Primary CHC COG-ACH findings
Basic Reading Skills
Basic reading skills (BRS) are primarily decoding and word recognition skills. Tests measuring basic reading skills typically include tasks such as reading real or nonsense words, an application of the alphabetic principle--knowing how sounds and symbols go together.
Broad CHC abilities and BRS.
The following broad CHC cognitive abilities were consistently significant (low, medium or high) in the prediction of BRS (see Figure 1) at one or more age group: comprehension-knowledge (Gc) (medium from ages 6-13; high at ages 14-19), long-term retrieval (Glr) (low at ages 6-8), processing speed (Gs) (medium at ages 6-13), and short-term memory (Gsm) (low at ages 6-8; high at ages 9-19).
It is not surprising that Gc has strong BRS relations as ample evidence exists that general language and vocabulary development, aspects of Gc, are necessary for acquiring reading skills (Cooper, 2006; Shaywitz, Morris, & Shaywitz, 2008; Torgesen, 2002; Vellutino, Tunmer, Jaccard, & Chen, 2007). Also, the ability to form, store, and retrieve sound-symbol relations and efficiently retrieve lexical and general knowledge (Glr) have all been linked to early reading development (Cooper, 2006; Perfetti, 2007; Shaywitz  et al., 2008; Vellutino et al., 2007). The importance of Gsm for reading is consistent with research that has implicated auditory/verbal/phonological working or short-term memory (Cooper, 2006; Hammill, 2004; Kintsch, 2005; Kintsch & Rawson, 2005). Finally, different researchers (Berninger, Abbott, Thomson, & Raskind, 2006; Kintsch, 2005; Kintsch & Rawson, 2005; Shaywitz et al., 2008; Wolf, Bowers, & Biddle, 2000) have emphasized a variety of speed or fluency constructs in early reading skill acquisition (e.g., rapid automatic naming; naming speed; speed of semantic or lexical access; verbal efficiency; automaticity), findings consistent with the significant Gs finding in this review. The consistency of significance of Glr and Gs tend to decline with age while the influence of other abilities, such as Gc and Gsm, increase with age (see Figure 1). It is likely that Glr and Gs are more important during the beginning stages of reading when basic skills are first being acquired and, once BRS are in place, Gc and Gsm become more important in the development of reading.
The broad abilities of auditory processing (Ga), fluid reasoning (Gf), and visual processing (Gv) were not consistently significantly related to BRS. Most surprising may be that Ga did not meet the criteria for low, medium, or high significance at any of the ages. The reason for the lack of broad Ga significance is apparent when one examines the results of the research at the narrow ability level.
Narrow CHC abilities and BRS
Phonetic coding (Ga-PC) was classified medium at all three age levels (see Figure 1), a finding supporting the importance of phonemic awareness in BRS, despite the lack of significance for a broad Ga/BRS relationship.  This finding is consistent with research (Berninger et al., 2006; Cooper, 2006; Shaywitz et al., 2008; Torgesen, 2002) indicating that awareness of sounds is a prerequisite skill for mastering the alphabetic principle in reading (e.g., Adams, 1990; Ehri, 1998) and that a phonological core deficit exists in many individuals with dyslexia (e.g., Morris et al., 1998; Stanovich & Siegel, 1994).
The broad Gc/BRS significant findings appear related to three different narrow Gc abilities.  General information (Gc-K0) was consistently related to BRS at all ages, with a trend towards increased importance with increasing age (low at ages 6-8; medium at ages 9-19). This finding is consistent with the importance of prior background knowledge, knowledge integration, and general fund of cultural knowledge in reading (Cooper, 2006; Kintsch & Rawson, 2005). Listening ability (Gc-LS) was classified medium at the youngest age group (6-8 years), a finding consistent with research that has implicated the ability to comprehend spoken language (i.e., listening comprehension) in reading development (Hoover & Gough, 1990; Joshi & Aaron, 2000). 
Three different narrow memory abilities (Gsm and Glr), particularly those of a short- term nature (Gsm), appear important for BRS. Memory span (Gsm-MS) was not significant at ages 6-8 but was medium for ages 9-19. In contrast, working memory (Gsm-MW) was consistently classified medium at all age levels (see broad Gsm discussion for references regarding the importance of memory span and working memory in reading). Associative memory (Glr-MA) was only related (low) to BRS at the youngest ages (6-8 years), a finding consistent with research that has demonstrated that paired-associate learning, such as learning phoneme-grapheme relationships (Cooper, 2006; Hammill, 2004; Perfetti, 2007; Shaywitz et al., 2008), makes a unique contribution to predicting early reading (Windfuhr & Snowling, 2001).
The driving force behind the broad Gs/BRS finding appears to be the influence of the narrow perceptual speed (Gs-P) ability, which was consistently significant at all ages (low at ages 6-8 and 14-19; medium at ages 9-13). The importance of Gs-P is not surprising given the confirmed relationship between perceptual speed, speed of processing, and the need for automaticity in integrating phonological and orthographic codes in word reading (e.g., Barker, Torgesen, & Wagner, 1992; Berninger, 1990; Hale & Fiorello, 2004; Joshi & Aaron, 2000; Urso, 2008).
Reading Comprehension
Reading comprehension (RC) is constructing meaning from text through a complex process that integrates multiple linguistic factors. Tests measuring reading comprehension include tasks that require word knowledge and understanding passages usually demonstrated through multiple-choice, open- ended, or cloze procedures.
Broad CHC abilities and RC. 
Several broad CHC abilities were consistently significant (low, medium, or high) in predicting reading comprehension at one or more of the age groups:  auditory processing (Ga) (medium at ages 6-8), comprehension-knowledge (Gc) (high at all ages), long-term retrieval (Glr) (low ages 9-13), and short- term memory (Gsm) (low at ages 6-8 and 14-19). 
Broad Gc displayed the most consistent relation to reading comprehension across all ages levels, a finding reinforced by studies that have demonstrated the important role of general language development and vocabulary (e.g., Baker, Simmons, &Kame’enui, 1995; Coyne, Simmons, Kame'enui &Stoolmiller, 2004; Jenkins, Van den Broek, Espin, & Deno, 2003; Perfetti, 2007) and prior knowledge (e.g., Anderson &Pearson, 1984; Kintsch & Rawson, 2005; Nation, 2005) in reading comprehension. In fact, Floyd, Bergeron and Alfonso (2006) reported broad Gc levels as the primary difference between individuals with good and poor comprehension. Research supporting the significant relations for Ga and Glr abilities with reading, in this case RC, was discussed in the previous basic reading skills (BRS) section and will not be repeated here.
Broad abilities not consistently significant at any of the three age groups include processing speed (Gs), fluid reasoning (Gf), and visual processing (Gv). However, Gs was classified tentative/speculative at the younger ages (ages 6-13), which is consistent with Keith’s (1999) research. The Gf tentative/speculative classification, only at the oldest age group (14-19 years), is suggestive of Gf involvement at higher-levels of reading comprehension, a finding consistent with other research linking Gf and RC (e.g., Floyd et al., 2006; McGrew, 1993; Nation, Clarke, & Snowling, 2002). The tentative/speculative RC findings for Gs and Gf may be partially explained by the narrow abilities in the current research synthesis.
Narrow CHC abilities and RC
Given the complex cognitive demanding nature of reading comprehension (Baddeley, Logie, Nimmo- Smith, & Brereton, 1985; Perfetti et al., 2007), it is not surprising that working memory (Gsm-MW) displayed a high classification at all ages. Memory span (Gsm-MS) was consistently significant (medium) only from ages 14-19.  We hypothesize that this finding is related to the inclusion of longer items (lengthy oral sentences) at the top end of most MS tasks, items which increase the demand for listening comprehension or listening ability (Gc-LS), versus simpler rote MS.  Listening comprehension is frequently cited as a good predictor of reading comprehension (Aaron & Joshi, 1992; Cooper, 2006).  The importance of broad Gc for RC appears due to the narrow abilities of general information (Gc-K0) and listening ability (Gc-LS) which were consistently significant (high for all age groups).
While broad Ga was only consistently significant (medium) at ages 6-8, phonetic coding (Ga-PC) was implicated at all ages (low at ages 6-8 and 14-19; tentative/speculative at 9-13). A possible explanation of these age-differentiated findings is the observation (from inspection of the on-line summary coding table for reading comprehension) that six of the nine significant PC-RC analyses came from McGrew’s (2007) multiple regression manifest variable study that used the WJ III tests (versus clusters) as IV’s. The WJ III Sound Awareness test has been reported to be a possible mixed measure of phonetic coding (Ga-PC) and working memory (Gsm-MS; see Schrank, 2006). When Sound Awareness was significantly related to a WJ III achievement dependent variable, McGrew (2007) double coded it as reflecting significance for both PC and MW. Thus, it is possible that the Ga-PC/RC significance may be related to influence of Ga-PC abilities at the youngest ages (6 to 8) and the more complex Gsm-MW component at the older ages (14 to 19). 
Again demonstrating the importance of narrow (vs broad) cognitive abilities in understanding achievement are the Glr and Gs broad and narrow ability findings. Meaningful memory (Glr-MM) had a high classification from ages 9-19 and naming facility (Glr-NA) was medium at ages 9-13 and low at ages 14-19, while broad Glr was only salient (low) at ages 9-13.  Individuals with RC difficulties often display problems with verbal fluency, word retrieval, naming facility, or speed and quality of lexical access (e.g., Kintsch, & Rawson, 2005; Nation, Marshall, & Snowling, 2001; Shaywitz et al., 2008) which is consistent with the Glr-NA/RC findings reported here. Similarly, despite broad Gs not being identified consistently significant at any age, narrow perceptual speed (Gs-P) was significant at all ages (medium, medium, low). A strong relationship between reading comprehension and quick and automatic processing of letters and words (fluency) and word reading speed (e.g., Fuchs, Fuchs, Hosp, & Jenkins, 2001; Jenkins, et al., 2003) is consistent with the strong perceptual speed (Gs-P) and RC findings.
Basic Math Skills
Basic math skills (BMS) include arithmetic and computational skills. Tests measuring basic math skills usually include tasks ranging in difficulty from basic math facts to solving more complex algorithmic computations.
Broad CHC abilities and BMS.
The following broad CHC cognitive abilities were consistently significant (low, medium, or high) in the prediction of BMS at one or more age group: comprehension-knowledge (Gc) (medium at ages 9-19); fluid reasoning (Gf) (medium at all ages); and processing speed (Gs) (medium at all ages). Language skills (aspects of broad Gc) have been linked to math (e.g., Fiorello & Primerano, 2005; Flanagan et al., 2006; Floyd, Evans, & McGrew, 2003; Fuchs et al., 2006; McGrew, 2008; Swanson & Jerman, 2006) especially as Gc relates to the development of number concepts (e.g., Carey, 2004; Gelman & Butterworth, 2005) and the retrieval of math facts (Chong & Siegel, 2008). The importance Gf in the prediction of math achievement is consistent with considerable research (e.g., Fiorello & Primerano, 2005; Floyd et al., 2003; Flanagan et al., 2006; Fuchs et al., 2006; Geary, 1993, 2007; Rourke & Conway, 1997).  The Gs-to-arithmetic skill link (Bull & Johnston, 1997; Fiorello & Primerano, 2005; Floyd et al., 2003; Fuchs et al., 2006) has been explained in terms of counting speed (Geary, 1993, 2007), numerical processing fluency (Swanson & Jerman, 2006) and efficiency and consistency of execution of simple cognitive tasks during math (Fuchs et al., 2006; Geary, 1993, 2007).
The broad abilities of Ga, Gv, Glr, and Gsm were not consistently significant at any age, findings inconsistent with prior research. Glr and Gsm were found predictive of math skills throughout childhood and adolescence by Floyd et al. (2003). Semantic retrieval, an aspect of Glr, has also been reported to contribute to math disabilities in college students (Cirino, Morris, & Morris, 2002). Further, the ability to fluently retrieve math facts from memory, a Glr function, is the most consistent BMS deficit associated with MD (e.g., Garnett, Frank, & Fleischner, 1983; Geary, 1990, 1993; Geary, Hamson, & Hoard, 2000; Goldman, Pellegrino, & Mertz, 1988). Most of the above inconsistencies can be further explained, and to some extent, resolved by inspecting the narrow ability findings for BMS.
Narrow CHC abilities and BMS. 
As was the case for BRS and RC, the current findings suggest that the narrow cognitive abilities may play an important role in the prediction of basic math achievement even when the corresponding broad ability does not. For example, broad Ga was not significant at any age group, but phonetic coding (Ga- PC) displayed a medium level of consistent significance at ages 6-13 and was tentative/speculative at ages 14-19. Phonological processing (Ga-PC in CHC taxonomy) has been reported to predict arithmetic achievement (e.g., Leather & Henry, 1994; Rasmussen & Bisanz, 2005) and is associated with MD and low math achieving children with fact fluency deficits (Chong & Siegel, 2008). Phonological processing has been hypothesized to influence computation skills since speech sound processes are used when solving problems (Bull & Johnston, 1997; Geary, 1993; Rourke & Conway, 1997) and counting requires retrieval of the phonological codes for number words (Geary, 1993; Logie & Baddeley, 1987).
Perceptual speed (Gs-P) was consistently significant at a high level for all age groups.   The Gs-P/BMS link may be a function of “subitizing,” which is the ability to instantly see “how many” without counting. Subitizing underlies development of fluency with math facts which is thought to be a core deficit in MD (e.g., Geary, 1993; Jordan, Hanich, & Kaplan, 2003).  Alternatively, since all the significant Gs-P findings involved the WJ III Visual Matching test (either alone or when combined with another perceptual speed test; Keith, 1999; McGrew, 2007; McGrew & Hessler, 1995)9, a test requiring rapid recognition of similar digit pairs in a line of numbers, an alternative explanation may be that the Gs-P/BMS may be due to number facility (Gs-N) ability. Working memory (Gsm-MW), which was consistently significant (high for all ages) is frequently cited as important for BMS (e.g., Geary, 1993, 2007; Geary, Brown, & Samaranayake, 1991; Hitch & McAuley, 1991; Passolunghi, Mammarella, & Altoè, 2008; Swanson & Jerman, 2006) and is also suggested as a core deficit for individuals with MD (e.g., Bull, Espy, & Wiebe, 2008; Chong & Siegel, 2008; Geary, 2003; Koontz & Berch, 1996; Passolunghi & Siegel, 2001).
Math Reasoning
Math reasoning (MR) is problem-solving skills in math. Tests measuring MR typically include word problems, number series, concepts, and application of mathematical operations and concepts. Achievement in MR will depend, to some extent, on proficiency with basic math skills.
Broad CHC abilities and MR.
Several broad CHC abilities were consistently significant (low, medium, or high) in predicting math reasoning at one or more of the age groups: comprehension- knowledge (Gc) (low at ages 6-8, medium at ages 9-13, high at ages 14-19); fluid reasoning (Gf) (high at ages 6-13 and medium at ages 14-19); processing speed (Gs) (mediumat ages 6-13); and short-term memory (Gsm) (low at ages 14-19). Much research supports the strong predictive nature of Gc for mathematics (e.g., Hale, Fiorello, Kavanagh, Hoeppner, &Gaither, 2001; Keith, 1999; McGrew et al., 1997) and the association between MD and limited oral language abilities (Fuchs et al., 2008; Proctor, Floyd, & Shaver, 2005). Furthermore, the importance of Gc increased with age, a finding consistent with the increased linguistic demands of more complex math reasoning tasks (e.g., Fuchs et al., 2006, 2008; Geary, 1994).
The Gf finding is consistent with a body of research that identifies Gf as important to math reasoning (e.g., Fiorello &Primerano, 2005; Floyd et al., 2003; Fuchs et al., 2006; Geary et al., 2007; McGrew, 2008; Rourke & Conway, 1997). Fluid reasoning is a strong predictor of math achievement (Hale, Fiorello, Kavanagh, Holdnack, & Aloe, 2007) and is often significantly impaired in individuals with MD (Geary, 2007; Proctor et al., 2005). Finally, Gs has also been identified as an important predictor of MR (e.g., Floyd et al., 2003; Geary, 2007; Swanson & Jerman, 2006) possibly facilitating reasoning by freeing up cognitive resources in working memory for higher level complex processing and thinking (e.g., Bull & Johnston, 1997; Fuchs et al., 2006).
The current review did not identify broad Ga, Glr, or Gv as consistently significant for math reasoning at any age group. While these non-significant findings are consistent with the Flanagan et al. (2006) review, other research is contradictory. Floyd et al. (2003) reported a moderate relationship between math achievement and Glr and Ga. As discussed next, the current review found several narrow Glr or Ga abilities to be significant predictors of math reasoning even though the broad cognitive abilities were not.
Narrow CHC abilities and MR. 
Phonetic coding (Ga-PC) was classified as medium in consistency of significance at ages 6-8 and low for ages 9-19. A number of studies have implicated the phonological system as underlying individual differences in math problem-solving (e.g., Furst & Hitch, 2000; Gathercole & Pickering, 2000; Geary & Brown, 1991; Swanson & Sachse-Lee, 2001). As noted for BMS, research has implicated the importance of perceptual speed (Gs-P), such as rapid processing of numbers and counting speed, for math performance (e.g., Geary et al., 2007; Fuchs et al., 2006; McGrew, 2008). This was supported in the current review when perceptual speed (Gs-P) displayed a medium level of consistent significance with MR across all age groups.
Two narrow Gsm abilities were important in the prediction of MR at one or more age group: memory span (Gsm-MS) was low for ages 6-8 and working memory (Gsm-MW) was high at all ages. Other research supports these findings as memory span (Gsm-MS) has been related to performing mental arithmetic and how quickly numbers can be counted (Geary, 1993; Holmes & Adams, 2006). Considerable research confirms the importance of working memory (Gsm- MW) for math reasoning (e.g., Fuchs et al., 2008; Geary, 2007; Passolunghi, 2006). Both the phonological loop (e.g., Furst & Hitch, 2000; Gathercole & Pickering, 2000; Geary, 2007) and visual-spatial sketchpad (e.g., Geary, 2007; Holmes &Adams, 2006), components of working memory (Gsm-MW), contribute to math reasoning performance.