In this review, as in most other prior CHC and non-CHC COG-ACH reviews, broad visual-spatial processing (Gv) was the “odd man out” as it was not found to predict reading or math achievement. How can this be when other research has implicated certain Gv abilities (e.g., visual-spatial; length estimation) as a core deficit in MD and as important for success in mathematics (Geary, 1993, 2007; Hale et al., 2008; Osmon, Smertz, Braun, &Plambeck, 2006; Pinel, Piazza, Le Bihan, & Dehaene, 2004; Rourke, 1993; Zorzi, Priftis, & Umiltá, 2002)?  Below is a brief discussion of possible explanations, together with two tentative/speculative Gv narrow ability findings that did emerge. This is followed by a brief discussion of the other tentative/speculative findings found in this review, findings that must be viewed as suggestive and in need of additional research, particularly since most of these findings are based on single WJ III tests from a handful of analyses.

Specification error, as described earlier in this manuscript, may be present in the current review. It is possible that those Gv abilities related to academic learning simply are missing from the current collection of intelligence batteries used in school achievement research. The types of Gv tests in current intelligence batteries (e.g., block design, spatial relations; memory for designs or pictures; etc.) may not measure the Gv abilities important for reading and math.  For example, the visual aspects of orthographic processing or awareness (the ability to rapidly map graphemes to phonemes; rapid processing of visual symbols; etc) have been reported as important for reading (e.g., Barker, Torgesen, & Wagner, 1992; Berninger, 1990; Berninger et al., 2006; Flanagan et al., 2006; Hale & Fiorello, 2004; Urso, 2008;) and are absent from intelligence batteries.  Additionally, more complex visual-spatial processing (not measured by current intelligence tests) may be important for school learning, such as Gv tasks that measure complex visual- spatial working memory (e.g., see Holmes, Adams & Hamilton, 2008; Maehara & Saito, 2007; Mammarella, Pazzaglia & Cornoldi, 2008).  It is also possible that the Gv mystery may be a DV or criterion variable problem. The math achievement DV measures used in the extant CHC COG-ACH research may not tap the higher level mathematics (e.g., geometry, trigonometry, calculus) that draw heavily on Gv abilities.

Second, lack of significance does not mean Gv abilities are not involved in reading and math. Obviously, individuals use their eyes when reading and when processing diagrams and figures during reading and math. Gv measures, as currently designed in intelligence batteries, simply may have no achievement variance to account for because the more powerful predictors (e.g., Gc, Gsm, Ga) account for the lion’s share of reliable variance in the achievement variables. To illustrate this concept we will use breathing. One must breathe to read and do math, yet breathing oxygen is not included as a predictor in COG-ACH research as it would not emerge as statistically significant. Like breathing, basic Gv processes may function as a threshold ability—you need a minimal amount to read and perform math, but beyond the minimal threshold level “more Gv”does not improve performance.

Two narrow Gv abilities were identified as tentative/speculative in the current review.  Visual memory (Gv-MV) was so classified at ages 14-19 for RC, possibly related to the positive effect of visual imagery on reading comprehension (e.g., Gambrell & Jawitz, 1993).  Spatial scanning (Gv-SS) was similarly classified at ages 6-8 for BMS.  Both of these isolated and tentative findings, which were based on single test indicators in a handful of studies, should be viewed with caution and warrant additional investigation. 

It is not surprising that quantitative reasoning (Gf-RQ) and general sequential (deductive) reasoning (Gf- RG) displayed significant relations with both math domains (BMS; MR).  Other research supports the relationship between mathematics and quantitative and deductive reasoning (e.g., Fuchs et al., 2005, 2006; Geary et al., 2007; Rourke & Conway, 1997).  These two narrow Gf ability findings also suggest that the broad Gf relation with math achievement may be driven largely by measures of deductive reasoning (e.g., WJ III Analysis-Synthesis), and/or tests that require the use of both inductive (I) and deductive (RQ) reasoning, but only when involving reasoning with numbers and numerical relations (e.g., WJ III Number Series and Number Matrices tests).  Quantitative reasoning (Gf-RQ) was also related to both domains of reading (BRS and RC), adding tentative support to the role of some aspects of Gf in reading, especially RC.

Ga:  Speech sound discrimination (US) and resistance to auditory stimulus distortion (UR) and reading and math. 

Ga-US/UR was related to BRS and MR at certain age levels.  These findings were due solely to the presence of the WJ III Sound Patterns-Voice test in a handful of analyses. However, research has supported the importance of sound discrimination abilities in learning to read (Berninger et al., 2006; McBride-Chang, Chang, Wagner, 1997).  Additionally, research has implicated speech sound processing, temporal processing, auditory perception, and encoding and maintaining phonological representations in working memory as related to math achievement (e.g, Fuchs et al., 2005; McGrew, 2008; Rourke & Conway, 1997; Swanson & Jerman, 2006). 

A potentially intriguing tentative finding was the significant relation between the WJ III Pair Cancellation test (classified as AC/EF by McGrew, 2007) and BMS and MR (but not reading) at the youngest age group (ages 6-8). It has been suggested that the WJ III Pair Cancellation test taps response inhibition, interference control, and sustained attention (Cooper, 2006).  Additionally, Poock (2005) reported that Pair Cancellation was one of three WJ III tests that reliably differentiated ADHD and non- ADHD subjects. Compromised executive functioning, including poor attention and inhibitory control, has been associated with the problems in development of math computation skills and with individuals with MD (Fuchs et al., 2006; Geary, 2007; Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007; McLean & Hitch, 1999; Swanson, 1993; Swanson & Jerman, 2006; Swanson &Sachse-Lee, 2001).

Listening ability (Gc-LS) was consistently significant in its relation with BMS at two ages and all ages for MR.   General information (K0) was also consistently related to MR at all ages.  These findings are consistent with the prior discussions of the importance of broad Gc and multiple narrow Gc abilities and mathematics.

Although broad Glr was not significantly related to BMS or MR in the current research synthesis, a number of narrow Glr abilities were identified as tentative/speculative. Naming facility (Glr-NA) was predictive of BMS at all ages and associative memory (Glr-MA) and meaningful memory (Glr-MM) were predictive of BMS and MR at one or more age levels. The importance for all three narrow Glr abilities is consistent with the finding that MD students often have difficulty forming and later retrieving or accessing long-term memory representations of math facts (Geary, 1993, 2007).  Learning math facts is a paired-  associate learning task requiring associative memory (Geary, 2007; Osman et al., 2006). Additionally, verbal counting, an aspect of naming facility (Glr-NA), has been mentioned as a precursor to early math achievement (Mazzocco & Thompson, 2005; Passolunghi, Vercelloni, & Schadee, 2007).