• Data Debriefings

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Intensive Immersion Institute
Katherine Foulser, Chelsea Public Schools Donna
Chevaire, Lawrence Public Schools Linda
Simeone, North Middlesex Regional School District
Claire Abrams, Lowell Public Schools Paula
Giaquinto, Fitchburg Public Schools Laureen
Cipolla, Leominster Public Schools Andrew Chen,
EduTron
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I3 Logic Model
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Evidence of Content GainsN 873

• Learn a great deal of mathematics content
• Feel smart Build up confidence
• Feel the need and urge to learn even more
• Know where students are heading
• Develop empathy for student struggles. Aspire to
  be kind, patient and compassionate
• Push/challenge students (set high expectations)

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Evidence of Pedagogy GainsN 873

• Ask probing questions as an integral part of
  teaching
• Questioning student answers is more powerful than
  answering student questions
• Constantly ask Why?
• Encourage students to struggle with unfamiliar
  mathematics and think by themselves
• Circulate and monitor student work as
  minute-by-minute ongoing assessment

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Evidence of Pedagogy GainsN 873

• Use the ongoing assessment as basis for providing
  optimized support
• Lead and empower students to realize and fix
  their own mistakes
• Use both solo work and group work formats in
  class
• Experience and appreciate multiple
  solutions/presentations of mathematics

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Evidence of Pedagogy GainsN 873

• Experience and appreciate cooperative learning
• Facilitate student discussions
• Differentiation through grouping and through
  demanding more from better students
• Use appropriate mathematical vocabulary
• Start with what students know
• Need to build positive and safe environment for
  students to struggle, take risks and learn

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• How do I start an Intensive Immersion
  Institute program?

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Characteristics of Ideal I3 Partners

• X-ray Vision
• accurate and honest self-diagnostics
• Long-term Vision
• think beyond Band-Aid and AYP
• Flexibility
• guts names on tests, weird hours, U, etc.
• Dedication
• passions to work beyond job description

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Moving Forward with I3

• STEP 1 Contact EduTron with
• X-ray - Self Diagnostics District/School
  specific problems and challenges
• Shopping List - Visions and plans on improving
  math teacher classroom performance
• YODA - Mechanism and personnel (solid in math)
  for long term local support

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Moving Forward with I3

• STEP 2 Plan
• Optimization No fixed curriculum or treatment.
  Refine customized plans. Focus.
• Funding

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Moving Forward with I3

• STEP 3 Sweat
• Intensive Immersion (work hard!)
• Differentiation (bring no ego!)
• Content Focus (integrate pedagogy organically!)
• Mid-course Corrections (use data seriously!)
• Growing YODAs (build sustainability!)

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8-Step Recipe for Success

• No Silver Bullet
• Hard Work
• Hard Work
• Hard Work
• Hard Work
• Hard Work
• Hard Work
• Hard Work

"It is a mistake to think that the practice of my
art has become easy to me. I assure you no one
has given so much care to the study of
composition as I. There is scarcely a famous
master in music whose works I have not frequently
and diligently studied." Wolfgang Amadeus
Mozart
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Intensive Immersion Institute

• Contact
• Andrew S. C. Chen 
• EduTron Corporation
• 5 Cox Road
• Winchester, MA 01890
• [phone]
• schen_at_edutron.com

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• This Space for Rent