Counting is a way to find out the exact number of objects in a set. In order to succeed in this, a child needs to learn the counting words of his language, to know the principles of counting, and provided with such an environment in which there are many opportunities for practicing counting.
VERBAL COUNTING — NUMBER SEQUENCES
Verbal counting means that a child can say number words, “one”, “two”, “three” etc, in a correct sequence both forwards and backwards. Learning number sequences often happens parallel with learning to count objects, such as toys. By the age of four most children have learnt to produce verbally the list of numbers from one to ten, and by the age of five also backwards with help of removing objects from a set (1). At around six years, most children are able to start verbally counting from a given number other than one (e.g., "Count from four to seven.") and can determine numbers just after or just before (e.g., "What comes just after six?") (2).
Gradually, children learn number sequences verbally first up to 100 and then up to 200 and even beyond. They also learn to skip count verbally (e.g., "10, 20, 30… 100") or when counting objects (e.g., "There are 2, 4, 6…12 sweets on the table."). Later on, children are able to count number words in both directions (forwards and backwards) and start using verbal counting as a strategy in early addition and subtraction.
OBJECT COUNTING – COUNTING PRINCIPLES
In order to solve a counting task correctly, there are some counting principles that a child needs to understand (3).
The stable-order principle. The child knows the conventional order of number words and uses them in counting of objects by saying counting words in a correct sequence until needed.
The one-to-one principle. This involves the the child assigns of one distinct counting word to each of the items to be counted, for example by pointing an object and saying a number word for it.
The cardinal principle. The child understands that the number word said to the final object in a collection represents the number of items in that collection.
The abstraction principle. The child understands that the above mentioned principles can be applied to any collection of objects, not only tangible but also non-physical things such as sounds and imaginary objects.
The order-irrelevance principle. The child knows that it does not matter in which order the objects are counted, as long as each the object in the collection is counted once and only once.
RELATION TO OTHER MATHEMATICAL SKILLS
There is general agreement that the role of counting skills, both verbal and object counting, is a significant predictor of early grades arithmetic skills, based on findings from several longitudinal studies (e.g., 4, 5, 6, 7). Studies focusing on low-performing kindergartners have shown that these children often face difficulties in counting skills (e.g., 8, 9)
IN OUR PROJECT
In our project, we assess children’s verbal counting skills, both forwards and backwards, in different number ranges.
(1) Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.) Handbook of Research on Mathematics Teaching and Learning, (pp. 243–275). Reston, VI: NCTM.
(2) Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research. Learning trajectories for young children. New York, NY: Routledge.
(3) Gelman, R., & Gallistel, C. R. (1978). The Child’s Understanding of Number. Cambridge, MA: Harvard University Press.
(4) Aunola, K., Leskinen, E., Lerkkanen, M.-K., & Nurmi, J.-E. (2004). Developmental dynamics of math performance from preschool to grade 2. Journal of Educational Psychology 96(4), 699–713.
(5) Bartelet, D., Vaessen, A., Blomert, L., & Ansari, D. (2014). What basic number processing measures in kindergarten explain unique variability in firstgrade arithmetic proficiency? Journal of Experimental Child Psychology, 117, 12–28.
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(7) Lepola, J., Niemi, P., Kuikka, M., & Hannula, M. M. (2005). Cognitive-linguistic skills and motivation as longitudinal predictors of reading and arithmetic achievement: A follow-up study from kindergarten to grade 2. International Journal of Educational Research, 43(4–5), 250–271.
(8) Hassinger-Das, B., Jordan, N. C., Glutting, J., Irwin, C., & Dyson, N. (2014). Domain-general mediators of the relation between kindergarten number sense and first-grade mathematics achievement. Journal of Experimental Psychology, 118, 78–92.
(9) Toll, S. W. M., & Van Luit, J. E. H. (2014). Explaining numeracy development in weak performing kindergartners. Journal of Experimental Child Psychology, 124, 97–111.