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Speeded naming tasks have been used to index the efficiency with which people retrieve familiar information from long term memory. In the traditional speed naming, or "Rapid Automatic Naming" (RAN) taska, people are required to name sequentially presented letters, digits, blocks of colour, or objects as quickly as possible (Denkla & Rudel, 1979; reviewed by Denkla & Cutting, 1999). RAN tasks consistently predict performance on complex tasks such as reading and mathematics. Although the requirements of the RAN tasks are apparently very simple, performance is consistently correlated with reading measures and is predictive of developmental reading difficulties (Wolf & Bowers, 1999; Wolf et al. 2002). RAN measures implicate a variety of cognitive processes including; feature detection of the symbol or item presented (e.g. letter, number, colour, or picture), accessing and retrieving the verbal name related to that item, and correctly articulating the information (Wolf et al., 2002). Presumably, deficits in the basic cognitive processes involved in the RAN also affect performance on complex tasks or interfere with children’s acquisition of relevant higher-level skills. These versions of speeded naming tasks which have 3 elements were developed to specifically assess speeded naming of the quantiites 1 to 3. Willburger, Fusseneger, Moll, Wood, and Landerl (2008) were the first to compare children’s performance on a quantity naming measure to that on more traditional RAN measures (i.e., objects, letters, and digits). However, naming of small quantities has a much longer history in research on numerical cognition. For example, Mandler and Shebo (1982) showed that adults can identify small quantities (up to 3 or 4), very quickly and accurately compared to the time it takes to count slightly larger amounts (see also LeFevre, Fast, et al., 2010). Subitizing speed is related to various early numeracy measures (LeFevre, Fast et al.) and children who have mathematical disabilities show relatively worse subitizing performance than typically-achieving children or than children with other learning disabilities (Willburger et al., 2008). The RAN-Quantities measure as formulated by Willburger et al. and in the present research is essentially an index of the speed with which an individual can name small quantities. It is not exactly a subitizing measure because the stimuli remain visible to the participants. The goal of developing these measures was to explore the relation between mathematical skills and the basic quantity processing skills. Research with more traditional RAN measures has been important in models of reading acquisition and thus a strong precedent exists for further work on the quantity version of the task. Both reading and mathematical ability are complex cognitive abilities that implicate processing speed, working memory, and attention (Geary, 2011). Completion of the RAN task requires similar cognitive abilities. Therefore, it is plausible that traditional RAN measures would be related to mathematical performance, specifically measures that involved fluent or speeded processing. Garnett and Fleischner (1983) completed some of the first research assessing the link between math ability and performance on traditional RAN tasks (letter, digit, colour, and object) with participants between the ages of 8 and 13. Participants also completed a measure of the speed and accuracy of written responses to simple addition, subtraction, and multiplication problems. On average, across the all of the RAN measures, students with learning disabilities were slower and less accurate on the arithmetic questions than students without learning disabilities. These results supported a relation between RAN performance and arithmetic, although it was not specific to individuals with learning difficulties in mathematics. Subsequent research has also shown a link between mathematical ability and performance on RAN tasks (e.g., Cirino, 2011; Geary, 2001). Geary (2011) found that traditional RAN measures (digits, letters, and words), and number-related competencies assessed in first grade predicted mathematical ability in fifth grade. In this study, the RAN task was used as an indicator of generic processing speed. In Cirino (2011), 286 kindergarteners were given the digit, letter, and object subtests of the RAN task. RAN performance was correlated with various mathematical abilities including number comparison, quantity discrimination, number identification, missing number indication, sequencing, dot comparison, oral counting, and counting down. The correlations were generally higher with RAN-digits than letters or objects. Variability in mathematics performance that was predicted by RAN tasks was independent of other correlates such as counting (Koponen et al., 2007), and working memory (Swanson & Kim, 2007). RAN-Quantity measures were not included, however, and so the domain-specificity of the correlations is unclear. Support for a domain-specific deficit in accessing quantity has been reported in comparisons of children with specific learning disabilities for mathematics versus reading (i.e., dyscalculia vs. dyslexia). Landerl, Bevan, and Butterworth (2004) showed that children with dyscalculia were slower than those with dyslexia or controls on subitizing groups of 1, 2, or 3 items. They were also slower and less accurate on other basic numerical abilities, including number naming, counting, and writing numbers. Van der Sluis, de Jong, and van der Leij (2004) administered the quantity, letters, digits, and object subtests of the RAN task to 19 children without a learning disability, 18 children with an arithmetic disability, 21 with a reading disability, and 16 with both reading and arithmetic disabilities. The children with an arithmetic disability were slower to complete the RAN-Quantities and the RAN-Digits version of the task in comparison to children without learning disabilities. In an extensive comparison of typically-developing children to those with dyscalculia, dyslexia, or both types of learning problems, Willburger et al. found that all groups of learning disabled children were slower than controls on RAN quantities whereas children with dyslexia were also slower than controls on RAN objects, letters, and digits. Willburger et al. argued that the deficit on RAN-Quantities reflected different processing limitations for the dyscalculic as compared to the dyslexic children. Specifically, these findings suggested that dyscalculic children have a deficit specific to quantity access whereas the dyslexic children have a more general naming speed deficit. Interestingly, dyscalculic children did not have a digit naming deficit whereas dyslexic children were impaired (in contrast to the results of van der Sluis et al. 2004). The results suggest that digit and letter name share more similar underlying processes (and these are important for reading) whereas the underlying quantity processes involved in quantity naming are specific to numerical tasks. Subsequent research suggested that the relation between quantity naming and performance was specific to certain aspects of numerical cognition: LeFevre, Fast, et al. (2010) reported a semi-partial correlation of -.32 (p < .01) between a non-symbolic arithmetic task and subitizing speed for 4- to 6-year-old children whereas subitizing speed was not related to digit naming performance (r = -.01). In summary, there is research linking mathematical and numerical performance to the RAN task however, the majority of that research has used letters, digits or colour versions. Research on the quantity subtest is limited.
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