Just a Fraction of What We Do

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Just a Fraction of What We Do
Michele Douglass and Judy
Timmerman
TechEd 01 Ontario, CA
March 27, 2001
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A NASA funded project of the San Bernardino
County Superintendent of Schools Office

• Project Purpose
• Project STEP is a highly focused research project
  involving a small number of volunteer schools (10
  schools).
• The purpose of the project is to increase the
  numbers of students achieving at higher levels of
  math and science.
• Focused on grades 4 - grades 9/10
• Math
• Science
• National Model

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Project Design
Project Areas The project is built on the belief
that educational improvement is not a function of
a single intervention, but a system of
interventions. Project STEP is centered on the
integration of the key components that support
powerful teaching and learning Professional
Development Standards Aligned Curriculum Evaluati
on Home Access/Parent Connection Technology/Infras
tructure
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Partnerships
JPL Curriculum development together Wheres the
Math? Tour Dryden Wheres the Science? Tour
summer opportunity, gather real data TEAMS
Orange County Office of Education Satellite
video lessons Outdoor Schools Web based
activities Treks 2000
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Technology Infrastructure
Transparent NOT THE FOCUS Web based - How do
we put in glass, what we do in class? Provide
support
SBCSS Servers Video development Web
development Least Expensive Solutions
Schools Home Classrooms not labs Survey what
parents have now Network WAN, LAN Cable
Providers WEB-TV for Internet access
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Parent/Home Connection
Develop a comprehensive system linking parents
and students at home to NASA and STEP
resources. Provide a system for timely
communications between members of the STEP
community Online Community Dr. Ruth Parker
Bulletin Board Listserves and Mailing lists TOA
home connection plans Parent feedback forms
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Evaluation
Provide Project STEP progress reports to all
project stakeholders through formative assessment
and feedback loops Dr. Carla Lane Technology
Education Coalition Observation, surveys,
interviews, reports Isolate Variables What
works and what doesnt?
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Curriculum Design
Develop/disseminate a standards aligned
curriculum, based on NASA resources related to
real-world problems STEP Website Standards
alignment National, State, Local Gatekeeper
concepts SAT 9-like Embedded Assessments Video,
Audio, Images and Animations
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Professional Development

• Just In Time
• Teacher Notes
• Web based
• Online learning - content and pedagogy
• Reciprocal teaching, cooperative learning,
  reflect and write
• Communication -
• Bulletin boards
• STEP Teacher Network
• STEP TOA Network
• Concept Institutes
• Gather best practices and intervention strategies

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The Concept Institute A Professional Development
Model How it came to be...
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Concept Institute on Fractions

• Strengthen students and teachers conceptual
  understanding of fractions
• Develop specific standards based interventions
• Gather best practices

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Hear, See, Do

• This piece of todays session will be conducted
  without spoken words.
• Please direct your attention to the screen for a
  brief overview of the philosophy and concepts
  that support our work, and also your journey as a
  critical friend to students.
• Feel free to read silently (or softly) to
  yourself, to a friend, or with a friend.

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What is the journey that brought you to where you
are now and led you to choose your particular way
of knowing and belonging to the world?
Stephanie Pace Marshall Executive Director,
Illinois Math Science Academy
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Beginners Mind
If your mind is empty, it is always ready for
anything it is open to everything. In the
beginners mind there are many possibilities in
the experts mind there are few. -
- Suzuki Roshi Zen Mind, Beginners Mind
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Division by fractions is an advanced topic in
arithmetic. Division is the most complicated of
the four operations. Fractions are often
considered the most complex numbers in
elementary school mathematics. Division by
fractions, the most complicated operation with
the most complex numbers, can be seen as a topic
at the summit of arithmetic. -Liping
Ma Knowing and Teaching Mathematics
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Reflection provides opportunities to consider
past and or current actions and thinking ...
in light of new information, feedback,
experience.
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The principle of moving from the concrete to the
abstract is extensively used in teaching the
addition of whole numbers, it is used much less
in teaching the division of fractions. The
inevitable result in that a student may be able
to use an algorithm by rote to divide fractions,
but the skill is useless because it is devoid of
meaning.
Understanding Partitive Division of
Fractions J.Ott, D. Snook, and D. Gibson
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The rate at which you learn...
will become the only sustainable competitive
advantage youll have in your life
Peter Senge quoting Arie de Geus
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We can learn something new any time we believe we
can.
---Virginia Satir
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This thing we call failure is not the falling
down it is the staying down.
Mary Pickford
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Mathematics instruction must be based on what is
known about how learning occurs. Old paradigms of
teaching and learning will not result in
mathematical power for teachers or students. We
need new paradigms that support teachers as
instructional decision makers and facilitators of
learning, that recognize children as capable
sense makers in control of constructing their new
understandings. - Ruth Parker
Mathematical Power Lessons from a Classroom
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Moral growth is not possible without the
discipline of regular personal reflection, which
is best described as a dialogue with
yourself. Anonymous
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5 percent technology95 percent psychology and
attitude

• The MISSING 95 percent is sociologypsychology
  anthropology.
• That is, the information technology - no matter
  how powerful - is merely an ENABLER. You can
  wire yourself up until you are blue in the face
  (and broke)but in the end its a people game.
• - Tom Peters, The Circle of Innovation

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Community of Learners
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the most important work we can do is to
engage one another in exploring our purpose
we need to explore why we have come
together ...Wheatley and Kellner-Rogers
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Working Agreements

• Listen
• No Turf, No Titles
• Suspend A/V/B
• Dialogue vs. Discussion
• Diversity
• Everyone Participates
• Work-in-Progress

• High Expectations, Low Attachment
• Protect, Respect, Reflect
• Co-learning and Colleagues
• Listen
• Enjoy!!!
• Do No Harm

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Concept Institute Participants reflection on the
working agreements.
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Content
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Reflection
What do you consider to be the Essential
Understandings of the concept of fractions?
Pair/Share
Find a colleague with whom to share your
thoughts, ponderings, and ideas regarding your
Essential Understanding of the concepts of
fractions.
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Standards

• Select a spokesperson for your group.
• Share why your group selected xxxx as the graphic
  representation that demonstrates the essence of
  the Standards.
• Each group will have 2 minutes to share.
• Listen and reflect.

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S T A N D A R D S
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S T A N D A R D S
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Concept Institute Participants engaged in whole
group Dialogue.
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Subject matter knowledge affects both what is
taught and how it is taught.
-Grossman
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L E A R N I N G E X P E R I E N C E S

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Learning Experiences

• You will participate in a series of learning
  experiences this afternoon.
• They are in a menu format.
• You may work on your own, with a partner, in a
  small group, or in any combination you like.
• Take your learning log with you to record your
  thinking.
• All the materials needed to complete each
  learning experience should be available. If not,
  let us know.

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Learning Experience B Picture This
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Pedagogy
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To be able to ask a question clearly is
two-thirds of the way to getting it answered.
John Ruskin
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D I S T R I B U T E D E X P E R T I S E
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The students engage with the mathematics...

• and the teacher mediates the relationship
  between the two.
• Stigler and Hiebert The Teaching Gap

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Pedagogical Content
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it is equally important to recognize that
standards and assessments, though necessary, are
not enough. What must be done now is to find ways
of providing students with the learning
opportunities they need to reach the new
standards. Stigler and Hiebert The
Teaching Gap
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Learning Experience B Picture This
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Dialogue

• Unpack the Learning Experience
• Share your learning in your group
• -What big ideas were uncovered?
• -What misconceptions might student have?
• WHIP around groups for Share Out.

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Modes of Representations

• Think of the value of 1/3
• Real-world application If you have a pizza,
  show what amount each of three people would get
  if they share equally.
• Manipulative materials Using pattern blocks,
  one blue diamond is 1/3 of a yellow hexagon since
  three blue diamonds equal one yellow hexagon.
• Pictures If you draw a rectangle and separate
  it into three equal sections, one section is
  shaded. A number line is separated into three
  equal lengths. The first length is one third of
  the whole.
• Spoken symbols Say the number one-third
• Written symbols Write the number one-third or
  1/3

Assessments should use as many of these within
each question as possible. For example, using
counters, show 2/3 times 3/4. Explain how you
would find the products.
Lesh, Landau, and Hamilton (1980) Rational number
ideas and the role of representational systems.
STEP - Concept Institute on Fractions
MLD/JST
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Misconceptions
Students were asked to compare the number of
girls to boys in the class. The class determined
there were 17 girls and 15 boys present. What
is the ratio of girls to boys? Several students
responded, seventeen to fifteen and wrote
17/15. Carmen blurted out, That cant be right.
You said that a fraction means the top divided
by the bottom. Thatll be more than the whole
class.
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Powerful Teaching and Learning
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Teachers should understand the subject in
sufficient depth to be able to represent it
appropriately and in multiple ways. They need to
understand the subject flexibly enough so that
they can interpret and appraise students ideas,
helping them to extend and formalize intuitive
understandings, and challenge incorrect
notions. -D. Ball
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Use two sets of tangrams. If Piece 3 1, what
is the value of the whole (both sets)?
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The piece from the Concept Institute on Fractions
that was most powerful for my teaching was the
knowledge that students need to struggle with
learning. - Institute Participant
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Collecting Evidence
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Learning is not the same thing as acquiring
knowledge
When you learn, your behavior changes.
Barbara Braham
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N E W S L E T T E R
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P R E and P O S T T E S T
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I N T E R V I E W S
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C O N C E P T M A P
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Our Findings
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I gained a confidence that I can do math, explain
it, and teach it!!! ---STEP
Concept Institute participant
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Institute Results
One of the largest areas of change for the CI
participants was their growth in understanding
of the conceptual basis of fractions.
Sixteen participants recorded at least one
idea relating to the whole/part construct in the
pretest, while all 19 participants identified
this construct as a major concept for fractions
in the posttest.
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Sharing with others and getting to experience the
menu activities instead of just hearing about
them was the most powerful part of the
institute. --STEP Concept
Institute participant
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Peer interactions is an ideal form for helping
learners take the leap to a higher level of
understanding. -Brown and Palincsar
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Institute Results
Participants changed their emphasis on topics
such as conventions and procedural knowledge from
the pre-test to the post-test.
Participants recorded a 21 decrease in their
concern for notation and procedures on the
post-test.
On the pre-test, 11 participants identified the
whole as The basis for understanding a
fraction. On the post-test, This number
increased to 18 participants, revealing an
Increase of 21 percent.
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The piece from the institute that was most
powerful for my teaching was to know that I now
have the knowledge to teach fractions
conceptually. --STEP Concept Institute
participant
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Institute Results
Experienced teachers were the only participants
that recorded notation as a major concept for
fractions on the pre-test. This association
dropped by 80 on the post-test.
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In just the 2 hours I was here, reassured me that
real education reform is in the hands and hearts
of teachers. . . --Terry Weatherby Mountain View
School District
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Institute Results
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Working on some of the projects with my group, I
saw how truly un-imaginative I have
become. --STEP Concept Institute
Participant
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Institute Results
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• The pre/post test examined computational and
  procedural skills.
• Each participant was asked to simplify four
  division problems.

• Results
• 4 out of 19 participants solved at least one
  computational
• problem incorrectly on the pre-test.
• Three of these four teachers solved the problems
  correctly
• on the posttest.
• Every participant provided a procedural solution
  on the pre-test.
• On the post test, six participants demonstrated
  solutions
• conceptually.

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Attempting to restructure classrooms at many
levels includes redesigning curricula,
introducing new roles for teachers, students, and
researchers, and re-conceptualizing
assessment. --Ann Brown
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Deltaing Up
Use Sticky Notes
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Questions . . . Thoughts . . . Comments . .
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www.step.k12.ca.us Judy Timmerman Michele
Douglass