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Sequence, Counting, and Cardinal aspects of number words

We are one of those crazy districts that starts school in August, and at the beginning of August, no less.  Because of that, I have been doing a lot of reading and thinking about all stuff school.  One of the books I am reading is entitled Primary Mathematics:  Teaching for Understanding, written by Patrick Barmby, Lynn Bilsborough, Tony Harries and Steve Higgins.  It is a fabulous resource, and as noted on the back cover, the authors’ intent is “to support and develop teachers’ understanding of the key primary mathematics topics. ”

One of the first topics our brand new kindergarteners tackle is counting.  They must count and count and count and then count some more, as they practice saying the number words in sequence.  In Chapter 2, Barmby, et al. discuss how children acquire the spoken representation of number and what that path might look like. “When mistakes occur in the use of sequence numbers, these are usually related to children’s developing skills rather than particular misconceptions” (Barmby, et al., pg. 17).

To move through the Early Learning Counting Trajectory (the developmental sequence described by Douglas Clements and Julie Sarama), from a “reciter”-says number words in order to a “counter and producer”-counts objects, counts out a specific number of objects, & uses cardinality, kids must count. They must count things, lots of different things, lots of times:  Unifix cubes, pebbles, toy cars, pencils, shiny markers, kids in their class, stickers, sea shells, and dots on five- and ten-frame cards.  The kiddos must count objects and they must talk about what they are counting.

They should build trains of Unifix cubes and talk about how many cubes in each train; chat about which train of cubes is longer, which train is the shortest, and which two might be of the same length. Kindergarteners must create sets of objects – buttons, shells, dice-shaped erasers, plastic pumpkins – and then, count and re-count how many objects in each of the sets.

So, have young kids count and chat, and explore and investigate, and converse and discuss-it’s good for them.

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