Supporting Mathematical Development in Young Children: Cardinality


Sudha: Cardinality basically means that you
count out a set of objects to determine the total quantity, and as you recite the number
words, you understand that the last number word you used tells you the total quantity in the set. Child: 1 block, 2 block, 3 block, 4 block,
5 block, 6 block, 7 block, 8 blocks. Sudha: Now, that’s a difficult concept.
We see a lot of children counting out, maintaining one-to-one correspondence, but not knowing
that the last number word they said is the total amount. Child: 24, 25, 26. Teacher: You have how many? Child: 46 Teacher: 46? Sudha: When we ask them, what is the total
number? How many did you count? Some of them go back to counting, “one, two, three”
and some others will just look at you. And while all of those tell you that they can
count, it doesn’t tell you that they can recognize the total quantity by the act of
counting. Sudha: Sometimes children count out, and we
hear that the last number word, they have a little rise in their tone. Child: 2,3,4 Sudha: And that gives you a sense that they
realize that, “I’ve come to the end of my number sequence. This number word is special.
It tells me something about the quantity.” And from that realization, they eventually
get to a point where they realize that the last number word is the total object. Teacher and Child: 5,6,7 Child 2: There’s seven. Narrator: Adults can support children’s
understanding of cardinality throughout the day. Narrator: Teachers frequently ask children
to count how many other children are in school that day. This provides an opportunity to
emphasize the total number in the group. Teacher: My friend Stephanie just counted
our friends. Look, I’m going to write the number eight. Narrator: Opportunities for supporting cardinality
can also come up naturally during children’s play. Teacher: How many people are going with you? Child: My whole family. Grammy, and this baby. Teacher: We have to know how many tickets
to buy. So should we make a list of everybody? Child: My sister’s number one. My baby’s
number two. 1, 2, 3, 4, 5, 6, 7. Teacher: Seven. So we need… Child: Seven people. Teacher: Seven people. Seven tickets you need
to buy, then? Narrator: It’s easy to assume that children
have cardinality when they count correctly, but in order to check their understanding,
adults can ask them how many in all. All children: Six, seven, eight. Teacher: So how many cubes are in the cup? 2 Children: Eight. Teacher: Eight. There were actually eight. Narrator: It’s also important for adults
to be deliberate in stating the total number. Child: 4, 5, 6 Teacher: Six. Six Blocks you used… Sudha: Cardinality develops gradually and
over repeated counting opportunities. You can support children’s understanding of
cardinality by modeling it for them. And by questioning and prompting them to state the
total quantity of their counting.