Transcript Math for Pre-Kindergarten

Math for Pre-Kindergarten
T/TAC at VCU
Activity
Your concerns
Students have difficulty with:
 Recognizing the numerals 1-10
 Counting
 One-to-one correspondence
 Half and whole
 Patterns
 Writing the numbers 1-10
How can we address them?
Let’s examine…
 Assessment
 Curriculum
 Instruction
You may see…
Four year olds:
- spontaneously use math to
solve real problems
- begin to develop one-to-one
correspondence with small
groups
- estimate quantities randomly
- sort objects by classifying
Five year olds:
- count objects up to 10 with
few mistakes
- recognize more complex
patterns
- enjoy beginning games that
involve moving markers around
a board
- use relationship words
- solve multi-piece puzzles
- sequence 5 or more objects
- classify objects into sets
- count a small number of
objects and recall that number
- confuse sets within sets
(Stupiansky and Stupiansky, 1992)
To make the best
instructional decisions for
children, teachers need to
assess each child’s pattern
of development, knowledge,
attitudes, and interests.
(Copley, 2000)
What is assessment?
It’s the process of observing,
gathering evidence about a
child’s knowledge, behaviors,
and dispositions; documenting
the work that children do and
how they do it; and making
inferences from that evidence
for a variety of purposes.
(Copley 2000)
Assessment Principles of
Early Childhood Math
Benefiting children
- takes place before, during, and after
instruction
- make adjustments to curriculum and
instruction
- identify the strengths and needs of
children
Observing and Listening
- observe children’s actions, behavior,
and interactions with others
- develop good questioning skills
- use the information to plan instruction
Use Multiple Sources of Evidence
- samples of children’s work
- anecdotal records
- audiotaped descriptions of problem
solving discussions
Assessing learning and development
- teachers assessing their own growth
- assessing children’s growth in math
understanding
(Copley, 2000)
We should not rely on a single
whole group assessment to measure
student’s mathematical
competence.
 Teachers must try not to allow
assessment to narrow curriculum
and inappropriately label children.
 The assessment process should
help build mathematical
competence and confidence. It
should be continuous, wellimplemented, and well-conceived.

(NAEYC, 2002)
Activity

With a partner

Read the enclosed scenario

Highlight the different principles
of assessment

Think of a time in your classroom
when you have had a similar
assessment experience with your
whole group
In your classroom

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What are the different ways you
assess and document your
children’s knowledge of concepts?
At what times and during what
activities do you assess and
document?
Documentation of Students’
Progress
Portfolios
 Individual and group products
 Observations
 Child self-reflections
 Narratives of learning experiences

(Helm & Gronlund, 2000)
Activity
Read about Rachel and Tiffany.
 What
do you know about Rachel?
 What
do you know about Tiffany?
NCTM Recommendations for
Mathematics Education for
3-6 Year Olds
Enhance children’s interest in
mathematics and their dispositions
to use it to make sense of their
physical and social worlds
 Build on children’s experience and
knowledge, including their family,
linguistic, cultural, and community
backgrounds; their individual
approaches to learning; and their
informal knowledge

Base mathematics curriculum and
teaching practices on knowledge of
young children’s cognitive,
linguistic, physical, and socialemotional development
 Use curriculum and teaching
practices that strengthen
children’s problem-solving and
reasoning processes as well as
representing, communicating, and
connecting mathematical ideas

Ensure that the curriculum is
coherent and compatible with
known relationships and sequences
of important mathematical ideas
 Provide for children’s deep and
sustained interaction with key
mathematical ideas
 Integrate mathematics with other
activities and other activities with
mathematics
 Provide ample time, materials, and
teacher support for children to
engage in play

Actively introduce mathematical
concepts, methods, and language
through a range of appropriate
experiences and teaching
strategies
 Support children’s learning by
thoughtfully and continually
assessing all children’s
mathematical knowledge, skills, and
strategies

Implications for your classroom
1.
2.
3.
4.
Examine your curriculum.
Whole group or individual
instruction?
Plan the environment and
activities to meet the needs of
the student(s).
Interact with the student(s) and
assist with the development of
mathematical language.
Examine your curriculum

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Are you integrating, i.e. thematic
units or the Project Approach, so
the skill can be in many areas of the
curriculum?
Have I specifically focused on this
concept/skill in my interactions with
the students?
Do I need to revisit this
concept/skill with the class?
Is it a developmentally appropriate
time to be doing this concept/skill?
Whole Group or Individual
Instruction
Who has not mastered this
concept/skill?
 Do I need to work with all of the
children, some of the children, or
one child?

Plan the Environment and
Activities
Do I have a math rich
environment?
 Do I have manipulatives available
to the children?
 Does my schedule provide time for
the students to interact with
others and to apply the
concepts/skills?
 Are the experiences meaningful,
active, naturalistic, and
developmentally appropriate?

Interactions with Students

Plan experiences when you can
guide a student’s understanding of
a concept through your use of
specific vocabulary and questioning
techniques.
Activity
How would you assist Rachel with
her mathematical understanding of
one-to-one correspondence and
seriation?
A Plan for Planning
It assists you with making decisions
for your students.
1. How will they demonstrate the
concept or skill in the classroom?
2. How can you set up my
environment?
3. What learning experiences will
we have?
One-to-one correspondence
and counting
SOL K.1:
“The student, given a set
containing 10 or fewer concrete
items, will identify and describe
one set as having more, fewer, or
the same number of members as
the other set, using the concept
of one-to-one correspondence.”
One-to-one correspondence
and counting
SOL K.2:
“The student, given a set
containing 10 or fewer concrete
items, will
a) tell how many are in the set by
counting the number of items
orally;
b) select the corresponding
numeral from a given set; and
c) write the numeral to tell how
many are in the set.”
One-to-one correspondence
and counting
Children often recite numbers as
they touch items to count them
without the awareness that each
item corresponds with one word in
the counting sequence.
 Children need to construct the
mental structure of number and to
assimilate the words into this
structure.

(Kamii, 1982)
One-to-one correspondence
and counting
Proportion of children who counted nine
objects correctly (Meljac, 1979):
Age
Proportion
4
4
5
5
6
6
6
7
years
years, 6 months
years
years, 6 months
years (K)
years (1st grade)
years, 6 months
years
0%
40
54
60
100
90
100
100
Developmental progression through
these abilities:
1. The ability to say the words in
the correct sequence.
2. The ability to count objects
(i.e. make a one-to-one
correspondence between the words
and the objects).
3. The choice of counting is the
most desirable tool.
(Kamii, 1982)
Implications for the classroom
Ask children to make sets, instead
of make a judgment about sets
 Provide opportunities to explore
with number concepts
 Encourage children to exchange
ideas with each other
 Observe the child’s behavior to
ascertain what he/she is thinking

(Kamii, 1982)
Patterns and Classification
SOL K.17:
“The student will sort and classify
objects according to similar attributes
(size, shape, and color).”
SOL K.18:
“The student will identify, describe, and
extend a repeating relationship (pattern)
found in common objects, sounds, and
movements.”
Patterns and Classification
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Identify the stage of development for
the child.
Most young children can classify
objects. It’s the vocabulary that they
may be missing. The lack of vocabulary
may be mistaken for lack of knowledge
or ability to classify. (Kriova &
Bhargava, 2002)
Exploring attributes, sorting, matching,
working with differences and gradual
variations, and creating patterns and
order assist young children to organize
and make sense of their world.
(Hohmann & Weikhart, 2002)
Implications for the classroom
Opportunities will arise through
play to support the development of
these concepts.
 Have a variety of materials
available to students.
 Provide many different learning
experiences for large group, small
group, and individual learning.
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In summary…
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Assessment is the first step.
Curriculum and instruction decisions
are made from on-going
assessments.
It’s a continuous process.
Additional Resources
Websites
 NCTM standards for PreK-2
 SOL Curriculum Framework
 Literature
 Software
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For additional information please visit our
website at: http://www.vcu.edu/ttac or
participate in our online community at
http://ttacoline.org