K. M. GADZICHOWSKI
However, children transition from one type of thinking in
preschool to a more complex cognition in early elementary
school, and patterning incorporates many of the improvements
in reasoning made during this time. Patterning may be interm-
ediate between seriation and transitivity, In seriation, a child must
understand how an item relates to the items that come before or
after it in the sequence. When looking at patterns, this same ru le
applies. In seriation, the relation is a simple one. Either the item
in question is smaller or larger than the other items in some
dimension (heig ht, width, weight, etc.). In patterning the re lat ion
is more complex; the relation might involve size, color, size and
color, shape, or other dimensions that are more abstract, and the
relationships can be multidimensional and much more comp-
licated.
Tran sitivi ty i s a mor e adv anced reasoning abili ty. Transitivity is
the understanding that if item A is related to item B in some
way, and item B is related to item C in some way, then the
relationship between A and C can be determined by comparing
these items to item B. The relationship between A and C (the
key items) is not directly observed but rather deduced by com-
paring the key items to another item. Both transitivity and pat-
terning incorporate the idea that an item is defined by, and sim-
ultaneously defines, properties of items that follow or preceed it.
The primary difference betwee n transitivity and patterning i s t h a t
patterning does not require an individual to utilize the relations
of A to B and C to B in order to determine the relation of A to
C. Transivity does require that one use those relations. Since a
child could make use of the transitive relation or alternatively
make use of the simultaneous presentation of all the items and
compare A to C directly, perhaps patterning is a precursor to
transitivity.
When a child understands patterns of items in which items
follow and precede other items, based on the rule of that pattern,
then the child can make inferences about a neighboring item by
looking at any one item in the pattern. A more advanced extr-
apolation would be to use a single item to make inferences
about both of the neighboring items successively or simultan-
eously. Being able to compare the two inferences about the
neighboring items in order to relate the neighboring items to
one another would be considered transitivity.
A first step in understanding patterning as an aspect of cog-
nitive development is to determine what kinds of patterns are
easy for children and what kinds are difficult. Does the dimen-
sion—colors, shapes, letters, etc.—make a difference, or do
children abstract the pattern rule independently of the d ime nsio n
in which it is presented? Gadzichowski, Kidd, and Pasnak (2010)
found that presenting preschoolers with oddity problems in dif-
ferent dimensions created large differences in the accuracy with
which these children applied the same simple rule (the oddity
principle). The same may well hold true for patterns early elem-
entary school children confronted with the more complex rules
involved in patterning. Further, not all of the rules which define
patterns are equally complex. Which pattern rules do children
grasp readily, without instruction, and which require improve-
ment in the kind of inferences the children can make? Answers
to these questions, which have never been asked by psycholo-
gists or educators, can inform investigations of how patterning
relates to children’s cognitive de velopment, and a lso a id ed u ca to rs
in determining what types of patterns can form the basis for the
most fruitful classroom instruction. The present study is an eff or t
to answer these questions by testing the following hypotheses:
Is children’s recognition of the same pattern equivalent reg-
ardless of the dimension which it is presented?
Are all pattern rules being tested in this study equally diffi-
cult for young children?
Method
Participants
Parental consent was obtained for 204 first-grade children fr om
an urban school district. There were 91 female and 113 male
participants. Of those participants 84 were African American,
73 were Hispanic/Latino, 32 were middle eastern, 5 were Cau-
casian and 10 were of an ethnicity other than those listed.
Materials
Because there are an infinite number of possible patterns, a
subset to compare had to be selected. Five different types of
patterns, subjectively estimated to range from easy to difficult
were constructed using Power Point so they could be presented
to the participants via a Dell Inspiron 1545 laptop. Each type of
pattern was constructed using letters, numbers, colors, shapes
and pictorial representations of objects (cars, flamingos, bees,
etc.). The first type of pattern (Type 1) was termed, simple
alternating “and used a rule of ABBABB, e.g., red, blue, blue,
red, blue, blue. This is the type of pattern children are usually
taught (Economopolous, 2008; Papic, 2007). A second type of
pattern (Type 2) was potentially a more difficult alternation. It
followed a rule of a constant alternating with a variable element
AEAZAF, e.g., green, purple, green, blue, green, red and was
termed “advanced alternation”. The third type of pattern (Type
3) was termed “symmetrical” and followed a rule of AKGGKA,
e.g. grey, black, orange, orange, black, grey. Another type of
pattern (Type 4) followed a rule termed “increasing”. The rule
was ABABBABBB, e.g., red, orange, red, orange, orange, red,
orange, orange, orange. Finally, the last type of pattern (Type 5)
was termed “arbitrary” and this included patterns such as:
AJDXNA, or yellow, blue, red, green, gray, yel low.
Procedure
The patterns were presented one at a time to each child indi-
vidually, and each child had unlimited time to respond. Each
child was shown 25 patterns in all; five shape, five color, five
letter and five objects patterns, one of each type for each of the
five pattern rules. The order of the presenta tion was complete ly
counterbalanced. The last item in each pattern was missing and
the children were asked to select the correct answer from four
possible options that were presented.
Analysis
Initial analyses were conducted with two factor ANOVA for
correlated measures. Inasmuch as each participant’s score on
each pattern was a one or zero (right or wrong), the interaction
of dimension and pattern type is the appropriate error term.
Results
There were no significant differences between the five dif-
ferent dimensions (letters, shapes, colors, numbers and objects),
F(4, 16) = 1.23, p > .05. There were however, significant dif-
ferences between the different types of patterns, e.g., arbitrary,
symmetrical, etc., F(4, 16) = 10.20, p < .001. Subsequent LSD
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