Teaching Young Learners with the Ohio Early Mathematics Standards in Mind

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Teaching Young Learners with the Ohio Early
Mathematics Standards in Mind

• Sponsored by
• the Ohio Department of Jobs and Family Services
• in collaboration with the Ohio Department of
  Education

Module One
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Overview of Seminar

• Module 1
• What are Standards, benchmarks and indicators?
• Supporting Childrens Early Concepts of Number
• Module 2
• Early Addition and Subtraction
• Patterns and Algebraic Reasoning
• Module 3
• Geometric Reasoning through Childrens Play
• Teaching Mathematics through Activity
  Measurement Data Analysis

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Themes for the Sessions

• Play
• Inquiry projects
• Home-school connections
• Adaptations for diverse learners
• Integration across the curriculum
• The connected nature of mathematical knowledge
• Role of conversation and questioning
• 3 levels of representational thinking

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Overview of Module 1

• What are the Ohio Early Learning Content
  Standards?
• What are the benefits of using standards?
• What are some of the challenges of using
  standards?

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The Ohio Standards

• What are the Ohio early learning content
  standards?
• How do standards, benchmarks, and indicators
  relate to one another?
• How should teachers think about using them?

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Imagine

• The Teacher as gardener
• The Learner as the growing plant
• Standards as a growers guide
• Early content standards as roots
• Environment and circumstances as sun, water,
  soil, geography

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We all begin young and full of potential
Seeds and seedlings need much care. The younger
the plant, the greater the need for careful
observation and responsiveness. The child as
learner needs similar support and responsiveness.
   
   
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We need strong roots
The roots of the plant develop first and are
critical to further growth, but they also
continue their importance throughout the life of
the plant.
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an appropriate environment
The sunlight, temperature, water, proximity and
types of other plants, soil, fertilizer, and
other environmental factors influence the
development of the plant. A childs environment
influences the development of his or her math
thinking
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and a gardener who knows our unique needs.
A growers guide is a generic guide for how MOST
plants grow. It provides benchmarks in the life
of a plant, and it gives assistance to the novice
gardener. It cant predict with certainty all the
specific needs of one particular plant. A skilled
gardener adjusts directions in order to create
the best environment for her particular plant.
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There are many plants and many learners.
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Ideas to Keep In Mind

• We cant depend on a guide to provide the
  schedule of care for each day.
• Too much of a good thing can be damaging.

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Ideas to Keep In Mind (Cont.)

• What worked with one plant will not necessarily
  work with another individualization is
  important.
• Patience is important for the gardener.

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Using the Standards Wisely

• The standards are like the
• growers guide.
• Teachers make educated judgments about necessary
  conditions for math learning. Each child is
  different.
• We reap benefits when we opt not to push children
  too hard or too quickly. Teachers need patience
  and direction.

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What is an early math standard?

• Standards are what we expect students to know and
  be able to use as they progress through school.
• Standards outline the foundational content and
  processes in mathematics.

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Standards are both content and process

• Number, number sense and operations
• Measurement
• Geometry and spatial sense
• Patterns, functions and algebra
• Data analysis and probability
• Mathematical processes

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What is an indicator?

• Indicators are specific skills and understandings
  that students demonstrate across the grade levels
• These indicators let us know that the student is
  making progress toward the benchmarks

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What are benchmarks?

• Benchmarks are particular indicators that are
  grouped in developmental chunks to indicate
  where students should be by a particular grade.
• For early childhood math, the benchmark is second
  grade.

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Number, Number Sense and Operations Standards
(by grade 12)

• Students will demonstrate number sense, including
  an understanding of number systems and operations
  and how they relate to one another.
• Students compute fluently and make reasonable
  estimates using paper and pencil,
  technology-supported and mental methods.

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2nd grade benchmark for number standard

• There are 13 indicators that a student has
  reached the 2nd grade standard for number, number
  sense, and operation.
• For example recognize, classify, compare and
  order whole numbers
• Model, represent and explain subtraction as
  comparison, take-away, and part-to-whole

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Mathematical Processes Standard

• Students use mathematical processes and knowledge
  to solve problems. Students apply
  problem-solving and decision-making techniques,
  and communicate mathematical ideas.
• Problem solving, Communication, Connections,
  Representation, Reasoning and Proof

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Benchmark for process standard

• Example indicator (there are 9 all together)
• Use a variety of strategies to understand problem
  situations, e.g., discussing with peers, stating
  problem in own words, modeling problems with
  diagrams or physical materials, identifying a
  pattern.

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Achieving Balance

• Children construct their own knowledge through
  play
• Teachers provide lots of time for free play with
  math materials
• Teachers place math related materials in every
  part of the room

• With Intentional Teaching, teachers can pay
  attention to curriculum standards and benchmarks
  as they prepare environments
• Teachers plan math experiences based on the
  standards, with developmental levels and culture
  in mind.
• Teachers assess where children are and provide
  next step experiences

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Backmapping

• How do we know we are providing experiences that
  support students progress toward the benchmark?
• We backmap!!
• Backmapping is a regular routine where you look
  back at curricular experience and ask which
  indicators have we been supporting?

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BREAK TIME
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Early number Concepts

• What understandings are young learners
  developing as they are developing their concepts
  about number?
• How do you support these early competencies?

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Early number -- sorting

• Free sorting activities what are they?
• Teachers roles providing sortable materials,
  conversation/questioning
• What did you find? What kinds of groups did
  you make? How did you put them together in
  different groups? I see you sorted them into
  colors!

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Structured Sorting Activities

• In the Loop The leader (adult or child) places
  one piece in the loop. Everyone else finds pieces
  from their pile to add to the loop
• Guess my rule The leader places several pieces
  in a loop everyone else guesses what s/he is
  thinking

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As early number concepts develop further

• Classification sorting according to attributes
• Patterns
• Comparisons of sets (more than less than)
• Ordering Sets (smallest to largest)

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As early number concepts develop further (Cont.)

• Conservation - Conservation is the recognition
  that the number, length, quantity, mass, area,
  weight, and volume of objects and substances are
  not changed by transformations in their
  appearance.
• Beginning to recognize how many in a small set
  without counting

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Early Counting Concepts and Skills

• What do you see when children count?
• How is learning to count similar to learning to
  read?

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Seven Candies

• While watching the children, notice what they do
  to count the candies
• What do they show us about their understanding of
  number and counting
• Take notes about individual childrens
• Strategies
• Physical behaviors
• Knowledge and competencies
• Misunderstandings or limited experience

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Seven Candies
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Seven Candies
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Seven Candies
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Seven Candies
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Seven Candies
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Seven Candies
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Developing Early Concepts of Number

• What do you do to foster childrens early
  development of counting?

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Components of Early Number Knowledge - Counting
Principles

• Production of numbers (standard list of counting
  words)
• One-to-one correspondence (one object for each
  number)
• Ordering or seriation (small to largest)
• Cardinality principle (last number is the number
  in the set)
• Which object in the set you start with doesnt
  matter
• Conservation number stays constant even if
  objects are rearranged

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Groups of 5 counters are arranged in the
following 3 patterns. Discuss the students
knowledge of counting principles on each of the
following slides
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A conversation with Stephen

• T Are there more red, blue, or yellow
  counters?
• S More blue.
• T How do you know?
• S I can tell by looking.
• T How many of each?
• S One, two, three, four, five... five red.
  One, two, three, four, five...five blue. One,
  two, three, four, five...five yellow.
• T Five of each?
• S Yes.
• T Do you still think there are more blue?
• S Yes, I can just see there's more blue.

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A conversation with Rebecca

• T Are there more red, blue, or yellow
  counters?
• R They're the same.
• T How do you know?
• R I counted them.
• T How many of each?
• R One, two, three, four, five...Five red.
  Five blue. Five yellow.
• T Five of each?
• R Yes.

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Counting Principles Stephen

• T Here are some blocks in a row. Start with
  this one on the end and count them.
• S One, two, three, four, five, SIX. There are
  six blocks.
• T What if you start at the other end of the row
  and count them?
• S One, two, three, four, five, SIX. There are
  six.

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Counting Principles Rebecca

• T Here are some red blocks in a row. Start
  with this one on the end and count them.
• S (Touches each of the 5 blocks) One, two,
  three, five, six. Six red blocks
• T Now count these blue blocks.
• S (Touches each of the 4 blocks) One, two,
  three, five. Five blue blocks.

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Counting Principles Sally

• T Here are some blocks in a row. Start with
  the one on this end and count them.
• S One, two, three, four, five, six. There are
  six.
• T What if you start at the other end of the row
  and count them?
• S I already counted them! There are six!

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Counting Principles Brenda

• T Here are some red blocks (4) in a row. Start
  with this one on the end and count them.
• S (Points to each but says two numbers with
  each point) One, two, three, four, five, six,
  seven, eight. Eight red blocks.

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Number Standard

• Age 3
• Counts Collection of 1 to 4 items
• Begins to understand cardinality
• Group recognition for collections of 1 to 3
• Adds and subtracts non-verbally low numbers

• Age 6
• Counts and counts out collections up to 100 using
  groups of 10
• Group recognition for patterned collections of up
  to 6 items
• Adds and subtracts using counting-based
  strategies such as counting on for numbers and
  totals less than 10