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Serious Fun: How Guided Play Extends Children around them, forming an equilateral triangle. The teacher, Juan, asked them what shape they made and how many angles and sides there were. He then asked one of the children to move, keeping the rope taut, and repeated the ques- tions. Juan also had children stand with a taut rope in groups of four, moving to create a rectangle with two long sides and two short sides, then moving to create four equal sides. He asked a series of questions: How many angles Does the shape have? How many sides? What is a rectangle with equal sides called? What do all rectangles have in common? Some of the children who were not participating directly in the shape activity climbed a play structure to see the shapes from above, and they eagerly called out answers to Juan's questions. In other classrooms. I have observed children enthusiastically count collections of erasers, small toy animals, col- colored cotton balls, and buttons, then represent their counts on paper often by drawing the objects or a circle to rep- resent each item and placing the objects on their representations to ensure an accurate count. I have watched young children play the card game War, counting the symbols (hearts, spades, clubs, diamonds) on each number card played to determine whose card has more. (Teachers can make the game more complex by having each child play two cards, add them, and then compare the sum with the another child's sum.) I have seen children hunt shapes in their classroom, debating whether a window with slightly curved corners is really a rectangle. I've witnessed a teacher read a picture book and ask children to find objects in front of, on top of, next to, and behind a house, and to identify the biggest and the smallest dogs in the illustrations Play Versus Academic Skills: It's Not a Zero-Sum Game Did the children who were engaged in these activities know they were participating in math lessons? Probably not. But they were indeed learning math through what I refer to as playful instruction. All of these activities were intentional on the part of the teacher, who had particular math learning goals in mind. All were carefully planned. All engaged children in active 73Serious Fun: How Guided Play Extends Children

For the children, this activity was a game. For Marylou, it was serious business. In this one lesson she had the children engaged in multiple components of the math curriculum categorization, basic number skills (counting, one- to-one correspondence, cardinality, writing numbers), graphing, and measurement. In another preschool I visited, children explored the defining qualities of shapes. On the playground, three children stood in equally spaced positions with a rope pulled taut Serious Fun: How Guided Play Extends Children pile. I soon understood, however, that this was a math activity. Marylou has drawn a 6 x 10 grid on a shower curtain spread on the floor. She asks the children to sort the shoes into six piles, according to certain attributes they have agreed on-sandals, slip-ons, shoes with laces, etc. Then, in the bottom row of the grid, they place one shoe from each pile in its own square, followed by the rest of the shoes from that pile, one each in the squares above the first shoe. After the children count the number of shoes in each column, Marylou asks them what they notice, and the children discuss which categories have the most and the fewest shoes. She follows up with questions: Are there any categories that have the same number of shoes? How many more sandals then slip-ons are there? Marylou replicates the grid on the chalkboard, and the children represent each shoe in each category with a letter (L for laces, etc.). Under each column, they write the total number of shoes in that cate- gory and continue the discussion: What kind of shoes did most children wear to school today? How many more Velcro shoes would they need for the Velcro column to be the same height as the slip-on column? BISI 71 Serious Fun: How Guided Play Extends Children Chapter Five Playful Math Instruction and Stan- dards Deborah Stipek As discussed in the introduction, playful learning might

be an activity that the teacher initiates with children and for which she has specific learning goals in mind. In the situations described in this chapter, children eagerly engage in sorting shoes, playing card and board games, and creating shapes with rope and then deter- mining the number of sides and angles-perhaps even without being aware that they're learning math concepts and skills. But the teachers have intentionally planned these activities to help children achieve not only math standards but also social skills in enjoyable, developmentally appropriate ways that provide for individualization. How does this chapter expand or challenge your idea of play and what playful instruction can look like? The children in Marvlou's preschool class were wearing only one shoe when I walked in the door. I was confused. I expected to sec a math lesson, and instead I saw children throwing their shoes into a 70Serious Fun: How Guided Play Extends Children thinking, participating, and communicating. Some had the added value of allowing children to move around, making the activity more engaging for those who find it difficult to sit in one place. And in all of these activities, the teacher had an opportunity to assess children's understanding through observation and by inviting particular children to contribute to the conversation This may not look like standards-based academic teaching, but it is. Many teachers of young children are understand- ably anxious about standards and accountability pressures that have been pushed down to preschool. Many have shared with me concerns about how these pressures can interfere with what young children really need-daily opportunities to learn through play. Some teachers are also worried that teaching academic skills at an early age may undermine children's natural curiosity and motivation. But these examples of playful math instruction make it clear that there is no need to choose between play and teaching academic knowledge and skills. Abundant research has demonstrated that young children enjoy learning math and can learn far more than was previously assumed--without a single flashcard or worksheet (Carpenter et al. 2016; 74 Serious Fun: How Guided Play Extends Children Clements & Sarama 2014; National Research Council

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2001). Playful math has an added bonus: Social skills develop- ment can easily be integrated into teacher-planned math activities. Research has shown that some types of board games (e.g., linear path games with lots of counting, like Chutes and Ladders) promote children's math abilities (Siegler & Ramani 2009). They also give children practice following rules, taking turns, and winning and losing gracefully. Similarly, children participating in Marylou's shoe categorization activity discussed and agreed on categories and raised their hands to answer questions, and Everyone had a chance to participate. In Juan's shape activity, children negotiated who moved where in response to teacher directions and collaborated with others on the shape. In such situations, children are not learning math instead of social skills; they are learning math and social skills. Teacher-Initiated Versus Child-Initiated Math Activities Why are intentional, planned activities necessary? Don't teachers need to weave academic learning into activities initiated by children to make them child centered? For example, couldn't a teacher take advantage of children building a fort with blocks to help them learn about relative size? Couldn't she spontaneously offer a counting and 75 Serious Fun: How Guided Play Extends Children comparison lesson to a group of children arguing about How many toy farm animals do they receive? Yes, teachers can and should seize on naturally occurring learning opportunities as children play and explore. But there must be a balance. Relying entirely on spontaneous, child-initiated teachable moments would leave the order in which math concepts are introduced or even whether they are introduced-too much to chance. Moreover, if teachers depend solely on child initiative, children's opportunities to learn will vary widely; some will have many opportunities, while others might have few. Playful instruction during planned small group and whole group activities provides systematic information about children's knowledge and skills, enabling teachers to keep track of what children understand and what support they need to grow and learn.

76 Serious Fun: How Guided Play Extends Children Making Standards, Accountability, and Packaged Curricula Work Math standards do not preclude teachers implementing playful, engaging activities. And they can help teachers determine the content and order of the activities they develop. While accountability can be beneficial or prob- lematic, depending on how it is implemented, math stan- dards are still useful. They have been carefully crafted and vetted by diverse groups of content area experts and educators so teachers don't have to figure out everything on their own. Standards can be intimidating, but they have value. The math standards developed in states, districts, and other organizations, such as Head Start, serve as a destination deemed desirable by experts. If teachers don't know where they want to end up, they will have a hard time figuring out how to get there. Still, standards should guide, not dictate, instruction. I have observed some teachers who, anxious about meeting standards or following a standards-based curriculum, teach concepts that are too advanced for some children. When this happens, the children quickly become restless and frustrated or just refuse to participate. Adhering strictly to standards can also lead to underestimating what some children are ready to learn. A study of a nationally representative sample of kindergartners found that before they entered kindergarten, children had already 77 Serious Fun: How Guided Play Extends Children mastered most of the mathematics skills kindergarten teachers reported teaching (Engel et al. 2016). For exam- ple, although the vast majority of children entered kinder- garten having mastered basic counting and were able to recognize simple geometric shapes, their teachers reported spending about 13 days per month on this content. And although very few of the children entered kindergarten already knowing basic addition and subtraction, only about 9.5 days per month were devoted to those skills. The research further found that spending more time on content that was new to children, such as basic addition and sub- traction, resulted in higher math achievement (Engel et al. 2016).

Ultimately, while standards help clarify annual learning goals, teachers must determine the short-term goals appropriate for their students. Children enter classes with varying knowledge and skills. Instruction needs to meet children where they are or just a bit beyond where they are, in what the Russian psychologist Lev Vygotsky ([1930-35] 1978) refers to as the zone of proximal devel- opment (what a child can do with a little help or guidance). As children progress through preschool and the carly elementary grades, some may need instruction focused on standards for children a year or two younger. They need to master those skills and that knowledge before they can tackle grade-level standards. This means that teachers need to adjust their instruction to help children master the pre- requisite skills, and ideally schools need to provide some students with extra support. Other children may be ready to move on to developing the knowledge and skills expected of children one or even two years older. In brief, standards provide useful goalposts, but only the children themselves can show you where to start. 78 Serious Fun: How Guided Play Extends Children Road Maps Help Knowing the final destination is a far cry from having a road map, which teachers also need for supporting children's progress. In addition to the standards, teachers need to know about the order in which children typically master math concepts and skills. By knowing typical learning tra- jectories, teachers can identify the next step in children's progression toward meeting a standard. And by under- standing how their own students learn best, teachers can plan engaging, playful activities that help move children's thinking forward and respond to their individual strengths and needs. Researchers now know a great deal about typical trajectories (c.g., see Clements & Sarama 2014). For example, when you add two objects to a set of six that a preschooler just counted and ask him how many are there now, most children will initially count the entire new set from the beginning (from one to six) before counting the last two. Later, at a more advanced level, they will "count on"-that is, start with the number of the previous set (six) and add the additional objects (seven, eight) to get the total (Siegler 2016). The child who starts again from the beginning

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needs help learning to remember the previous count. The teacher might play a "hide the set" game by putting her hand or a cup over the set and asking the child if she can figure out how many there are without seeing the items she already counted. The child who counts on might be given 70 Serious Fun: How Guided Play Extends Children larger sets or asked to solve problems that involve remow- ing items (counting down). Another example of a learning trajectory is that children are often able to identify basic shapes before they can articulate the shapes' defining qualities. Once children have a general idea of, and names for, basic shapes, teach- ers can use activities such as the rope game and the shape hunt, mentioned earlier, to help the children understand the defining characteristics of particular shapes. Children with these understandings might be ready for more complex shapes. Because identifying the next step requires knowing where a child is in relation to typical learning trajectories, 80 Serious Fun: How Guided Play Extends Children activities that provide information about the child's current knowledge and skills are valuable. While math learning trajectories of individual children do not conform exactly to what researchers have summarized as "typical," based on studying large numbers of children, research on trajectories provides some guidance on the order in which new math concepts should be introduced Using a curriculum with a research-based scope and sequence can assist teachers in introducing math concepts in an appropriate order, but packaged curricula are not necessary (and not all packaged curricula are based on sound research). Many schools and teachers develop their own math activities based on standards and research on math learning trajectories. And even if a school uses a packaged curriculum, teachers can supplement it with their own activities, those developed by colleagues, or ones found on the internet. Curricula can serve as helpful resources, but teachers know their own students better than curriculum developers, and they need to make adaptations to meet their students' needs and use materials and strategies that make sense within the children's social and cultural con- texts. Teachers occasionally say that administrators pressure

them to follow a strict pacing guide connected to the curriculum they use, moving to new concepts based on the time of year rather than children's mastery. Pacing guides are designed to ensure that all of the material is covered and that teachers give all children access to a rigorous curriculum. But pacing guides do not guarantee that all children achieve the ultimate learning goals. Some children begin far behind their age-mates or are not yet proficient in the language of instruction. Others enter the classroom having already mastered the knowledge and skills they are expected to obtain it by the end of the year. Strict adherence to pacing guides often results in instruction that is too hard for some children and too easy for others. Teachers required to use pacing guides can usually make adaptations within the context of particular math skills, such as by varying the difficulty level of the problems they give children or making manipulatives available to children to solve problems. Providing some extra instruction with small groups of children for example, those who need 81 Serious Fun: How Guided Play Extends Children more support or additional challenges--is another strategy to help meet students' diverse needs. Conclusion Standards and accountability have value, but we must make sure they do not get in the way of being child-centered. developmentally appropriate, playful learning. The kind of teaching described in this chapter requires teachers to be intentional, to plan lessons carefully, and to provide direct guidance, at least for some math activities. But as the examples illustrate, children are not likely to notice any difference between playing and learning mathematics concepts and skills. Try This! › Plan a playful activity to extend children's understanding about carly mathematics concepts (e.g., categorization, counting, cardinali- ty, shape concepts). How will the activity support the learning goal? How will you adjust the demands of the task to be appropriate for different skill levels? How will you determine whether the activity was effective? › Make materials that lend themselves to math activities (e.g., card and board games, sorting activities) easily available to children. Observe

what they do with them and try out strategies for encouraging engagement with the materials that will support math learning. > Give children a math activity to do in pairs (c.g., sorting materials, playing a card game, finding all the rectangles in the classroom) Observe children's social behaviors (e.g., negotiating the task, taking turns, winning or losing gracefully) and consider ways you can promote their social skills in the context of other math activities. › Observe children during free play and find ways to encourage math learning, such as ask- ing them how many times they can bounce the 82 Serious Fun: How Guided Play Extends Children Chapter Six Fostering Positive Experiences in the Math Center for African American Boys Danielle B. Davis and Dale C. Farran Young African American boys are often left behind in mathematics, an essential content area for future school success and careers. Fostering positive math out- comes for them, and for every child, requires self- reflection on your part. Do you hold high expectations for all the children you work with? How well do you understand the children's cultural contexts? What mathematical concepts and skills might individual children be ready to learn next? The goal is to make math activities, including those that invite independent exploration in the math center, a magnet for learners so that math is approachable and enjoyable yet sufficiently challenging. Keeping the idea of playful learn- ing in mind, what materials and activities will be appealing to the children you work with and engage them in higher-order thinking and problem-solving experiences- -and set them on a positive course for the future? 84 Serious Fun: How Guided Play Extends Children In a prekindergarten classroom in an impoverished section of the city, Ms. Shepherd announced to the

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children that they were all going for a walk in the neighborhood. The classroom theme for that month was buildings. During the walk, the class came upon a house under renovation where the construction workers and electricians were happy to take a break to talk to the children. The children paid rapt attention to measurement, construction plans, and plumb lines and levels. Over the next few weeks, Ms. Shepherd and the children returned to the building site several times, observing from a safe vantage point as the house took shape, cheering on the carpenters. Back in the classroom, interest in construction was high, and the children engaged in a variety of hands-on activities centered on buildings. With Ms. Shepherd modeling the building process, the class constructed plans to build and design a birdhouse. Each week Ms. Shepherd introduced new ideas around buildings, connecting them to the questions and observations that arose from the class's visit to the construction site. The teacher also provided mathematical tools in the math center for the children to use as they planned, measured, and constructed. Several children created buildings in the block area, taking tools and measuring devices from the math center to help with their construction. Ms. Williams, the teacher assistant, outlined a skyline of the city for the dramatic play area, and the children added windows and other touches to the mural. The class also inter- viewed a father who worked for a construction company, and he spent one morning showing the children the basics of how to measure and assemble a house. Throughout the class's building theme, mathematical content was integrated everywhere! While young children often eagerly play in the dramatic play, art, and block areas, they may have little interest in exploring the math center without prompting. As university-based researchers and consultants, we spent a year intensively observing the math centers in eight publicly 85 Serious Fun: How Guided Play Extends Children funded pre kindergarten classrooms in a southern US city. We sought to understand children's natural interactions with math manipulatives and materials during center time.

All of the classrooms were relatively well supplied with math-related materials, but in some cases the centers were not set up to foster children's sustained interest or develop their mathematics understanding. Materials were similar across classrooms, but they did not change over time and were not organized in ways that provoked students' curios- itv or attention. Two major research findings support the importance of mathematics learning in urban pre kindergarten classrooms that primarily serve children of color. One is that early Math knowledge is a strong predictor of later school success-in reading as well as math (Duncan et al. 2007). The other is that racial disparities in children's math achieve- ment are present at kindergarten entry (Friedman-Krauss 2016)and these gaps remain large throughout elementary, middle, and high school (National Assessment of Educational Progress [NAEP] 2015). In this chapter, we argue that creating engaging early math-learning opportunities is critical, especially for African American boys, and we recommend ways teachers can choose materials and design environments to optimize early math learning. Supporting African American Boys At an early age, African American boys become aware of racialized stereotypes regarding their own math abilities (Nasir & Shah 2011). On average, African American boys are overrepresented in negative educational outcomes and underrepresented in positive outcomes. Although it is well established that these disparities are due to a wide range of issues regarding opportunities to learn (see Bowman, Comer, & Johns 2018), a misperception remains among some members of the public (including some educators) that these disparities are due to innate differences in abilities. As a result, many African American boys are often confronted with lowered expectations even when they are high achieving (Berry III 2008; Zilanawala et al. 2017). Lowered expectations can lead to these children being denied access to rigorous math curricula, feeling unsupported in their math trajectories, and developing a negative attitude toward (or perception of) their abilities to do math that is, their self-efficacy (Berry III 2008; Nasir & Shah 2011). Making matters worse, new research finds that

Young children's attitudes toward math are a powerful predictor of their achievement, even after controlling for cognitive abilities (Chen et al. 2018; Digitale-Stanford 2018). Setting expectations and attitudes aside, research also finds clear disparities in access to high-quality math learning across educational settings. Young children of color attending urban schools in low-income areas tend to have fewer opportunities to master math knowledge. A study of urban pre kindergarten classes showed that math teaching and activities take place much less frequently than literacy teaching and activities (Farran et al. 2017). Studies have also found that in the elementary grades (and beyond), African Americans are underrepresented in gifted pro- grams. For example, a careful examination of gifted referrals in kindergarten, first grade, and third grade found that when Black children had a Black teacher, they were far more likely to be referred and assigned to gifted programs than when they had a non-Black teacher (Grissom & Red- ding 2016). Given these disparities in opportunities to lear throughout early childhood and elementary school, perhaps it should come as no surprise that, according to the National Assessment of Educational Progress (2015), only 13 percent of African American eighth-grade boys were proficient in math, compared with 43 percent proficiency among White boys. Early exposure to high-quality math environments is increasingly important in determining students' career trajectories. In 2002, according to the National Science Foun- dation (NSF), African American college students received only 7 percent of the science, technology, engineering, and mathematics (STEM) bachelor's degrees awarded. In in 2014, this percentage remained roughly unchanged. While STEM careers have typically been male dominated, this is not the case among African Americans. Fewer than half of the STEM degrees awarded to African Americans in 2014 went to males (NSF 2017). 87 Serious Fun: How Guided Play Extends Children African American males' accomplishments in mathematics remain an under researched topic, especially from an early childhood perspective. Many successful African American men who have STEM careers have attributed their achievement largely to positive early math experiences. This suggests that by offering more challenging and supportive math learning

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environments, especially when children are young, teachers can improve children's math proficiency and, over time, open doors to STEM careers (Berry ITI 2008; MeGee & Pearman II 2014; Zilanawala et al. 2017). Providing engaging carly math experiences is not simple, however. Significant efforts-such as reducing teacher turnover, increasing spending, and hiring more qualified teachers--have had little impact on improving African American males' math trajectories (Zilanawala et al. 2017). Increasing math involvement in early childhood classrooms serving children of color from low-income families requires fundamentally rethinking math learning opportunities. 88 Serious Fun: How Guided Play Extends Children Choosing Appropriate Math Materials Based on questions from teachers, and on the day-to-day challenges we observed in their classrooms, we developed the following guidelines and strategies for selecting appropriate math materials and using them in enriching ways. Teachers should be mindful of children's unique interests and abilities as they structure the math learning environ- ment. Provide Sequential Activities In early childhood, the most effective math materials involve sequential learning. Sequential materials give children a logical order or sequence of steps to follow and often involve children creating a working plan, or blueprint, of how they will accomplish the task. Using these types of materials, children engage in higher-order think- ing, planning, reflecting, and problem solving. More engagement in sequential activities is linked to higher gains during preschool in both math and self-regulation skills (Farran et al. 2017). Teachers can spark children's interest in sequential materials by introducing and model- ing the materials before setting them out for children to independently engage with. For 3- to 5-year-olds, provide materials like tangrams (matching patterns of increasing complexity), peg-sorting boards, and learning cubes with design cards (3-D construction based on 2-D pictures). Select Materials that Give Children Feedback 89 Serious Fun: How Guided Play Extends Children

While teacher-directed math instruction is important, math centers offer great opportunities for children to explore and learn independently. One way to do this is to provide mate- rials that automatically provide feedback (sometimes called autodidactic or self-correcting), allowing children to independently sec when they have gone off course and need to rethink their approach. A simple example is a jigsaw puzzle with pieces that fit together only one way. The self-correcting feature allows children to consistently rein- force their initial ideas about math, leading to sustained math learning and enhanced working memory (Kirschner, Sweller, & Clark 2006; Willingham 2017). Activities like these also may challenge children to try more and more difficult materials as they succeed. One way to maintain children's interest in sequential materials is to scaffold the complexity of the material over time. For example, initially you might have children use the numerals 1-10 in a number game, then expand to 1-20 once they have grasped the concept. When choosing math materials, consider how much sup- port children are likely to need in order to understand and learn from the activity. It is reasonable to introduce a mate- rial and provide occasional support, but if children are likely to need continual guidance, the material may be more appropriate for a small group or one-on-one activity. Offer Problem-Solving Opportunities Extending children's initial interest in mathematical activities involves setting high expectations and inviting children to make sense of the world through problem solving. Positive carly math experiences are a wonderful way to foster young children's natural curiosity. In our observations. we have found that boys are often attracted to open-ended building materials such as LEGO bricks, Bamboo Building Blocks, and Magna-Tiles because they allow for exploration and creativity. However, children often need some adult assistance to use these materials in ways that provoke more complex thinking. Teachers should scaffold children's play by asking thoughtful questions, increasing challenges, and sparking new explorations over time. They can also encourage children to share their discoveries and their thinking with each other.Materials such as LEGO bricks and Magna-Tiles allow students to plan elaborate structures with some teacher assistance. For example, a teacher might help a child draw his plans and choose appropriate materials, then later ask

detailed, open-ended questions about the child's structure. Pictured is a young boy independently engaged in building stairs for a structure. To determine the height of the stairs, He measured the stairs against the height of the LEGO container. This required the boy to complete several phases of rebuilding and remeasuring to ensure that the stairs fit the structure properly. After several attempts, he was able to transfer the stairs to the structure, and the stairs fit. Play like this involving complex problem solving- is essential to developing the executive function skills (e.g., shift- ing attention between multiple components of a task) discussed in "Why Is Math So Important?". While solving this challenge, the child remained deeply engaged in his project for the remainder of math center time (roughly half an hour). Providing models (like a laminated poster of stairs) with corresponding plans to follow and suggestions from the teacher can help children enjoy the cognitive ben- efits- -and fun- -of more sophisticated play. Step 3: Transferring the stairs to the structure Why Is Math So Important? Exposure to high-quality carly math experiences and environments allows children to plan, focus, and build on past experiences-actions that develop executive function skills. These skills include the ability to suppress distract- ing information, shift attention between multiple components of a task, and retain and process information, all of which facilitate learning and performance in the class- room (Clements, Sarama, & Germeroth 2016; Fitzpatrick et al. 2014). Engaging in math activities-like playing 94 Serious Fun: How Guided Play Extends Children board games and sorting toys into sets (by color, shape, etc.) -enriches these essential skills. The connection between math and executive function is especially important for children growing up in homes with low income and under resourced communities. which as of 2016 included 34 percent of Black children (Annie E. Casey Foundation 2018). Recent neurological evidence shows that the areas of the brain most affected

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By early exposure to poverty are the ones related to executive function skills and reasoning (Noble et al. 2015). Because children from low-income families and under resourced communities tend to have less-predictable routines and be exposed frequently to high-stress environments, they are less likely than children from wealthier families to have well-developed executive function and math skills (Ursache & Noble 2016). Boys in particular have a hard time focusing and persisting without strong environmental support, and boys from low-income, high-stress households have the most difficulty. Younger children are more dependent on the organization of the environment than older children. It is important to note that environmental support does not mean more teacher direction and control. Often, it Means creating a math learning center that has enticing materials that support carly math skills, minimal distractions, and accessible organization to facilitate children's attention. It can also mean that teachers support and extend children's mathematical ideas by providing comments, questions, and suggestions as children explore the materials. The choice of materials matters (as outlined in the chapter), with some offering more support for learn- ing than others Add a Variety of Explicit Math Content In the prekindergarten classrooms we observed, many of the materials in math centers were variations of sorting and block building. But there is much more to math learning than these two activities. Moreover, sorting and building can happen without children actually learning much math. Boys may be attracted to these types of activities, but the math center should represent a wide range of math content, 95 Serious Fun: How Guided Play Extends Children from patterns to counting and cardinality to spatial relations. Materials that do not at first seem math related can become so with the addition of supporting resources. For example, we have observed that children often use count- ing bears for dramatic play. If children do not know how to count, having counting bears will not, by itself, teach them. However, providing a lazy Susan with numerals or dots (or a combination of either with color coding) with the counting bears can provide children with actual math Iearning. The lazy Susan allows children to physically count the quantity of counting bears and match it to the

quantity of dots displayed on the lazy Susan (i.e., one-to- one correspondence). We often saw Bristle Blocks in math centers even though They teach little to no math. While some spatial learning may occur with materials like Bristle Blocks, too often children merely attach them without reference to con- structuring a shape. For Bristle Blocks to enhance math, teachers need to add some creative suggestions for how children can interact with the blocks. Take advantage of how attractive the blocks are to children by adding measuring tapes, rulers, and suggestions for their usage, giving children a means to use these materials mathematically. Avoid Materials that Distract from Math Learning Be aware of the non mathematical aspects of materials and activities that may compete for children's attention. For example, young children are often distracted by the features of a math manipulative, particularly color, and may 96 Serious Fun: How Guided Play Extends Children have trouble recognizing the mathematical concept (Willingham 2017). Consider if color is being used for mathematical purposes (such as comparing the quantities of red cars and blue cars) or if it is simply a distraction (such as a rainbow of hues in a game intended to focus on one-to-one correspondence or counting on). It is important to note that materials in which a nonmathematical concept is redundant with the mathematical concept may impair children's math learning. For instance, many materials that aim to focus on sorting allow for both numerical and color sorting; it is very possible for children to sort entirely by color and be correct without attending to the math features at all. In addition, recent research has shown that preschoolers can become overstimulated by materials with multiple features and can have trouble distinguishing which one is most relevant (Willingham 2017). When materials have multiple features, children may need adult support to identity and attend to the mathematical aspects. For independent learning in math centers, materials with a minimal number of distracting features may be more effective. Incorporating STEM into Early Learning Realizing that all young children have enormous capacity for STEM learning can go a long way toward intention- ally providing opportunities for that learning. You can incorporate engaging STEM practices in your classroom

in simple ways -you don't have to be an expert, and 97 Serious Fun: How Guided Play Extends Children STEM can happen as part of children's play and other activities you are already doing. You Don't Have to Be an Expert Many people believe that supporting STEM learning means having STEM expertise. But, as in other academic domains, learning happens best for young children in the context of play. Educators do not need to be STEM experts but instead can support children's growth by encouraging and practicing STEM habits of mind, like curiosity, exploration, and natural experimentation. By combining hands-on explorations with stories and questions that inspire curiosity, you provide children with opportunities to develop conceptual understanding, acquire new facts, and engage in essential skills such as observing, forming hypotheses, collecting evidence, revising hypotheses, and devising experiments (NSTA 2014). Children develop STEM understandings and habits of mind as they act on their curiosity while playing and interacting with their everyday environments, sup- ported by adults. An effective STEM teacher often resists directly answer- ing children's questions. Ask purposeful questions and then support children as they investigate for themselves. This fosters self-reliance and resilience, two characteris- tics that are foundational to STEM inquiry and practices (Van Meeteren & Zan 2010). Supporting children's curiosity and self-direction requires intention and practice. Learn to facilitate children's open and focused exploration, and encourage them to reflect on their experiences through representation and talking over their ideas (Hoisington 2010). One of your most important roles in encouraging children's natural STEM capacity is to help children persist when they might otherwise give up. When a child encounters frustration, avoid the temptation to resolve the tension with an answer. Instead, help the child develop persistence by showing enthusiasm about the challenge, modeling won- der and curiosity. Ask questions that re-engage her intrinsic desire to understand the issue. In contrast to questions

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that imply a single correct answer (e.g., "Did the ball go up or down?"), questions that encourage experimentation (such as "What do you think would happen if .. ?") help 98 Serious Fun: How Guided Play Extends Children children persist, problem solve, and experience the won- der of discovery (Hoisington 2010). When you get into the habit of asking questions like these, you may find that you yourself enjoy this experience of encouraging children to dig deeper. STEM Can Happen Within Your Existing Curriculum The concepts, vocabulary, and habits of mind children develop when they engage in STEM activities that are transferable. The activities therefore strengthen many skills, including literacy and attention development. In other words, STEM learning is not an additional task to include on top of other demands: When you view early STEM learning as the development of both knowledge and inquiry-based habits of mind, you discover ways to infuse STEM practices and concepts into your existing curriculum. For example, STEM and literacy skills go hand in hand. Many of the books you already read aloud to children include STEM-like features: a problem to be solved, an evidence-driven solution that is attempted (and often iterated and reattempted), and the discovery of a method that works. Use these opportunities to illustrate that STEM is everywhere and that there is inherent drama to STEM exploration. Explicit STEM-based activities can be used to enhance children's engagement and understanding of narratives as well. For example, one preschool class was exploring the book Lost and Found, by Oliver Jeffers, about a lost penguin finding his way home on a boat. Teachers asked the 3-year-olds to build and test boats made from aluminum foil to transport a small penguin figure across the water table. The children were deeply engaged in this immersive and meaningful STEM experience, which enhanced their experience with the book and encouraged them to talk at length about the story (Draper & Wood 2017). Once you start to embed these approaches to supporting children's explorations, you'll be in a prime position to

help families and other educators see the remarkably sophisticated, and often hidden, STEM capacity of young children and to see how powerful carly STEM experiences can be in shaping the minds of the next generation. Adapted from F. McClure, "More Than a Foundation: Young Children Are Capable STEM Learners," 2017, Young Children 72 (5): 83-89 Organizing the Environment to Maximize Learning Young children are highly dependent on the organization of the environment to be able to engage with math materials in a meaningful way. A space that is neatly organized, labeled, and engaging will garner far more attention than a poorly arranged center. When children can easily see all available materials, they can better plan their math-related play, be it building a pyramid or copying a design or sort- ing toy animals into different types of sets (perhaps by tail length). Maintaining their interest throughout the year requires adding new materials and/or enhancing old mate- rials with new resources that allow children to do more with what is at hand. For example, you could provide children with sets of pattern blocks and simple designs to copy. As the children gain mastery, you can add more complex designs and invite children to create their own using the shapes. Teachers can also expand this design copying using other materials, such as beads or LEGO bricks. 100 Serious Fun: How Guided Play Extends Children Shells Cookie Cutters •Fun -Foam Rocks Finger Lights Pipe Cogners Containers for materials are often labeled to make cleanup easier, but there is a more important benefit to labeling. Appropriately labeling materials with photos and/or text helps children access them easily. Labels can also be

enhanced to remind children of more challenging ways to play with the materials. Children can then independently navigate centers, making informed decisions and plans about what supplies to work with. Many materials fit well into tubs that are easy to label. Oddly shaped and large materials can be placed on labeled shelves. To re engage children and maintain their attention, refresh materials after every unit of study by adding new items and changing the supporting materials. For example, if counters in the math center are used only to practice one- to-one correspondence, you can add pattern cards that prompt children to use the counters in new ways. There is not one prescribed time frame for rotating materials. When you observe fewer children choosing the math center, it's a strong indication that the materials need updating. Conclusion Fostering high-quality early math experiences can have a tremendous effect on the long-term school success and career trajectories of African American males. While the guidelines we have outlined here are beneficial to all preschoolers, they are critically important to male children of color. Far too many schools are not providing the vigor- 101 Serious Fun: How Guided Play Extends Children ous math activities, materials, and supports that children of color need, hampering their opportunities to later engage in advanced math courses or enter STEM-related fields. Early childhood teachers can foster productive math experiences for African American boys by having positive individual interactions, providing opportunities for exploration, extending children's initial interests, and structuring the environment to continuously attract and engage children in math learning. The way in which teachers and parents approach and com- municate the importance of math learning has a direct link to a young boy's perception of his ability to enjoy and excel in math. It also impacts his self-regulation skills. Therefore, making math a meaningful and inviting experience is vital in all early childhood classrooms-especially those serving African American boys growing up in under- resourced communities. Try This! > Make a list of resources suggested in the chap- ter that promote engagement with mathematical concepts (e.g., tangrams, peg sorts,

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number cubes, design cards, jigsaw puzzles, puzzle boards, color tiles, counting cars and bears, materials for design copying and building, and board and card games). Choose three and jot down what children can learn as they manipulate the materials and play. How might you support and extend their learning? › Refresh your mathematics materials. Organize your setting with ample table space. Redesign the storage area for easy access with containers that are labeled and have photos of contents. What activities, games, and resources can you add? Think about whether children would ben- efît more from an introduction to new additions or from simply exploring materials on their own at first. > Use math talk to solve simple daily problems throughout the day.

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