Academic journal article School Psychology Review

Determining Early Mathematical Risk: Ideas for Extending the Research

Academic journal article School Psychology Review

Determining Early Mathematical Risk: Ideas for Extending the Research

Article excerpt

The National Mathematics Advisory Panel (2008) specifies that children should be able to fluently add and subtract whole numbers by the end of third grade. Mathematical understanding of addition and subtraction emerges well before formal mathematic instruction begins, and when it emerges it reflects competence in a number of prerequisite skills and concepts. 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. There is agreement about which early mathematics skills are thought to be essential to longer term success (e.g., U.S. Department of Health and Human Services, 2001; National Council for Teachers of Mathematics, 2008) and, in fact, there has been relatively strong correspondence in the skills assessed by researchers in this area (Hojnoski, Silberglitt, & Floyd, 2009).

It also seems clear that understanding of important mathematical concepts occurs as young children interact with adults, children, and materials in their environments. For example, there is some suggestion that subitivity (the ability to instantly recognize object sets ranging in size from 1 to 5) precedes the ability to count and may emerge in infancy (Clements, 1999). In turn, automatic recognition of object set sizes can facilitate the development of procedural skills like counting (one-to-one object correspondence and cardinality). The ability to count forward and backward fluently belies an understanding that numbers occur in a fixed position, with higher numbers representing greater quantity or magnitude than lower numbers. This understanding both prepares a child to understand that 1 is less than 2, and later, to understand negative numbers.

For example, if I ask my 2-year-old whether she would like to have 2 M&Ms or 5 M&Ms, she will think for a moment and say "5!" But if I ask her whether 5 is more than 2, she may not answer as readily or correctly. She intuitively knows that 5 appears later in the sequence of numbers and suspects that it is more than 2. Her suspicion is confirmed (and rewarded) when she receives 5 M&Ms instead of only 2. These everyday experiences lay the foundation for a child understanding that 1 1/2 is more than 1 but less than 2, and this expectation may be tested and verified when helping to bake a cake with a parent or dividing a single item with a sibling, for example. Big ideas in mathematics are generally well established for children before procedural instruction even begins.

Unfortunately, and as noted by others (Ginsburg, Lee, & Boyd, 2008), adults are fairly unresponsive to young children's mathematical development. Mathematic deficits are apparent by preschool and are often associated with other risk factors (e.g., socioeconomic status; Jordan, Huttenlocher, & Levine, 1992). Early intervention is necessary for some children and can successfully resolve early deficits and prevent longer term consequences (Gersten & Chard, 1999). In what is likely to be a seminal study, Slavin and Lake (2008) synthesized mathematics instruction studies for elementary-aged students and their findings echo the need for adults to be responsive to young children's mathematical development. Of the 256 studies reviewed, 87 met their rigorous inclusion criteria. Studies were categorized as curricula studies, computer-assisted instructional programs, or "instructional process" studies. Instructional process studies included studies that used procedures to adjust the instructional interaction between teachers and students in the classroom. The curricula studies had the greatest methodological limitations and also the lowest effect size (+0. …

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