Creative Education
2012. Vol.3, No.5, 632-635
Published Online September 2012 in SciRes (
Copyright © 2012 SciRe s . 632
Patterning Abilities of First Grade Children:
Effects of Dimension and Type
K. Marinka Gadzichowski
George Mason, Fairfax, USA
Email: Kgadicho@gm
Received July 18th, 2012; revised August 20th, 2012; accepted August 29th, 2012
In the United States children receive instruction on recognizing patterns beginning most often in kinder-
garten and continuing on through early elementary school years. Although widely accepted and included
in curricula, patterning instruction has not been based on empirical research. The current study is the first
attempt to determine how the dimension, e.g. color or shape, in which a pattern is displayed impacts chil-
dren’s ability to understand the pattern. This study is also an initial exploration of whether the overall
“rule” of the pattern impacted a child’s ability to recognize a pattern. Five types of patterns displayed in
five different dimensions were presented to 204 first grade children in a completely counterbanced order.
Results indicated that the dimension in which a pattern was displayed made no difference to the children.
Patterns with alternating elements were significantly easier than any others, and those with increasing
numbers of elements were significantly more difficult. Implications for instruction in patterning were
Keywords: Patterning; Cognitive Development; Education
Children of elementary school age in most school districts in
the United States are taught how to recognize patterns made up
of letters, numbers, shapes and colors. This instruction is term-
ed “patterning”. There are several manuals in existence that
provide directions on how to go about teaching patterning
(Burton, 1982; Ducolon, 2000; Jarboe & Sadler, 2003). The use
of patterning in current curricula nationwide is based on a con-
sensus of educators who believe that patterning has educational
value because it improves children’s cognitive abilities (e.g.,
National Council of Teachers of Mathematics, 1993). The im-
provement in thinking ability would lead to improved under-
standing of classroom instruction.
Suggested improvements in thinking include increased sensi-
tivity to critical differences or sameness in items (Papic, 2007),
identifying repetitions (alternations) and increases or decreases
in the number of items (Economopolous, 1998), and detecting
and apply ing relationships between items (Threlfall, 1999). The se
supporting abilities are thought to facilitate the development of
prealgebra (Papic, 2007; Warren, Cooper, & Lamb; 200 6). Th e re
is no direct proof that this supposition is correct, but White,
Alexander, and Daugherty (1998) found that mastery of pat-
terns wherein elements alternated (e.g. red, blue, red, blue) was
correlated with analogical reasoning, which would contribute in
turn to an understanding of prealgebra.
The literature in this area is quite limited; there are only two
studies that address how patterning instruction impacts achieve-
ment. In 1973, Herman gave 24 lessons on patterns made from
alternating shapes, sizes or colors to kindergarten children from
impoverished backgrounds. Her findings were that African-
American children who received this instruction made gains in
numeracy skills but Latino/Hispanic children did not. In 2006,
Hendricks, Trueblood, and Pasnak expanded the depth of pat-
terning instruction to incl ude 480 color, size, number, letter, an d
time (clock face) patterns ranging from alternations to unidime-
nsional orderings to matrices presenting patterns in two dimen-
sions. The children who received this type of instruction made
greater academic gains than children in their control groups who
received instruction focused specifically on academic material
that had been developed upon the recommendation of teachers.
These two studies constitute the entire set of empirical evidence
that patterning has an effect beyond becoming better at pattern-
ing per se. However, it is clear that patterning instruction has
become a fixture in education, and for that reason deserves
To date, very little research exists that has been designed to
determine which types of patterns are the easiest or hardest for
children to learn. It has been theorized that patterning was a
stepping stone toward a very early form of analogical reasoning,
and this type of reasoning was related to mathematical learning.
(White, Alexander, & Daugherty, 1998; Clements & Sarama,
2007a, 2007b, 2007c). Patterning may also contribute to
prealgebra since it is an early, age-appropriate form of
instruction in rules and relations (Threlfall, 2004). Clements and
Sarama (2007c: p. 507) theorized that “algebra begins with a
search for patterns. Identifying patterns helps bring order,
cohesion, and predictability to seemingly unorganized situa-
tions and allows one to recognize relationships and make
generalizations.” Therefore when children learn a patterning
rule and then learn to apply that rule when they are presented
with a pattern made up from new a child is sho win g “a lge bra ic
insight”—the understanding that a relation is not tied to
pa rt i cu la r c o nc re t e it e ms . He n ce , “recognition and analysis of
patterns are important components of the young child’s
intellectual development because they provide a foundation for
the development of algebraic thinking” (Clements & Sarama,
2007b: p. 524).
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-
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
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?
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.
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.
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.
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.
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
Copyright © 2012 SciRe s . 633
post hoc analyses revealed that Type 1 patterns (simple alterna-
tions) were significantly easier than Type 2 patterns, p < .05
and also significantly easier than Type 3 and Type 4 problems,
p < .005 and p < .001 respectively. Type 4 (increasing) patterns
were significantly more difficult than all other types of patterns,
p < .01. There was no significant difference between pattern
Types 2, 3 and 5. The percentage correct for each dimension
and type of pattern is presented in Table 1.
Because the patterning instruction observed in local elemen-
tary schools was conducted almost exclusively on patterns con-
structed from shapes, colors and numbers, it was assumed that
those dimensions would be significantly easier for the children.
However, the first grade children were able to recognize pat-
terns constructed using letters, numbers, colors, shapes or ob-
jects with equal accuracy. They did not have the difficulty app-
lying the same rule to different dimensions that Gadzichowski
et al. (2010) reported for preschoolers who attempted to apply
the oddity principle to stimuli varying in color, size, shape, or
orientation. It appears that by first grade, children are able to
abstract relations between stimuli with less attention to their
perceptual characteristics.
The most basic alternating patterns, e.g., red, blue, red, blue,
red, blue or red, blue, green, red, blue, green are often taught
toward the end of the kindergarten school year and the begin-
ning of the first grade school year. Therefore, the findings that
the participant’s performance on such patterns (ABBABB) was
better than performance on other pattern types makes sense.
The Type 4 patterns were the most difficult, indicating that
the idea of a constant object alternating with an increasing numbers
of objects is a complex concept and beyond the ability of most
first grade children at the beginning of that academic year. Sinc e
the most common mistake in “solving” this type of pattern was
to pick the answer choice that would have made the pattern a
simple alternation, it appears t hat the idea of an increa sing el em ent
was lost on the participants.
Perha ps the most surpri sing finding was that the Typ e 5 p at t er n
problems were solved with almost as much accuracy as the
ABBABB patterns. These Type 5 patterns had no discernible
rule; a child would have to reach the understanding that the
pattern is random and merely repeats itself.
In sum, these findings show that children’s ability to understand
patterns is not so much impacted by the dimension in which the
pattern is presented, as it is by the over arching structure of the
pattern itself. The implications for educators are two-fold. First,
it appears that there need not be much concern about the
dimension in which a pattern is presented. Second, alternation
patterns are those with which instruction in patterning should
start, because those are the easiest and would hence be best for
Table 1.
Percentage correct for five types of patterns presented in five different
61.27 Shape:
51.67 Object:
62.75 Letters:
57.45 Numbers:
Type 1 Type 2 Type 3 Type 4 Type 5
86.18 AEAZAF:
64.41 AKGGKA:
19.80 AJDXNA:
beginners. Third, and perhaps most important, patterning instr-
uction should not stop with alternation patterns. T he first gr ad ers
in the present study had received patterning instruction in kin-
dergarten, as part of the curriculum of the local school system,
and perhaps in preschool as well. Yet they did not generalize to
more advanced patterns, particularly those with increasing num-
bers of elements. Comprehending systematic increases is
integral to mathematics, so it appears that instruction on these
types of patterns, and on advanced types of patterns in general
would be beneficial to children as they develop their mathe-
matic skills.
Since pattern analysis is a cognitive skill that develops natu-
rally, but has scarcely been investigated, and because it is also
taught in American educational systems, developmental psycho lo -
gists should not continue to neglect it. In order to better under-
stand how it develops and how formal instruction in abstract
cognition such as patterning impacts not only the development
of that ability, but also other areas of cognition, patterning is a
topic that should continue to be explored. Future research should
explore other types of patterns, and attempt to further determine
which patterns are easiest and which are harder so as to estab-
lish a more complete knowledge base for including patterning
instruction in formal education.
The author acknowledges the constructive assistance of Ro bert
Pasnak and the gracious participation and cooperation of Dr.
Monte Dawson, Kristen Clark, and the principals, teachers, and
students of the Alexandria City Public Schools.
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