Block play and mathematics learning in preschool: The effects of building complexity,peer and teacher interactions in the block area,and replica play materials

Abstract

Block play has been included in early childhood classrooms for over a century, yet few studies have examined its effects on learning. Several previous investigations indicate that the complexity of block building is associated with math ability, but these studies were often conducted in adult-guided, laboratory settings. In the present investigation, the relationship of block play variables to both the complexity of block structures and math learning was studied in naturalistic free play settings. A total of 41 preschool children were videorecorded playing with blocks. Time in blocks, number of structures built, levels of social participation, frequency of teacher interactions, percentage of buildings without replica play toys, and structure complexity were coded. Findings indicated that level of social participation and percentage of structures built without toys predicted the complexity of children’s buildings. This building complexity was, in turn, associated with growth in math learning, as measured by Tools for Early Assessment in Mathematics. Based on these findings, a path model was constructed to hypothesize causal relationships between block play features, structure complexity, and math learning.

Keywords

child development early childhood education mathematics in young children play preschool

Play has been associated with young children’s social, emotional, and intellectual development (Bergen, 2002; Lillard et al., 2013). However, surprisingly, little research has been conducted on block play, even though it has long been considered a major form of play in early childhood (Piaget, 1962) and has been a standard activity in preschool and kindergarten classrooms for over a century (Froebel, 1895). The few studies that have been conducted indicate that there are relationships between block play and important areas of learning and development (Cohen and Uhry, 2007; Sluss, 2002; Sluss and Stremmel, 2004). Of particular relevance to our research are investigations indicating an association between block play in preschool and growth in math ability (Ramani et al., 2014; Wolfgang et al., 2001). These previous studies on blocks and mathematics were conducted in adult-guided or laboratory settings. Few naturalistic studies have been conducted that capture specific elements of a real classroom block play center, such as types of materials available or interactions with peers and teachers during play. In the present investigation, we examined the contributions of these various elements on children’s block building and, in turn, on the relationship of such building to mathematical thinking.

Background

Block play and math learning

Researchers have noted that block play provides many opportunities for early mathematical thinking (Kamii et al., 2004; Ness and Farenga, 2007). Ginsberg (2006) offers a rich description of math conversations and problem solving that arise as children build. In block play, he indicates, children think and talk about shape, size, length, area, and number. Other researchers have observed that block play includes high levels of math talk—conversations about mathematics (Ramani et al., 2014; Trawick-Smith et al., 2016). Frequency of math talk has been found to predict early math learning (Boonen et al., 2011; Klibanoff et al., 2006; Levine et al., 2010; Trawick-Smith et al., 2016).

The relationship between block building and math learning has rarely been studied directly. In two investigations, the complexity of children’s block structures was found to predict performance on math achievement measures (Ramani et al., 2014; Wolfgang et al., 2001). In another study, however, no association was found between preschool block abilities and math knowledge (Hanline et al., 2010). These previous investigations were conducted in adult-guided, laboratory settings, not in naturalistic classroom play areas. Also, blocks were the only available choice of play material, children were assigned to perform tasks with the blocks, and children built alone or with a researcher-assigned peer. Therefore, previous research has not taken into account the many other aspects of naturalistic block play settings—peers, teachers, and the other play materials that are available there. In this study, we examined naturalistic play in preschool classroom block areas, including how people and toys affect building and growth in math ability.

Peer interactions in block play

Research has indicated that block play is highly social and verbal. Complex language interactions among peers have been observed in classroom block centers (Cohen and Uhry, 2007; Sluss, 2002; Sluss and Stremmel, 2004). In one study, more social interaction was recorded when children were playing with blocks than when using any other kind of play material (Trawick-Smith et al., 2016). Such peer interactions—occurring in any area of a classroom—have been found to predict math ability at the end of a year of preschool (Bulotsky-Shearer et al., 2014; Tarim, 2009).

Why would peer interactions in the block area have a particularly strong effect on math learning? One theory is that social interactions during children’s block play include a great deal of math content. Ginsberg (2006) describes anecdotally how children collaborate on naturally occurring math problems as they build together. In a small descriptive study, children were found to engage in more math discussions and to solve more mathematical problems when they were building collaboratively than when playing alone (Trawick-Smith and Savalli, 2013). Such math-rich peer interactions might contribute directly to math learning. A question we examined in this study was whether the level of social participation in the block center—cooperative play versus parallel, solitary, onlooker, or unoccupied behavior (Parten, 1933; Rubin, 1989)—would contribute to complexity of block building and subsequent math learning.

Teacher interactions in block play

There has been a growing interest in the influence of teacher–child interactions in preschool on learning and development (LoCasale-Crouch et al., 2007; Mashburn et al., 2008; Trawick-Smith et al., 2016). Several studies have shown that conversations about mathematics between teachers and preschool children can enhance math learning. Wood and Frid (2005) describe the impact on children’s thinking of mathematical discourse—teacher language that is rich in math content. These researchers found that preschool teachers naturally used a variety of verbal strategies, such as asking open-ended, math-related questions, to extend thinking during problem solving. Larger scale studies have reported that a high frequency of adult–child math discourse in preschool classrooms or in homes predicts later math achievement (Klibanoff et al., 2006; Levine et al., 2010; Trawick-Smith et al., 2016). In the present investigation, we explored how natural adult–child interactions in the block center affected both block play complexity and math learning.

Block center materials

The materials available to play with in preschool block centers vary across classrooms (Prochner et al., 2008), yet little research has examined their effects. Several studies have focused on the influence of various literacy items in the block area (Pickett, 1998; Stroud, 1995). Not surprisingly, the presence of books and writing materials was found to increase literacy behaviors during block play. However, the effects of such materials on block building, itself, were not studied. Replica play toys—small people, animals, or vehicles that are commonly provided in preschool block areas—have not been studied, in spite of the fact that they have been recommended to teachers for decades (Doctoroff, 2001; Frost et al., 2011; Harms et al., 2014; Hirsch, 1984). No research has been conducted on what children do with these toys, what effects they have on block building, or whether their inclusion is beneficial. Such toys, while supportive of make believe, may distract children from actual building. Findings of a qualitative investigation of block center interactions confirm this (Trawick-Smith and Savalli, 2013). Children were observed building more complex structures and cooperating more frequently with peers in centers without these toys. In the present investigation, we assessed the impact of replica play toys by alternating observations weekly between blocks-only and blocks-with-toys play areas.

Method

Participants

Participants were 41 preschool children enrolled in four mixed-age (3- and 4-year-olds) classrooms in an American child development center with a teacher–child ratio of 1–7, a wide variety of learning and play materials, safe and well-designed indoor and outdoor spaces, and a planned curriculum that addresses national learning standards. Two hours of indoor free play are offered each day—once in the morning and once in the afternoon—in which children are able to choose activities in various play areas—books, blocks, pretend play, puzzles, math, science, and writing. The curriculum includes regular experiences and play materials to support children’s mathematics learning in the areas of number, geometry, and measurement. For example, each classroom has a special math area with games and activities that are related to math concepts. The classrooms were staffed by four lead teachers who hold master’s or bachelor’s degrees, four assistant teachers with bachelor’s degrees, and eight university student assistants who are studying early childhood education. A total of 21 participants were aged 4 at the time of enrollment in their classrooms and 20 were aged 3. Children were of diverse cultural and socioeconomic backgrounds—19 were Euro-American, 14 were Latino, and 8 were of other ethnic backgrounds; 16 were of middle socioeconomic status (SES) and 25 were of low SES, based on family eligibility for free or reduced lunch; and 21 were females and 20 were males.

Each of the classrooms included a block center comprising a large open space for building, with blocks stored on shelves along the periphery. Each block center was equipped with a set of unit blocks—hardwood blocks of varying lengths, shapes, and sizes that are common in preschools around the world. In addition, each block center contained a set of large hollow wooden blocks to create larger structures. Toy people, animals, and vehicles were also available to play within these centers during one half of the study. As part of this investigation, these materials were removed during the other half of the study.

We videorecorded all children who played in the block center of their classroom over a 6-month period in 125 separate, 20-minute observation periods during naturalistic free play in each classroom. All elements of block play captured on video that were of interest in the study were coded each time a child entered the block area, including a code for the complexity of each distinct structure a child built there. Because recordings were made in naturalistic play settings, there was variation in the number of block building episodes that were analyzed across individual children, ranging from 5 to 111, with a mean of 19 over the course of the study.

Measures

Tools for Early Assessment in Mathematics

Children’s math knowledge was assessed at the beginning of the study, in October, and again in April, at its conclusion, using the Tools for Early Assessment in Mathematics (TEAM; Clements et al., 2013). This instrument is used regularly in preschool research and measures knowledge of number, geometry, measurement, patterns, and other math concepts of children aged 3–8 years. TEAM was selected for use in the investigation because it measures a range of math abilities, not just number. Because it includes items on patterns, geometry, and measurement as well, it was deemed ideal for examining the impact of block building, which presents children with regular problems of shape, height, length, area, and patterning.

TEAM was administered individually to each participant by one of four trained research assistants in a quiet area outside the classroom. TEAM has been found to be a reliable and valid instrument (Clements et al., 2013). Item reliability for a group of 360 3- and 4-year-old children of diverse backgrounds was determined to be very high (r = .98) (Von Eye and Mun, 2005). The developers of TEAM also established construct validity using the Rasch modeling technique (Clements et al., 2013).

Number of structures and time in blocks

Frequency of block building was measured in two ways. The number of distinct block structures that each child built, individually or with peers, was tallied over the course of the study. The duration of block building was measured by summing the minutes that each child spent building in the block area during the 20-minute observation periods, across the 6 months of the investigation.

Block structure complexity

Each block structure that was built by a child during recorded observations was rated on its complexity, using a modification of an instrument developed in previous research (Hanline et al., 2010; Trawick-Smith and Savalli, 2013). An overview of this instrument is presented in Table 1. As shown in the table, a score of 1–10 was assigned for each structure, with simple stacks or rows being assigned lower scores and more complex and representational structures higher scores. If children played in the block area, but did not build at all, they were assigned a 1 for the entire 20-minute observation. Two independent researchers coded 100 percent of block structures; reliability coefficients indicated a sufficiently high level of agreement (Von Eye and Mun, 2005), kappa = .85. Mean complexity scores were computed for each child to obtain a measure of complexity that was independent of the number of structures built.

Table 1.

Summary of a block structure complexity scoring instrument, adapted from the previous research (Hanline et al., 2010).

Score	Type of structure
1	No building
2	Stacks (vertical piles, one block on top of the other)
	Lines/roads (horizontal rows, one block after the other)
3	Two or more adjoining piles or rows
4	“Fences” (rows of blocks lined on their edges)
5	Simple enclosures (“pens” or “houses” with blocks on edge, closing around a space)
	Simple bridges (rough bridging where a single cross-block does not precisely span uprights)
6	Complex enclosures (enclosures with blocks coming together completely in “corners” and/or adjoining multiple “chambers” are created)
	Complex bridges (elaborate or multiple bridges; cross-blocks fit uprights relatively well)
7	Complex enclosures with “roofs” or “flooring”
8	Obviously representational structures (interior spaces are decorated, individual blocks represent objects (tree, door, stairs, driveway, chair), the structure “looks like something,” and/or the building is named)
9	“Towns” (several separate or adjoined structures that are obviously representational are built that clearly represent different buildings)
10	“Towns” with a sense of scale (multiple buildings are roughly built to scale—for example, a house is smaller than an apartment building

Social participation in block play

Social participation during block play was rated from 1 to 5, using a modification of the Play Observation Scale (Rubin, 1989). Researchers coded the highest level of participation for each child who was captured in each recorded 20-minute period: cooperative play, parallel play, solitary play, onlooker behavior, or unoccupied behavior. Interrater reliability for this scale has been established in previous research. In this study, two independent researchers coded 100 percent of video and achieved a sufficiently high level of agreement (Von Eye and Mun, 2005), kappa = .84. Children’s mean levels of social participation across the course of the study were computed and used in our analysis.

Teacher interactions in block play

Coders tallied the number of teacher–child interactions that were observed for each child on each block play video. An interaction could be verbal or nonverbal (assisting a child with block building), but was only counted if a teacher obviously directed the interaction to a particular child. An interaction was considered to be completed once a teacher disengaged from the child. Ending a conversation and observing, interacting with another child, or leaving the play area are examples. Two independent researchers coded 100 percent of teacher interactions and achieved a kappa coefficient of .82, which indicates a high level of agreement, based on psychometric tradition (Von Eye and Mun, 2005). Mean frequencies of teacher interactions were computed and used in our analysis.

Percentage of building without toys

As noted, children’s block play was recorded in play spaces that included replica play toys—miniature vehicles, people, and animals—during half of the study and in block play spaces without these toys during the other half of the study. This allowed us to examine the effects of these toys on block structure complexity and math learning. Each block structure built by a child was coded as either being built in a space with or without toys. Agreement between co-raters was 100 percent for this coding. The percent of block buildings constructed without toys was computed and used in our analysis to obtain a measure of replica toy effects that was independent of overall block building frequency.

Results

Mean values, standard deviations, and bivariate correlations among all variables of interest in the study are presented in Table 2. As shown in the table, a number of significant associations were found among pairs of variables. One correlation—that between social participation and block structure complexity—was particularly high, r = .86. A correlation of .90 or higher is considered a cause for concern regarding potential collinearity among independent variables (Alin, 2010). We conducted collinearity diagnostics for all pairs of variables, including this particular association. Tolerance statistics were found to be above .10, and the variance inflation factor (VIF) was below 5, indicating that collinearity was not a concern.

Table 2.

Correlations among TEAM scores and all demographic and block play variables of interest in the study.

	Mean	SD	TEAM pretest	TEAM posttest	Age	SES	Gender	Ethnicity	Structure complexity	Time in blocks	Social participation	Teacher interactions	Percentage with no toys
TEAM pretest	12.54	10.05	1
TEAM posttest	21.77	15.39	.90**	1
Age	3.51	.51	.40**	.40**	1
SES	1.85	.96	.02	.02	−.10	1
Gender	1.49	.51	.03	.06	.17	.15	1
Ethnicity	1.73	.78	−.14	−.12	−.15	−.16	.21	1
Structure complexity	4.46	1.61	.46**	.72**	.31	.03	−.03	−.02	1
Time in blocks	15.13	3.95	.11	.18	−.05	−.10	.23	.05	.32*	1
Social participation	3.67	1.55	.59**	.78**	.43**	.12	.02	.20	.86**	.23	1
Teacher interactions	.76	.32	−.15	−.12	−.04	.07	.54	−.18	−.22	−.13	−.26	1
Percentage with no toys	.56	.51	.26	.50**	.05	−.08	.20	−.14	.71**	.31*	.52**	−.06	1

TEAM: Tools for Early Assessment in Mathematics; SD: standard deviation; SES: socioeconomic status.

p < .05; **p < .01.

We conducted hierarchical multiple regression analyses to examine two distinct research questions: (1) Which demographic and block play variables predict the complexity of young children’s block structures? (2) Which of these variables—including block play complexity—predict children’s posttest performance on TEAM?

Block play complexity

To answer the first question, we conducted a two-stage hierarchical multiple regression analysis with demographic variables, block play factors, and pretest TEAM scores as independent variables and block structure complexity as the dependent variable. The results of this analysis are presented in Table 3. As shown in the table, in the first stage, we fitted a model in which only demographic variables and pretest TEAM scores were entered as independent variables. These factors were entered first, since they reflect general childhood characteristics and indicators of development for participants prior to the beginning of the study.

Table 3.

Multiple regression analysis with block structure complexity as the dependent variable and TEAM pretest scores, demographic variables, and classroom block play factors as independent variables.

	Independent variables	Beta	t	Significance
Model 1	Age	.19	1.12	.272
	Socioeconomic status	.08	.51	.614
	Gender	−.11	−.65	.516
	Ethnicity	.10	.62	.537
	TEAM pretest	.40	2.57	.010
Model 2	Age	−.09	−.91	.369
	Socioeconomic status	−.04	−.52	.610
	Gender	−.15	−1.63	.112
	Ethnicity	.21	2.27	.091
	TEAM pretest	−.01	−.10	.925
	Time in the blocks	−.03	−.28	.780
	Number of structures	.10	1.10	.281
	Social participation	1.05	9.09	.000
	Teacher interactions	.08	.96	.346
	Percentage of building with no toys	.25	2.73	.010

TEAM: Tools for Early Assessment in Mathematics.

This model was found to explain 24 percent of variance in participants’ block structure complexity, R² = .24, F(5, 35) = 2.30, p < .05. However, only one of these variables, TEAM pretest scores, contributed significant independent variance to structure complexity in this model, β = .40, t(40) = 2.57, p < .01. As shown in Table 3, in the second stage of the regression analysis, we added classroom block play factors as independent variables—time spent in the block area, number of structures built, social participation in blocks, teacher interactions in blocks, and percentage of structures built without toys available. This model was found to predict 82 percent of variance in block structure complexity, R² = .82, F(5, 30) = 14.06, p < .001. The addition of these block play variables explained an additional 58 percent of block structure complexity over Model 1, R² change = .58, F(8, 32) = 21.14, p < .001. Two variables in Model 2 contributed significantly to block structure complexity—level of social participation in block play, β = 1.05, t(40) = 9.09, p < .001 and the percentage of block structures with no toys, β = .25, t(40) = 2.73, p < .01. When classroom block play variables were entered into this regression model, TEAM pretest scores were no longer a significant predictor of structure complexity.

TEAM posttest scores

In order to answer our second research question about which factors predict math learning, we conducted a two-stage hierarchical multiple regression analysis, the results of which are presented in Table 4. As shown in the table, at stage 1, we fitted a model with age, SES, gender, ethnicity, and TEAM pretest scores as independent variables. These were entered first since they are indicators of participants’ characteristics and math learning prior to the beginning of the study. These factors were found to explain 81 percent of variance in participants’ TEAM posttest scores, R² = .81, F(5, 35) = 30.41, p < .001. As shown in the table, only pretest scores in this model contributed significant variance to posttest scores, β = .88, t(40) = 11.02, p < .001.

Table 4.

Multiple regression analysis with TEAM posttest scores as the dependent variable and TEAM pretest scores, demographic variables, and block play factors as independent variables.

	Independent variables	Beta	t	Significance
Model 1	TEAM pretest	.88	11.02	.000
	Age	.04	.50	.623
	SES	.01	.10	.923
	Gender	.02	.21	.834
	Ethnicity	.01	.03	.974
Model 2	TEAM pretest	.71	12.58	.000
	Age	−.05	−.92	.365
	SES	−.04	−.83	.416
	Gender	.02	.29	.778
	Ethnicity	.02	.42	.678
	Complexity of structures	.27	2.60	.011
	Time in the blocks	−.07	−1.33	.196
	Number of structures	.07	1.37	.181
	Social participation	.25	2.12	.042
	Teacher interactions	.08	1.80	.082
	Percentage with no toys	.07	1.37	.181

TEAM: Tools for Early Assessment in Mathematics; SES: socioeconomic status.

In stage 2, we fitted a model that added classroom block play factors as independent variables, as shown in Table 4. This model explained 95 percent of variance in posttest TEAM scores, R² = .95, F(6, 29) = 45.25, p < .001. Therefore, classroom block play factors contributed an additional of 13 percent of variance in children’s TEAM posttest scores over and above the influence of TEAM pretest scores and other factors included in the first model, R² change = .13, F(6, 29) = 11.59, p < .001. As shown in the table, three variables in this second model contributed significant variance to TEAM posttest scores: TEAM pretest scores, β = .71, t(40) = 12.58, p < .001; complexity of structures, β = .27, t(40) = 2.60, p < .01; and level of social participation, β = .25, t(40) = 2.12, p < .05.

Discussion

In this investigation, we explored the demographic and block play factors that contribute to block building complexity and growth in math abilities in preschool.

Block structure complexity

The question of which variables predict children’s block play complexity is an important one, since previous research has indicated that in teacher-guided or laboratory settings, the complexity of structures was related to math and literacy abilities later in school (Hanline et al., 2010; Ramani et al., 2014; Wolfgang et al., 2001). We found that pretest scores on TEAM (Clements et al., 2013), along with gender, age, SES, and ethnicity—when examined alone—accounted for 24 percent of block structure complexity. When we added five classroom play factors to the analysis—time spent in the blocks, number of structures built, social participation, teacher interactions, and percentage of time building without replica play toys—an additional 58 percent of variance in block structure complexity was explained. This indicates that classroom block play factors are important predictors of children’s building complexity—stronger predictors than previous math knowledge and other child characteristics. It suggests that a large amount of children’s block building ability can be affected by things teachers and children do in the classroom during a year of preschool.

Our finding that none of the demographic variables predicted structure complexity is consistent with results of some previous studies, but not others. We found no age differences in block complexity—a finding similar to that of a prior investigation (Ramani et al., 2014). Other studies indicate that children’s structures become more elaborate as they get older (Hanline et al., 2001, 2010). This inconsistency across studies may be due to differences in the age range of children studied. Age variance in our investigation was quite narrow, compared to that of previous work in which children as young as 16 months and as old as 5.5 years were included (Hanline et al., 2001). The fact that there were no age differences in structure complexity suggests that becoming a more sophisticated block builder is not a matter of simple maturation—of getting older over the course of the year. At least for the narrow age range of participants in our study, other factors, such as building experiences with peers, not age, explained increases in building complexity. Our finding of no gender differences in block structure complexity contrasts with early investigations reporting that boys construct taller, more varied structures (Goodfader, 1982; Leaper and Gleason, 1996), but is congruent with more recent studies reporting no gender differences (Hanline et al., 2001, 2010; Ramani et al., 2014).

Similarly, our finding that neither SES nor ethnicity predict block play complexity is inconsistent with early studies reporting that children of historically underrepresented groups generally show play deficits (Lovinger, 1974; Saltz et al., 1977), but is consistent with more recent investigations indicating no ethnic or SES differences in block building (Jirout and Newcombe, 2015).These shifts in play findings over several decades of research may reflect increased commitment to fostering gender, SES, and ethnic equity in modern preschools and an effort to assure equal play opportunities (Derman-Sparks and Edwards, 2010). Our findings on demographics suggest that complex block building is now a classroom experience from which children of all backgrounds and characteristics might equally benefit.

We found that children’s prior math ability—as measured by pretest scores on TEAM—predicted structure complexity, when block play variables were not included in the analysis. This supports a long-held theory that block building is a highly mathematical activity (Ginsberg, 2006; Kamii et al., 2004; Ness and Farenga, 2007; Reifel and Greenfield, 1983). However, this relationship between math and block complexity was no longer significant when block play factors were entered in the analysis. This is likely the result of the strong association between TEAM pretest scores and one of our block play factors—social participation in blocks. It may be that both math ability and social participation share some common underlying cognitive or social foundations. When both are entered into the analysis, social participation emerges as the stronger predictor of building complexity.

Social participation was one of two block play variables that contributed significant independent variance to block structure complexity. The fact that this variable was associated with complex building is consistent with research indicating that play with peers is more sustained (Butler and Walton, 2013; Qu, 2011; Warneken et al., 2012), includes greater cognitive flexibility (Qu et al., 2001), and involves more planning and goal setting (Ramani et al., 2014). Our findings are similar to those of recent work showing that children more successfully complete difficult tasks when working with peers, rather than alone (Park and Lee, 2015). Block play is replete with challenges for children to overcome—a tall structure keeps toppling or there are no more blocks of the length needed to complete a bridge or enclosure. Children may simply become better at solving such problems when they have input from peers.

In the present investigation, we informally observed numerous instances in which play with peers extended and enhanced building. Children encouraged one another to add more blocks, create more elaborate block structures, or stay longer in the area to keep building. When children built together, they often planned out what they would build, how they would build it, and what parts each player would construct.

The percentage of block buildings created in the play space without replica play toys was also found to contribute significant, independent variance to block structure complexity. This finding runs counter to conventional wisdom and traditional practice in early childhood education. For decades, such toys have been recommended as necessary accessories in the block play areas of preschools (Doctoroff, 2001; Frost et al., 2011; Harms et al., 2014; Hirsch, 1984). Our finding suggests that the presence of such toys may actually diminish the complexity of block building. This possibility is supported by a descriptive study in which children’s block structures were found to be more sustained and elaborate in block centers without toys (Trawick-Smith and Savalli, 2013).

The presence of replica play toys may simply provide an alternative activity to block building. When pretending to drive cars or carrying out make-believe roles with plastic people or animals, children may no longer engage in complex construction. The presence of replica play toys may also limit the types of structures that are built. Toy vehicles, for example, may inspire simple roads to drive on. Toy animals might prompt simple enclosures as fences or pens. The blocks-only center may encourage a wider range of possibilities for what can be built. In our investigation, we informally observed a greater variety and novelty of structures when children played blocks only. It is important to note that we studied only block play in this investigation, not pretend play that is more likely to be promoted by replica play toys. However, if complex building is the primary goal of blocks, then centers without toys may have the greatest impact.

TEAM posttest scores

Our second research question was related to the block play factors that predict growth in math learning—that is, scores on the TEAM posttest. We found that demographic variables and TEAM pretest scores, alone, predicted 81 percent of variance in TEAM posttest scores. When classroom block play factors—including structure complexity scores—were entered into the analysis, along with demographics and pretest scores, an additional 13 percent of variance in posttest scores was explained. Given the many other ways that children learn math in the preschools—math lessons, children’s books with math content, or math learning centers (Ginsberg, 2006)—this finding suggests an important contribution of these block play factors to growth in math abilities from pretest to posttest.

Demographic variables were not associated with math abilities at the end of the study, once we controlled for pretest math abilities. Boys and girls and children of varying SES and ethnic backgrounds achieved the same levels of math ability during our investigation. The absence of gender differences is consistent with new research reporting that a gender gap in early math ability exists primarily for children of very high math ability, those of high SES, and for children 8 years of age or older (Hyde and Mertz, 2009; Penner and Paret, 2008). Similarly, our finding of no ethnic differences is congruent with research showing that ethnic background does not predict early math learning, when SES is held constant (Fryer and Levitt, 2004). The fact that SES did not predict posttest scores in our study, however, is inconsistent with findings of previous investigations. Young children in poverty have been found to score lower on math assessments in previous work (Lee et al., 2008; Trawick-Smith et al., 2016). It may be that participants in our study did not face the extreme levels of poverty of participants in other investigations. Also, our research was conducted in a high quality child development center with a prescribed curriculum and clear goals for math learning, which might have served to reduce SES differences. Age was also not a significant predictor of TEAM posttest scores. However, this is likely explained by the strong bivariate correlation between TEAM pretest scores and age. When pretest performance was included in the analysis, age effects on posttest scores were diminished.

Pretest math scores continued to be the strongest predictor of posttest TEAM scores, even when block play variables were included in the analysis. This supports previous research indicating that home or child care math experiences prior to age 3 can lay a foundation for later preschool learning (Baroody et al., 2008; Franzén, 2015; Palmér et al., 2015). Mean block structure complexity scores were also significantly related to posttest TEAM scores. Neither time in the blocks nor number of structures built were associated with growth in math ability, as has been reported in other studies (Hanline et al., 2001, 2010). Our findings suggest that it is the quality of building—as indicated by structure complexity—not the amount of time building or the number of structures built that predicts math learning. This finding is similar to those of earlier studies showing that complexity of block play in adult-guided or laboratory settings predicts math ability (Hanline et al., 2010; Ramani et al., 2014; Wolfgang et al., 2001). Our finding extends this previous work by demonstrating that free play with blocks has this same impact on learning.

One explanation for why complex structures are related to math ability may be that building them poses many math-related challenges. For example, creating complex enclosures may require reflection on area, shape, parts of shapes (e.g. angles), spatial knowledge, and number. Similarly, constructing a complex bridge may cause children to think about length and measurement. More elaborate structures may include more blocks, providing greater opportunities to think about larger numbers of objects. Such mathematical challenges in block building have been documented in other investigations (Jirout and Newcombe, 2015; Ramani et al., 2014).

A second significant predictor of posttest TEAM scores was social participation while playing with blocks. This association was significant, even when controlling for the influence of block play complexity. This suggests that social participation in blocks has a dual influence on math learning. It predicts more complex structures, which, in turn, are associated with math ability, as described previously. But it also directly promotes math growth, over and above its effects on what children are building. Previous research may provide explanations for the independent impact of social participation on math ability. In all peer interactions, children have been found to engage in more mathematical discourse—math talk—far more than they do when playing alone (Levine et al., 2010; Trawick-Smith et al., 2016). Also, cooperative play and group work—compared to individual experiences—have been found to promote math learning in preschool and later grades (Artut, 2009; Bulotsky-Shearer et al., 2014; Park and Lee, 2015; Tarim, 2009). The interchange of math ideas among peers in blocks may, similarly, extend children’s exposure to and understanding of math concepts.

The frequency of teacher interactions was not significantly related to TEAM posttest scores or to block structure complexity (p = .08). This finding raises questions about the benefit of teacher–child contact in block play. Previous research has found that certain teacher–child play interactions predict positive outcomes in preschool (LoCasale-Crouch et al., 2007; Mashburn et al., 2008; Trawick-Smith et al., 2016). Teacher conversations with children that include math content have been associated with math learning (Klibanoff et al., 2006; Levine et al., 2010). In one study, however, only “good-fit” interactions—those that supported, rather than interrupted, children’s play—were associated with growth in math ability (Trawick-Smith et al., 2016). A limitation of the present investigation was that specific types of teacher interactions were not coded. It may be that not all such interactions in our study were a good fit with what children were playing, explaining the lack of a strong association between teacher involvement and block building or math learning. We informally observed interactions that both supported children’s block play and interrupted it. Future research should examine the precise types of teacher–child interactions that support or interfere with block play and learning.

Implications: a path model for block play and math learning in classrooms

Using results of our multiple regression analyses, we constructed a path model that hypothesizes causal relationships among the variables of interest in our study. The model is illustrated in Figure 1. The figure includes all significant associations among variables. Beta-weights are presented to show the strength of each relationship. This model holds several important implications for classroom practice and future research. As shown in the figure, TEAM pretest scores are highly related to posttest scores. We hypothesize that children’s math knowledge prior to a year of preschool strongly affects growth in children’s math learning over the subsequent year. This suggests that teachers, parents, and other caregivers of toddlers and younger 3-year-olds should provide age-appropriate classroom math experiences. Research suggests that such experiences at these young ages will enhance children’s understanding of such foundational domains as number and simple spatial relationships (Baroody et al., 2008; Palmér et al., 2015; Stock et al., 2009). Additional research is needed to identify specific math-related abilities in the first 3 years of life that support later learning in preschool.

Figure 1.

Proposed path model for the relationships between block play behaviors, block structure complexity, and math ability, with beta weights from multiple regression analyses showing the strength of each association.

As shown in the figure, two block play variables are associated with block play complexity, which, in turn, is related to math learning. We propose that the percentage of buildings that children create when replica play toys are not available promotes overall complexity of structures. Complex block structures, as shown, enhance math ability. An implication is that teachers should periodically remove miniature people, cars, and animals from the block center, so children can focus exclusively on building. Centers with and without toys might be alternated from week-to-week. Another option might be to create distinct replica play centers for these toys and separate blocks-only areas (Trawick-Smith et al., 2016). Future research might explore the balance of toy and no-toy block play opportunities that are optimal for promoting building complexity and math learning, along with the pretend play benefits of replica play materials. Additional studies might focus on other materials commonly available in block centers. What are the influences of various types of blocks—hardwood unit blocks, large hollow blocks, small table blocks, and other construction toys—on building and math learning. Previous research has indicated that different kinds of building toys can have unique effects on play and learning (Trawick-Smith et al., 2015; Wolfgang et al., 2003).

The path model shown in Figure 1 indicates that the level of social participation in the block area also predicts block complexity and, in turn, posttest TEAM scores. One implication is that block play spaces, peer groups, and teacher interactions should be planned to promote collaboration in building. For example, larger play spaces and a relaxation of limits on how many children can play in them at one time might promote greater social interaction. Teachers might actively facilitate cooperative building with peers (e.g. “Why don’t the three of you make a farm together.”) Such strategies might lead to more complex structures and gains in math learning. Based on previous research, however, such interactions should be a good fit with what children are currently playing.

The path model suggests that social participation in blocks contributes directly to math ability, independent of its effects on structure complexity. Simply interacting with peers at high levels in the block center, regardless of the structures being built, may contain math conversations or other interactions related to math. A major implication is that children be encouraged to play together in blocks, regardless of what they play. Future research might examine the components of peer collaboration in blocks that lead to these positive outcomes—planning, negotiating, verbalizing play ideas, or engaging in specific types of math talk.

The model in Figure 1 suggests that block play complexity, social participation, as well as previous math knowledge may promote math learning. Caution is urged in assuming that these are causal relationships, however. It is possible that findings of this investigation are the result of other, unknown factors in a child’s classroom or home environment that contribute to both block building complexity, social interactions, and growth in math ability. Experimental studies might be designed to compare math growth of children randomly assigned to block play or no block play treatments in order to verify a causal relationship.

Future research might be conducted to identify other methods—beyond increased social participation and building without toys—to encourage children to build more elaborate structures. Specific types of teacher questions or comments might increase complexity (e.g. “Are you going to build any more rooms for your house?” “Will you make a bridge between this building and that one?” or “What could you build for the animals, so they won’t run away?”). Providing photos or books showing real buildings with unique architectural designs might have an effect on building complexity.

Future research should also examine the effects of different types of blocks on block building and math learning. Do large hollow blocks, hardwood unit blocks, or small table blocks influence play and learning in different ways? Finally, studies might be conducted to examine how teacher characteristics, such as education level or depth of math knowledge, affect teacher interactions with children in blocks.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article

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