24 Sep 2013 - Rational versus Rote Counting

Today's lesson started with discussing about 'Rational Counting' and 'Rote Counting'. So how do we teach these concepts of counting to young children?

Rational Counting
- one and only one number name is assigned to each object in a group, and the last number name said is understood to name the quantity in the group (eg. 5 apples).

When talking about rational counting, I think of some nursery rhyme songs that can be used to teach the toddlers (e.g. "Ten Little Indian Boys"), "Five Little Ducks", "Five Little Monkeys", "Ten in the Bed", "Ten Green Bottles"). However, the concept taught in the songs, ""Five Little Ducks", "Five  Monkeys", "Ten in the Bed", "Ten Green Bottles" differs from the song taught in "Ten Little Indian Boys" (Counting back from 10 versus counting up to 10).

Using the Bruner's Concept-Pictorial-Abstract (CPA) approach, I will introduce concrete materials (eg. 5 apples, 10 spoons) to teach young children to do rational counting. When they are able to grasp the concept using real objects, I will introduce the below activity sheet(pictorial/abstract). After which, can ask the children "How many are in the group?" and that the total number will be the cardinal number.

Rote Counting
- is the naming of the number words in the correct sequence (eg, 1, 2, 3, 4, 5).

In reference to the CPA approach, counters can be used to teach this concept of rote counting. After which, the below number cards can be used to teach the sequence of numbers.

 

The attached resources are retrieved from the below link:
 http://illuminations.nctm.org/LessonDetail.aspx?ID=U147
This link has good resources to teach children mathematical concepts.