LeFevre - numeracy and mapping

I would say that the next level of early numeracy knowledge in particular that children need to acquire is the knowledge of how quantities, once they know how to determine those quantities through counting, how those map onto written symbols. So, if we think about the three kinds of representations that you can have of a number: the quantity, the verbal number word and the written symbol- learning the links between those we usually refer to as mapping. So children need to learn the mappings among those three representations.  

In research that we’ve done, children as young as 2 and 3 years of age, a lot of them know how to name the symbols. So if you show them a 4, they’d be able to say 4 and they can say the count sequence up to 10 pretty easily. They may or may not know how to actually count the set of objects. So that’s kind of the difficult part.  

So between about 3 and 5, they’re mastering that counting objects part of it with the goal eventually of being able to look at a written symbol and know how many that that symbol stands for without having to have five things in front of them. They know that the symbol 5, what it stands for. 

So being able to map across those three different representations kind of forms the foundation for a lot of additional kinds of knowledge that children have to acquire. They have to understand for example, that six things is more than four things. They could do that if you show them six things and four things by counting them at one point, you know by probably 5, most children would be able to do that. But you also want them to be able to look at the digit 6 and the digit 4 and know that the digit 6 represents more objects than the digit 4 does.  

So it’s kind of- the research that we’ve been doing suggest that that process of moving from external concrete objects to understanding the verbal symbols and being able to map them between words and written symbols and then being able to work with those symbols as if you had the objects in front of you kind of from 2 to 6, those are the critical early mathematical processes that children have to acquire.