Transcript numerical operations - State of New Jersey

Understanding Numerical
Operations in Preschool
Developed by
Carmen Davis, Hoa Ly, Ryan Ratajski & Johari Sykes
Camden City School District
Standard 4.2 Children demonstrate an initial
understanding of numerical operations.
Match The Cards
• Select a piece of paper from the
bag provided on your table.
• Try to find a member of the
group with the matching half
of the phrase.
• After matching the phrase, take
this opportunity to talk to your
partner about some things you
know about numerical operations.
Today’s Objectives
 To define numerical operations, giving teachers a deeper
understanding of what the math content means.
 To describe how this standard translates into practice during small
group times, large group times, and as a choice embedded in
classroom centers.
 To highlight math practices that can be used while teaching about
numerical operations.
 To accentuate that the quality of the teacher-child interactions is
key to enhancing children’s outcomes as they develop an initial
understanding of numerical operations.
2004: Math Expectation 1
Children demonstrate an understanding of
number and numerical operations
Preschool Teaching Practices
• Make materials and books that promote number exploration
accessible to the children.
• Encourage children to compare numbers frequently through
questions and graphing.
• Integrate purposeful counting experiences throughout other
learning opportunities.
• Encourage and support individual attempts to learn to count
numbers. Encourage counting to 30+.
2004: Math Expectation 1
Children demonstrate an understanding of
number and numerical operations
Preschool Teaching Practices (cont’d.)
• Provide children opportunities to use estimation skills during
daily activities by asking interesting and relevant questions.
• Model addition for children by using counting to combine
numbers.
• Model subtraction for children by using counting to separate
numbers.
• Foster one-to-one correspondence throughout the day.
2004: Math Expectation 1
Children demonstrate an understanding of
number and numerical operations
Preschool Learning Outcomes
1.1 Demonstrates understanding of one-to-one correspondence.
1.2 Spontaneously counts for own purposes.
1.3 Learns to say the counting numbers.
1.4 Discriminates numbers from other symbols in the
environment.
1.5 Recognizes and names some written numerals.
2004: Math Expectation 1
Children demonstrate an understanding of
number and numerical operations
Preschool Learning Outcomes (cont’d.)
1.6 Compares numbers in different.
1.7 Uses estimation as a method for approximating an appropriate
amount.
1.8 Adds two groups of concrete objects by counting the total.
1.9 Subtracts one group of concrete objects from another by taking
some away and then counting the remainder.
What does “numerical operations” mean for
our preschoolers?
Numerical Operations
Preschool Learning Outcomes
4.2.1
Represent addition and subtraction by manipulating up to 5 objects:
(a) putting together and adding to (e.g., “3 blue pegs, 2
yellow pegs, 5 pegs altogether.”); and
(b) taking apart and taking from (“I have four carrot sticks. I’m
eating one. Now I have 3.”).
4.2.2
Begin to represent simple word problem data in pictures and
drawings.
Number Sense + Numerical Operations
= Number & Operations
• Counting (1, 2, 3…one-to-one correspondence)
• Quality (sense of number; three fingers = 3; subitizing)
• Order (sequence – first, second, third…)
• Numerals (seeing numbers and what they represent)
Number Sense + Numerical Operations
= Number & Operations (cont.)
• Comparisons (more/less; more/fewer)
• Combining operations (adding)
• Separating operations (subtracting)
• Sharing operations (dividing)
• Set-Making operations (multiplying)
Numerical Operations
Preschool Learning Outcomes
4.2.1
Represent addition and subtraction by manipulating up to 5 objects:
(a)putting together and adding to (e.g., “3 blue pegs, 2 yellow
pegs, 5 pegs altogether.”); and
(b)taking apart and taking from (“I have four carrot sticks. I’m
eating one. Now I have 3.”).
4.2.2
Begin to represent simple word problem data in pictures and drawings.
Numerical Operations
What Preschoolers Can and Cannot Do
 Preschoolers typically:
 Believe that two sets of objects have
the same number if the objects are
close to one another.
 Solve subtraction problems before
they can solve addition problems.
 Think about small numbers
without having the physical
objects.
 Preschoolers typically do not:
 Understand mathematical words in
abstract thinking without the use of
real objects present.
 Connect the idea on large quantity
schema.
 Easily keep track of what they have
counted or not counted.
Teaching Practices and Classroom
Environments that Make the Difference
Preschool teachers will:
 Model addition for children by using counting to combine numbers (e.g.,
“Maria has two blocks and Justin has three. There are five blocks altogether:
1, 2, 3, 4, 5.”).
C: I hit all them pins down, but I
can pick them back up.
T: How many green stripes do you
have?
C: (counts) 1, 2.
T: How many yellow stripes do you
have?
C: (counts) 1, 2, and one glitter one,
too.
T: Good. So how many do you have
in total? That means altogether.
C: (counts) 1, 2, 3, 4, 5. I got five
stipers!
T: Why would you do that?
C: Because if I pick one up, then
it’s one and then if I pick up
this one, it’s two of them.
(counts) 1, 2, 3, 4, 5, 6, 7, 8. It’s
eight of them still down.
T: This is a number sentence. How
many children are here?
C: (counts) 1, 2, 3. 3.
T: Plus how many children?
C: One.
T: Equals…
C: (counts) 1, 2, 3, 4. Four kids. It’s
four.
T: Can you find that card in your
hand?
C: Yes. (selects the number 5 card
and holds it up)
Video #1
Scaffolding Activity
 What did you see and hear in this clip? Use the checklist to guide a discussion
at your table.
 How does this teacher’s activity support Standard 4.2.1:
Represent addition and subtraction by manipulating up to 5 objects?
 Then, as a group, use the 5 objects in the brown bag to modify the activity seen
in the clip or to develop a new activity. Think about children in the group who
might be at earlier stages of understanding and/or children with more
advanced thinking.
 To debrief, we’ll have one person from each group sum up the group’s
discussion and another person from each group describe the activity developed
by the group.
Materials to Use
Play people
Collections of natural objects
Linking cubes
Counting bears
Preschool teachers will:
Develop addition and subtraction stories with small groups of children
using story mats and flannel board scenes with small quantities of objects
and pictures/drawings.
Preschool teachers will:
Use fingers, chalk, wipe-off markers and/or whiteboard technology to tell
and draw addition and subtraction stories with small groups of children.
Preschool teachers will:
Provide writing materials and/or handheld devices with appropriate
applications in classroom centers so that children can choose to view, solve,
and create addition and subtraction stories.
Figure 1
Figure 2
Let’s try it!
 Represent this math problem
 With pictures
 With objects
 By acting it out
Video #2
Assessing Your Current Practice
From Preschool to Kindergarten
 Do you know what the Common Core asks of children in
kindergarten?
New Jersey Preschool Teaching and Learning Mathematics Standards Aligned to
the Common Core Mathematics Standards for Kindergarten – DRAFT
Making It Happen
References
 The Creative Curriculum for Preschool -Volume 4
Mathematics by Juanita V. Copley, Candy Jones, and Judith
Dighe
 The Young Child and Mathematics by Juanita V. Copley
Resources for Further Use
 http://www.naeyc.org/positionstatements/mathematics
NAEYC/NCTM position statement on Early Childhood
Mathematics: Promoting Good Beginnings
 Teaching and Learning Math: The Learning Trajectories
Approach by Douglas H. Clements and Julie A. Sarama
 http://www.youtube.com/watch?v=wV85P07K1mU
The Building Blocks of Math: Lessons from Research, featuring Dr.
Doug Clements