## Publications and Findings |

A description of the shortened number sense battery can be found in:

Jordan, N. C., Glutting, J., & Ramineni, C. (2008). A number sense assessment tool for identifying children at risk for mathematical difficulties. In A. Dowker (Ed.),Mathematical difficulties: Psychology and intervention(pp. 45-58).San Diego, CA: Academic Press.*****************************************************************************************************

Nancy C. Jordan, David Kaplan, Chaitanya Ramineni, & Maria N. Locuniak (2008)

Developmental Science, 11(5), 662-668.

Children's change over time in frequency of finger use on number combinations was examined in relation to their change in accuracy. Performance was tracked longitudinally over 11 time points, from the beginning of kindergarten (mean age = 5.7 years) to the end of second grade (n = 217). Accuracy in number combinations increased steadily during the time period while frequency of finger use declined. Correlations between finger use and accuracy decreased gradually, ranging from .60 in kindergarten to -0.15 at the end of second grade. Low-income children showed linear growth in frequency of finger use while middle-income children slowed down by second grade and even started to decline. Although girls and boys showed similar growth patterns in frequency and accuracy, boys used their fingers less often than girls and were more accurate. The findings indicate that finger use is most adaptive when children are first learning number combinations, but this benefit lessens over time.

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Maria N. Locuniak & Nancy C. Jordan (2008)

Journal of Learning Disabilities, 41(5), 451-459.

Children’s number sense in kindergarten was used to predict their calculation fluency in second grade (n = 198). Using block entry regression, usual predictors of age, reading, memory, and verbal and spatial cognition were entered in the first block and number sense measures were added in the second block. The number sense measures contributed a significant amount of variance over and above the more general predictors (from 26% to 42%). Uniquely predictive sub-areas were active memory for numbers, number knowledge, and number combinations, with number combinations standing out as the strongest single predictor. 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 relation of early number skills to later calculation fluency has important implications for math screening and intervention.

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Nancy C. Jordan, David Kaplan, Maria N. Locuniak, & Chaitanya Ramineni (2006)

Learning Disabilities Research & Practice, 22(1),36-46.

Number sense development was tracked from the beginning of kindergarten through the middle of first grade, over six time points. Children (n = 277) were then assessed on general math achievement at the end of first grade. Number sense performance in kindergarten, as well as number sense growth, accounted for 66% of the variance in first-grade math achievement. Background characteristics of income status, gender, age, and reading ability did not add any explanatory variance over and above growth in number sense. Even at the beginning of kindergarten, number sense was highly correlated with end of first grade math achievement (r = .70). Clarifying the observed slope effect, general growth mixture modeling showed that children who started kindergarten with low number sense but made moderate gains by the middle of kindergarten had higher first-grade math achievement than children who started out with similarly low number sense with flat growth. The majority of children in the low/flat growth class were from low-income families. The findings indicate that screening early number sense development is useful for identifying children who will face later math difficulties or disabilities.

Nancy C. Jordan, David Kaplan, Leslie Nabors Olah, & Maria N. Locuniak (2006)

Child Development,77(1), 153-175.

Number sense development of 411 middle- and low-income kindergartners (mean age 5.8 years) was examined over 4 time points while controlling for gender, age, and reading skill. Although low-income children performed significantly worse than middle-income children at the end of kindergarten on all tasks, both groups progressed at about the same rate. An exception was story problems, on which the low-income group achieved at a slower rate; both income groups made comparable progress when the same problems were presented nonverbally with visual referents. Holding other predictors constant, there were small but reliable gender effects favoring boys on overall number sense performance as well as on nonverbal calculation. Using growth mixture modeling, 3 classes of growth trajectories in number sense emerged.

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