Jennifer Kearns-Fox, Mary Lu Love & Lisa Van Thiel
Institute for Community Inclusion
University of Massachusetts Boston
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Apply understanding of how children develop
mathematical concepts to curriculum
Use rich language to expand vocabulary
Implement Houghton Mifflin Pre-K math
curriculum, differentiating instruction to
support children along a developmental
continuum
 What
math
concepts might
children be
learning in each
center?
Emphasize a vision of mathematics for young
children that:
 builds upon young children’s experiences with
mathematics,
 establishes a solid foundation for the further
study of mathematics,
 incorporates assessment as an integral part of
learning events,
 develops a strong conceptual framework that
provides anchoring for skill acquisition,
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involves children in doing mathematics,
emphasizes the development of children’s
mathematical thinking and reasoning
abilities,
includes a broad range of content, and
makes appropriate and ongoing use of
technology, including calculators and
computers.
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Problem-Solving
Connections
Reasoning
Representation
Communication
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There are 7 girls on a bus.
Each girl has 7 backpacks.
In each backpack, there are 7 big cats.
For every big cat, there are 7 little cats.
How many legs are there on the bus?
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What was your first response when you read
the question?
What problem-solving skills did you use?
How did you connect to the problem?
What reasoning skills did you use or follow?
Did you use any forms of representation to
assist you? If so, what?
Describe how communication impacted your
thinking.
Content and Process Standards
Number & Operations
•Numbers can be used to tell us how
many, describe order, and measure;
they involve numerous relations, and
can be represented in various ways.
Algebra
Patterns can be used to recognize
relationships and can be extended
to make generalizations.
Problem
Solving
Connections
•Operations with numbers can be used
to model a variety of real-world
situations and to solve problems; they
can be carried out in various ways.
Communication
Data Analysis
•Data analysis can be used to classify,
represent and use information to ask
and answer questions.
Geometry
•Geometry can be used to understand
and to represent the objects, directions,
and locations in our world and the
relationships between them.
•Geometric shapes can be described,
analyzed, transformed, and composed
and decomposed into other shapes.
Measurement
•Comparing and measuring can be used to specify
“how much” of an attribute (e.g., length) objects
possess.
•Measures can be determined by repeating
a unit or using a tool.
Reasoning
Clements and
Sarama, 2004
Line up according to your comfort with
math.
phobic
genius
What should every fouryear-old know and be
able to do?
1.
2.
3.
4.
5.
Number Sense &
Operations
Algebra
Geometry
Measurement
Data Analysis
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Count off by fives.
Work with other group members in pairs or
triads. (10 minutes)
Join small group. Select a recorder, facilitator,
and reporter. (10 minutes)
◦ Establish benchmarks for 4-year-olds in your
strand.
◦ Develop a list of potential vocabulary to expand
children’s academic language.
◦ Prepare to share with the larger group.
What should every fouryear-old know and be
able to do?
1.
2.
3.
4.
5.
Number Sense &
Operations
Algebra
Geometry
Measurement
Data Analysis
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Assess
Choose learning outcome
Plan experience for learning
Select materials and resources
Facilitate learning experience
Assess what learners have learned
(Brewer and Kallick, 1997)
Robert Pianta
Bridget Hamre
Karen LaParo
Result of using 3-second pause:
 For children:
◦ Larger number of correct answers
◦ Longer answers
◦ Fewer “I don’t know” answers
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For adults:
◦ Ask more varied questions
◦ Ask additional questions for more complex
processing
(Stahl, 1994)
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Provide opportunities for informal
reflection to express reasoning
Facilitate problems during center time
(versus being the answer giver)
Connect knowledge to prior knowledge
Connect tasks/routines to mathematics
Ask questions to promote problem
solving, prediction, reflection
Use and encourage use of math terms
Knowledge
Comprehension
and
Application
Higher Level
Thinking:
Analysis,
Synthesis,
Evaluation
Popham (2002)
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Focuses on
knowledge level:
◦ Fails to capture
creativeness
◦ Classroom is
humdrum
◦ Teaching becomes
mundane
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Focuses on higher–
order thinking:
◦ Classroom is more
interesting
◦ Children show more
enthusiasm for
learning
◦ Children discover
knowledge and
concepts
The more we relinquish the role of
problem solver, the more children
will assume it. (Carol Gross)
Teacher as
Problem
Solver
Child as Problem
Solver
Understand
the
problem
Devise a
plan
Carry out
the plan
Answer the
question
Evaluate
the answer
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Language should describe children’s
thinking, as best you understand it
Suggest possible solution – tentatively
(What if…?; Have you thought about…?)
Encourage multiple ways to get to answer
Reflect on the process of problem solving
As children engage in problem solving,
teacher is thinking about:
1. Where is the child now?
2. What is the next logical step for the child
to learn?
3. What should the child do to accomplish
this
objective?
4. What materials should be used?
5. Do the plan and materials fit the
expectation as indicated by the objective?
6. Has the child learned?
Multiple Means
of
Representation
Multiple
Means of
Expression
Multiple
Means of
Engagement
 Differentiated
instruction is a
teaching theory based on the
premise that instructional
approaches should vary and be
adapted in relation to individual
and diverse students in
classrooms (Tomlinson, 2001).
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Watch the video.
What process and
content standards are
being taught?
What strategies are being
used to teach the
concepts?
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Watch the video.
What process and content standards are
being taught?
What strategies are being used to teach the
concepts?
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Individually read the vignette.
In small groups, discuss:
◦ What does the teacher say/do to support
students’ learning?
◦ How does she respond differently to different
students, and why?
◦ What else might you do to extend learning?
Children’s literature creates a natural context
for talking about mathematics (see Hellwig, Monroe, and
Jacob, 2000; Moyer, 2000)
◦ To launch conversation around the mathematical
story line
◦ To make meaning
◦ To Illustrate use of process standards
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Model and demonstrate
Ask thought-provoking questions
◦ How do you know?
◦ Tell me about your thinking.
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Facilitate support and enhance
exploration
◦ Open-ended and focused questions
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Engage students in higher-order thinking
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Predictions
Classification and comparison
Evaluation
Opportunities to explain their thinking and
reasoning to others
Provide opportunities for children to plan,
anticipate, reflect on, and revisit their own
learning experience
Students feel secure and comfortable enough to:
 Share beliefs
 Ask questions
 Hypothesize
 Express ideas
 Make mistakes
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Questions - no incorrect answers
Allow time before sharing with classmates
Discuss ideas with a partner before sharing with
entire group
Social learning is learning, not “cheating”!
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Does anyone want to add anything to the
list?
Tell me about your thinking.
What is one take-away you have from this
morning’s session?
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Integrated approach to
aligning OWL and HM
Pre-K Math
Room 2039
Teachers
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Preview Pre-K Math
activities and
extensions; develop
HOT language
Room Tigers Den
Annex
Instructional Partners
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If you had a budget of
$50.00, how would you
engage families in
literacy?
Describe the purpose
and goals of your family
literacy event.
How would you measure
success?
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What is one thought
you will take away
from today’s
session?
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Reflect on today’s professional development.
Establish a goal for yourself.
What are one or two ideas you will take away
from today’s session?
Design an action plan for yourself.
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What is your goal?
What supports will you need?
How will you use your coach as a resource?
What changes do you expect your coach to observe
in the classroom?