# Determining Early Mathematical Risk: Ideas for Extending the Research

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```					School Psychology Review,
2010, Volume 39, No. 2, pp. 196 –202

COMMENTARY

Determining Early Mathematical Risk: Ideas for
Extending the Research

Amanda M. VanDerHeyden
Education Research and Consulting, Inc.

The National Mathematics Advisory                   It also seems clear that understanding of
Panel (2008) speciﬁes that children should          important mathematical concepts occurs as
be able to ﬂuently add and subtract whole           young children interact with adults, children,
numbers by the end of third grade. Mathe-           and materials in their environments. For ex-
matical understanding of addition and sub-          ample, there is some suggestion that subitivity
traction emerges well before formal math-           (the ability to instantly recognize object sets
ematic instruction begins, and when it              ranging in size from 1 to 5) precedes the
emerges it reﬂects competence in a number           ability to count and may emerge in infancy
of prerequisite skills and concepts. By the         (Clements, 1999). In turn, automatic recogni-
time children begin to formally learn the           tion of object set sizes can facilitate the devel-
procedures associated with addition and sub-        opment of procedural skills like counting
traction, they will already understand that num-    (one-to-one object correspondence and cardi-
bers have a ﬁxed sequence, that numbers appear-     nality). The ability to count forward and back-
ing earlier in the sequence represent lower mag-    ward ﬂuently belies an understanding that
nitudes or quantities than do numbers appearing     numbers occur in a ﬁxed position, with higher
higher in the sequence, that objects can be         numbers representing greater quantity or mag-
counted, and that quantities can be compared        nitude than lower numbers. This understand-
and shifted by moving objects between sets and      ing both prepares a child to understand that 1
so on. There is agreement about which early         is less than 2, and later, to understand negative
mathematics skills are thought to be essential to   numbers.
longer term success (e.g., U.S. Department of              For example, if I ask my 2-year-old
Health and Human Services, 2001; National           whether she would like to have 2 M&Ms or 5
Council for Teachers of Mathematics, 2008)          M&Ms, she will think for a moment and say
and, in fact, there has been relatively strong      “5!” But if I ask her whether 5 is more than 2,
correspondence in the skills assessed by re-        she may not answer as readily or correctly.
searchers in this area (Hojnoski, Silberglitt, &    She intuitively knows that 5 appears later in
Floyd, 2009).                                       the sequence of numbers and suspects that it is

and Consulting, Inc., 102 Ashton Court, Fairhope, AL 36532; E-mail: amandavande@gmail.com
Copyright 2010 by the National Association of School Psychologists, ISSN 0279-6015
196
Determining Early Mathematical Risk

more than 2. Her suspicion is conﬁrmed (and         ably measured for particular types of decisions,
rewarded) when she receives 5 M&Ms instead          and when instruction can (and ought) to be ini-
of only 2. These everyday experiences lay the       tiated or intensiﬁed. Being able to quantify early
foundation for a child understanding that 11⁄2      mathematics skills will allow teachers and par-
i
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Description: By the time children begin to formally learn the procedures associated with addition and subtraction, they will already understand that numbers have a fixed sequence, that numbers appearing earlier in the sequence represent lower magnitudes or quantities than do numbers appearing higher in the sequence, that objects can be counted, and that quantities can be compared and shifted by moving objects between sets and so on. Because children in kindergarten and preschool are just beginning to be exposed to formal mathematics instruction, it is particularly important to identify measures that are matched to the students' level of proficiency.
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