In this study, Koponen and colleagues reviewed data from 38 studies that included 7,135 participants and examined the relationship between RAN tests and mathematical functioning.
In a Rapid Automatized Naming (RAN, or rapid naming) test,
the child is shown a page filled with rows of stimuli, and is asked to name the
stimuli as quickly as possible. The stimuli may be five letters or five digits repeated
in random order or five pictures of familiar objects, such as a cat or a fork,
repeated in random order. Sometimes a larger number of pictures of familiar
objects appears, in which case they are repeated fewer times.
Because the test does not assess general knowledge, the
stimuli in a RAN test are familiar and easy to identify. The test assesses the ability to
access the knowledge store quickly and fluently and retrieve from it the names
of the stimuli — that is, the phonological sequences required in order to say
the names of the stimuli. Therefore, the test assesses the broad ability of
retrieval fluency.
The difference between letter RAN and digit RAN, on the one
hand, and object RAN, on the other, is that letters and digits are highly
practiced stimuli, whose retrieval is expected to be very automatic. Children
and adults have practiced retrieving the word “three” when seeing the digit 3
many more times than they have practiced retrieving the word “cat” when seeing
a picture of a cat. Therefore, letter and digit RAN tests assess fluent retrieval of highly practiced
stimuli, whereas object RAN assesses fluent retrieval of less practiced
stimuli.
Reading is a highly practiced function. In everyday life,
we repeatedly practice retrieving the meaning of common written words, and also
retrieving their phonological code when we read them aloud. Therefore, there is
a much stronger relationship between letter and digit RAN and reading decoding —
not reading comprehension — than between object RAN and reading decoding. The
correlations between all types of RAN and reading decoding range from 0.38 to
0.51.
Like words, single-digit addition and multiplication facts
are also highly practiced and are stored as phonological representations in
long-term memory, for example: “two times three is six.” Therefore, there
should be a relationship between the ability to retrieve such facts quickly and
fluently and performance on RAN tests.
Researchers Noël and Rouselle, who specialize in the field
of numerical cognition, argue that the central difficulty of children with
mathematical disabilities lies in the ability to connect a digit with its
quantitative value. If so, digit RAN should be more strongly related to
mathematics than letter RAN or object RAN.
Butterworth, also an expert in numerical cognition,
proposes, in contrast, that the central difficulty of children with
mathematical disabilities lies in processing quantities of any kind — digits,
such as 3, or sets of objects or dots, such as OOO. According to this view,
children with mathematical disabilities will have difficulty both with digit
RAN and with quantity RAN. In a quantity RAN test, the child must say as
quickly and continuously as possible the quantities of circles shown to them,
for example O, OOOO, OO, OOO, usually arranged like dots on a die. Children
whose difficulty is processing quantities are not expected to have difficulty
on letter RAN or object RAN.
There is also a third possibility. It may be that children
with mathematical difficulties have a general difficulty in learning and
retrieving associations or connections between a visual stimulus and an
auditory stimulus. Such children will have difficulty saying that 3 is “three,”
and to the same extent will have difficulty saying that T is “Tee.” Children
like these will show low performance on all types of RAN tests.
In this meta-analysis, Koponen and colleagues found a significant correlation
of 0.37 between the various RAN tests and mathematical functioning. Stronger
correlations were found between RAN tests and solving arithmetic problems than between RAN and tests
that assessed not only calculations but also topics such as understanding the
decimal structure, fractions, or geometry. This makes sense, because tests that
assess a variety of different mathematical skills do not assess only the
ability to retrieve stimuli fluently.
Stronger correlations were found between RAN tests and
speed in solving single-digit arithmetic problems than between RAN tests and
speed in solving two-digit arithmetic problems, such as 32 × 51. Although
solving a two-digit problem requires retrieving the solutions to single-digit
problems, it requires not only retrieval but also the application of a
procedure.
In
addition, the researchers found that all types of RAN tests — digits, letters,
and objects — were related to mathematical functioning to more or less the same
extent. This may suggest that children with mathematical
difficulties have a general difficulty in learning and retrieving
visual-auditory associations. The implication is that one can test a
kindergarten child using an object RAN test, and low performance on this test
may predict future difficulties in the rapid retrieval of arithmetic facts.
This is very important to examine, because rapid retrieval of arithmetic facts
helps not only with simple arithmetic problems but also with multi-step
problems, such as two-digit calculations, and with solving mathematical word
problems. When a child quickly retrieves the answer to an arithmetic problem,
they do not need to calculate it, and they can then free up working-memory
resources and invest them in other aspects of a multi-step calculation or a
word problem.
Koponen, T., Georgiou, G., Salmi, P.,
Leskinen, M., & Aro, M. (2017). A Meta-Analysis of the Relation Between RAN
and Mathematics. Journal of Educational Psychology, 109(7), 977–992.
https://doi.org/10.1037/edu0000182
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