Next, I asked her to count starting at 76. She counted 76, 77, 78, 79, 30, 31,
32, 33, 34, 35. Then I asked her count from 93. She counted from 93 to 100, then
paused. I encouraged her to continue. She counted from 100 to 109. She stopped
at 109 and said that she forgot what comes next. Kristen’s knowledge of the
counting sequence started to break down after 40. She was able to count correctly
between the multiples of 10s, but she was unsure of what to do when going over
a decade, sometimes losing track of the sequence (e.g., 79, 39).
In a related task, I asked Kristen to say the number word that comes after a
given number. She was unsure of the number after 19. She said, “91.” After 12,
she paused for several seconds, then responded in a questioning voice: “13?” After
29, she said: “22?”
Kristen also could not identify some numerals. For the number 13, she said
“31.” When she wrote numbers backward, I had assumed that this was simply a
writing reversal. In fact, she confused the names of the two numbers, and at times
needed to count from 1 on the number line to figure out which number is correct.
She was also unable to count backward from 15. When asked to say the number
that comes before a given number, she found it difficult to say the number words
before numbers that have 0 in the 1s place. She also struggled to recall which
numbers come before 11, 13, and 14. Although she was able to say the correct
numbers, she required extra think time.
I presented her with the following missing addend task: “Here are 4 green
counters under this paper. While you look away, I’m going to put some yellow
counters under the paper.” I added 2 more counters that she could not see. “Now
there are 6 counters. How many more counters did I put under the paper?” Kristen
responded, “Six?” She had no way into this task so I lowered the numbers. This
time I showed her 3 counters. I asked her to turn away while I added some more.
I said, “Now there are 5 counters. How many more counters did I just put under
the paper?” Once again, Kristen responded, “Six?”
These assessment tasks provided me with valuable information about
Kristen’s mathematical understanding. I came away from these brief meetings
with a better understanding of why Kristen was struggling with the second-grade
curriculum. Her knowledge of numbers, beginning with the number sequence,
particularly around the multiples of 10, and her numeral recognition were very
fragile. The work of the second-grade curriculum seemed beyond her reach. The
accommodations I was making, such as simply changing the numbers in word
problems, were not enough to address her needs.
It did not appear that Kristen expected math to make sense. She seemed to ap-
proach problem solving in a hit-or-miss fashion, unable to consider the reasonable-
ness of her answers. She needed to connect more meaning to numbers before she
could consider the reasonableness of her answers. I wanted Kristen to experience
Assessing and Developing Early Number Concepts