DEVELOPING EARLY

NUMBERS

Prof Madya Dr. Noor Shah SaadFakulti Pendidikan & Pembangunan Manusia

INTRODUCTION Children are aware of number names long before they begin to count

• How old are you? “Two”• On what floor is your house? “Four”• How many sisters do you have? “one”• What cannel should we watch? “Nine”

Such early experiences introduce number names as well as symbols – for example, “9” on the channel indicator or “4” on the elevator

Helping children develop number concepts and counting skills has a high instructional priority.

PRENUMBER CONCEPTS

Numbers are everywhere, and thus children get a vast amount of early number experiences.

Need to help children to organize their prenumber development

Many different steps are involved in developing these prenumber concepts that will lead eventually to meaningful counting skills.

CLASSIFICATION

• In learning to count, children aware of number as a characteristic of different things. They must first know what to count.

• The ability to separate and distinguish one thing from another (such as books, toys, people, etc ) is essential to number development – This is classfication in action.

• Experience in classifying toys or any materials that interest children will be valuable in stimulating children’s observational skills.

• At this point, there may be no counting as materials are classified, yet words such as more, few, many, most, none will likely be used in describing the resulting collection. (Figure 1 )

• Classification allow us to reach general agreement on what is to counted.

• Look at figure 1, and consider the question: How many pieces of fruit are shown?

The answer is a number that tells how many

When a number is used in this way, it is called a cardinal number.

• Before finding the specific cardinal number

Must classify which are fruits or other objects and distinguish from the figure 1

This means, we must classify the fruits or object and distinguish it from other things in figure 1.

• Classification provides opportunities for children to sort objects to:

What belongs to what The object has been classified

ATTRIBUTE BLOCKS

Sometimes called “Logic Block”, provide an excellent model for classification activities. These blocks may differ in color, shape, and size.

Example: attributes for a set of 24 blocks may be as follow:

Color : red, black, green, yellow

Shape : triangle, square, pentagon

Size : small, large

• Children at all grades can benefit from some structured activities with these materials.

COMPARISON

• Comparison of quantities is the next important step toward counting and also is essential in developing number awareness.

• Comparison are plentiful in classrooms as children use materials.

• Teacher-led activities occur frequently and provide opportunities for questions such as:

Does everyone have a piece of paper? Are there more pencils or desks?

• These questions either directly or indirectly involve comparison, which may lead to the very important and powerful mathematics notion of one-to-one correspondence.

Example: Look at figure 2 and consider these question,

“Are there more heart or cookies?

i. Counting would provide a solution, particularly with cookies scattered on a plate.

ii. If cookies are arranged in an orderly fashion, we can make direct comparisons and answer the question without counting

• When making comparison: Students must be able to

discriminate between important and irrelevant attributes.

• Several different but equally valid verbal descriptions may be given for this situation:

Example:

Salim has more leaves than Aminah

Aminah has fewer leaves than Salim

• Children need to be familiar with descriptions of relationships such as:

“more than” “less than” “as many as”

• A grasp of these terms is followed by more explicit characterization.

Example:

Salim has one more leaf than Aminah Aminah has one less leaf than Salim

• In this cases the notion of order and succession are being developed.

• Children must come to realize that four is the number between five and three as well as one more than three and one less than five.

• Such relationships can evolve naturally as comparisons are made and discussed

• When comparisons are made among several different things, ordering is involved.

• For example:

children can physically compare their names with others

o Who has the longest name?o Who has the shortest name?o Can you find someone with a name the same

length as yours?

o Can you find someone with one more (less) letter than your name?

GROUP RECOGNITION

• Prior to counting, children are aware of small numbers of things: one nose, two hands, four tires etc.

• Research shows that most children entering school can identify quantities of three things or by inspection alone without the use of counting techniques.

• One instructional goal for first grade is to develop immediate recognition of groups up to five or six.

• Sight recognition of quantities up to five or six is important for several reasons:

i. It saves time. Recognition of the number in a small group is much faster than

counting each individual member of that group.

ii. It is more accurate. Children often mess up counting small groups, even when their counting skills are well developed.

iii. It is the forerunner of some powerful number ideas. Children naming small groups give evidence of knowing early order relations:

e.g.:

three is more than two and one is less than four.Some may also realize that three actually contains a group of two and a group of one.

iv. It help develop more sophisticated counting skills. Children who recognize the number in a small group will more quickly begin counting from that point.

v. It accelerates the development of addition and subtraction.

COUNTING• Children may count apples, blocks, cards, rocks, stones, even petals of flower.

• You should try counting the petals on the flowers. They provide a very interesting setting for practicing counting, and they remind us that numbers are everywhere in nature.

• What is counting?- Process by which children call number values by name.

COUNTING PRINCIPLE

• How do children count?

• Let’s look at actual counting situation. Suppose seven blocks are to be counted.

• A child who is what we will call a ‘rational counter’ might say each number name as the blocks are counted. The last number named ‘seven’ would report the total.

one two three four five six

seven

i. Each object to be counted must be assigned one nd only one number name.

ii. The number-name list must used in a fixed order every time a group of objects is counted. The child started with one and counted two, three, …, seven, in a specific order.

iii. The order in which the objects ate counted doesn’t matter. The child can start with any block and count them in any order.

iv. The last number name used gives the number of the objects.

COUNTING STAGES

• Several different stages of counting that children typically demonstrate during the primary grades.

ROTE COUNTING

• The number names and proper sequence are known up to a limit of ten or so, which is an important prerequisite for all counting.

• Thus, a rote counter may say, “one, two, three, four, … “

• The rate of saying the number names is not coordinated with the objects being counted.

POINT COUNTING

• A correct number name is given as each object is pointed to in succession.

• A point counter will say the number-name string beginning with one and point to a different objects as each number name is spoken.

• Although the one-to-one correspondence principle is well established, it is possible for a child to be able to point- count and still not know how many objects ave been counted.

RATIONAL COUNTING

• Rational counting includes being able to answer the question about the number of objects being counted.

• Rational counting is an important skills for every primary grade child.

• Once mastery of rational counting to 10 or 20 has been reached, more efficient and sophisticated counting strategies should be encouraged, such as:

COUNTING ON

• Here correct number names are given as counting proceeds, but the starting point is flexible.

• Children can start at any number and being counting.

• Counting on is also an essential strategy in developing a addition.

SKIP COUNTING

• Correct names are given, BUT instead of counting by ones, the child counts by twos, fives, tens, or other values.

• The starting point and direction are optional.

• To provide many patterns, skip counting provides valuable readiness for multiplication and division.