Early math matters: Kindergarten number competence and later mathematics outcomes.

Abstract

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.,...

Individual variance in responsiveness to early computerized mathematics intervention

“…Understanding of ordinal numbers and the ability to order sets of objects predict later math achievement (Duncan et al, 2007) and, more specifically, counting fluency (Koponen, Aunola, Ahonen, & Nurmi, 2007), so ordering tasks were added to the second version of GGM. Finally, early numerical competence (i.e., a sense of quantities and numbers) predicts calculation fluency (Locuniak & Jordan, 2008) and applied problem solving skills (recently Jordan, Kaplan, Ramineni, & Locuniak, 2009). For this reason, various types of comparison tasks were included in GGM (e.g., non-symbolic and symbolic approximate and exact comparison tasks, such as more / less, the most / the least, one more / one less, two more / two less).…”

“…Preventive Support for Kindergarteners (Jordan, Kaplan, Ramineni, & Locuniak, 2009). Furthermore, when exact object counting skills develop, they can be used for composing and decomposing quantities ) as well as for adding and taking away.…”

Measurement in education

“…Especially, counting out loud (e. g. Aubrey et al, 2006;Jordan et al, 2009;Kolkman et al, 2013;Krajewski & Schneider, 2009;Passolunghi et al, 2007), other tasks of distinguishing different counting principles (e. g. Jordan et al, 2006), or number line tasks on the spatial representation of magnitude (e. g. Geary et al, 2009;Kolkman et al, 2013;Nuerk, Geppert, van Herten, & Willmes, 2002; are often assessed or theoretically considered. Although not exactly the same, the available items cover all the factors of number sense, which have been identified before (see e. g. Aunio et al, 2004;Aunio & Niemivirta, 2010;Kolkman et al, 2013).…”

“…All of the studies confirm a sizable predictive power for later mathematic achievement level above, and beyond demographic characteristics, and in the case of Jordan et al (2010) controlling for general cognitive ability. Furthermore, Jordan et al (2009) report a positive association of high number sense values with high growth rates in mathematic achievement. Additional results are again the major importance of early symbolic number knowledge , as well as that the strength of prediction does not weaken over the first three years .…”

“…Many longitudinal studies analyze the relevance of specific operational definition of numbers sense for later mathematic achievement (e. g. Aubrey, Godfrey, & Dahl, 2006;Aunio & Niemivirta, 2010;Jordan et al, 2010;Jordan, Kaplan, Locuniak, & Ramineni, 2007;Jordan, Kaplan, Ramineni, & Locuniak, 2009;Kolkman et al, 2013). Each article uses a different operationalization.…”