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The Importance of Counting
The Importance of Counting
Counting is a prominent aspect of much of the so-called 'mental arithmetic' or mental computation done be children in the primary years and beyond.
Counting is a prominent aspect of much of the so-called 'mental arithmetic' or mental computation done be children in the primary years and beyond.
Levels of Sophistication in Counting
Levels of Sophistication in Counting
There are various levels of mathematical sophistication in the ways children use counting and it is important for teachers to have some understanding of these. Teachers who have a good knowledge of these are better able to develop instructional approaches focused on developing more sophisticated arithmetical strategies in their children.
Counting versus Saying a Number Word Sequence
Counting versus Saying a Number Word Sequence
In Number Words and Numerals we did not use the word counting to describe the process. It was referred to as FNWS. This is because we find it useful to distinguish between, on the one hand, the activity of merely reciting the sequence of number words and, on the other hand, the activity of saying the words in a context where the child is purposefully keeping tract of items.
Perceptual Counting
Perceptual Counting
Refers to situations in which the items to be counted are available for the child to see. Counting that is not perceptual counting refers to situations in which the child knows how many counters are in a small collections that is screened.
- Using Perceptual Counting to Establish the Numerosity of a Collections- ( The numerosity of a collection is its how-manyness. That is counting the number of items in a group to determine how many are there)
- Using Perceptual Counting to Establish a Collection of Specified Numerosity- (The counting out of a number of items from a large group)
- Using Perceptual Counting to Establish the Numerosity of Two Collections- (Counting the total number of a group of differing types)
Beginning Addition through Counting
Beginning Addition through Counting
Perceptual counting is where students can see the objects referred to. More advanced levels of counting occur when children count to solve problems involving items which are not seen. If items were screened in two different groups and briefly displayed and then the child asked to determine the total. The adult prospective this is trivial but from the child it is problematic. The arithmetical idea of addition is currently somewhat remote for the child. This is an additive task involving two screened collections of counters.
Counting-from-one versus Counting-on
Counting-from-one versus Counting-on
Children who are capable of perceptual counting when presented with a screened task (example 2 different screens with different amounts of counters) will respond in one of four ways:
Children who are capable of perceptual counting when presented with a screened task (example 2 different screens with different amounts of counters) will respond in one of four ways:
- The Perceptual Counter- is unable to use counting to solve the ask.
- The Figurative Counter- count from on screen from one and then continues their count from the second screened set. This strategy is described as counting-from-one. The significant aspect of the figurative counter is that they count from one to count the first collection, which from an adult perspective is redundant.
- The Counting on Child- looks at the first screen and states the number that is under it (without counting). This is referred to as counting-on-to solve an additiye task and is regarded as more advanced than perceptual and figurative counter.
- The Non-count-by-ones Child- uses a strategy that does not involve counting-by-one. By determining the number to be added to the first screened set to make ten. Then partitioning the second screened set into a group that will allow them to make 10 then adds the remaining count.
Counting as Coordinating Words and Items
Counting as Coordinating Words and Items
In counting a child coordinated each number word with an item. The perceptual, figurative and counting-on child coordinate number words with items. The difference is that the perceptual counter is directly perceiving(seeing) the items, whereas the figurative counter and the counting-on child imagine or visualize the items to be counted. For this reason the figurative and counting child is regarded as cognitively and arithmetically more advanced than perceptual counting.
Emergent , Perceptual and Figurative Counting
Emergent , Perceptual and Figurative Counting
There are three areas of focus in this section: Emergent, Perceptual and Figurative Counting. The term 'emergent' is used in cases where the child is not able to count perceptually. Thus the child is unable to count a collection of say 12 or 16 counters. They might not know the number word sequence or might not correctly coordinate each number word with tn item to be counted.
Determine the Most Sophisticated Level
Determine the Most Sophisticated Level
It is not unusual for children to use a level of counting less advanced than they are capable of. It is our task to elicit the most advanced kind of counting that the child can use spontaneously and with certitude. Only classify a child as perceptual if you are certain that they are not able of figurative counting or counting-on to solve a task. Typically, it is necessary to present the child with several tasks rather than just one, in order to elicit the most advanced kind of counting.
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