Abstract
How does symbolic number knowledge performance help identify young children at risk for poor mathematics achievement outcomes? In research and practice, classification of mathematics learning disability (MLD, or dyscalculia) is typically based on composite scores from broad measures of mathematics achievement. These scores do predict later math achievement levels, but do not specify the nature of math difficulties likely to emerge among students at greatest risk for long-term mathematics failure. Here we report that gaps in 2nd and 3rd graders' number knowledge predict specific types of errors made on math assessments at Grade 8. Specifically, we show that early whole number misconceptions predict slower and less accurate performance, and atypical computational errors, on Grade 8 arithmetic tests. We demonstrate that basic number misconceptions can be detected by idiosyncratic responses to number knowledge items, and that when such misconceptions are evident during primary school they persist throughout the school age years, with variable manifestation throughout development. We conclude that including specific qualitative assessments of symbolic number knowledge in primary school may provide greater specificity of the types of difficulties likely to emerge among students at risk for poor mathematics outcomes.
Highlights
Some aspects of number knowledge involve an awareness of the meaning of somewhat arbitrary symbols that are used on a daily basis
We demonstrate that basic number misconceptions can be detected by idiosyncratic responses to number knowledge items, and that when such misconceptions are evident during primary school they persist throughout the school age years, with variable manifestation throughout development
We focus on behaviors that would be readily assessable in informal environments, and evaluate whether early indicators of atypical number concepts are associated with future computational fluency
Summary
Some aspects of number knowledge involve an awareness of the meaning of somewhat arbitrary symbols (such as Arabic numerals and number words) that are used on a daily basis This knowledge is an important predictor of later mathematics achievement (Rousselle and Noël, 2007; De Smedt et al, 2009; Krajewski and Schneider, 2009), which makes it a useful indicator of risk for mathematics learning difficulties (Mazzocco and Thompson, 2005; Jordan et al, 2007; Stock et al, 2010; Desoete et al, 2012). A challenge for educators is knowing what observable behaviors (such as counting or labeling sets) map on to important elements of number sense and how these behaviors are typically manifested in early childhood. Educators may want to know what a weak number sense looks like, and which numerical behaviors reflect typical or atypical development
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