Revisiting Counting
My assessments of Kristen’s work forced me to revisit what I thought I knew about
counting. I began to refine my thinking and worked to identify the specific ideas
about counting that form the foundation for numerical thinking and number
sense. I wanted her to understand that counting is more than a sequence of num-
bers, that each number has a quantity attached to it. My most immediate goal, in
a nutshell, was that she develop a deep understanding of small numbers, up to
about 20, and specifically that she develop fluency in sequencing them forward
and backward, attach quantities to each, and compare amounts. Kristen needed
to develop counting as a tool that would help her develop an understanding of the
important number relationships that will lead to a stronger number sense. Instead
of providing her with various supplemental counting activities from the kinder-
garten and first-grade curriculum, I realized that I needed to develop a deeper un-
derstanding of how the activities in those grade levels build the ideas about
counting that Kristen needed to understand. I needed to plan a consistent series
of activities that would allow her to build this understanding while exposing her
to some of the activities in our second-grade curriculum.
On most mornings, when the rest of the class was working on independent
morning work, Kristen played games from the first-grade curriculum that allowed
her to work on her fluency with numbers to 20. She often played these games with
a partner who needed extra practice. I focused on games that could be modified
by changing the size of the numbers. In this way, I only needed to teach her a lim-
ited number of games and she was able to put more of her thinking into the math-
ematics of the game, rather than learning and remembering directions. She
played Start With/Get To, in which numbers are chosen from a set of number
cards. She identified the numbers, found them on a number line, and then
counted from one to the other. This game helped her develop fluency with the
rote counting sequence, both forward and backward. By varying the size of the
numbers, I could easily adjust the game. Compare Dots is a game in which two
players compare dot cards and decide which player has more dots on their card
(Russell et al. 2008f). Once she was familiar with that version of the game, she
played Double Compare Dots, in which both players turn over two cards and de-
termine which player has the most dots. Here again, by changing the cards, I
could easily adjust the game.
I also had Kristen work on modified versions of some second-grade games.
When the rest of the class was playing Get to 100 (Russell et al. 2008g), Kristen
played Get to 20. This game involves rolling two multiples-of-5 number cubes,
finding the sum, and moving a game marker that many spaces on a 100 chart.
Kristen played with one number cube. Like the rest of the class, she recorded her
Assessing and Developing Early Number Concepts