Educators have many tools to screen students early for future reading problems, but few tools to screen them for future math difficulties. While researchers are still trying to root out the sources of math difficulties, a study in the Journal of Learning Disabilities reports that simple number-sense tests in kindergartners could predict calculation fluency in 2nd grade and assist educators in better focusing their efforts on the students who need help.
“We suspected that basic skills related to counting, number knowledge, and simple arithmetic would be more predictive of calculation fluency than more general cognitive competencies,” write the authors of this study of 198 children.
Counting by kindergartners was less predictive of 2nd grade fluency than other number-sense tests such as number knowledge and sense of number combinations, the researchers report (see descriptions below).
“Our data suggest that screening for number sense in kindergarten would successfully rule out most of the children who are not at risk for fluency difficulties,” the researchers report.
“Number sense screening in kindergarten, using ‘at-risk’ versus ‘not-at-risk’ criteria, successfully ruled out 84% of the children who did not go on to have calculation fluency difficulties and positively identified 52% of the children who later showed fluency difficulties.”
The 198 children at the center of this study attended six schools in a school district in northern Delaware. The children were recruited in kindergarten. All of the schools used the same math curriculum (Teaching Integrated Math and Science Curriculum, 2004).
The number-sense battery used by the researchers (Jordan, Kaplan, Olah and Locuniak, 2006) had a total of 50 items and included the following categories:
- Enumeration – Children were shown a series of five stars and
asked to count them and then to state how many stars were on the paper. The same
procedure was followed with seven stars. - Count sequence – Children were asked to count as high as
they could. They were stopped once they reached 50. Self-correcting was allowed.
- Counting principles – Children were shown a finger puppet
and told the puppet was learning to count. The puppet counted 8 sets of
alternating blue and yellow dots, consisting of either 5 or 9 dots. The children
were instructed to tell the puppet whether he counted OK or not OK for each of
the sets. The puppet counted in unusual ways, but correctly, in some of the
sets–counting only blue dots first followed by yellow dots and vice versa. The
puppet also counted incorrectly by, for example, double counting the first dot. - Number recognition – Children were asked to name four
numbers: 2, 8, 9, and 13. - Number knowledge – Children were shown a number and asked to
name the number that followed and and the number that followed 2 numbers after
that one. Then children were given pairs of numbers and asked to identify which
number was bigger or smaller. Children also were shown 3 numbers in the corners
of an equilateral triangle and asked which was closest to a target number. - Nonverbal calculation – Using chips, the tester presented
simple addition and subtraction calculations (e.g. 2 + 1, 4 + 3, 7 — 3) to the
children. Chips were covered and the child told how many chips were under cover.
Then one at a time, chips were added or subtracted. Children had to indicate how
many chips were hiding under cover either verbally or by placing the appropriate
number of chips on the table. - Story problems – The tester gave children 4 addition and 4
subtraction story problems. The stories were presented orally, one at a time. - Number combinations – 4 addition and 4 subtraction
calculations were presented orally.
Number sense and early reading skills were assessed in the spring of kindergarten, cognitive measures were given in the winter of 1st grade and the calculation fluency measure in the winter of second grade. The researchers note that other research suggests number sense measures could be taken by mid-year in kindergarten.
Useful for ruling out students
“Number sense predicted calculation fluency over and above general predictors of age, reading, oral vocabulary, memory and spatial reasoning,” the researchers write. Although working memory was also uniquely predictive of 2nd grade fluency, the researchers note that it is a more generalized indicator and not as relevant for teaching math. The study used a cut-off criterion of <25th percentile for calculation fluency in 2nd grade. In view of the high false-positive rate (48%), the researchers indicate that testing for number sense was more reliable for ruling out children than for positively identifying those who were likely to have future math difficulties. Of the 48 children who were positively identified by the number sense predictors, only 25 went on to have fluency difficulties in 2nd grade, although half of them did go on to be low fluency performers (between 25th and 50th percentiles).
Besides number sense, children were also evaluated for:
- Reading, with Dynamic Indicators of Basic Early Literacy Skills
DIBELS–letter-naming fluency, phoneme-segmentation fluency and nonsense-word
fluency. - Cognitive abilities, with Wechsler Intelligence Scale for Children and
Wechsler Abbreviated Scale of Intelligence. - Calculation fluency, with Assessment of Math Fact Fluency
The researchers note that calculation fluency is not sufficient for learning high-level mathematics but it is a necessary sub-skill. “This ‘necessary but not sufficient’ relationship is analogous to the connection between decoding fluency and comprehension in reading,” the researchers write. “Deficient calculation fluency is a defining characteristic of math difficulties and disabilities.” Further research is needed to show if early instruction in number sense could prevent or reduce future math difficulties, the researchers say.
“Using Kindergarten Number Sense to Predict Calculation Fluency in Second
Grade,” by Maria N. Locuniak and Nancy Jordan, Journal of Learning Disabilities,
September/October 2008, Volume 41, Number 5, pp. 451-459.