Hi everybody..
We meet again in the second entry..
In the previous entry we learned about how the young children learn mathematics looking at the beginning process illustrated by Iron (1999). In this entry, I will focus on how the children learn numbers looking at the substising, counting and number word sequences.
Before, we go further, do you know that in the early number sense, children actually developing the concept of number through the beginning process? For example, teacher can introduce the early children to the number concept through sorting, comparing, ordering and patterning.
Example: Sorting
1) Ask the students to group the buttons according to the same colour (attribute)
2) Ask the students to give the number of the button for each of the colours.
In the early number sense, the teacher must create activities that develop numeral skills in recognizing, identifying and writing. Recognizing-teacher selects a named numeral from a randomly arranged group of displayed numbers; identifying - students are to state the name of the displayed number; writing - students practice writing the numeral, focusing on numeral shape. This process helps the children in matching the symbols to the name and to the quantity.
Thus, in the teaching model, learning must be consisted of the concrete object, symbol and language.
According to Doverborg, Elisabet and Samuelson (2000) as stated in Gelman and Gellistel (1978), there are five principles that can help the early number sense children to develop counting skills.
One-to-one principle
When counting, only one number word is assigned to each object. On the other word, children must be able to match and pair objects according to the same quantity.
Stable-order-principle
When counting, number words are always assigned in the same order. An example of this would be understanding that after 7 comes 8 then 9 and 10 (Doverborg, Elisabet and Samuelsson, 2000, p. 85).
Cardinal principle
The possession of the skill of knowing that the last listed number is in fact the number of objects present in the counted quantity (Doverborg, Elisabet and Samuelsson, 2000, p. 85). Example is shown below.
Q What is the last listed number?
A 9.
Q How many objects are there?
A 9(this is an example of cardinal principle being acquired).
Abstraction Principle
A concept of all appropriate objects of a well-defined capacity being counted irrespective of the kind of objects present (Doverborg, Elisabet and Samuelsson, 2000, p. 85).Example, a rectangular prism and a cylinder both being counted regardless of their differing shapes.
Order-irrelevance principle
When counting the number of objects in a set, the order in which they are counted is not important, but rather simply that all objects are counted.
Online programs such as Five Little Ducks and 1O Fat Sausages can assist the students in promoting the development concept. The audio, which is the songs help the children to listen and at the same time do the counting.
As, the children are able to mastering all the five principles in counting, the teacher can teacher the teach the children to the number word sequences.
1) Forward Number Word Sequence
The number sequence is from ascending to descending order.
Q Looking at the number sequence above, what number would come after 5?
A 4
2) Backward Number Word Sequence
The number sequence is from descending to ascending order.
Q Looking at the number sequence above, what number would come before 6?
A 5
However, if you ask the young children about the quantity of an object, they will confidently say "three flowers" without counting. Hence, Piaget called this ability to instantaneously recognise the number of objects in a small group as 'subitising'.
Subitising is defined as the side recognition of a quantity. They are two different recognize forms of substising:
Perceptual subitizing - Distinguishing a number without using any other form of mathematical process, for example children seeing and recognising the number ‘4’ without any taught mathematical familiarity (Clements, 1999, p. 402).
Conceptual subitizing - “Recognizing the number pattern as a composite of parts and then together as a whole, for example an eight dot domino" (Clements, 1999, p. 402)- children will automatically say two rows of four dots as eight without counting.
Teacher can develop students' learning experience on substizing through simple activities in the classroom. Example of the activities are shown below.
This activity develop students' skill on substizing. Children have to recognize the number on the dice and on the pictures in order to complete the 'Humpty Dumpty puzzle'.
Q What is the number on the Humpty Dumpty's hat?
A 4.
Q How did you know this?
A There are 2 and 2 dots, which together equal 4.
As Clements (1999, p. 403) explained, subitizing along with tens frames can help with early addition for students to understand addition combinations. The game pictured below is the example of subtizing with the tens frames.
In this game students will substizing through out the rolling dice. When the dice shows the same number as appears on their koala's line, their can move the koala ahead. The first koala that can reach home is the winner.
As an adult that played those activities in the tutorial class-Humpty Dumpty puzzle and Koala race for example, I can see games that include dice, domino or playing card help the children to recognize and identify the quantity in numbers. Indirectly, it develops students' substising skill in counting.
