Supporting Early Math Learning with a Targeted Number Sense Intervention

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Supporting Early Math Learning with a Targeted
Number Sense Intervention

• Nancy Dyson
• University of Delaware

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Developing Number Sense in Children at Risk for
Mathematics Learning Disabilities funded by the
National Institute of Child Health and Human
Development (5R01HD059170),Nancy C. Jordan,
Principal Investigator2009 - 2014
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Components of Number Sense
NUMBER OPERATIONS
COUNTING SKILLS

• 11 Correspondence
• Stable order
• Cardinality

• Numbers represent sets that can be broken into
  smaller sets or combined to make larger sets
• Symbols , -,

NUMBER SENSE
QUANTITIES, NUMBERS, NUMERALS
MAGNITUDE COMPARISON

• Numbers represent quantities
• Numerals represent numbers

• Compare sets larger or smaller
• Compare numbers larger or smaller

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Number Sense Development
QUANTITY

• Very young children are sensitive to number
• 
  
  (Dehaene,1999)
• 6 month old children can distinguish between
  quantities
  (Feigenson, Dehaene, Spelke, 2004)

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Number Sense Development
QUANTITY

• SUBITIZE the ability to recognize small
  quantities without counting
• Perceptually subitize collections of 1- 4
  objects. (Gelman Tucker,1975 Starkey Cooper,
  1995)
• Conceptually subitize larger quantities based on
  arrangement of objects or quick calculation

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Number Sense Development(Griffin Case,1997)
QUANTITY
4 Year Old
COUNTING

• QUANTITY

VERBAL
VISUAL
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Number Sense Development(Griffin Case,1997)
6 Year Old
CENTRAL CONCEPTUAL STRUCTURE FOR WHOLE NUMBERS
COUNTING

• QUANTITY

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Number Sense Development

• MENTAL NUMBER LIST
• As you go up the list, the quantities get larger
• Each number is one more than the number before it
  and one less than the number after it. (Baroody,
  Eiland, Thompson, 2009)

1 2 3 4 5 6 7 8 9 10
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Number Sense Development
NUMBER OPERATIONS
1 2 3 4 5 6 7 8 9 10
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Number Sense and Math Difficulties

• Subitizing has been found to be linked to early
  counting skills (Kroesbergen, Van Luit, Van
  Lieshout, Van Loosbroek, Van de Rijt, 2009)
• Subitizing may help children form principles of
  cardinality (Butterworth, 2005)
• Deficits in number relations are associated with
  mathematics learning disabilities (Rousselle
  Noël, 2007)

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Number Sense and Math Difficulties

• Kindergartners abilities to compare numbers and
  solve number combinations, in particular, are
  unique predictors of calculation fluency in
  second grade, over and above working memory,
  spatial ability, and language. (Locuniak, M. N.,
  Jordan, N. C. , 2008).
• Number combinations -- even at the very beginning
  of kindergarten are strongly predictive of math
  achievement from first through third grades.

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Number Sense Income Gap

• The average cognitive scores of entering children
  in the highest SES group are 60 above the
  average scores of the lowest SES group (Lee
  Burkham, 2002).
• Many children enter school behind in number
  skills most are children living in low income
  communities (Jordan et al,2007)
• Low-income children are often nearly two years
  below the level of their middle-income peers in
  developmental tests of number knowledge (Griffin,
  Case, Siegler, 1994)

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Number Sense Income Gap

• Data from the Early Childhood Longitudinal Study
  Kindergarten Cohort (ECLS-K)
• Gap between kindergarten children with two or
  more family risk factors and children with no
  risk factors more than doubled by the time the
  children reached third grade (Rathburn West,
  2004).

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Early Screening and Intervention

• Early screening and intervention has proved very
  successful in reading same is needed for
  mathematics
• Early screening for childrens gaps in Number
  Sense allows for identifying potential problems
  and developing effective teaching approaches.

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NUMBER SENSE SCREENER (NSS)Developed by Nancy
Jordan, Joseph Glutting, Nancy Dyson

• Research-based tool for screening early numerical
  competencies
• Kindergarten and early first grade
• Aligned with Common Core State Standards in
  Kindergarten
• Aligned with NCTM Focal Points for Kindergarten

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Number Sense Intervention Materials and Procedures
QUANTITY
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Number Sense Intervention Materials and Procedures
QUANTITY
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Number Sense Intervention Materials and Procedures
PART/WHOLE RELATIONSHIPS
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Number Sense Intervention Materials and Procedures
PART/WHOLE RELATIONSHIPS


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Number Sense Intervention Materials and Procedures
Linear Representations of Number

1 2 3 4 5 6 7 8 9 10

• NUMBER COMPARISON
• Before / After n-1 / n1 Bigger / Smaller

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Number Sense Intervention Materials and Procedures
PUTTING IT ALL TOGETHER

Sam has three pennies. Kisha gives him two more
pennies. How many pennies does Sam have now?
325
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NUMBER SENSE SCREENER
NON-VERBAL CALCULATION DOTS UNDER the BOX
MATCHING GAME

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NUMBER SENSE SCREENER


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PARTNERS
Number Sense Intervention Materials and
Procedures
EQUATIONS

1 3 4
STORY PROBLEMS
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Number Sense Intervention Materials and Procedures
PROBLEM SOLVING STRATEGIES
Finger Counting
Drawing Problems
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More Sophisticated Drawing
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Number Sense Intervention Materials and
Procedures
MAGIC NUMBER
 
 
 
 
 
 
 
 
10
7
 
 
 

 
 
 

• Count to 17 while sequencing number cards
• Number Recognition game
• Before / After game

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Number Sense Intervention Materials and Procedures

• THE GREAT RACE
• (Ramani Siegler, 2008)

START
1
1
2
-1
-2
2
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Thank you! Questions? Nancy Jordan njordan_at_udel
.edu Nancy Dyson ndyson_at_udel.edu Casey
Irwin cmw_at_udel.edu
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NUMBER SENSE SCREENER

• Standardized measure designed to be used by
  teachers, school psychologists, learning
  specialists, and other school-related personnel.
• Norms for the fall and spring of kindergarten and
  the fall of first grade
• 29 Items
• Counting Knowledge Number Recognition
  Number Comparisons
• Nonverbal Calculations Story
  Problems Number Combinations
• 15- 20 minutes

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NUMBER SENSE SCREENER

• COUNTING KNOWLEDGE
• Task 1 Here are some stars. I want you to count
  each star. Touch each star as you count.
• Task 2 Turn over paper and ask, How many stars
  were on the paper you just saw?

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NUMBER SENSE SCREENER

• NUMBER RECOGNITION
• Im going to show you some numbers. I want you
  to name the number when I show it to you.
• 4, 9, 13, 16, 28, 37, 82, 124

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NUMBER SENSE SCREENER

• NUMBER COMPARISON
• 7
• What number comes right after 7?
• What number comes two numbers after 7?

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NUMBER SENSE SCREENER

• NUMBER COMPARISON
• 4
• What number comes right before 4?
• What number comes right before 6?

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NUMBER SENSE SCREENER

• NUMBER COMPARISON
• 5 4
• Which is bigger 5 or 4?
• Which is smaller 8 or 6?
• Which number is closer to 5 6 or 2?

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NUMBER SENSE SCREENER

• NUMBER COMPARISON
• 5
• 6 2
• Which number is closer to 5 6 or 2?

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NUMBER SENSE SCREENER

• STORY PROBLEMS Addition
• Task 1 Jill has 2 pennies. Jim gives her 1 more
  penny. How many pennies does Jill have now?
• Strategy fingers, count (w/o fing), no
  observable strategy
• Task 2 Sally has 4 crayons. Stan gives her 3
  more crayons. How many crayons does Sally have
  now?
• Task 3 Jose has 3 cookies. Sarah gives him 2
  more cookies. How many cookies does Jose have
  now?

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NUMBER SENSE SCREENER

• STORY PROBLEMS Subtraction
• Task 1 Kisha has 6 pennies. Peter takes away 4
  of her pennnies. How many pennies does Kisha have
  now?
• Task 2 Paul has 5 oranges. Maria takes away 2 of
  his oranges. How many oranges does Paul have now?

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NUMBER SENSE SCREENER

• NUMBER COMBINATIONS
• How much is 2 and 1?
• How much is 3 and 2?
• How much is 4 and 3?
• How much is 2 and 4?
• (These questions are a little bit different.
  Listen carefully.)
• How much is 7 take away 3?
• How much is 6 take away 4?

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NUMBER SENSE SCREENER
STORY PROBLEMS NUMBER COMBINAION STRATEGIES

1 2 3 4 5 6 7 8 9 10

     
     
     
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NSS Case Study 1--Celine

• Celine is in a bilingual kindergarten classroom.
  Spanish is the primary language spoken by her
  parents. She came to testing with a shy and
  quiet demeanor. She worked diligently throughout
  the assessment but had trouble with individual
  items throughout the various subareas. Below is
  a summary of her scores on the subareas
• Sub-Area Totals
• Counting Total 3 /3 Nonverbal
  Calculation Total 3 /4
• Number Recognition Total 1 /4 Story
  Problems Total 0 /5
• Number Comparisons Total 4 /7 Number
  Combinations Total 6 /6

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NSS Case Study 2--Eric

• Eric arrived at testing eager to participate in
  the assessment. He informed the examiner that he
  was good at math. He easily completed the
  counting tasks and readily counted to 20 without
  error. He could name 13, 37, and 82 but missed
  124. Eric performed well on Number Comparisons
  missing only two after 7. While working
  through the Nonverbal Calculation subarea his
  only error was for 4 3 ? .
• When Eric reached the Story Problems, he was
  able to answer the first problem Jill has 2
  pennies. Jim gives her 1 more penny. How many
  pennies does Jill have now? He quickly
  responded, 3.
• Sub-Area Totals
• Counting Total 3 /3 Nonverbal
  Calculation Total 3 /4
• Number Recognition Total 3 /4
  Story Problems Total 1 /5
• Number Comparisons Total 6 /7
  Number Combinations Total 1 /6