From Vygotsky to neurobiology, there is a solid theoretical base that supports the potential positive impact that play can have in the classroom. Vygotsky (1967) created a coherent theory about play in which the very act of play put the child into a zone of proximal development. Vygotsky theorized that play provided the most efficient means by which the child could pass through the zone of proximal development.  In other words, play was the fastest way to learn.

         Decades later, neurobiologists have found empirical evidence to support the benefits of play.  Although play remains an emerging area of research in neurobiology, there is growing evidence of its influence on development. Byers and Walker (1995) found that play and growth of the cerebellum peak at the same time in childhood.  Pellis, Pellis, and Whishaw (1992) found that play-deprived rats, at puberty, had less mature than expected patterns of neuronal connections in their medial prefrontal cortexes.  Spinka, Newberry, and Bekoff (2001) concluded that play amounted to training for the unexpected and contributed to more flexible patterns of thinking.  Finally, Bateson (2005) suggested that play helped an individual avoid false endpoints.   

         The focus of this study was to perform exploratory research on the impact of play on attitudes toward mathematics.  The primary research question was: Does play in a middle school mathematics classroom have a positive impact on the attitudes of students toward mathematics?

Methods & Data Sources

This exploratory study was conducted from August to May of the 2009-2010 school year.  Participants (n=49) were 6^th, 7^th, and 8^th grade mathematic students at a private school in the Southeastern United States.  Students received 50 minutes of math instruction per school day.  The study design required incorporation of math play (see Table 1) into the standard curriculum. Typically, there were two opportunities for math play per week.  Math play was defined as an activity that fit into one of seven categories proposed by the National Institute for Play.  Play activities were brief, lasting about ten minutes. 

Institutional permission for the research was granted, and participants voluntarily completed a forty question Attitude Toward Mathematics Inventory (ATMI). Responses were gathered in August, December, February, April, and May. The data can be thought of as five repeated observations within an individual. For this reason hierarchical linear modeling and specifically growth curve modeling was employed.  The researchers used HLM 6.02 developed by Bryk and Raudenbush to analyze the data.

Table 1

Patterns of Play and Examples from this Study

Pattern	Examples from Classroom Research
Body Play & Movement	Students perform pantomimes that demonstrate various slopes.
Object Play	Students play with balance scales and small objects in order to discover how to balance an equation.
Social Play	Students create and tell math jokes.
Imaginative & Pretend Play	Students pretend to conduct TV interviews of celebrity mathematicians.
Storytelling-Narrative Play	Students write trailers for a new movie on a specific math topic.
Transformative-Integrative & Creative Play	Students imagine and describe life on a 2-D planet.

Note. Patterns of play adapted from The National Institute for Play. Retrieved from    http://www.nifplay.org/states_play.html

Results

            To determine if responses on the ATMI were clustered within students, an unconditional model was run. The Interclass correlation coefficient was .64 and it indicated the degree to which the responses over the five time periods showed clustering within the student.  An ICC of 0 would have indicated there was no clustering of student responses over time within the student.  However, the non-zero ICCs suggest the hierarchical analysis was more appropriate, because this analysis accounts for the nesting of individual responses over time within the student. Recall that for repeated measures designs it is not uncommon to see ICCs of .50 and greater.  HLM estimation method is restricted maximum likelihood. For Model 1 there is significant within student variability (Level-1 intercepts) in attitude toward math of 188.03; there is significant between student variability (Level-2 intercepts) in attitude toward mathematics of 362.2; and there is significant variability when predicting student attitudes toward mathematics over the five time periods of 15.77 (Time Slope). These results remained constant across all models.

            For Model 4, the predicted initial attitude toward mathematics when Gender and Grade are held constant at 0 is 141.93. Further, the effect of being a male or female student in Grades 6 through 8 on the predicted initial attitude toward mathematics is not significant. While there is more male regression lines clustered around the intercept value of 178.1 overall the males and female intercept values are not significantly different.

            Model 4 predicted attitudes toward mathematics will improve 5.11 points on the ATMI index for every one time unit increase. So, from August 2009 to May of 2010, for every time unit increase students attitudes toward mathematics will increase 5.11 units on the ATMI scale when holding gender and grade (6 through 8) constant. Finally the deviance statistic in Model 4 (1566.36) is an improvement over Models 1, 2 or 3, suggesting that Model 4 fits the data best.

Educational Importance

         The results of this exploratory study indicate that, for this group of students, eight months of infusing play into middle school math classes had a positive impact upon student attitudes toward mathematics.  Evidence suggests that time (exposure to play) was significantly related to increases in attitude, and that gender and grade level were not related to change in attitude. Due to the exploratory nature of the research, such results must be interpreted with respect to whether future research in this area is warranted.  We conclude that these results strongly support further experimentation with play in the middle school math classroom.  Teacher attitude toward math was a potential confound in this study.  We recommend that future research employ an experimental design with random assignment to the play condition across multiple schools or classrooms. 

         We believe that this study on play produces some interesting implications for such serious topics as the Common Core mathematical practices.  We will discuss how four of these practices might be strengthened through the use of play. 

References

Bateson, P. (2005). The Nature of Play: Great Apes and Humans. New York, NY: Guilford.

Byers, J. A., & Walker, C. (1995). Refining the motor training hypothesis for the evolution of play. American Naturalist, 146(1), 25-40.

Pellis, S. M., Pellis, V. C., & Whishaw, I. Q. (1992). The role of the cortex in play fighting by rats: Developmental and evolutionary implications. Brain, Behavior and Evolution, 39(5), 270-284.

Spinka, M., Newberry, R., & Bekoff, M. (2001). Mammalian play: Can training for the unexpected be fun? Quarterly Review of Biology, 76, 141–176.

Vygotsky, L. S. (1967). Play and its role in the mental development of the child. Soviet Psychology, 5(3), 6-18.