Notes
I. Overview
a. Numerals
i. Number symbols are called numerals
ii. Each numeral represents an amount and acts as a shorthand for
recording how many
iii. The young child sees numerals all around
1. Has some idea of what they are before he can understand and
use them
2. Sees that there are numerals on his house, the phone, the
clock, and the car license plate, etc.
iv. Sometime between the age of two and the age of five a child learns to
name the numerals from zero to 10
1. Child is usually four or more when he begins to understand that
each numeral stands for a group of things of a certain amount
that is always the same
v. Can be confusing to the child to spend time on drills with numerals until
he has had many concrete experiences with basic math concepts
1. Most experiences with numerals should be naturalistic and
informal
II. The Number Symbol Skills
a. Six number symbol skills that young children acquire during the
preoperational period:
i. She learns to recognize and say the name of each numeral
ii. She learns to place the numerals in order: 0-1-2- 3-4-5-6-7-8-9-10
iii. She learns to associate numerals with sets: “1” goes with one thing
iv. She learns that each numeral in order stands for one more than the
numeral that comes before it
v. She learns to match each numeral to any set of the size that the
numeral stands for and to make sets that match numerals
vi. She learns to reproduce (write) numerals
b. Assessment
i. Teacher should observe whether the child shows an interest in
numerals
1. Does he repeat the names he hears on television?
2. Does he use self-correcting materials that are described in the
part of this unit on informal learning and teaching?
3. What does he do when he uses these materials?
III.
Naturalistic Activities
a. As the young child observes his environment, he sees numerals around him
b. Usually children start using the names of the number symbols before they
actually match them with the symbols
IV.
Informal Activities
a. Experimentation and practice in perception with sight and touch are most
important
b.
c.
d.
e.
i. These experiences are made available by means of activities with selfcorrecting manipulative materials
1. Self-correcting materials
a. Those the child can use by trial and error to solve a
problem without adult assistance
b. Made in such a way that it can be used with success with
very little help
2. Manipulative materials
a. Things that have parts and pieces that can be picked up
and moved by the child to solve the problem presented
by the materials
b. Teacher observes the child as she works
c. Notes whether the child works in an organized way, and
whether she sticks with the material until she has the task
finished
There are four basic types of self-correcting manipulative math materials that
can be used for informal activities
i. Can be bought, or they can be made
ii. Four basic groups of materials are those that:
1. Teach discrimination and matching
2. Teach sequence (or order)
3. Give practice in association of symbols with sets
4. Combine association of symbols and sets with sequence
Child can learn to discriminate one numeral from the other by sorting packs of
numeral cards
i. Can also learn which numerals are the same as she matches
ii. Another type of material that serves this purpose is a lotto-type game
1. Child has a large card divided equally into four or more parts
2. Must match individual numeral cards to each numeral on the big
card
3. She can also experiment with felt, plastic, magnetic, wooden,
rubber, and cardboard numerals
There are many materials that teach sequence or order
i. May be set up so that parts can only be put together in such a way that
when the child is done, she sees the numerals are in order in front of
her
ii. Sequence is also taught through the use of a number line or number
stepping-stones
The hand calculator lends itself to informal exploration of numerals
i. First, show the students how to turn the calculator on and off
ii. Tell them to watch the display window and then turn on the calculator
1. A 0 will appear
2. Explain that when they first turn on their calculators a 0 will
always appear
iii. Then tell them to turn on their calculators and tell you what they see in
the window
1. Have them practice turning their calculators on and off until you
are sure they all understand this operation
iv. Next, tell them to press 1
1. Ask them what they see in the window
2. Note if they tell you they see the same number
v. Next, have them press 2
1. A 2 will appear in the window next to the 1
2. Show them that they just need to press the C key to erase
3. Then let them explore and discover on their own
4. Help them by answering their questions and posing questions to
them such as, “What will happen if _______?”
f. Many materials can be purchased that help the child associate each numeral
with the set that goes with it
i. Large cards that can be placed on the bulletin board give a visual
association
ii. Numerals can be seen and touched on textured cards, which can be
bought
iii. Numeral cards can be made using sandpaper for the sets of dots and
for the numerals
iv. Other materials require the child to use visual and motor coordination
v. Teacher can make cards that have numerals and dots the size of
buttons or other counters
g. Materials that give the child experience with sequence and association at the
same time are also available
i. Can be seen that the basis of the materials is that the numerals are in
a fixed order, and the child adds some sort of counter that can be
placed only in the right amount
h. Teacher’s role with these materials is to show the child how they can be used
and then step back and watch
i. After the child has learned to use the materials independently, the
teacher can make comments and ask questions:
1. How many pegs are on this one?
2. Can you tell me the name of each numeral?
3. You put in the four pegs that go with that numeral 4.
4. How many beads are there here? (point to stack of one)
a. How many here? (stack of two, and so on)
5. Good, you separated all the numerals into piles
a. Here are all 1s, and here are all 2s
i. Numerals can also be introduced informally as part of daily counting activities
j. Most children will learn through this informal use of materials to:
i. Recognize and say the name of each numeral
ii. Place the numerals in order
iii. See that each numeral stands for one more than the one before it
iv. Associate numerals with amounts
V. Structured Activities
a. By the time young children finish kindergarten, they should be able to:
VI.
VII.
i. Recognize the numerals from 0 to 10
ii. Place the numerals from 0 to 10 in order
iii. Know that each numeral represents a group one larger than the
numeral before (and one less than the one that comes next)
iv. Know that each numeral represents a set of things
b. They may not always match the right numeral to the correct amount, but they
will know that there is such a relationship
i. The five-year-old child who cannot do one or more of the tasks listed
needs some structured help
c. Most of the software programs described in Unit 9 include numeral
recognition
d. Number symbols can be incorporated in other content areas
Ideas for Children with Special Needs
a. Cristina Gillanders examined the factors that enabled an English-speaking
prekindergarten teacher to successfully teach Latino English Language
Learners (ELLs)
i. First and foremost were the teacher’s efforts to develop a positive
relationship with the students
1. Teacher took the time to learn some Spanish, which gave the
Latino children social status
2. They were then accepted by the English-speaking students as
play partners
3. The teacher’s experience as a second language learner gave
her empathy for the Latino students’ struggles with learning
English
ii. Providing one-to-one attention and a consistent routine helped the
Latino children feel comfortable
1. Teacher spoke some Spanish in the classroom and included
Spanish materials in her program
2. Some of the English-speaking children became enthralled with
the bilingual songs and videotapes included in the program
iii. She also enlisted the help of the Latino children in translations
1. Spanish became valued in the classroom and supported cross
language cooperative play
b. How does this example relate to mathematics and science?
i. In any classroom ,the quality of the social/emotional climate is
important
ii. In math and science, presenting some concepts using Spanish or other
primary language vocabulary can make children feel comfortable as
their primary language and culture becomes a valued part of the
classroom culture
Evaluation
a. Teacher may question each child as she works with the self-correcting
materials
i. Should note which numerals she can name and if she names them in
sequence
ii. May interview her individually using the assessment questions in this
unit and in Appendix A
© 2010 Wadsworth, Cengage Learning.