Children's number competencies over 6 time points, from the beginning of kindergarten to the middle of 1st grade, were examined in relation to their mathematics achievement over 5 later time points, from the end of 1st grade to the end of 3rd grade. The relation between early number competence and mathematics achievement was strong and significant throughout the study period. A sequential process growth curve model showed that kindergarten number competence predicted rate of growth in mathematics achievement between 1st and 3rd grades as well as achievement level through 3rd grade. Further, rate of growth in early number competence predicted mathematics performance level in 3rd grade. Although low-income children performed more poorly than their middle-income counterparts in mathematics achievement and progressed at a slower rate, their performance and growth were mediated through relatively weak kindergarten number competence. Similarly, the better performance and faster growth of children who entered kindergarten at an older age were explained by kindergarten number competence. The findings show the importance of early number competence for setting children's learning trajectories in elementary school mathematics. Keywords number competence; mathematics achievement; longitudinal studiesPoor achievement in mathematics is a major concern in U.S. schools. Advanced study in high school mathematics is a pillar for success in college science (Sadler & Tai, 2007) and serves as a gateway for a wide range of vocations in science, technology, engineering, and mathematics disciplines. Unfortunately, many U.S. students do not develop the foundations for learning advanced mathematics. Mathematics difficulties are cumulative and worsen with time. For example, difficulties with whole numbers are obstacles to learning fractions, and difficulties with fractions lead to failure in algebra (National Mathematics Advisory Panel, 2008). Mirroring U.S. national trends, recent data from the state of Delaware showed approximately 25% of students failed to meet state mathematics standards in third grade, with © 2009 American Psychological AssociationCorrespondence concerning this article should be addressed to Nancy C. Jordan, School of Education, University of Delaware, Newark, DE 19716. njordan@udel National statistics in the United States reveal persistent income disparities in mathematics achievement across grade levels, with low-income students scoring substantially lower than middle-income students (National Assessment of Educational Progress, 2007). Yet, lowincome youth who acquire strong mathematical skills by the end of middle school are much more likely to graduate from college than their peers who do not acquire such skills (National Mathematics Advisory Panel, 2008). Early Number CompetenceThere is growing consensus that many mathematics difficulties in elementary school can be traced to weaknesses in basic whole number competencies, that is, in understanding the meaning of numbers and number relationships (e.g.,...
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.
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 percent of the variance in first-grade math achievement. Background characteristics of income status, gender, age, and reading ability did not add 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 = 0.70). 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.
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. Number sense measures contributed a significant amount of variance over and above the more general predictors (26%–42%). Uniquely predictive subareas 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.
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 0.60 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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