Gf: Quantitative reasoning (RQ) and
general sequential reasoning (RG) and reading and
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
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).
Attention/concentration (AC) and executive
functions (EF) and math.
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).
Gc: Listening ability (LS) and
general information (K0) and math.
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.
Glr: Associative memory (MA),
meaningful memory (MM), and naming facility (NA) and
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).