Math for Pre-Kindergarten

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Math for Pre-Kindergarten
T/TAC at VCU
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Activity
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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

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How can we address them?
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Lets examine

• Assessment
• Curriculum
• Instruction

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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

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• 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

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• - 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)

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• To make the best instructional decisions for
  children, teachers need to assess each childs
  pattern of development, knowledge, attitudes, and
  interests. (Copley, 2000)

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What is assessment?

• Its the process of observing, gathering
  evidence about a childs 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)

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Assessment Principles of Early Childhood Math
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• 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 childrens actions, behavior, and
  interactions with others
• - develop good questioning skills
• - use the information to plan instruction

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• Use Multiple Sources of Evidence
• - samples of childrens work
• - anecdotal records
• - audiotaped descriptions of problem solving
  discussions
• Assessing learning and development
• - teachers assessing their own growth
• - assessing childrens growth in math
  understanding
• (Copley, 2000)

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• We should not rely on a single whole group
  assessment to measure students 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, well-implemented, and
  well-conceived.
• (NAEYC, 2002)

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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

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In your classroom

• What are the different ways you assess and
  document your childrens knowledge of concepts?
• At what times and during what activities do you
  assess and document?

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Documentation of Students Progress

• Portfolios
• Individual and group products
• Observations
• Child self-reflections
• Narratives of learning experiences
• (Helm Gronlund, 2000)

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Activity

• Read about Rachel and Tiffany.
• What do you know about Rachel?
• What do you know about Tiffany?

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NCTM Recommendations for Mathematics Education
for 3-6 Year Olds

• Enhance childrens interest in mathematics and
  their dispositions to use it to make sense of
  their physical and social worlds
• Build on childrens experience and knowledge,
  including their family, linguistic, cultural, and
  community backgrounds their individual
  approaches to learning and their informal
  knowledge

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• Base mathematics curriculum and teaching
  practices on knowledge of young childrens
  cognitive, linguistic, physical, and
  social-emotional development
• Use curriculum and teaching practices that
  strengthen childrens problem-solving and
  reasoning processes as well as representing,
  communicating, and connecting mathematical ideas

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• Ensure that the curriculum is coherent and
  compatible with known relationships and sequences
  of important mathematical ideas
• Provide for childrens 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

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• Actively introduce mathematical concepts,
  methods, and language through a range of
  appropriate experiences and teaching strategies
• Support childrens learning by thoughtfully and
  continually assessing all childrens mathematical
  knowledge, skills, and strategies

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Implications for your classroom

1. Examine your curriculum.
2. Whole group or individual instruction?
3. Plan the environment and activities to meet the
   needs of the student(s).
4. Interact with the student(s) and assist with the
   development of mathematical language.

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Examine your curriculum

• 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?

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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?

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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?

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Interactions with Students

• Plan experiences when you can guide a students
  understanding of a concept through your use of
  specific vocabulary and questioning techniques.

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Activity

• How would you assist Rachel with her
  mathematical understanding of one-to-one
  correspondence and seriation?

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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?

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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.

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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.

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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)

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One-to-one correspondence and counting

• Proportion of children who counted nine objects
  correctly (Meljac, 1979)

Age Proportion
4 years 4 years, 6 months 5 years 5 years, 6 months 6 years (K) 6 years (1st grade) 6 years, 6 months 7 years 0 40 54 60 100 90 100 100
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• 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)

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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 childs behavior to ascertain what
  he/she is thinking
• (Kamii, 1982)

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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.

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Patterns and Classification

• Identify the stage of development for the child.
• Most young children can classify objects. Its
  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)

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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

• Assessment is the first step.
• Curriculum and instruction decisions are made
  from on-going assessments.
• Its a continuous process.

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Additional Resources

• Websites
• NCTM standards for PreK-2
• SOL Curriculum Framework
• Literature
• Software

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