Rozencwajg, P., Schaeffer, O., & Lefebvre, V. (2010). Arithmetic and aging: Impact of quantitative knowledge and processing speed. Learning and Individual Differences, 20(5), 452-458.
The main objective of this study was to examine how quantitative knowledge (Gq in the CHC model) and processing speed (Gs in the CHC model) affect scores on the WAIS-III Arithmetic Subtest (Wechsler, 2000) with aging. Two age groups were compared: 30 young adults and 25 elderly adults. For both age groups, Gq was an important predictor of Arithmetic score variance (R² = 48% and R² = 45%, respectively). However, in line with Salthouse, the results showed that processing speed predicted Arithmetic scores only for the older adults, not for the younger ones (additional 9% of the variance for the elderly vs. 1% of the variance for the young adults). These results can clarify the ambiguous evolution of Arithmetic scores with aging: Arithmetic performance with aging seems to follow an intermediate path between Gc and Gf. This suggests that both Gq and Gs have an impact on Arithmetic in aging.
Additional quotes from the article
Today, “the CHC model (Cattell–Horn–Carroll theory of cognitive abilities) used extensively in applied psychometrics and intelligence testing during the past decade is a consensus model” (McGrew, 2005, p. 149). CHC is a hierarchical model (Fig. 1) with three strata: factor g (Stratum III), broad abilities (Stratum II), and narrow abilities (Stratum I). Broad CHC abilities (Stratum II) include Gf (fluid intelligence/reasoning), Gc (crystallized intelligence/knowledge), Gv (visual–spatial abilities), Gsm (short-term memory), Gs (cognitive processing speed), and Gq (quantitative knowledge). [Click on images to enlarge them]
In contemporary assessments of intelligence (Flanagan & Harrison, 2005), the Cattell–Horn–Carroll Theory (CHC model) plays an important role in interpreting the scores underlying the Wechsler Scale Subtests. There is some controversy, however, as to the constructs measured by each subtest. As stated above, authors disagree on how to classify Arithmetic in this model.
The first hypothesis tested here concerns the role of quantitative knowledge (Gq) in Arithmetic Subtest performance. Gq has been defined as the wealth (breadth and depth) of a person's “acquired store of declarative and procedural quantitative knowledge. Gq is largely acquired through the ‘investment’ of other abilities, primarily during formal educational experiences. It is important to recognize that RQ (narrow ability, Stratum I), which is the ability to reason inductively and deductively when solving quantitative problems, is not included under Gq, but rather is included in the Gf domain (broad ability, Stratum II). Gq represents an individual's store of acquired mathematical knowledge, not reasoning with this knowledge” (McGrew, 2005, p. 156).
Yet when we look at the performance curve with age (see Fig. 2), we can see firstly that the mean scores on Digit Span (Gsm) and Matrix Reasoning – which is a typical test of fluid intelligence (Gf) ([Schroeder and Salthouse, 2004] and [Verhaeghen, 2003]); – start to decline gradually at the age of 25, whereas the mean score on Arithmetic remains stable until age 70. Secondly, the mean score on Vocabulary – which is a typical test of crystallized intelligence (Gc) (Verhaeghen, 2003) – is close to the teenage level (age 16) after the age of 70, whereas performance drops well below that level on Arithmetic. Analyses of age effects on the WAIS-III subtests among American subjects indicate the same phenomena ([Ardila, 2007] and [Ryan et al., 2000]). Finally, Arithmetic performance with aging seems to follow an intermediate path between Gc and Gf (see Fig. 3). This result is similar to that found by Schroeder and Salthouse (2004), see their [Fig. 1] and [Fig. 2] p. 399 and 400): “All the factors were also influenced by knowledge (vocabulary), with the largest knowledge effects on the numeric/fluency factor” (p. 400).
.....the high correlations obtained between the scores on the Arithmetic Subtest and the new quantitative test, both for the young and older adults, support the hypothesis that the Arithmetic Subtest belongs to factor Gq in the CHC model ([Flanagan and Harrison, 2005] and [Flanagan and Kaufman, 2004])
CHC theory intelligence Cattell-Horn-Carroll WAIS III French WAIS III Gq Gsm Gs Gf working memory Aging IQs Corner Wechslers School psychology Neuropsychology Cognitive abilities
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