Young children's block play and mathematical learning.
Abstract. This qualitative study investigated young children's mathematical engagement in play with wooden unit blocks. Two boys, ages 6 and 7, were independently observed completing the task of filling outlined regions with the various sets of blocks. Three major mathematical actions were observed: categorizing geometric shapes, composing a larger shape with smaller shapes, and transforming shapes. Results indicated that young children's block play with designed tasks promoted mathematical actions, which may cement the foundation for advanced mathematics learning.
Almost every preschool classroom in the United States has a block play center. Despite a widespread belief that block play helps young children's development and learning, many early childhood teachers do not fully recognize the educational value of block play (National Association for the Education of Young Children [NAEYC], 1996; Wellhousen & Kieff, 2000; Zacharos, Koliopoulos, Dokomaki, & Kassoumi, 2007). In reality, many teachers provide young children with didactic activities, such as worksheets or other academic tasks, to "teach" literacy, math, social studies, and other subjects, rather than provide opportunities to choose free-play activities, such as block building, pretend play, puzzles, and other games. Paper-pencil tasks are perceived to be developmentally inappropriate, because preschoolers and children in primary classrooms are in the pre- or concrete-operational stages of cognitive development. The use of worksheets is counter to the need for hands-on activities with concrete objects, which is how children learn at these stages of cognitive development (NAEYC, 1997).
While it is often perceived that mathematics may be too difficult of a subject for young children, children are exposed daily to various opportunities to learn mathematics. By age 5, children generally acquire the skills of comparing, counting, classifying, measuring, ordering, and using fractions (Varol & Farran, 2006). Such mathematics skills could be promoted by block play, using different types of blocks (Wolfgang, Stannard, & Jones, 2001). As preschool teachers recognize the importance of block play, they can guide children's play activities, promote their mathematical actions, and ultimately support their learning. Such involvement by teachers significantly influences preschool-age children's math learning (Klibanoff, Levine, Huttenlocher, Vasilyeva, & Hedges, 2006), whereby teacher input has been shown to promote children's math learning in a preschool classroom by: 1) talking to children using number words (Mix, Huttenlocker, & Levine, 2002); 2) asking the quantity (Wynn, 1990); and 3) directing children's attention to such concepts as equivalence and non-equivalence (Klibanoff et al., 2006). Block play consistently provides opportunity for teachers to help young children's mathematics learning through various types of teacher input.
While block play is beneficial for all children, children of families with more limited economic resources might benefit more from their mathematics learning through block play. Many research studies suggest that young children from families with more limited economic resources have lower levels of mathematics achievement than their more economically affluent peers (Jordan, Huttenlocher, & Levine, 1992; Saxe, Guberman, & Gearhart, 1987). Other studies suggest that the quality of environmental input from parental involvement or through preschool programs (Klibanoff et al., 2006) also influences one's achievement in mathematics. Although parents of children from families with more limited economic resources may often be less involved in their children's education because of time constraints and financial circumstances, children's mathematics learning may be enhanced with appropriate teacher input through block play.
The current qualitative research study was based on task interviews with two boys, ages 6 and 7. Both children were from families with limited economic resources and neither child had attended preschool. Neither child had extensive experience playing with wooden unit blocks before the interview. Before interviewing the boys, the researchers provided a two-hour session, during which the two boys had free play with the wooden unit blocks. The purpose of the free play was for the children to become familiar with the unit block pieces. In addition, the research team gathered background information on the children regarding their communication skills, attention spans, and mathematical skills.
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The tasks developed for the children were to fill outlined diagrammed regions with blocks (see Figure 1). The regions presented to the children were shaped like a car and a house. We prepared four sets of blocks for each region, which included some extra pieces. For example, one set included multiples of square blocks and two different triangular blocks, and another had both triangles and rectangles for the body of the car-shaped region (see Figure 2). In the second set of blocks provided to the children, triangular blocks could form rectangular blocks, while the two triangular blocks in the first set were extra and not needed to complete the fill task.
We interviewed the two participants independently on the same day with the same tasks. We interviewed the 6-year-old boy, Tony, with the first task (filling the car-shaped region), and continued the second task with the house-shaped region after a half hour break. We interviewed the 7-year-old boy, Corey, without a break after asking him whether he was willing to continue on another task. For each task, the interview took about 15-20 minutes, and the interview was video-recorded for further analysis.
Our data analysis was informed by an iterative video analysis process (Lesh & Lehrer, 2000). This process included examining the video for identified portions when the children showed potential mathematical actions. While watching the video repeatedly, we developed thematic categories of mathematical actions. After repeated viewings of the video, categories were modified to strengthen our analysis. Once we had finalized the categories, we identified the properties of the categories to describe the children's mathematical actions.
Results from our analysis suggested three major mathematical actions that children performed when completing block tasks. The first finding indicated that children categorized block pieces according to their geometric shapes. Both children were able to label the block pieces as geometric shapes. That is, they could tell various shapes, such as triangles, rectangles, and squares. When presenting the outlined regions, we asked them to label the blocks in the prepared sets. Tony labeled each block by its individual shape, using geometric terms. Regarding two triangular pieces, an isosceles right triangle (half of a square piece) and a 3060-90 degree triangle (half of the 2 by 1 rectangle piece), he recognized that both were triangles, but differentiated them by their sizes. He named the 30-60-90 degree triangle as the "big triangle." He also named a half-circle shape piece as a "U-block" by attending to the fact that the circular curve looked like an alphabet letter U.
The second participant, Corey, labeled blocks by relating them to familiar objects. He could note that both an isosceles right triangle and a 30-60-90 degree triangle were triangles. In order to differentiate them, Corey named an isosceles right triangle as a "roof-top" and a 30-60-90 degree triangle as a "diamond." He called a half-circle shape piece a "half-wheel" by explaining that two pieces of the shape made a wheel. Unlike Tony, Corey named block pieces by connecting the shapes with familiar objects to him. The children demonstrated common mathematical actions. Both were able to recognize geometric shapes (e.g., triangle, rectangle, etc.) in blocks and differentiate the types of geometric shapes by attending to their characteristics, such as size or connection to shapes in everyday life (see Table 1).
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The second finding from our analysis, where we provided a variety of block sets to fill an outlined figure, suggested that children composed the same shapes with smaller block pieces. In terms of rectangular blocks, we used four types: 3" by 3" square, 6" by 3" rectangle, 12" by 3" rectangle, and 3" by 1 1/2" rectangle. Both children easily figured out the relationship among the four different rectangular blocks, and they were able to replace a bigger rectangular block with smaller ones in performing the tasks. However, the children had difficulty understanding the relationship between triangles and rectangles. That is, while they visually noticed that the 12" by 3" rectangle was composed of two 6" by 3" rectangles without physically trying to put together the smaller pieces, neither of the children could figure out how two isosceles right triangles made a 3" by 3" square. After several trials, both children were finally able to put two isosceles triangles together to make a square.
The third finding indicated that children were able to manipulate the blocks, through turning and flipping, to compose a desired shape. In several tasks, the children were to put two 30-60-90 degree triangles together to make a 6" by 3" rectangle, which was quite challenging for them. They randomly put two triangular pieces together to form the rectangle and did not succeed. When they became frustrated, we demonstrated how the two pieces should be put together in order to motivate them to continue trying. Despite this demonstration, they did several more random trials, and finally they tried turning and flipping the block pieces systematically (see Figures 3 and 4). They fixed one triangle, and turned or flipped the other without repeating previous trials. This indicated that they began to notice the orientation of the triangles, and thus rotation (turning action) and reflection (flipping action) became purposeful strategies to them at the end.
The results of our analysis suggest that children's first free exploration experience with unit blocks allowed them to engage in mathematical actions, discover mathematical concepts, and relate objects to their personal lives. During our observations, the children did not state that they were engaged in mathematical actions. However, they started to understand relationships between different geometric shapes and constructed the foundation for later geometric learning. The children also had many chances to count, compare, measure, and reason during the block play session. Because unit blocks are open-ended learning materials, there was not only one way of using the materials, and each child could interact with the blocks on his own learning level.
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Implication and Discussion
Our study demonstrated that block play provides an opportunity for young children to learn complicated mathematical concepts in lieu of the more traditional mathematics lessons, such as paper-pencil tasks and worksheet exercises. In particular, with appropriate tasks, child engagement in higher levels of mathematical thinking was increased and children were observed making complex mathematical conclusions earlier than typically perceived.
For example, because the children in this study were asked to fill the shapes with provided sets of blocks, they had an opportunity to develop their knowledge of geometric concepts, such as angle, length, orientation, and area. Using the various sets of blocks at increasing difficulty levels, the children realized that the exact same shape could be filled with various compositions. That is, the 6" by 3" rectangular block could be replaced with two 3" by 3" square blocks, four isosceles right triangular blocks, or two 30-60-90 triangular blocks in the tasks. It means that they had to examine and compare the angles, lengths, and orientations of smaller blocks in each given set in order to try to cover the same area of the 6" by 3" rectangle blocks. Thus, we believe that the tasks in this study created a context in which children could investigate and develop the targeting geometric concepts while engaging in a play activity.
Consequently, teachers of young children can plan similar or modified tasks in consideration of what mathematical skills are available to their children and what geometric concepts are targeted. We also encourage early childhood teachers to have children verbalize what they themselves can do, and try to do, while doing block play, so that the children can acknowledge and reflect upon their attempts to foster mathematical concepts.
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The findings of this study reconfirm the preceding studies that emphasize teachers' roles in developing young children's mathematics learning through play. As they perceive the importance of block play, the early childhood teachers are able to provide a developmentally appropriate learning environment that stimulates young children's mathematical thinking. A block play center would become one of the critical parts of the environment because young children would learn mathematics through block play, giving children many hands-on activities with concrete objects. As taught via block play, mathematics is not a too-difficult subject for early childhood teachers to teach, nor for young children to learn. In the block play center, teachers are there to guide children's play with questioning, scaffolding, and modeling, and the children will construct math concepts on their own without any rote memorization or mere drilling, as these activities ignore their developmental status. Children from low-SES families, like the participants of this study, will benefit from block play because they have limited access to educational resources at home. Those children's block play at school will not only compensate for the academic disadvantage, but also provide them less stressful learning experiences and more emotional support from adults than would traditional mathematics lessons. In a future study, we want to investigate those benefits for children from low-SES families in depth.
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University of North Carolina at Charlotte
Barbara Foulks Boyd