Abstract. In 1982, an intact group of 37 preschoolers (age 4)
attending a play-oriented preschool were tested using the Lunzer Five
Point Play Scale (1955) to obtain a block performance measure. To
statistically control for social economic status (SES), IQ and gender,
the McCarty Scales of Children's Abilities (1972) were given, the
gender determined, and an SES score obtained (Hollings head &
Redlick, 1958). In 1998, after these same participants had completed
high school, their records were obtained. Outcome measures for the 3rd,
5th, and 7th grades included standardized tests and report card grades
in mathematics. High school achievement was determined by using 1)
number of courses, 2) number of honors courses, 3) advanced math courses
taken, and 4) grades. While controlling for IQ and gender, the block
performance measure was correlated and regressed against these outcome
variables. No significance was found at the 3rd- and 5th-grade levels by
evaluating report card grades and standardized math scores. At
7th-grade, there was a significant correlation between blocks and
standardized math scores, but not report card grades. At the high school
level, there was a positive correlation with all high school outcome
variables. There was no correlation between block performance and
standardized math tests or grades at the elementary school levels.
However, at the beginning of middle school, 7th grade, and in the high
school grades, a positive correlation between preschool block
performance and math achievement was demonstrated.
Historically, the education of preschool children, ages 3 to 5, has
produced widely varying philosophies on effective and developmentally
appropriate curriculum models (Bereiter & Englemann, 1966; Biber,
Shapiro, & Weckens, 1971; Montessori, 1912; Weikart, Rogers, Adcock,
& McClelland, 1971). Many of the designers of these early childhood
educational models were critical of the theoretical, philosophical, and
practical applications used by competing early education models
(Bereiter, 1972, 1986; Schweinhart, Barnes, & Weikart, 1993;
Schweinhart, Weikart, & Larner, 1986). At the same time, there has
been limited research on the long-term effects of specific activities
involved in these models. The often-cited research that does exist looks
primarily at the whole program's effect (Lee, Brooks-Gunn, Schnur,
& Liaw, 1990) as it correlates to later longitudinal effect on
larger social variables such as arrests (Bereiter, 1986), welfare,
graduation from high school, income, and owning a home (Barnett, 1993;
Schweinh art et al., 1993; Schweinhart & Weikart, 1997; Sevigny,
1987). There appears to be limited research evidence (Miller &
Bizzell, 1983) that looks at the effects of specific learning activities
on young children's later school achievement in reading, math,
science, and similar content areas.
The National Association for the Education of Young Children
(NAEYC) guidelines for developmentally appropriate practices (DAP)
(Bredekamp & Copple, 1997) support an active play curriculum and
self-initiating play activities. The DAP document, although widely
disseminated, has limited empirical longitudinal research for the
positions taken in the support of play learning and curriculum. It now
becomes incumbent upon early childhood researchers to test these DAP
assumptions and the specific value of play activities, in terms of how
they affect preschoolers' development and learning; learning in
their later developmental stages; and their effectiveness at the
elementary, middle, and secondary school levels.
Playing with blocks is a central activity in play preschools (Biber
et al., 1971; Weikart et al., 1971; Wolfgang & Wolfgang, 1999).
Thus, this study attempts to establish a correlation between the levels
of young children's block play and their performance in mathematics
in later school levels. The generally accepted definition of play would
include three large categories: 1) sensori-motor play (large and small
motor activity); 2) symbolic play, which involves representational
abilities and includes the fantasy play of socio-dramatic play; and 3)
construction play, which involves symbolic product formation with
blocks, Lego, carpentry, and similar materials (Piaget, 1962; Smilansky,
1968; Wolfgang & Wolfgang, 1999). Although there is a host of
empirical research on symbolic play (e.g., Cook, 1996; Dodge &
Frost, 1986; Fein, 1981; Pellegrii, 1980), the literature regarding
construction play, especially longitudinal studies, is limited (Miller
& Bizzell, 1983).
Playing with blocks has historically been a central play activity
and found is found in play-oriented preschools (Hartley, Frank, &
Goldenson, 1957; Hirsch, 1996; Isaacs, 1933; Provenzo, 1983). Playing
with blocks, as a form of construction play (Piaget, 1962), requires the
young child to build spatially with large numbers of pieces of unit
blocks of wood to produce representations of objects, or products. These
products, at the higher levels of block building, can be labeled as
imaginary structures representing real objects (Hirsch, 1996; Lunzer,
1955; Reifel, 1996b). Construction play with blocks offers the preschool
child the opportunity to classify, measure, order, count, use fractions,
and become aware of depth, width, length, symmetry, shape, and space
(Hirsch, 1996); thus, one can make a direct relationship with the skills
acquired in block play as being foundational for the later cognitive
structures (Kamii, 1972, 1982; Piaget & Szeminska, 1952) needed for
number and math skills and learning (Fennema et al., 1996; Ginsburg,
Balfanz, & Greenes, 1999; Ginsburg, Inoue, &Seo, 1999; Liedtke,
1995; Reifel, 1996a; Vondrak, 1996; Zammarelli & Burton, 1977). The
question is whether preschool age children who have intensive play
experiences in play-based preschools and who can perform at high levels
of block building, also show high levels of mathematical achievement
later in formal school settings.
This correlational study uses statistical regression to establish a
relationship between preschoolers' levels of block play with later
school achievement in mathematics at the elementary, middle, and high
school levels, while controlling for SES, IQ, and testing for the
effects of gender.
The 37 participants were selected in 1982 as an intact group of
preschoolers enrolled in a play-based preschool (later NAEYC-accredited)
located in a southeastern U.S. city of about 212,000 people, a
substantial portion of whom were employed in government-related fields.
In 1998, the school records of these same participants were obtained
after they had completed high school, to permit a longitudinal
comparison. Table I provides characteristics of participants in 1982
(when their block-building abilities were measured) and in 1998 (when
the longitudinal data was captured).
Ten participants (27%) could not be contacted. The racial mix of
these potential participants was six Caucasians, two African Americans,
and two Asian Americans. Of these, four were males, and six were
Lunzer Five-Point Play Scale. The Lunzer Scale, based on the
Piagetian theoretical framework, was used to rate the preschool players
"adaptiveness" in the use of the blocks, as well as their
"integration," or play complexity, on a five-point scale. One
(or the lowest score) would be defined as "the materials [blocks]
are used without regard to their physical or representational
properties." The highest score of five would define play as using
"the materials [blocks] ... in a highly insightful manner, adapted
to a concept that clearly transcends it." Thus, the higher score
signified a more development play performance with blocks. The Lunzer
(1955) research reports a .91 reliability with similar age participants,
while this research produced a 94 percent interjudgmental reliability.
McCarty Scales of Children's Abilities. A general cognitive
score, or IQ, was attained from summing the verbal, perceptual
performance, and quantitative scores on the McCarty Scales of
Children's Abilities (McCarty, 1972). This test was administered to
each participant at the preschool center by a professor of early
childhood education. The raw subscale scores were used, because the
indexed scores were normed by age level and would, therefore, have
reduced variance across participants.
The California Achievement Test. The California Achievement Test
(CAT) was administered by school officials in the normal routine of
standardized testing, beginning in grade 1, and continuing through grade
8. The CAT score was the mathematics computation and mathematical
concepts, using the national percentile score ranging from 1 to 99
points. Scores on tests administered at grades 3, 5, and 7 were used for
Mathematics Grades. Report card letter grades on mathematics, taken
from the participants' elementary records (grades 1 through 5),
were scaled as 0 (Unsatisfactory), 1 (N-needs improvement), 1.5(S
minus-satisfactory), 2 (S-satisfactory), 2.5 (5 plus-satisfactory), and
3 (E-excellent). Middle school (grades 6 through 8) letter grades on
mathematics taken from the participants' school records were scaled
as 0 (F-failure), 1 (D-below average), 2 (C-average), 3 (B-above
average), and 4 (A-excellent).
Higher Mathematics Courses Taken in High School. From high school
records for 9th through 12th grades, higher math courses (algebra 1, 2,
and 3; algebra 2 honors; mathematical analysis; geometry; geometry
honors; analytical geometry; trigonometry; calculus; advanced placement
calculus; and advanced placement statistics) were counted, with heavier
weightings given to "honors" courses. The score for the
variable "higher mathematics courses taken" was obtained by
adding the number of courses with a score of 1 for regular math courses.
A second variable was established comparing the number of honors courses
taken. Finally, a weighted combined point value of mathematics courses
taken was determined by summing all courses taken and giving a score of
2 for those labeled as honors and advanced courses.
The predictor variables of levels of block play (SES and IQ) were
measured in the fall of 1982 by testing a group of 3- and 4year-old
preschoolers. The longitudinal effects were later examined and gender
factored in after these same participants had completed high school.
Their school records--at the elementary, middle, and high school
levels--were obtained in 1998. During the preschool phase of data
gathering, the participants were rated by a researcher with the use of
Lunzer Five Point Play Scale (Lunzer, 1995); the researcher had been
trained and had demonstrated an interjudgmental reliability of 94
percent. This scoring was done while the participants were engaged in
block play on three different days in the natural classroom setting,
without any facilitation from their teacher. Participants were simply
instructed by the teacher at the beginning of the play session, "Do
the best block play that you can do today, and use as many blocks as you
can!" The researcher used the best of the three scores as the in
dependent or predictor variable.
Because IQ has been determined to correlate to school achievement
in mathematics (Aiken, 1976; Campbell & Ramey, 1995), and accounts
for a large percentage of the variance in play research (Smilansky,
1968; Smilansky & Shefatya, 1990), the researcher also administered
the McCarty Scales of Children's Abilities (McCarty, 1972) to
obtain an IQ score. Since gender has also been shown to be correlated to
various play abilities and mathematics (Casey, Pezaris, & Nuttal,
1992; Fennema & Sherman, 1978; Leder, 1985; Leder & Fennema,
1990; Meyer & Koehler, 1990), gender was established as a
dichotomous variable. The dependent or outcome variables obtained from
school cumulative records included: 1) results from the California
Achievement Test, 2) the grades in mathematics courses, and 3) higher
mathematics courses taken in high school.
Statistical Analysis. Using the SPSS (Statistical Package for
Social Science), two statistical analyses were used in this
study--hypotheses that state a relationship were tested with simple
regression, while those requiring control for IQ and gender used
The Elementary Grade Levels
Correlational analysis and regression techniques were used to
determine the relationship between block play and mathematical
achievement. The researchers' initial set of analyses addressed the
between-year interrelations among construction play with blocks, and
their measures of mathematical achievement. The correlation coefficients
are presented in Table 2. These analyses indicated that there were not
significant correlations between measured block play and the
students' 3rd-, 5th-, and 7th-grade standardized test scores.
Similarly, there were no significant correlations between the measure of
block play and the student's mathematics grades at the 3rd-, 5th-,
and 7th-grade levels.
The second set of analyses addressed the researchers'
hypotheses concerning the predictive relations between measures of
children's block play and their mathematical achievement in 3rd,
5th, and 7th grade. Using hierarchical regression techniques, the
analysis were designed to control contributions due to IQ and gender
respectively. Because gender and intelligence have been related to
mathematics achievement in previous research, they were used as a
control variable in all analyses. A two-step hierarchical regression was
performed for each of the mathematics achievement measures. These
analyses were based on the assumption that the association between the
variables of interest was linear. Furthermore, it was assumed that the
conditional variance was equal and that the conditional values on the
dependent variables were normally distributed. Examinations of the
residuals revealed no apparent violation of these assumptions. Gender
and IQ were entered as control variables at step one and measures of
block play we re entered at step two. Findings indicated that
children's play with blocks reliably predicted mathematical
achievement at the 7th-grade levels (F = -3.78, p = .03).
High School Level
Similar analyses were conducted to determine the relationship
between block play and the participants' mathematical achievement
at the high school level. For these analyses the researchers examined
the predictive relationship between participants' block performance
and 1) the number of higher mathematics courses taken in high school, 2)
the number of honors classes taken, 3) participants' average high
school mathematics grades, and 4) a weighted high school mathematics
"points" score that was created to give more weighting to
honors mathematics courses.
Analyses indicated that there was a significant relationship
between preschool block performance and the number of higher mathematics
courses taken, F = 4.18, p = .02. Similarly, there was a significant
relationship between preschool block play and the number of honors
courses taken, F = 4.05, p = .02. The relationship between the
participants' high school mathematics grades also yielded a
significant relationship, F = 5.6, p = .01. Finally, the relationship
between block play performance and the mathematics "points"
score was judged significant, F = 4.6, p = .01.
In summary, the researchers' hypotheses were supported to the
extent that children's play with blocks reliably predicted
mathematical achievement at the 7th-grade and high school levels. Thus,
with controls for IQ and gender, preschool block performance accounted
for nontrivial portions of variability.
Block performance during the preschool years and the later variable
of students' letter grades and mathematical achievement on
standardized tests did not demonstrate significance at the 3rd- and
5th-grade levels. At the same time, no significance was found at
7th-grade level on teacher-awarded grades. A clear significance was
found, however, for standardized testing at this same level. Also, since
all other outcome variables at the middle school and high school
levels--such as number of classes taken, number of honors classes taken,
average mathematics grades, and a combined weighted value of all
mathematics course taken--were all significant, the authors conclude
that there is a statistical relationship between early block performance
during preschool and achievement in mathematics, although not at the
elementary school years, but rather at the later middle and high school
levels. The question is raised as to why this same significance does not
appear at the 3rd- and 5th-grade levels.
One possible answer could be that children near the age of 11, or
the beginning of middle school, typically begin to acquire formal
operational thinking (Piaget, 1977), which enables the child to reason
in abstract terms and separate from the need to rely as heavily on
concrete objects (Forman & Kuschner, 1984). From a Piagetian
framework, the acquisition of knowledge is cumulative, drawing on the
motor activities of the preoperational years and stages (like block play
during the preschool school years and concrete use of objects during the
concrete operational period during the elementary school years).
Although a causal relationship was not established in this study, one
may still hypothesize that those preschool age participants who
demonstrated high levels of performance with block building were
developing the basic underlying cognitive structures that would permit
them to perform well in higher abstract mathematics, such as geometry,
trigonometry, and calculus. This can been seen as early as the 7th grad
e on standardized tests of mathematics skills. In turn, grades awarded
by teachers, and the standardized testing during the elementary years
(in grades 3 and 5), only test minimum skills and memorization, and thus
the researchers found no correlation between elementary mathematics and
block performance during this preoperational period. This finding may
suggest that the real and lasting effects cannot be demonstrated by
academic measures during the elementary school years, but rather can be
seen at the beginning of the middle school years. Support for this
assertion can be found in the research literature (Schweinhart, Weikart,
& Larner, 1986).
Follow-up studies on the effects of compensatory early preschool
education demonstrate that the effects on these children, who were
followed beginning in the 1st grade, were minimal and not found later in
the elementary grades (Luzar, 1981). The findings shown here as to the
lack of statistical significance at the elementary school level conforms
to these previous studies; however, later findings at the middle school
and high school levels suggest that earlier findings on the lasting
effects of preschool experience on the students were premature. Only
later can these effects be determined; namely, after students have
obtained formal operational thinking, and when students study school
subjects that require true higher-order thinking. Other researchers have
found this latency effect (Anderson, 1992; Campbell & Ramey, 1995;
Lee et al., 1990). These findings would support the inclusion of blocks
and block play in the play curriculum of preschool age children.
* Special acknowledgement and thanks are given here to the Creative
Center for Childhood Research and Training, 2746 West Tharpe Street,
Tallahassee, Florida 32303 and to its director, Dr. Pamela Phillips, who
supported this research effort through their resources, data gathering,
Aiken, L. R. (1976). Update on attitudes and other affective
variables in learning mathematics. Review of Educational Research, 26,
Anderson, B. (1992). Effects of day care on cognitive and
socio-emotional competence of thirteen-year. old Swedish school
children. Child Development, 63, 20-36.
Barnett, W. S. (1993). Benefit-cost analysis of preschool
education: Findings from a 25-year follow-up. American Journal of
Orthopsychiatry, 63, 500-508.
Bereiter, C. (1972). An academic preschool for disadvantaged
children: Conclusions from evaluation studies. In J. C. Stanley (Ed.),
Preschool programs for the disadvantaged: Five experimental approaches
to early childhood education (pp. 1-21). Baltimore: The Johns Hopkins
Bereiter, C. (1986). Does direct instruction cause delinquency?
Early Childhood Research Quarterly, 1, 289-292.
Bereiter, C., & Englemann, S. (1966). Teaching disadvantaged
children in preschool. Upper Saddle River, NJ: Prentice-Hall.
Biber, B., Shapiro, E., & Weckens, D. (1971). Promoting
cognitive growth: A developmental-interaction point of view. Washington,
DC: National Association for the Education of Young Children.
Bredekamp, S., & Copple, C. (Eds.). (1997). Developmentally
appropriate practice in early childhood programs. Washington, DC:
National Association for the Education of Young Children.
Campbell, F., & Ramey, C. (1995). Cognitive and school outcomes
for high-risk African-American students at middle adolescence: Positive
effects of early intervention. American Educational Research Journal,
Casey, G., Pezaris, L., & Nuttal, M. (1992). Spatial ability as
a predictor of math achievement: The importance of sex and handedness
patterns. Neuropsychologia, 30, 35-45.
Cook, D. (1996). Mathematics sense making and role play in the
nursery school. Early Childhood Development and Care, 121, 55-65.
Dodge, M. K., & Frost, J. L. (1986). Children's dramatic
play. Childhood Education, 62, 166-170.
Fein, G. (1981). Pretend play in childhood: As integrative review.
Child Development, 52, 1095-1118.
Fennema, E., & Sherman, J. (1978). Sex-related differences in
mathematics achievement and related factors: A further study. Journal
for Research in Mathematics Education, 9, 863-870.
Fennema, M., Carpenter, A., Franke, R., Levi, W., Jacobs, R., &
Empson, J. (1996). A longitudinal study of learning to use
children's thinking in mathematics instruction. Journal for
Research in Mathematics Education, 27, 8-25.
Forman, G., & Kuschner, D. (1984). The child's
construction of knowledge: Piaget for teaching children. Washington, DC:
National Association for the Education of Young Children.
Ginsburg, H. P., Balfanz, R., & Greenes, C. (1999). Challenging
mathematics for young children. In A. L. Costa (Ed.), Teaching for
intelligence II: A collection of articles (pp. 245-258). Arlington
Heights, IL: Skylight Press.
Ginsburg, H. P., Inoue, N., & Seo, K. (1999) Preschoolers doing
mathematics: Observations of everyday activities. In J. Copley (Ed.),
Mathematics in the early years (pp. 88-89). Reston, VA: National Council
of Teachers of Mathematics.
Hartley, R E., Frank, L., & Goldenson, R. M. (1957). The
complete book of children's play. New York: Crowell.
Hirsch, E. (1996). The block book. Washington, DC: National
Association for the Education of Young Children.
Hollingshead, A. B., & Redlick, F. C. (1958). Social class and
mental illness. New York: John Wiley & Sons.
Isaacs, S. (1933). Intellectual growth in young children. New York:
Kamii, C. (1972). An application of Piaget's theory to the
conceptualization of a preschool program. In M. C. Day & R. K.
Parker (Eds.), The preschool in action: Exploring the early childhood
program (pp. 363-420). Boston: Allyn and Bacon.
Kamii, C. (1982). Number in preschool and kindergarten. Washington,
DC: National Association for the Education of Young Children.
Leder, G. (1985). Sex-related differences in mathematics: An
overview. In E. Fennema (Ed.), Explaining sex-related differences in
mathematics: Theoretical modes. Educational Studies in Mathematics, 16,
Leder, G., & Fennema, E. (1990). Gender differences in
mathematics: A synthesis. In F. Fennema & G. Leder (Eds.),
Mathematics and gender (pp. 188199). New York: Teachers College Press.
Lee, V., Brooks-Gunn, J., Schnur, E., & Liaw, F. (1990). Are
Head Start effects sustained? A longitudinal follow-up comparison of
disadvantaged children attending Head Start, no preschool, and other
preschool programs. Child Development, 61, 495-507.
Liedtke, W. (1995). Developing spatial abilities in the early
grades. Teaching Children Mathematics, 21, 12-18.
Lunzer, E. A. (1955). Studies in the development of play behavior
in young children between the ages of two and six. Unpublished doctoral
dissertation, Birmingham University, London.
Luzar, E. (1981). As the twig is bent: Lasting effects of preschool
programs. Hillsdale, NJ: Consortium for Longitudinal Studies.
McCarty, D. (1972). McCarty scales of children's abilities.
New York: The Psychological Corporation.
Meyer, M., & Koehler, M. (1990). Internal influences on gender
differences in mathematics. In E. Fennema & G. Leder (Eds.),
Mathematics and gender (pp. 60-95). New York: Teachers College Press.
Miller, L., & Bizzell, R. (1983). Long-term effects of four
preschools: Sixth, seventh, and eighth grades. Child Development, 54,
Montessori, M. (1912). The Montessori method. New York: Schocken
Pellegrini, A. D. (1980). The effects relationships between
kindergartners' play and reading, writing, and language
achievement. Psychology in the Schools, 17, 530-535.
Piaget, J. (1962). Play, dreams, and imitation in childhood. New
York: Norton Press.
Piaget, J. (1977). Problems in equilibration. In M. Appel & L.
Goldberg (Eds.), Topics in cognitive development: Vol. 1.
Equilibrations: Theory, research and application (pp. 3-13). New York:
Piaget, J., & Szeminska, K. (1952). The child's concept of
number. London: Routledge and Paul Kegan.
Provenzo, E. (1983). The complete block book. Syracuse, NY:
Syracuse University Press.
Reifel, S. (1996a). Block construction: Children's
developmental landmarks in representation of space. Young Children, 48,
Reifel, S. (1996b). Spatial representation in block construction.
Paper presented at annual meeting of the American Educational Research
Association, Montreal, Canada.
Schweinhart, L., Weikart, D., & Larner, M. (1986). Consequences
of three curriculum models though age 15. Early Childhood Education
Quarterly, 1, 15-45.
Schweinhart, L. J., Barnes, V., & Weikart, D. P., with Barnett,
W. S., & Epstein, A. S. (1993). Significant benefits: The High/Scope
Perry Preschool study through age 27. Monographs of the High/Scope
Educational Research Foundation, 10.
Schweinhart, L. J., & Weikart, D. P. (1997). Lasting
differences: The High/Scope preschool curriculum comparison study
through age 23. Monographs of the High/Scope Educational Research
Sevigny, K. E. (1987). Thirteen years after preschool: Is there a
difference? (ERIC Document Reproduction Service No. ED 299287).
Smilansky, S. (1968). The effects of sociodramatic play on
disadvantaged preschool children. New York: John Wiley & Sons.
Smilansky, S., & Shefatya, L. (1990). Facilitating play: A
medium for promoting cognitive, socioemotional and academic development
in young children. Gaithersburg, MD: Psychosocial & Educational
Vondrak, M. (1996). The effect of preschool education on math
achievement. (ERIC Document Reproduction Service No. Ed 399017).
Weikart, D. P., Rogers, L., Adcock, C., & McClelland, D.
(1971). The cognitively oriented curriculum: A framework for preschool
teachers. Urbana, IL: University of Illinois Press.
Wolfgang, C. H., & Wolfgang, M.E. (1999). School for young
children: Developmentally appropriate practices. Boston: Allyn and
Zammarelli, J., & Burton, N. (1977). The effects of play on
mathematical concept formation. British Journal of Psychology, 47,
A Comparison of Demographics on Participants at Preschool and High
Participants as of
Number of participants 37
Ages: 3 years, 10 months to
4 years, 11 months
Racial mix: Caucasian 74%
African American 17%
Asian American 9%
Gender: Males 51%
Age at entry: Before age 1 42%
Before age 2 34%
Before age 3 17%
Before age 4 7%
SES: Level 1 (lowest) 20%
Level 2 29%
Level 3 36%
Level 4 11%
Level 5 (highest) 3%
Type of school: Public school -
Private school -
University lab school -
education: Attending -
Not attending -
Participants as of
1999 (graduating high school)
Number of participants 27
18 years, 10 months to
19 years, 11 months
Racial mix: 85%
Age at entry: 55%
SES: Not Available
Type of school: 81%
Correlation Matrix of Grades 3, 5, 7: Mathematics and Blocks
Standardized Test Score Grade
Grade 3 Grade 5 Grade 7 Grade 3 Grade 5
Blocks 0.3158 0.0296 0.2785 0.1374 0.0665
(p=.101) (p=.452) (p=.105) (p=.313) (p=.384)