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How many times do you have to see something before you have learned it and committed it to memory? In this video, a preschool teacher talks about how she incorporates a single math concept, such as shapes, into many different activities. With this approach she exposes the children to the concept many different times and in many ways. As you watch, pay close attention to the different ways that the students are learning about shapes.In your initial response, answer the following questions: List the basic mathematical concepts covered in the video. Describe an activity to use in a Math or Activity Center. Identify the age group and choose a developmentally appropriate concept. Use this guide to help select a concept that follows the math sequence development for your chosen age range. ages 1-2: size; shapes; position words (top, bottom, middle); counting. ages 3-5: patterning; sequence; counting; numeral recognition; numeral formation. ages 5-8: addition; subtraction; money recognition. With your peers, discuss the activity ideas for a Math or Activity Center that you each shared. Suggest variations to the activities (such as a different age group and/or a different Learning center – dramatic, art, water, language, movement, etc.). Sorenson Squeeze Encoded by A A 19-2aFormal Science Formal science  experiences are planned by the teacher to develop particular skills (see  Photo 19-2 ). A formal science experience that develops young children’s fine-motor skills might involve pouring and measuring with tools in the sand and water area. The teacher would plan to include a specific item such as a funnel hung low over the water table or funnels attached to each end of a length of plastic tubing that would serve a specific purpose—the development of fine-motor skills. Although other learning might occur because of these implements’ inclusion, they serve a specific developmental purpose. Photo 19-2 The child is observing the effects of light as part of his teacher’s planned, formal science activity. Casper Holroyd 19-2bInformal Science Unlike formal science,  informal science  calls for little or no teacher involvement (see  Photo 19-3 ). Children work on their own, at their own rate, and only when they feel like it. They select the kinds of activities that interest them. They spend as much or as little time working at a given activity as they desire. It is when this sort of openness is available to children that creative potential begins to develop. Photo 19-3 Playing with sand and other materials fosters many informal science experiences. Casper Holroyd Most informal science activities occur in the discovery (science) center. The discovery center is an area in the early childhood classroom where children can participate in a variety of informal science activities that stimulate curiosity, exploration, and problem solving. In the discovery center, young children develop many skills and concepts in their active exploration of such things as sand, water, magnets, and a multitude of other real-life objects. A more specific discussion of the discovery center follows later in this chapter. 19-2cIncidental Science Incidental science  cannot be planned. It sometimes does not take place once a week or even once a month. Just what is incidental science? A city or town may be struck by a violent windstorm. Limbs of trees are knocked down; whole trees are uprooted. Great sheets of rain fall, and streets become flooded. Children are frightened by the great noise and wild lightning as the storm passes. Finally the storm is over. Is this the time for an incidental science experience? Of course it is! This is the time for children who are interested to learn many things. They can study the roots of trees; they may have the chance to observe growth rings. They are able to examine tree bark. They can observe what happens to water as it drains from a flooded street. Some might want to talk about their feelings as the lightning flashed and the thunder crashed. Some may want to create a painting about the experience. A teacher cannot plan such an experience. A good teacher can, however, take advantage of such an opportunity by letting children explore and seek answers to questions. A teacher can encourage children to be more inquisitive and creative. Did You Get It? · A group of young children take magnifying glasses from a box, and then run around the schoolyard looking at insects and plants through the magnifying glasses. In which type of learning are they engaged? 1. scientific method 2. creative learning 3. informal science 4. formal science Take the full quiz on CourseMate. Inquiry-Based Learning LO 3   Inquiry-based learning  is a term often used when discussing science experiences for young children. Inquiry refers to investigating to gather information, which is part of human behavior from birth. For children, it is a way of learning about the world driven by interest, wonder, and curiosity. For teachers, it is a way of learning about children’s interests, abilities, and theories in order to plan appropriate activities. Because inquiry is such a basic human learning strategy, it makes sense for teachers to use an inquiry-based approach in their science activities with young children. Inquiry-based learning is an approach to learning that involves a process of exploring the natural or material world that leads to asking questions and making discoveries in the search for new understandings. There are several ways to promote inquiry-based learning in the early childhood classroom: · Ask questions that invite constructive input and validate prior knowledge. For example, instead of “Has anyone ever seen a rock before?” ask, “What do you know about rocks?” Ask open-ended questions. For example, “Tell me about what you’re wondering.” “What do you think might happen if…?” “What do you notice?” · Encourage children to wait a few seconds before giving an answer to allow time for thinking. Tell the children you are going to ask a question, but you would like them all to close their eyes and think about it for a few seconds before answering. · Repeat or paraphrase what the children say without praising or criticizing. This encourages children to think for themselves instead of seeking teacher validation. “Scott thinks that sand comes from rocks, and Claire says it is dirt from the ocean. What do you think? Where does sand come from?” In science activities, encourage children to look closely, notice details, pose questions, and reflect on what they learned. Children’s wonderings and reflections are essential to the learning process. Also, talking about their experiences with others allows children to articulate what they have seen or done in a way that makes sense. By listening to what others have experienced, children can understand multiple perspectives. Listening to others’ insights and opinions and learning that these are of value is a key skill taught in an inquiry-based classroom (see Photo 19-4). Photo 19-4 In an inquiry-based classroom, children need to ask questions, but they also need to learn to listen to other’s insights and opinions. © Cengage Learning TeachSource Video © 2015 Cengage Learning School Age: Cooking Activities · 1. What type of science activity is being presented by this teacher? Give a specific reason for your choice. How could you present this activity in one of the other types of science activities? · 2. Is this teacher using inquiry-based learning techniques? Use specific examples from the video in your reply. · 3. How could this activity be enhanced so that it involves aesthetics and science? Did You Get It? · A preschool teacher is careful to always use an inquiry-based method of teaching because she wants her students to learn social skills. Inquiry-based learning can promote social skills because children learn to 1. obey the teacher. 2. listen to others’ opinions. 3. listen instead of asking questions. 4. share their materials. Take the full quiz on CourseMate. National Science Education Standards LO 4 The National Research Council (NRC) defined performance standards for children at each grade level, from kindergarten through high school back in 1996. These standards present an outline of what students in kindergarten through grade 12 need to know, understand, and be able to do to be “scientifically literate” at each grade level. They promote a dynamic understanding of scientific principles that is always open to review and revision. Since the introduction of these standards, a joint effort between the NRC, the National Science Teachers Association (NSTA), and the American Association for the Advancement of Science (AAAS) is underway to create the  Next Generation Science Standards (NGSS) , the foundation for all students to have a solid  science education. The NGSS will be  science standards created through a collaborative, state-led process. The new standards being drafted are based on the  Framework for  Science Education , which identifies the key scientific ideas and practices all students should learn by the end of high school. Many states have begun work to implement the framework. The vision laid out in the framework identifies what students should know and be able to do to be a functional citizen, which includes being scientifically literate and an effective member of the U.S. workforce. 19-4aStem/Steam Science, Technology, Engineering, and Math (STEM)  curriculum areas have become a major focus in education because of the concern that the United States is falling behind in scientific innovation. The pressure is on educators to start early and provide learning experiences in these areas for young children. STEM is a buzzword even referring to preschool (Ashbrook, 2010; Moomaw & Davis, 2010). STEM has quickly taken hold in education policy circles, but some experts in the arts community and beyond suggest it may be missing another initial to make the combination still more powerful. The idea? Move from STEM to STEAM, with an A for the arts. Some experts perceive a special connection between the arts and the STEM fields. A 2008 study led by Robert Root-Bernstein of Michigan State University found that Nobel Laureates in the sciences were  more likely than scientists in general to be involved in the performing arts (2008). Others note that Albert Einstein was an accomplished violinist. And then there’s the Renaissance figure viewed by some as the personification of STEAM: Leonardo da Vinci, the Italian painter and sculptor who also made a name for himself as a scientist, engineer, and inventor. Because the arts are a natural part of early childhood education, adding this element may help more teachers find ways to work STEM concepts into the curriculum. STEM is more about facilitating inquiry-based thinking and discovery than about teaching facts and giving answers. Did You Get It? · While teaching three-year-olds about mixing colors, the teacher has them experiment with mixing different colors and seeing what happens when they add more water to the paint. The teacher’s actions reflect the ___________ policy. 1. STEM 2. STEAM 3. creative arts 4. color teaching Take the full quiz on CourseMate. Aesthetics and Science LO 5 As we have learned earlier in this text, having aesthetic awareness means being sensitive to beauty in nature and art. Such sensitivity is fostered not by talking about beauty but by experiencing it in a variety of forms—the sight of snow on evergreen boughs, the smell of the earth after a spring rain, the sound of a bird singing overhead, and the feel of a kitten’s fur or the moss on the side of a tree. It is easy to forget how amazing a pebble or a pinecone can be to a young child. For the young child, the world of nature is an especially appropriate avenue for developing aesthetic sensitivity. An early snowfall in winter may provide a child with his or her first remembered experience of snow. Seeing a rainbow in the sky may be something a  has never experienced before. Watching a butterfly move from flower to flower may provide a visual feast that a child has not yet come to take for granted. Beauty is not just in what can be seen. It is present also in what can be touched, felt, and listened to. Because the world of nature is so full of sights, sounds, and textures, it can serve as an incredibly rich and readily available resource for the development of aesthetic sensibilities in young children. 19-5aScience and Art Materials/Activities Children working with art materials make scientific observations noting, for example, that water makes tempera paint thinner and that crayons become soft if they are left near the heat. Evelyn looks at her wet, drippy painting and says, “I wonder if I can blow it dry with my wind.” Drew finds that his clay figure left on the windowsill overnight has “gotten all hardened up” because it is no longer wet. Experimentation with art materials may lead to many other discoveries about cause and effect. Children notice that colors change as they are mixed and that the sponges used for printing absorb liquid. In contrast, other materials such as plastics are found to be nonabsorbent. In using many materials, children observe differences between liquids and solids and see that other items such as wax crayons and oil paints resist water. In mixing paint from powder, children learn that some materials dissolve in water. The operations of simple machines can be understood through using tools such as scissors and hammers. The potential for developing science concepts is in the art materials and in the processes—ready to be discovered and applied. These experiences are consistent with the national science standard that states that children should understand the properties of materials. 19-5bAnimals Link Science and Art Young children’s natural love of animals is a good place to begin when planning art activities that encourage science experiences. Children are intrigued by animals. Studying animals is consistent with the national science standard calling for the study of animals and their environments (see  Photo 19-5 ). Yet, animals provide more than a science experience for children because they stimulate children’s artistic exploration as well. Young children, after touching, seeing, hearing, or smelling animals, will be stimulated to use art media for animal representations. Children with an emotional attachment to household or school pets will be additionally motivated to create visual images. Teachers create opportunities for guided learning about animals by providing art media and materials for children to use, by engaging children in discussions about animals, and by reading stories, showing pictures, and singing songs about animals. Photo 19-5 This science activity combines drawing, language arts, and scientific observation. Casper Holroyd Sometimes after a trip to a zoo or farm, children will be stimulated to visually express their ideas about animals. After the class trip to the zoo,  Aiden painted an elephant immediately upon returning to school. “Look! Elephants are so funny because they have a tail on both ends,” he announced. The teacher accepted his work but, realizing his confusion, clarified the differences between a trunk and a tail. This example shows how art can serve as a vehicle for direct learning by helping children express their understandings. At the same time, the art responses give the teacher clues for further planning. The following are some activities that expand further on the concept of animals/pets and art activities. · Encourage older children to draw, paint, or model representations of their pets doing something characteristic of that animal. · Suggest to children that they find pictures for collages showing animals that live in different places, move in various ways, or have different body coverings. · Provide opportunities for children to make their drawings, paintings, or cutout animals into booklets, murals, jigsaw puzzles, or puppets. · Offer a variety of boxes, trays, and found objects that children can use to make zoo cages or farm environments for toy animals or models they create. · Provide scraps of furry fabrics, yarns, and spotted and striped papers in different shapes for children to paste on a background and then add appendages for real or imaginary animals. · Make a variety of boxes, cardboard tubes, and other found objects available so children can create real or imaginary creatures. · Provide Styrofoam trays on which children can draw simple animal forms. Pierce the outline at regular intervals for younger children to stitch. Older children can pierce through the trays themselves. · Transfer children’s animal drawings onto felt or burlap. Cut out two duplicate shapes, stitch together, and fill with beans, seeds, or shredded nylon hose for use as toys to toss. At the end of this chapter, you will find many ideas that may be used as the basis for planning both formal and informal science activities. These, of course, are meant to be starting points. Teachers will think of many more activities that suit their particular groups’ interests and abilities. Did You Get It? · A four-year-old notices that when she rubs her hand over her drawing, the lines she drew with pastels meld and soften. She is learning 1. scientific inquiry. 2. the aesthetic principle. 3. cause and effect. 4. operation of simple machines. Take the full quiz on CourseMate. The Discovery/Science Center LO 6  The discovery center can be open ended (for example, present students with a box of magnets and electrical supplies with the instructions to see how the items interact), or they can work toward a specific outcome (for example, ask students to find out which items sink or float). The discovery center should have things for the children to “do.” It is not a center where children just look at objects. Most teachers use a sand and water table in the discovery center. Here various materials—sand, water, sawdust, mud—can be made available for children to explore, measure, and pour. Sand and water activities are usually informal science and open ended; that is, children can freely explore and manipulate materials with no definite or specified purpose to the activity. Another type of activity that usually is done in a discovery center is cooking. Recipes that children can prepare individually with a minimum of teacher supervision work well in the discovery center. There are many simple recipes that do not require cooking (see Chapter 21 for examples of such recipes). If heating equipment is used, an adult must always be present to supervise and assist. The discovery center can house plants and animals for the children to observe. In addition to caring for them, children can also record information about them, such as the amount of food given to the guinea pig each day, the amount of water used for the plant, or the amount the plant has grown (see Photo 19-6). Photo 19-6 A discovery center can keep animals for children to observe and to keep track of the amount of food they eat. © Cengage Learning “Please touch!” is the implied invitation of an interesting, ever-changing discovery center. Many teachers begin the school year with noble intentions of welcoming nature finds and other objects of scientific interest that children bring from home. Perhaps they initiate the project attractively with a bird’s nest propped in a small tree branch, some special rocks, and a recently shed snake skin. If the goal of a changing display is forgotten, the old things will lose their meaning. Because there is little appeal in a dusty nest or a tattered snake skin, it is better to retire the too-familiar objects. 19-6aDiscovery Centers—Setup Try to locate the discovery center in an area that both invites children’s participation yet controls distractions. Varying the location to fit the requirements of the activity builds interest. Science is very popular on the days when it takes place under a blanket-covered table! Careful planning of space, materials, and time for science will allow children to work as safely, independently, and successfully as possible. In preschool and kindergarten classrooms, and in elementary classrooms organized with learning centers, many science activities can be set up for independent use. Printed activity directions can be prepared to guide reading students. Recorded guides for nonreaders can also be made to reduce the amount of direct supervision needed for small-group learning activities. 19-6bDiscovery Centers—Younger Preschool Children Although the activities in this text are intended for children  of age and older, many can be adapted for younger preschool children. Two-year-olds can enjoy simple sensory explorations such as feeling air as they move it with paper fans, spinning pinwheels, or swinging streamers on a breezy day. They can feel rock textures and weights, touch ice and then the water it melts into, and watch and then move like a goldfish. They can taste raw fruits and vegetables that have grown from plants, listen to loud and soft sounds, or gaze through transparent color paddles to see their surroundings in a new light. Three-year-olds might be expected to engage in similar activities, taking in greater detail. They will be able to direct deeper attention to such things as exploring new dimensions with a magnifying glass. This group can enjoy some of the classifying experiences on a beginning level: sorting rocks from objects that are not rocks; things that float from those that do not float; and objects that are attracted by a magnet from objects that are not attracted. In formal science activities, younger children need easily distinguished materials and clearly defined steps. For instance, the seeds in a planting experience should be large and easy to see. A fine, dark lettuce seed is hard to distinguish from a bit of dirt, and a child may not be sure of what he or she has actually done after planting it. A large, pale bean or pumpkin seed that is obviously different from the soil would be a better choice. Very young children can be easily sidetracked in their reasoning by what they observe. To keep the objective of science experience evident to them, avoid using materials with irrelevant, distracting details. For instance, if size comparisons are to be made with measuring cups, use cups of the same color and shape to help children focus on size. Younger children will still be exploring materials with their mouths as well as with their fingers. Nonfood materials must not be small enough to swallow. Foods such as peanuts and popcorn should not be given to children too young to chew them well. As a matter of course, adults should closely supervise any activity for very young children. Thoughtful questioning, careful listening to children’s replies, and comments from the teacher guide formal science activities in the discovery center. Open-ended questions such as “What happens when you…?” help children focus their thinking. A question such as “Why do you suppose…?” allows children to share their reasoning. Many of us use the pattern of stating the answers we hear from children in the form of a question. We may say, “So the cup of snow melted into a smaller amount of water, right? Isn’t that what you found?” This style of questioning reduces children’s need to discover answers for themselves, or tells them that the main discovery is to find out what the teacher wants them to say. 19-6cDiscovery Walks An easy way to keep the science discovery area new and exciting is to plan nature discovery walks as a regular part of your curriculum. The desire to collect things is strong in young children. A discovery walk can be a springboard to some memorable science experiences. Give children shopping bags and take them on a mini field trip to a nearby playground or sidewalk. Ask them to collect anything interesting to add to their bag (keeping safety in mind, of course). You’ll be amazed at what your young collectors find, including flattened bottle caps, blades of grass, and even an occasional penny. Sorting and representing. Ask children to unload their collections into a plastic tray or pan. Start sorting, comparing, classifying, and ordering. Have a sheet of paper and markers on hand so that they can trace and label their collections. A closer look. A magnifying glass is great for helping children examine their discoveries (see Photo 19-7). Children can sort their collections by lines, textures, colors, or any other art element. You might add magnetic strips to the backs of rocks and place them in categories (big/little, smooth/rough, shiny/dull, and so on) on a magnetic board. Photo 19-7 A magnifying glass is an excellent tool to help children examine their discoveries. © 2015 Cengage Learning Displaying objects in the discovery center. When a child brings a collection of objects from home, provide a special place for this temporary display. For objects collected by the class, you can organize and store the displays in clear plastic boxes. This way, the displays can be easily rotated among children. When you have popular items in your discovery center such as prisms or magnets, have duplicates on hand or use a sign-up system. Two to four children can sit on the floor and explore a collection out on a small carpet square or a bathmat. Four chairs set at a table invite four science investigators. If you have access to a digital camera, snap a photo of each child’s collection and print a large, one-page photo of each collection. Below the picture, write a short “I spy” description of a few items in the collection. For example, write, “I spy an item that is round and has lines on it.” This invites children’s investigation and close observation. You can also use interesting collections as table centerpieces for special occasions. If you have access to a video camera, you can make a video about the children’s collecting and investigating process and share it with parents. This One’s for You! Making Sense of Data: a Twenty-First-Century Science Skill Knowing how to read, interpret, and see trends in graphs is a critical twenty-first-century skill. All learners use this skill throughout their lives because it helps judge whether a claim is supported by evidence. A major aspect of doing science (in and out of the classroom) is asking questions about how the world works and then designing investigations to collect and analyze data that will provide solutions to those questions (McNeill & Krajcik, 2011; NRC, 1996, 2000). But after your students collect data, how can you help them make sense of it? Young students are capable of asking a, “How many different types of birds come to our bird feeder?” question, designing and carrying out investigations, and then analyzing data to use as evidence to support claims that respond to their questions (NRC 1996, 2000). Data organization and analysis is the process of making observations, taking measurements, and sorting out the information in ways that facilitate sense-making, allowing possible patterns to become apparent (Krajcik, 2011). The ability to analyze data is an essential aspect of scientific literacy and will be critical for young children as they grow in a world that is filled with information. To make sense of data, scientists transform it into various representations. By creating tables, graphs, diagrams, or other visualizations, children can transform data into different forms that will allow them, just as it allows scientists, to see patterns and trends. Let’s go back to the bird feeder scenario. This could be an area where children can practice making sense of data. The children might make a record of the type and number of birds that visit the feeder. A simple list of information might be difficult for children to see a pattern. Children can create a table to more clearly see the pattern of type of bird and how frequently each type visits the feeder. The transformation from list to table helps learners see trends in data—for example, sparrows are the most common bird. After students have constructed their tables, they can write summaries describing what their tables mean. Such summaries are another way to transform data—from numbers to words. Children could also create graphs of data to make visual representations. Transforming data into graphs will help students see trends in quantitative data. To continue with our bird example, rather than a count of the type of birds, students could create a bar graph. A bar graph of the number versus types of birds is much easier for students to “read” because it more effectively illustrates patterns. In elementary classrooms, students can transform their data into pie charts, bar graphs, and line graphs (NCTM, 2000). Another way to support students in learning this data-analyzing skill is to have them come up with statements that describe what the graph means. Have them look for a pattern or a trend in the shape of the graph. After students have written their own interpretation, members of the group can compare the statements. If your students are too young to write, you can have them say what they see. Providing opportunities for students to ask questions about scientific phenomena they encounter in their world is a critical aspect of students learning science. Creating such learning activities will support all students in developing critical scientific practices and developing twenty-first-century capabilities that they will use throughout their lives (Krajcik, 2011). 19-6dNature-Related Materials in Different Learning Centers To the language-experience center, you can add books and pictures about nature. You can also add stuffed animals, animal puppets, and a variety of plant and animal flannel-board characters (see  Photo 19-8 ). Choose pictures and other representations of animals that are as realistic as possible versus those that have a cartoonlike appearance. Photo 19-8 Stuffed animals are just one type of item that can be added to a nature-related learning center. Casper Holroyd To add nature-related materials to the manipulative center, you might choose simple puzzles with nature themes (animals, plants, and so on) and shells or pebbles of different colors and sizes. You might also add pinecones, small pieces of bark, dry wood, and other objects found in or near the yard. Similar items could be introduced into the block center as well. Materials from the outdoors also make wonderful additions to the art center. Dried leaves or small pieces of bark can be used for rubbings; seeds, shells, dry grasses, and feathers can be used for collages; evergreen sprigs can be used as paintbrushes. To the music or listening center, you might add audiotapes of bird songs, ocean sounds, rainforest noises, and other sounds from nature. The dramatic play area can also be enriched with materials from the outdoors. Such materials include camping equipment, garden tools, and a picnic basket filled with a variety of picnic items. Did You Get It? · A teacher gives each of her three-year-olds three identically sized ice cubes so they can compare how long each cube takes to melt in different assigned places in the classroom. Why should she be careful to give each child three identically sized ice cubes? 1. to minimize jealousy among the students 2. to avoid them from becoming sidetracked by irrelevant details 3. to ease the job of giving out the ice cubes and managing the experiment 4. to ensure their satisfaction with the experiment Take the full quiz on CourseMate. Environmental Education LO 7 “We do not inherit the earth from our ancestors, we borrow it from our children.” — Native American proverb Ecologists have varied estimates on how much time is left before we will have wasted natural resources and polluted the Earth to the point where we can no longer survive. Some fear the damage is already irreversible. Others believe that there is still time—provided a profound change in attitude and behavior occurs. For adults, this change means finding new values. For children, it means growing up with an understanding of the environment and a desire to conserve and protect those things essential for continued life on this planet. If children are to grow up in a world fit for human survival, the environment must be protected. Children should learn about nature from their earliest years. Nature is not the only part of a child’s environment, however. Home, school, and neighborhood are all parts of the child’s environment. In fact, everything that contributes to children’s experiences—good or bad—is part of their environment. Can a child learn creativity by learning about the environment? Can a child learn to improve the environment? Can young children learn about ecology? The answer to these questions is “yes.” Most of all, learning about these things can and must begin when a child is young. Their environment is one of the most important influences in the lives of children. They need an environment full of love. They need an environment that provides for their other basic needs: water, food, clean air. Children need an environment that provides for their safety, that helps them grow intellectually, and that they can understand and control. In other words, children need to learn about their environment because their lives depend on that environment. This learning can be done in a very creative way. Activities that help children understand their environment can also help them become more creative thinkers. (Bredekamp 2009). Main content 19-7aTypes of Environments For the purposes of this chapter, the term  environment  refers to two things: man-made and natural things that children meet in their surroundings. Streets, houses, and schools are examples of man-made things in the environment. Trees, grass, and birds are parts of nature. Streetlights, cars, and buildings are man-made. Animals, clouds, and snow are natural things. Noise, light, and smells may be man-made or a part of nature. Children have many environments in which they live. Home is one. It may be a pleasant part of a child’s life or an unpleasant one. School is another environment that influences a child’s life, and it, too, may be an enjoyable experience or an unpleasant one. The neighborhood environment may be friendly and safe, or it may be hostile and dangerous. Many people are also part of a child’s environment: parents and neighbors, grocers and police officers, and teachers and doctors. The people who make up the communities in which children live may make children feel very good about their lives, or they may make the children feel unhappy. In these environments, there are also natural things and natural happenings: grass, trees, and flowers; rain, wind, and earthquakes; cats, rats, and beetles. All these things are part of a child’s environment. They all affect one another. Nature influences people; people influence nature. Think about It Eight-Year-Olds Publish Study Biology Letters published a report conducted and written by a group of - to  olds from an English elementary school investigating the way bumblebees see colors and patterns. The scientific organization—which is more than three centuries old and includes some of the world’s most eminent scientists—said the children reported findings that were a genuine advance in the field of insect color and pattern vision (Hui, 2010). Working with a neuroscientist from University College London, the children carefully documented their methodology and discussed the data they collected. The group trained bees to go to targets of different colors by giving them a sugar reward, and they reported that the insects are able to learn and remember cues based on color and pattern. The study successfully went through peer review, and the scientists who commented on the students’ report in the journal said although the experiments were modest and lacked statistical analyses, they were cleverly and correctly designed. The studies held their own compared to those conducted by highly trained specialists. Beau Lotto, the scientist who coordinated the study, said she hoped the project could inspire people to approach science in a way that’s creative and fun (Hui, 2010). 19-7bEcology Ecology  is the study of all elements of an environment, both living and nonliving, and the interrelation of these elements. The term comes from two Greek words: ecos, meaning the “place to live” or “home,” and ology, meaning “study of.” If we stop to consider our work with young children, we have probably touched on the subject of ecology frequently. For example, we notice the changes in the weather and discuss how these affect plants, birds, animals, and ourselves. When we plant seeds, hatch eggs, or care for a pet, we notice those things that are necessary for life and growth—nourishment, light, heat, nurturing. We like to examine and observe many organisms, but if we remove an insect from its home, we take care to restore it unharmed to its place after our observation is finished. Consequently, children learn that all life is precious, and no creature is more or less worthwhile than another. Those of us in early childhood education are also old hands at recycling materials and using up discards. Bits of paper left over from cutting shapes find their way into the collage box instead of the wastebasket. Empty boxes evolve into constructions, large and small. The blank sides of printed sheets of paper are used for drawing. Old newspapers are used for many art projects. We all think twice before throwing anything away, and with a little encouragement, children and their parents soon catch the saving habit. By our example, we can teach other ways of living a more ecologically sound lifestyle. For example, using durable dishes for food service rather than disposable dishes is an ecologically sound practice. When food and beverages for snacks and meals come in bottles or cans, these containers should be cleaned and the cans flattened and deposited at a recycling center. The use of personal cloth towels instead of paper towels is another good ecological practice. To encourage parents to recycle, you might consider establishing a collection site at your school, perhaps making it a cooperative project run by the parents. To truly grasp the concept of ecology, young children need opportunities to observe the total process rather than just a portion of it or only the finished product. Help children understand the total process when you explain the need for conservation. Describing how the paper-making process begins with the cutting down of a tree in the forest and ends with the paper products that we use every day helps children understand why it is important that they use only one paper towel to dry their hands. Incorporating the subject of ecology into the early childhood curriculum is endorsed in the National Science Education Standards. It is particularly relevant to the standard that states that children should develop an understanding of “types of resources” and “changes in environments” (NRC, 1996). These early experiences in ecology will provide students an eventual understanding and appreciation for their part in protecting the environment. 19-7cEcology and Art Art, music, dance, movement, and storytelling all provide opportunities for children to express their interests and discoveries developed through environmental education. Setting up easels outdoors may inspire children to paint trees or their feelings about trees. Modeling clay outdoors may encourage children to create their own versions of natural objects in their outdoor play space. Use types of clouds to inspire soft sculptures: stratus, cumulus, and so on. (See Chapter 14 and the appendices for play dough and other modeling material recipes.) In movement activities, children may reflect the wiggle of caterpillars they observed on the playground. In music, the sounds of birds and crickets can be reflected with rhythm instruments or their own voices. They may dance the story of birds, flowers, and animals awakening to the springtime sun. Children’s books are also excellent for further expanding a child’s understanding and appreciation of the earth. Children’s science books are an excellent way to address the national science standard that states, “It is important for students to learn how to access information from books” (NRC, 1996, p.). The preceding are all general ideas on how to incorporate environmental education and ecology into your early childhood program. The following are some more specific activities related to environmental education and ecology for children of all ages: · When someone in the classroom breaks a toy or piece of equipment, use the opportunity to talk with children about the consequences—that no one can play with the toy or use the equipment until it is repaired and that if it cannot be repaired, no one can ever use it again. Have children discuss ways of preventing this problem. · Help children (and by your own example) use materials—paint, paper, crayons, and the like—conservatively by saving scraps, storing unused paint, completing a picture before starting another, and keeping pencils and crayons off the floor. · Encourage children to help care for and clean classroom furniture. Provide cleanup materials for washing off tables and chairs and cleaning up spills. · Before looking at books, discuss with the children the importance of caring for them. Suggestions might include washing hands, turning pages at the corner, and putting them in a special place away from pets and younger brothers and sisters. Remind them of their disappointment over a missing page in a story. · Snack time offers an opportunity for children to learn to conserve. The same applies to older children at lunch time. Persuade them to take only what they will eat, to eat all they take, and to refuse what they do not want. Each child should frequently have the opportunity to clean up after snack. Before going on a class picnic, remind children to pick up their trash in the park and discuss with them why this is important. · During the year, encourage appreciation for the jobs of the school custodian, the garbage collector, and others whose work is essential to maintaining a clean and pleasant environment. Invite these helpers to talk with children about what they do and how the children can help make their job easier. · Avoid frightening children with threats about results of things they cannot control. (Example: What will happen when there is no clean air left?) Concentrate instead on the things they can do, such as keeping their own yards and school grounds neat, putting their own waste in proper receptacles, having a litter bag in the car, avoiding open burning, keeping pets clean, and so on. 19-7dEnvironmental Activities in School A child first learns about caring for the environment by caring for his or her most immediate environment, that is, home, school, playgrounds, and parks. In the early childhood years, the teacher can use everyday experiences to point out to children the importance of caring for the environment. Getting started. Getting young children outdoors to touch and experience nature is the starting point for learning about ecology and the environment. Unfortunately, a visit to many early childhood classrooms reveals the obvious: indoor time and space are given far more priority than outdoor. Many early childhood programs allot only a short daily period of outdoor time for children’s energy release and motor development. In the elementary grades, with state-mandated curriculums, it becomes even more difficult to find time to go outdoors to study and still accommodate all the mandated subjects and time requirements. Increased time for outdoor learning experience can be worked into the daily routine without difficulty, however, at least in good weather (see Photo 19-9). Music, movement, and art acquire new dimensions outside; there is often plenty of space for construction with large blocks, boxes, tires, and boards; and snack and lunch times become picnics. Best of all, the outdoors provides a natural setting, complete with props, for dramatic play. Middle- and upper-elementary-age students enjoy reading and working on projects outdoors. Small reading groups, project work, and other academic activities can often be done just as effectively in the outdoors. Just think how much you, as a student, enjoy reading outside on a sunny, pleasant day! Photo 19-9 It’s important to work outdoor learning experiences into the day. © Cengage Learning Even if the outdoor space is a concrete-covered square, children experience more of nature than they would inside. They know the warmth of the sun, the power of the wind, and the coolness of shade; they find plants that spring up in cracks and insects that crawl or fly; and they experience weather in its many forms. Obviously, the more natural an environment is, the better. Slightly unkempt spaces are more interesting to investigate than blacktop or grassy lawns. In many areas, the edges of property lines where the mower does not reach hold the greatest promise for exploration. As stated in the national standards on earth and science (Content Standard D), it is important that “all students develop an understanding of the properties of the earth” (NRC, 1996). Young children are naturally interested in everything they see around them—soil, rocks, streams, rain, snow, clouds, and rainbows. During the first years of school, they should be encouraged to observe closely the objects and materials in their environment, note their properties, distinguish one from another, and develop their own explanations of how things become the way they are. Teacher’s role. To be involved with nature, all you need are curiosity, joy of exploration, and a desire to discover firsthand the wonders of nature. Young children are naturals at this. Adults take a little longer. The teacher’s most important role is sharing enthusiasm, curiosity, and wonder. Adults can best do this by using their legs—stopping and getting down to see what has caught a child’s attention (see Photo 19-10). Just the focusing of attention, perhaps with an expression of wonderment—“Look how pretty!” or “Great, you found something amazing!”—can encourage exploration and child–adult conversation. When we share our own ideas and feelings with a child, it encourages that child to explore his or her own feelings and perceptions. In middle- and upper-elementary grades, as children become more familiar with their world, the teacher guides them to observe changes, including cycle changes such as cycles of the moon, predictable trends such as growth and decay, and less consistent change, such as weather. Photo 19-10 Teachers can share in young children’s natural curiosity and wonder by getting down to look at what has caught their attention. © Cengage Learning This One’s for You! Where the Wild Things Are In an attempt to give the public a peek into the secret lives of wild animals, Smithsonian Institution researchers have collected all of their motion-triggered camera shots from the field in one place, the Smithsonian Wild website. Before consolidation, these candid photos of vampire bats, jaguars, and everything in between were lodged on various computers, neglected and at risk of being lost. All over the world, researchers have set up “camera traps,” often along forest trails or in trees, which take a photo when the camera’s sensor recognizes movement or body heat. Researchers often employ camera traps instead of walking forest trails and carefully watching and recording every sign of an animal’s presence. But these line-transect surveys often fail to catch shy, small, or rare species, like the snow leopard, which the cameras have successfully captured. You can check the website to see what work has been done on any particular species in any area of the world. The pictures are just like collecting a specimen. The Smithsonian plans to enlarge the current cache of  images with contributions from individuals and researchers associated with institutions and schools (Schipani, 2011). Source: Schipani, V. (2011). Works in progress: Where the wild things are. Reprinted from The American Scholar, Volume 80, No. 3, Summer 2011, p. 14. Copyright © 2011 by the author. Pets in the classroom. The best way for young children to learn about animals is to have them in the classroom. Through observing and caring for pets in the classroom, children can do the following. · Grow in understanding the needs of animals for food and water, as well as safe, clean housing and attention. · Grow in appreciation for the beauty, variety, and functional physical characteristics of animals (for example, the protective shell on a turtle, the webbed feet on a duckling, and the sharp teeth and claws on a hamster). · Grow in compassion for and humane treatment of animals. · Obtain inspiration for many language experiences and creative activities. · Good classroom pets are guinea pigs, rabbits, parakeets, white mice, hamsters, turtles, salamanders, gerbils, and goldfish. Good short-time (an hour or so) classroom pet visitors are chicks, ducklings, puppies, a setting hen, kittens, and turkey poults. Of course, before purchasing or adopting any pet, be sensitive to the needs of children with allergies. Children can help plan for the pet by building the cage or preparing the terrarium or aquarium. The necessary food and water pans can be obtained, a food supply can be stored up, bedding can be prepared, and the handling of the pet can be discussed. Arrangements must be made for pet care during all holidays and vacation periods. A trip to a pet shop would be an excellent experience. Children should help with the care of the pet after it is obtained, but in the final analysis, the teacher is responsible for seeing that the pet is treated well. Children should learn that pets are not toys, that they have feelings, and that when provoked, some of them defend themselves by biting. Children should not be allowed to handle pets excessively or without supervision. It is cruel to let them wrap pets up in blankets and take them for walks in a doll buggy or to allow any other activity foreign to the pet’s nature—and children should be helped to understand why. Neglected or mishandled pets give a negative message about responsibility and respect for life. Besides learning how to care for pets, children can participate in the following activities: · They can discuss the way pets feel, how they look, the sounds they make, the way they move, the purpose of various parts of the body, the need for food, their homes, their reproduction habits, and other attributes. · They can create experience charts about an animal’s care and characteristics. · They can tell original stories based on the pet and tape these stories. · They can draw, paint, or model the pet out of clay. · They can dramatize the pet’s movements. · They can take a trip to a pet shop or zoo. · They can show pictures of animals, telling which are tame and which are wild; which fly, hop, or swim; and which live in water or on land. · They can tell animal stories, recite animal poems, and sing animal songs. · Older children can write journal entries about their daily observations of the classroom pet. · They can write stories with the pet as the main character. Outdoor science. Many activities work well inside the school. Others are more suited to the area outside the school building. All of the following activity suggestions are consistent with National Science Education Standards. They apply most specifically to Content Standard D in Earth Science. This standard is focused on the child’s developing an understanding of: properties of earth materials, objects in the sky, and changes in earth and sky. Beginning activities. Children can learn many different things about nature by being outdoors. However, many young children come to school with limited direct experiences with natural environments. Thus, they may have little understanding and great fear about what may happen to them in their encounters with nature. They may fear the darkness of a wooded area. They may think that all bugs and insects bite or sting. In their minds, an earthworm may be a poisonous snake. Such children need a gradual exposure to the world of nature. They need to become familiar with the trees and bushes in the schoolyard before they feel comfortable hiking in the woods. They need to observe and care for classroom animals before they are asked to welcome a caterpillar crawling across their hand or feel the woolly head of a lamb while on a field trip to a farm. Young children also need to realize that nature is all around them and that wildlife can be found anywhere. Some children seem to think that wildlife is somewhere very separate and far away from where they live. When asked where he might look to find wildlife, one little boy responded, “Africa.” For such children, one of the most meaningful lessons would focus on becoming aware of and comfortable with wildlife in their immediate environment. Ideas on how to begin with simple experiences include the following. · Have students watch a bean seed sprout in the classroom and then attempt to plant and tend a vegetable garden. · Allow children to play with snow in the texture table before making and crawling through tunnels of snow in the schoolyard. · Have children watch birds and squirrels from a “window on nature” before suggesting that they let a goat eat from their hands. · Have children walk barefoot in puddles, and then observe their footprints made on the sidewalk. Bird feeders. Children can design and build bird feeders with the assistance of their parents or another adult. Professionally built bird feeders can also be used outside the classroom. Children can try to discover what food attracts various kinds of birds. Where is the best place to put a bird feeder? When is the best time of year to watch for birds? What time of day is best for bird watching at a feeder? Older children enjoy learning the names of the birds they see at the feeders. A book with colored illustrations of local birds can be a research source for this activity. Children can keep records of which birds frequent certain feeders more than others and speculate as to why this is the case. They can make graphs representing use of each feeder. Cloud and sky watching. On a mild, partly sunny, or cloudy day, children can learn much about their environment. They can lie on the ground and look up at the sky. They may see distinct clouds of many shapes or clouds that join together. The sun may disappear. It may get cool very suddenly. Birds may fly past. Children may have many different feelings as they lie still and watch the sky. Questions may arise. How do clouds seem to move? What do they look like? Are there many colors in the clouds? What do clouds look like just before a storm? The teacher might have children make up a story about clouds or suggest they paint a picture about their cloud watching. The sounds of nature. Walking in the woods or along a busy street can be made exciting by listening to the sounds. In the area next to a school, there are many sounds, too. When most of the children are indoors, one or two supervised children may want to go outside and simply listen. They can take a cassette tape recorder along and record sounds, too. Play the tape and encourage children to move like the sounds make them feel. How many different sounds can they hear? Can they hear sounds made by birds? By animals? What do the leaves in the trees sound like? How do trees without leaves sound? What other sounds can be heard? How do noises made by cars differ from noises made by trucks? How does a person feel if there is too much noise? What happens to rain water? After a rainstorm, children can try to follow the paths taken by the water. Does all of the water flow into a sewer? Does some of it go into the ground? What happens in paved areas compared to grassy areas? What happens in dirt areas compared to grassy areas? Older children can learn about the effects of erosion in their own parks and playgrounds. This can easily be done after a heavy rainstorm on the playground or in a nearby park. Making mud pies and mud finger painting are great follow-up activities to these observations. Animal hiding places. There may be a small hole in the ground or a sand hill in a crack on the playground. Thick grass or bushes serve as hiding places for animals. Under a large rock or near the foundation of the school, there may be places for living things to hide. Children seek answers to many questions about animals. Why do animals need hiding places? Can a child create a place where an animal will choose to hide? How many natural hiding places can be found? Can children create hiding places for themselves? How do they feel when they are in their hiding places? Can they move like an animal looking for a hiding place? Can they move like that animal as it goes into its hiding place? If creativity is to be a part of activities such as these, decisions must be left to children. Help from the teacher should not take the form of orders about what to do and what not to do. Advice is good; orders or carefully worded cookbook directions are not. Plants in the environment. Probably the best way to observe the magnificent color and variety to be found in plants is to visit the places where they can be seen firsthand. The school grounds are the closest source. Children can hunt with you for the tallest tree, the one with the roughest bark, and the ones with needles, pinecones, or smooth leaves. They can hunt for plants that are growing in cracks in the sidewalk, for plants that have been eaten by insects, and for seeds, berries, and roots that are exposed. Going beyond the schoolyard, trips can be made to the grocery store, supermarket, or farmers’ market to examine firsthand the potatoes, carrots, onions, eggplants, peas, cabbages, beets, and other foods. Vegetables are beautiful and occur in many colors, shapes, and sizes. One of each kind brought back to the classroom would provide a wonderful opportunity for children to make comparisons among them. The same kind of observations can be made with fruits, or with flowers at a greenhouse, shrubs at a nursery, or plants in an arboretum, small neighborhood garden, or truck farm. Plants can be looked at, cooked, taken apart, tasted, felt, counted, smelled, and weighed. They could be compared for color, texture, juiciness, shape, kind of leaf, aroma, size, and outside covering. They could be classified by the preceding characteristics as nuts, seeds, fruits, roots, leaves, stems, or vegetables, usually eaten raw or usually eaten cooked. If trips are not possible, each child could be asked to bring one fruit, vegetable, or other plant to school, or the teacher could supply the necessary items from the school budget. Some other suggestions follow. · Have seed catalogs available in the book center for children to browse through. · Have children plant seeds in pots, or better yet, if a small garden plot is available, have children use it for planting and nurturing a “crop.” Seed dealers can advise you on types that germinate quickly and what care they need. Press a stick such as a tongue depressor down into the soil by the seed when it sprouts. Have children mark the height of the sprout each week as it grows. The date and name of the plant can be put on the stick. If the seeds in some pots don’t grow, dig them up to see what happened to them. · Help children build a model greenhouse in the block center, using planks, large blocks, and packing boxes. They can put their plants in the greenhouse, as well as small trowels, watering cans, a bag of potting soil, and experience charts. · Have children start plants from seeds, cuttings, bulbs, roots, and tubers. Sweet potatoes, placed in glasses so that half the potato is under water, will produce roots and a luxuriant vine. (Try to find potatoes that aren’t bruised.) Bulbs of all kinds can be started. Geraniums and philodendron will produce roots from cuttings placed in water and can then be potted. Pussy willow twigs will grow roots in water. · Show children how to make top gardens by cutting off about an inch from the top of root vegetables, such as carrots. When children place the cut end in water, new, leafy growth will shoot up. · Have children break or cut apart seeds of various kinds to study the small plant inside. Then have a plant tasting party. Examples: Seeds—sunflowers; roots—carrots; stems—celery; leaves—lettuce; flowers—cauliflower. · Help children sprout seeds so that their growth can be studied. A satisfactory way to do this is to cut up blotting paper or paper towels. Place a couple of layers in the bottom of a saucer, moistening the paper thoroughly. Drop six to ten radish seeds on the blotter. Smear a little Vaseline around the edge of the saucer and cover with a piece of window glass. Tiny white root hairs will develop. · To see roots, stems, and leaves form, have children make a plastic bag greenhouse. They can place folded paper towels inside a plastic, self-locking bag, then staple a line across about  from the bottom. Children can fill the bags to just below the line of staples with water, and then drop in seeds. Seal the bags and display them on a bulletin board for children to observe their growth and development. Children will be able to see the roots, stems, and leaves form. Water play experiences. No matter in what quantity or container water is available—in a pool or basin, in a puddle or cup—there are ways to take advantage of its learning potential! A wading pool or large basin lends itself to pouring, sprinkling, and mixing with water, while a cup or a puddle is ideal for floating tiny objects like foil boats or cork stoppers and for dissolving small quantities of sugar or drink mix. Whatever facilities can be provided, water provides a marvelous science experience for young children (see Photo 19-11). Photo 19-11 Playing at the water table, children learn many science projects. © Cengage Learning Organizing the play space for water play is a matter of selecting and arranging suitable containers and appropriate equipment. A laundry tub or plastic wading pool can be placed outside with a bench or table nearby to hold objects. If water play is to take place inside, the floor covering must be water repellent, and a shelf can be used for equipment storage; a plastic tablecloth can be a weatherproof carpet and a small card table can substitute for the shelf. Plastic aprons are ideal for clothing protection, but garbage bags with neck and armholes cut serve well, too. Objects that lead the child to science experiences might include the following: · Sponges, corks, and light pieces of wood · Funnels, strainers, colanders, plastic tubing, and siphons · Spray containers, sprinkling cans, squeeze bottles, and rubber balls · Plastic pitchers, margarine tubs, plastic cups, and yogurt containers · Paintbrushes, paint rollers, and washcloths · Spoons, dippers, plastic syringes, and plastic medicine droppers Occasionally, bubble bath, cornstarch, food coloring, or other mixables can be added to vary the appearance and physical properties of the water. Safety tips. Always have an adult with the children in any water play situation. Never leave a child unattended. Use only unbreakable materials for water play activities: never use glass, ceramic, porcelain, pottery, china, or other breakable materials. Always gather materials ahead of time so you do not have to leave children unsupervised. Develop water play rules with children. Discuss and generate a list of rules that are appropriate to your situation and revise them as needed. For example, you will need one set of rules when children are playing at the water table and another set for the outdoor pool. Appropriate rules are presented here. · No splashing is allowed. · Keep the water in the containers. · Mop up spills immediately. Specific activities for water play are included at the end of this chapter. Did You Get It? · A kindergarten teacher explains to her students that the six-pack rings that hold together soda bottles are dangerous to marine wildlife. She is teaching them about 1. informal science. 2. scientific inquiry. 3. ecology. 4. cause and effect. Take the full quiz on CourseMate. Think about It Two Approaches to Teaching Science to Young Children In this study, researchers examined two common but different instructional approaches to teaching young children science concepts, vocabulary, and scientific problem-solving skills. One of the approaches was responsive teaching (RT), which involves a child-initiated and child-directed perspective in which teachers provide materials and opportunities for exploration and experimentation but without explicitly and systematically teaching specific concepts. Teachers who use this approach follow a child’s lead and facilitate children’s exploration by using strategies such as modeling, imitating, describing what children are doing and saying, and providing materials in an environment that challenges children’s thinking (Hong & Diamond, 2012). The second teaching strategy was one that included more explicit instruction (Responsive Teaching + Explicit Instruction: RT+EI). This approach includes guiding and supporting children’s learning using explicit as well as implicit strategies that best fit each child’s level of understanding and skills. Specific strategies in this approach include explicitly introducing concepts and vocabulary words to which children may not be familiar, directly asking open-ended and challenging questions, and conducting experiments, along with responsive teaching approaches. Researchers hypothesized that children whose teacher provides both explicit and implicit (responsive) instruction (RT+EI) will outperform children receiving only responsive instruction (RT) on all three issues (that is, concepts and vocabulary, content-general, and content-specific problem-solving) (Hong & Diamond, 2012). Participants included  children ( boys and  girls) aged  to  attending early childhood programs in a mid-sized Midwestern community. Children were randomly assigned to small group instruction with one to three classmates, and the small groups were then randomly assigned to an instructional condition: Responsive Teaching (RT), Responsive Teaching and Explicit Instruction (RT+EI), and Control. Four  intervention sessions focused on objects’ floating and sinking were implemented with the two intervention groups, and four book-reading sessions were provided for the control group. The full cycle of each intervention took approximately  to . Each session was videotaped. Assessments of science concepts and vocabulary and scientific problem-solving skills related to sinking and floating were completed about  before and after the four intervention sessions. In the RT intervention, the lessons were taught by choosing and providing materials that would promote an understanding of sinking and floating. In contrast, Responsive Teaching and Explicit Instruction (RT+EI) used both implicit and explicit strategies to teach science vocabulary, concepts, and problem-solving skills by providing a brief lesson  at the beginning of each session. Results revealed significant effects of instructional approaches on children’s learning of science concepts. Children in both intervention groups significantly outperformed those in the control group on measures of science concepts and science vocabulary. There was a significant difference in performance between children in the two intervention groups. These findings suggest that the combination of implicit and explicit teaching strategies may be more effective in teaching new concepts and vocabulary than implicit teaching strategies. In addition, there was a significant difference in children’s performance on content-specific scientific problem-solving skills (that is, making floating and sinking experiments) that were taught as part of the EI intervention. Children in the RT+EI group received significantly higher scores than did children in the control group on these tasks. The performance of children in the RT group was not significantly different from the performance of children in either the RT+EI group or the control group. This study provides evidence that preschool-aged children can learn science concepts, vocabulary, and age-appropriate scientific problem-solving skills when appropriate guidance and instruction are provided. Both responsive teaching and explicit instruction are useful approaches to teaching young children science concepts, vocabulary, and scientific problem-solving skills at a basic level. However, incorporating explicit strategies into teaching was found to be more effective in promoting children’s understanding of science concepts related to objects’ floating and sinking (Hong & Diamond, 2012). Source: Hong, S-Y & Diamond, K. E. (2012). Two approaches to teaching young children science concepts, vocabulary, and scientific problem-solving skills. Early Childhood Research Quarterly 27(3), 295–305. Chapter 20 Creative Mathematics Chapter Introduction © Cengage Learning Early childhood teachers face the challenging responsibility of opening young children’s eyes to the world of mathematics. We can provide creative, stimulating, hands-on experiences that can initiate long-term positive feelings about mathematics, or we can provide a boring stream of workbook pages and dittos. In such a situation, where children are required to sit down, quiet down, and write it down, excitement about math may never have a chance to emerge. Math in the early childhood setting is not a sit-at-your-desk-with paper-and-pencil activity. It is a part of a young child’s active life. Learning Objectives After studying this chapter, you should be able to: · 20-1Discuss the developmental pattern of learning mathematical concepts. · 20-2Explain the purpose of national mathematics standards in the early childhood program. · 20-3Discuss how mathematics learning occurs in learning centers in the early childhood classroom. · 20-4Define rote counting and rational counting. · 20-5Discuss classification and sorting. · 20-6Discuss comparing. · 20-7Discuss ordering. · 20-8Describe how to present shape and form concepts to young children. · 20-9Describe mathematical concepts appropriate for children in grades 3–5. NAEYC Program Standards · 1a Knowing and understanding young children’s characteristics and needs. · 5a Understanding content knowledge and resources in academic disciplines. · 5b Knowing and using the central concepts, inquiry tools, and structures of content areas or academic disciplines. DAP Criteria · 3A1 Teachers consider what children should know, understand, and be able to do across disciplines, including mathematics. · 3c2 Teachers carefully shape and adapt the experiences they provide children to enable each child to reach the goals outlined in the curriculum. All young children need opportunities to explore their world and experience mathematics through their play. Early mathematical experiences include such basic events as placing crackers in a toddler’s hands while saying, “Here are two crackers—one, two,” or allowing a -year-old to choose how she wants her sandwich cut—into triangles, rectangles, or small squares. As a child arranges stuffed animals by size, a teacher might ask, “Which animal is the smallest?” or “Which is the largest?” Such questions reveal mathematical ideas involved in simple activities and lay the foundation for children’s understanding of more complex mathematical concepts as they grow older. When children recognize a stop sign from the back, focusing on the octagonal shape rather than the red background and the word “STOP,” adults have an opportunity to talk about different shapes in the environment. Teachers in any setting can help children look for mathematical connections and relationships, encourage their questions, and promote mathematical discussion about topics that interest them. The most powerful mathematics learning for a child is seldom acquired sitting down in a group lesson. In this chapter, the emphasis is on this active exploration of mathematical concepts as a natural part of the early childhood program. Developmental Pattern of Learning Mathematical Concepts LO 1   It is possible to look at the child’s construction of mathematical concepts the same way we look at literacy development—as emergent. The idea that literacy learning begins the day that children are born is widely accepted in the early childhood field. Mathematical learning can be viewed in a similar way. Children begin to build the foundation for future mathematical concepts during the first few months of life. In fact, from the moment they are born, children begin to construct ideas about mathematics through everyday routines, experiences, and, most importantly, caring interactions with trusted adults. A key aspect of these interactions involves language—how we talk with infants, toddlers, and young children. Long before children formally use numbers, they are aware of them through daily experiences. For example, children become aware of sequences in events before they can talk about what is first, second, or third. At the age of  or , they know that one block on top of another is two blocks, and they know that if they add more, they will have three, even though they may not know the words two and three. When they lift objects, they experience lightness or heaviness. Cuddling up in their mother’s lap, they feel themselves small and her big. They know all this by the reality of their experience—through living and doing. Thus, children are able to tell differences in sizes of people, animals, and toys before they have any idea about measurement. They recognize, too, the difference between one and many and between few and lots before they acquire real number concepts. They develop a sense of time long before they can tell time by a clock. Their ideas about time grow out of hearing statements like the following: “It’s time for lunch.” “It’s time to go to bed.” “We’re going for a walk today.” “We went to the park yesterday.” In such instances, parents reinforce mathematical concepts every day in life’s normal routines. Thus, when the child enters an early childhood program, he or she has already experienced many basic mathematical learnings. This pattern of early use of numbers is similar to the general-to-specific pattern of physical growth (see Chapter 9). In these early stages of mathematical thinking, the child has a general understanding of numbers that will gradually move toward a more specific understanding as the developmental process continues. Thus, a general understanding of time (“It’s time for lunch.”) develops in a gradual process to a more specific understanding of time (“Twelve o’clock is lunch time.”). Children gradually associate 12 o’clock with lunchtime. They learn with their senses, with their whole bodies. Their understandings become parts of themselves. Only after this has happened can they name these experiences. By the time they learn the words big, small, light, heavy, or the names of numbers, they will know by their own senses what these words mean. (Geist, 2009). 20-1aParents as Partners in Mathematical Learning Because young children begin to learn mathematics from the day they are born, parents are obviously an early childhood teacher’s partner in mathematical learning. Early childhood teachers can explain to parents how infants and toddlers begin to notice relationships as they interact with their parents or primary caregivers through songs, rocking, and other verbal and nonverbal communication. They can help parents understand that as a baby crawls through a tunnel or in and out of a cardboard box, he is using his whole body to explore and learn. Placing infants in different positions to encourage the child to pay attention to where things and spaces are in relation to one another is another mathematical learning early childhood teachers can point out to parents. In the same way, early childhood teachers can explain to parents that physical activities introduce spatial relation and set the stage for later understandings of geometry and numbers. Teachers need to encourage parents to allow their children freedom to explore how their bodies fit in space and to see things from different perspectives, such as “inside” and “outside,” and “high” and “low.” The teacher may suggest activities to parents to reinforce these concepts, such as providing an expanding tunnel or making one by taping together several cardboard boxes. Also, parents may encourage children to climb on a stack of pillows for the same reasons. Encourage parents to talk about what the child is doing so they can begin to learn the words that describe mathematical concepts: “You were on the pillow, and then you climbed off. You climbed up on the box, and then you jumped off.” Parents can also use sequential words to describe events or tasks in order to help children develop mathematical concepts. For example, when the parent explains the day’s schedule, the use of sequential words helps children connect events with the order of time: “First, we will go outside. After we go outside, we will go to the playground. Next, we will have lunch. Later, we will come home for a nap.” Parents are, and will continue to be, the most important math teachers our students will ever have. Here are a few additional suggestions to help parents help you. · Provide parent workshops. Have them try some of the exploratory, hands-on lessons they might see in their children’s classroom. Explain how the concepts fit into the curriculum and why a student-centered, investigative approach is so valuable. · Offer family mathematics challenges. Group activities can be fun, simple ways to tackle math together. A math scavenger hunt—in which families identify the math they encounter and do over a weekend—is one example. · Foster positive attitudes. Help parents understand that mathematics is the doorway to many professional careers and that every child can be successful in math. · Encourage parents to be positive about their own view of math, even if they must acknowledge that it can be challenging. Did You Get It? · A teacher of two-year-olds likes to hold her students on her lap, saying that it helps her students develop math skills because cuddling · a. helps them to understand that one plus one equals two. · b. sparks creativity, which helps develop mathematical ability. · c. helps them recognize the difference between people of different sizes. · d. is directly correlated with mathematical ability. Take the full quiz on CourseMate. National Council of Teachers of Mathematics (NCTM) Standards LO 2 Recognizing the importance of these early experiences in mathematics, the National Council of Teachers of Mathematics (NCTM) has developed a set of Principles and Standards for Children Pre- (2000). These standards propose mathematical content and processes students should know and be able to use as they progress through school. There are  standards— content standards and  process standards—that apply across the pre- grade span. (See Figure 20-1 for a summary of these standards.) Within each standard, a number of focus areas are to be emphasized at each grade level. Figure 20-1 Overview of the National Council of Teachers of Mathematics National Standards for grades pre-K–12. Content · Five standards describe the mathematical content that students should learn. · number and operation · patterns, functions, and algebra · geometry and spatial sense · measurement · data analysis, statistics, and probability Process · Five standards describe the mathematical processes through which students should acquire and use their mathematical knowledge. · problem solving · reasoning and proof · communication · connections · representation Societal Needs for Mathematics · Mathematical literacy. The underpinnings of everyday life are increasingly mathematical and technologic. Our students will live in a world where intelligent decisions often require quantitative understandings. · Cultural literacy. Mathematics is a great cultural and intellectual achievement of human kind, and our citizens should develop an appreciation and understanding of that achievement. · Mathematics for the workplace. Just as the level of mathematics needed for intelligent citizenship has increased dramatically, so too has the level of mathematical thinking and problem solving needed in the workplace increased. · Mathematicians, scientists, engineers, and other users of mathematics. Equity and excellence both must be the object of school mathematics programs. If schools enfranchise more students while maintaining high standards, there will be a larger number available to pursue these careers. 20-2aCommon Core State Standards for Mathematics (CCSSM) The  Common Core State Standards for Mathematics (CCSSM)  build on the NCTM standards, but they also introduce significant changes to how mathematics is to be taught. The Eight Standards for Mathematics Practice (see Figure 20-2) describe varieties of expertise that mathematics educators at all levels should seek to develop in their students (CCSSM, 2010). Each standard has broad clusters of goals for each grade level, which are further grouped under broad mathematical concepts called domains (CCSSM, 2010). Figure 20-2 Common Core State Standards for Mathematical Practice. These Standards define what students should understand and be able to do in their study of mathematics. The Standards set grade-specific standards but do not define the intervention methods or materials necessary to support students who are well below or well above grade-level expectations. Standards define what students should understand and be able to do. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning (CCSSM, 2010) The  standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions, and decimals. This helps young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications. These standards build on the best state standards to provide detailed guidance to teachers on how to navigate their way through topics such as fractions, negative numbers, and geometry, and do so by maintaining a continuous progression from grade to grade (CCSSM, 2010). Suggested activities addressing the Common Core Math standards are at the end of this chapter. Let us now take a look at mathematics in action in the early childhood program. Did You Get It? · In planning her math activities, a kindergarten teacher uses clusters of goals for kindergarten students, as recommended by the · a. National Council of Teachers of Mathematics. · b. State Board of Creativity and Mathematics. · c. Federal Guidelines for Kindergarten Teachers of Mathematics. · d. Common Core Standards for Mathematics. Take the full quiz on CourseMate. Mathematics Learning in the Early Childhood Classroom LO 3   Everything we know about young children tells us that early math experiences must be hands-on, filled with play and exploration. Young children’s understanding of mathematical ideas takes place in an action-based learning environment. Mathematics learning can occur throughout the early childhood curriculum. The following information provides examples of how this can be achieved. 20-3aMathematics in the Movement Center As we observe in the movement center, we see children climbing over, ducking under, crawling through, and walking around several pieces of climbing equipment. Anthony approaches a ladder bridge suspended between two climbing frames and hesitates. He ducks under it, just clearing the ladder. He looks back to see what he did and repeats this action several times. “What would happen if you didn’t duck?” asks the teacher. Anthony silently stands beside the ladder and indicates with his hand where he would hit his head (an example of measuring vertical distance by eye and comparing lengths). At the trampoline, Christina counts as Justin jumps. “After , it’s my turn,” she tells Justin (an example of using a cardinal number to obtain access to classroom equipment). The rest of the children begin to count Justin’s jumps. “I can jump highest because I am the tallest,” comments Juliette (an example of explaining measurement between object and event). The children in line begin to measure themselves against each other (comparing height). When the teacher asks who jumped the highest today, the children all agree that it was Amanda. “Is she the tallest?” the teacher asks. “Well, tomorrow I’m going to jump the highest because it’s my birthday,” says Justin. “Amanda jumps in the middle of the trampoline,” observes Juliette (showing she is thinking about location). “I’m going to try that tomorrow.” These specific learning experiences in the movement center fall under the three mathematics content standards of number and operation, measurement, and spatial sense. In the preceding scenes, we see how moving their own bodies through space helps children learn these specific mathematical concepts. Playtime will allow children many chances to explore, extend, and refine their spatial discoveries. The children playing on the trampoline are learning to share power, space, things, and ideas as well as to use counting for access and comparing their jumping skills by measuring in a nonthreatening way. 20-3bMathematics in the Language Arts Center   Very few teachers need convincing of the benefits of using children’s books in the early childhood math program. Children love being read to, and books provide rich sources for learning math (see  Photo 20-1 ). Teaching math through children’s books motivates children to learn math in exciting new ways. Learning math through the use of children’s books encourages students to think and to reason mathematically while building students’ appreciation for both math and literature. Photo 20-1 Pretend reading is an important step in a child’s developing literacy. © Cengage Learning Evaluating Children’s Books for Math Learning. When evaluating which books to incorporate in a math activity, first judge the book as a worthy piece of literature. It must have an engaging story line, beautiful language, and a sense of wonder about the world (Eisenhauer & Feikes, 2009). Appropriate picture books present math concepts accurately with visual and verbal appeal. The illustrations and text must engage the reader. The reader or listener must be able to find real-world connections in the way concepts are presented. Concepts must also be presented in a way that truly engages the specific audience of young children. Ask yourself these questions when considering a book for a math lesson. 1. Would I read this book to the children even if I weren’t choosing it for a math lesson? Books should be used in the classroom because they are enjoyable, not because they teach a lesson. For a book to promote interest in reading as well as be appropriate for math, it must be memorable, use natural language, have captivating images, and stand up to multiple readings. 2. Does the book stimulate curiosity and a sense of wonder? Are children inspired to do their own investigations? In the reading of these books, concepts that a teacher may be required to teach, such as proportion, measurement, weight, and shapes, become topics that children want to investigate on their own. 3. Is the book meaningful to children? Can they make personal connections? Children should be able to identify with the characters in the book as having similar life experiences, doing activities children normally do. 4. Are the math connections natural? When math connections are embedded in a story, the reader not only enjoys the book but also is intrigued by the math concepts. Mathematical ways of thinking are emphasized; they are not facts presented in an authoritarian tone. As such, children have opportunities to question and pursue solutions (Charlesworth, 2011). An Example of Using a Children’s Book for Math Learning. You will find that children’s books can be used to launch many interesting math learning activities. Eric Carle’s The Very Hungry Caterpillar, which describes the life cycle of a caterpillar through the use of vibrant, collage-like designs, is an excellent example of children’s literature that can provide math experiences for a young audience. Teaching comparisons. Size comparison is the most obvious prenumber concept that can be drawn from this book. The caterpillar changes from a tiny egg laid on a leaf to a small, hungry caterpillar to a big, brown cocoon, and finally to a large, beautiful butterfly. After reading the book to the class, the teacher might discuss with the children the size relationships depicted. Later, children can compare cutouts of phases of the caterpillar’s life cycle and arrange them from largest to smallest. Teaching ordering. The prenumber skill of ordering can be related to both the days of the week and the caterpillar’s life cycle. Ask children to tell the order of the days of the week or stages of the life cycle told in the book. Ordering the days of the week in this way can promote an interest in the calendar for daily record keeping of days gone by. The life cycle can be used in a game-like situation in which children order the pictures of the cycle. This sequencing can be made self-correcting by writing the numerals  through  on the back of the pictures. Teaching one-to-one correspondence. The fact that the caterpillar ate through a variety of foods one by one can be used to emphasize one-to-one correspondence. A learning center follow-up might require children to match pom-pom caterpillars to plastic fruits to see if there is an equal match or if there are more caterpillars than fruit. Teaching rational counting. Children can also be asked to rationally count the number of pieces of food the caterpillar ate in the story by counting the number of fruits and then the number of other foods eaten. They might also count the number of days of the week and the life cycle changes. A later concrete learning activity would be to have children count out pieces of fruit or other similar foods eaten by the caterpillar to eat in their own particular snack time. Learning center games could involve the counting of food cutouts found in plastic containers. Teaching cardinal numbers. The teacher might use a story to emphasize the prenumber skill of recognizing cardinal numbers. As children look at the book, the teacher might ask: “How many things did the caterpillar eat on Saturday? How many on Monday?” Later, children can work with a learning center activity that involves counting holes made by the hungry caterpillar in card stock leaves to determine how many bites the caterpillar took. A self-correcting feature can be included by simply writing the answer on the backs of the leaves. 20-3cMathematics in the Art Center   Much incidental learning related to mathematics occurs during art activities. When materials are used for a particular process, children need to remember quantities and their order of use. Children can frequently be heard explaining a process to classmates by saying, “First you tear the strips, then you add the paste, and then you stick them on the balloon.” As art projects are planned, children learn to consider the number of items needed and often the shapes that will be required. This experience relates directly to problem solving and measurement—two of the content standards in the national mathematics standards for children. We hear, “My truck will have four wheels,” and “I need a triangle shape of wood for the roof on my house.” Children learn to decide “how many” as they draw and paint: how many eyes on the face, fingers on the hand, and buttons on the coat. Differences and equivalences in number and size frequently concern children. Six-year-old Jonathan calls out, “I want  feathers on my peacock, and I have only .” Bernardo, sitting next to him, responds, “I have more than you; I have  feathers.” Children also learn about one-to-one correspondence as materials are chosen and distributed to classmates. Four children need four scissors; five paste cups need five lumps of paste; three needles need three lengths of yarn—all direct, hands-on experiences with the standard of number and operation. The following scenario further demonstrates how art activities can be used to provide children practice in areas related to national mathematics standards. Two children are making headbands using shape stamps to make designs on paper strips that will fit around their heads. “This is a skinny square,” says Casper, referring to his rectangle stamp. Claire laughs and looks through the shape set. She picks up an oval shape, “This is a skinny circle!” The children laugh some more as they assign names to the other shapes. (Comparing shapes provides experience with the geometry and spatial sense standard.) Soon they are finished, and Casper holds the strip while Claire measures and cuts the correct length (measurement standard). On the first try, the strip is too short, and they come to the teacher with the problem. “How could you make it longer?” she asks. Claire thinks they can add some paper to one end of the strip (an example of extending length to make an object longer). Eventually the children make the headbands fit. When two different children approach the center later, Casper says, “You should cut the paper first to be sure it fits.” One child takes this advice, but the other ignores him and begins to make designs on the paper strips. The children in the preceding scenario had a prolonged opportunity to explore and talk about the characteristics of shapes. This was a fun, hands-on learning experience involving the mathematical concepts of shape, measurement, and problem solving. 20-3dMathematics at the Water Table   Some of the greatest opportunities for integrating math in children’s play occur at the water table. Constant “watery” sounds are heard as children fill containers with water and pour the water back and forth. “This won’t hold all the water,” Grace comments (an example of measuring volume). Elbert picks up a bottle and says, “This one is taller. It will hold the most.” Grace disagrees. “This one might hold a lot because it’s very fat all the way up.” (She is comparing size and capacity of containers.) She suggests that they count how many cups each holds and begins to count, but Elbert just continues to pour water from one container to another. (He is comparing capacity by direct measure.) “This one holds six cups!” says Grace (an example of measurement). “How much does yours hold?” Elbert then begins to fill his bottle with water, using the cup and a funnel. Grace counts the cups and explains, “It’s four and a little bit more—not the whole thing” (a real-life use of measurement—fractions). Teachsource Video Exploring Math Concepts Through Creative Activities: Integrated Curriculum in Early Childhood © 2015 Cengage Learning 1. What basic mathematical concepts are covered in this video? 2. When the child answers, “three” for number of sides on the diamond, how else could the teacher handle this child’s number error? 3. What additional center(s) could be included in this shape lesson? Include in your answer the specific center, number concept, and activities you would use. In the preceding scene, play reveals a progression of mathematical thought. In this situation, the children’s processing of their own experiences shows the way they grow in measurement thinking. They were not concerned with a particular goal or end as much as with the means to achieve it. They did not have a clear plan in mind, and their goals and ends were self-imposed and changed as the activity proceeded. In addition to these spontaneous mathematical experiences, you can also plan activities at the water table to build children’s mathematical concepts. For example, a teacher may construct a math puzzle with three empty plastic glasses. Pour water up to the brim on the first glass. Then fill the second glass halfway, and leave the third empty. Ask children to identify which glass is empty, which is full, and which one is half-full. Children generally understand the meaning of full and can identify the full glass of water. Most children will also understand the concepts of empty and more, but many children have trouble with half and less. This experience at the water table may be continued in the manipulatives area by providing measuring cups of beads, buttons, or other materials for children to further explore the concepts of full, empty, fewer, and less. Through repeated interactions and dialogue, children learn some of the vocabulary and concepts that underlie mathematics, such as equations, fractions, and the notion of zero. At the water table, these math concepts are experienced and learned by repeated activity rather than by sitting at a desk trying to do math worksheets. 20-3eMathematics in the Dramatic Play Center   Two children are rocking their dolls and sharing a book about a hospital adventure. Suddenly, Corazon stops and says, “My doll is so sick. I have to call the doctor.” She looks at a list posted near the telephone and dials (reading and using numbers). “His number is 919-555–1234” (ordering a sequence of single numbers). “Hello, doctor? My baby is so sick. What should I do? Goodbye. My doctor says I have to give my baby eleventeen pills.” “Oh, well,” says Meg. “My baby was so sicker the other day before today” (time sequence). “He had eleventy-seven pills” (using numbers from the teens to the over-twenty digits). The children continue to rock their babies and share the book. These children are using play to translate their understanding of adult activities into their own actions. Corazon understood how adults use numbers to make telephone calls. Play activity also involves intelligence. Corazon used her understanding of the pattern of telephone numbers—three digits followed by seven digits—to make her call. Her comment to Meg that her baby needed “eleventeen pills” showed her developing number sense; to Corazon, teen numbers indicate a larger quantity of an item than single digits. Meg’s comeback indicated that she, too, is developing a sense of numbers because she knew that numbers ending with -ty are larger than numbers ending with teen. Meg’s verbal description of yesterday was understood by her friend and will be replaced later with the appropriate terms after more experiences over time. This scenario can also be related directly to the national standards in math. Two of the standards—“communication” in a mathematical sense and “connections” between mathematics and everyday life—were obvious in the children’s play experience. 20-3fMathematics in the Block Center   The block center is a perfect place for math experiences. Blocks are especially good for learning math because they are real-life examples of geometric shapes and solids. The block center is usually set up in preschool rooms, but it is just as important in the early elementary classroom. Figure 20-3 lists some suggested goals and block materials to make this center as complete a learning place as possible. Figure 20-3 Suggested Goals and Activities for a Block Center. Goals Activities in this center afford the child experiences in · creating real and imaginary structures. · differentiating between sizes and shapes. · classifying according to size and shape. · selecting according to space. · conceptualizing about space, size, and shape. · defining geometric shapes. · developing perceptive insight, hand–eye coordination, imagination, and directionality. Materials · Set of solid wooden unit blocks (approximately 200) · Small wheel toys · Puppets (to use with puppet stage or theater) · Dolls (from housekeeping center) · Dress-up clothes, especially hats · Set of hollow blocks (varying in size) · Miscellaneous construction sets: Tinkertoys, Lego® blocks, Lincoln Logs, Bristle-blocks, Connectos, etc. · Rubber animals (zoo, farm) · Small plastic/rubber people (family, farmer, firefighter, etc.) · Planks, tiles · Old steering wheel · Packing crates, boxes, and ropes · Traffic signs · Books related to building · Pulleys and ropes · Large quantities of “junk” construction materials, egg cartons, milk cartons, rods, spools, small rectangular boxes, etc. · Measuring tapes and unusual things to measure · Pan balance for exploring weight · Playing cards or cards with dots, numerals, or both TeachSource Digital Download: Download from CourseMate. To encourage rich and varied mathematical experiences in the block center, you need to carefully plan the appropriate equipment in this center. For example, the younger the children, the larger their first blocks should be. Smaller blocks can come later, when children feel the need to supplement larger blocks. If you give too many small blocks to children early in the year and insist that they reshelve them neatly, children may come to dislike blocks, defeating your purposes in having them at all. Aside from this, block building is a tremendously satisfying activity that nourishes minds, imaginations, and the development of mathematical concepts. If your block area is popular, and children must wait for turns, make a waiting list—printed neatly for children to read—and set a timer. When you use a timer, children discover that turns are coming around in a fair way. You may also want to post stick-figure pictures indicating how many children can be in the area at one time. A child building with blocks has many experiences related to math, such as classification (grouping by the same size, for example) and order (putting blocks in order of largest to smallest). Many other basic math ideas are also learned through block building, such as length, area, volume, number, and shape (see Photo 20-2). Both small- and large-motor skills are also developed as children play with blocks. Photo 20-2 While playing with blocks, young children learn many basic math concepts. © 2015 Cengage Learning Cleanup in the block center is another good chance to practice math skills. The following suggestions can help you make this cleanup a true learning experience. · Ask children to pick up all of the blocks that are curved. · Ask children to pick up blocks of three different lengths. · Ask children to pick up blocks according to size. · Ask children to pick up blocks similar to a specific block that the cleanup director names. · Ask children to pick up blocks different from a specific block that the cleanup director names. · Ask children to put away all of a particular shape or size block, and ask how many of that block were used. · Ask children to stack all of the blocks that go in the lower-left section of the blocks shelf, then stack the lower middle shelf, and so on. · Ask children to put away blocks in groups of twos, threes, fours, and so on. · Ask children to put away one dozen long unit blocks. · Ask children to put away blocks according to size, beginning with the biggest or longest and ending with the smallest or shortest. · Select certain children to put away certain shapes, for example, rectangles and cylinders. · Select certain children to collect blocks according to weight. · Have children put away a certain unit of blocks and all of the blocks that are a fraction of that unit block. · Use an assembly line to put away blocks. This encourages cooperation. · Ask children to pick up a number of blocks that are greater or lesser than the number of blocks the cleanup director is holding (Hirsch, 2000; Sarama & Clements, 2009). See Figure 20-4 for more information on all of the learning opportunities possible in the block center. Figure 20-4 Learning Opportunities in the Block Center. The block center abounds with learning opportunities for young children. Listed below are a few of them. In the block center, children learn: Science and math · Discover that one long block is equal to two short blocks (proportion, fractions). · Match block shapes to shelf labels (spatial sense). · Make patterns (triangle, triangle, square, square, and so on). · Arrange blocks in order of size (sequencing). · State the number of blocks (counting). · Stand net to a block tower (comparing, measuring). · Build ramps and pathways, then race cars and marbles (measuring, spatial reasoning). Language and literacy · Learn vocabulary – shapes (arch, cylinder); comparisons (taller, heavier); building terms (enclosure, bridge) – in English and their home languages. · Talk about structures before, during, and after their creation. · Make books about structures using photos and text dictated to a teacher. Social and emotional skills · Rebuild after a block tower falls (self-confidence, perseverance). · Put away blocks when finished building (self-regulation, sense of community). · Offer dress-up items to a friend so they can both be construction workers (cooperation, self-regulation). · Share ideas with a friend whose building keeps toppling (friendship). · Construct roads and buildings with a small group (cooperation, sense of community). TeachSource Digital Download: Download from CourseMate. Did You Get It? · A teacher reads his preschoolers a book about flowers. The book shows what flowers are growing each month of the year. Which math skill are the children likely to learn from this book? · a. flowers and where they grow. · b. how to care for flowers. · c. counting the pages as the teacher turns them · d. understanding ordering from the progression of months Take the full quiz on CourseMate. Numbers: Rote and Rational Counting LO 4   In our preceding discussion, many references were made to various mathematical concepts young children develop through everyday experiences in early childhood learning centers. The following information provides a brief description of these basic mathematical concepts and suggests some related activities for development of these specific concepts. Children learn numbers by rote. A child often has no comprehension of what these abstract terms mean, but as a result of relevant experiences, he or she begins to attach meaning to numbers. Children talk about monetary values in their play, usually without any comprehension of what a dime or a quarter is. While playing store, Irene glibly sold the apple for a dollar and later sold the coat and hat for . Before the child is  old, he or she often can count to  in proper order. Such counting (called  rote counting ), however, may have little specific meaning for the child. The words may be only sounds to him or her—sounds repeated in a particular sequence, like a familiar song. This rote counting is similar to the stage in the development of speech (see Chapter 18) when a child can repeat words without really understanding their meaning. Quite different from and much more difficult than rote counting is understanding the numerals as they apply to a sequence of objects: that each numeral represents the position of an object in the sequence (button 1, button 2, button 3, and so on). Equally or more difficult to understand is the idea that the last number counted in a sequence of objects represents all the objects in the sequence, the total number of objects counted. This is called  rational counting . For example, in counting six buttons, the child must grasp the idea that six, the last number counted, tells him how many buttons he has—that he has six buttons in all. Rational counting, a higher-level number understanding, develops slowly for most children. However, carefully structured activities that take one idea and present it to children one step at a time help them grow from a general to a more specific understanding of numbers. Young children frequently hear counting—as steps are being climbed, objects are being stacked, foods are being distributed, finger plays are being played, familiar nursery rhymes and songs are being enjoyed, and during many other activities. This repetition helps the child memorize the sequence and sounds of numbers, even before the meanings of these numbers are understood. Songs, finger plays, and nursery rhymes using the fingers as counting objects should be common practice in early childhood programs to help young children practice the sounds and sequence of numbers. True counting ability (rational counting) is not possible until the child understands one-to-one correspondence. In other words, to rote count (to say the number sequence) is one thing, but to count items correctly—one number per item—is more difficult. Very often when a young child is given a series of things to count, the child counts two numbers for one item or two items while saying only one number. Thus, as rote counting develops, teachers should also encourage the skills of  one-to-one correspondence . Having children touch each object as they count is one way to encourage their grasp of one-to-one correspondence. Repeating this exercise in various experiences throughout the day reinforces the concept of one-to-one correspondence. Young children should be asked to count only with number names that are meaningful to them, that is,  cardinal numbers  (the numbers one, two, three, and so on). Young children just learning numbers often have difficulty in understanding the relationship between counting and numbers. For example, Beatrix may count, “One, two books.” Later, when asked to bring two books to the table, she may count, “one, two” and bring only the second book.  Ordinal number  refers to the place of an object in a series of numbers. The second book in the preceding example is an ordinal number. (The cardinal number is two.) Did You Get It? · A six-year-old child counts his pennies, pointing to one at a time as he says the numbers. When he has finished counting them, he proudly proclaims, “I have six pennies!” This child has learned · a. pre-operational counting. · b. numeral counting. · c. operational counting. · d. rational counting. Take the full quiz on CourseMate. Classification and Sorting LO 5   Classification and sorting activities are the beginnings that help children perceive a variety of relationships among things in their world.  Classification , putting together things that are alike or that belong together, is one of the processes necessary for developing the concept of numbers. In order to classify, children must be able to observe an object for likenesses and differences, as well as for attributes associated with purpose, position, location, or some other factor. Children progress through the following stages as they develop the skill of classifying: · Sorting into graphic collections without a plan in mind. Children may put all of the blocks with a letter on them together and then, ending with a blue letter, continue by putting all blue blocks with the group. When the grouping is complete, they won’t be able to tell you why the blocks belong together, only that they do. · Grouping with no apparent plan. When asked why all the things go together, children respond with some reason but one not immediately clear to the adult: “Well, all these are like Kimiko’s.” · Sorting on the basis of some criterion. Children proceed to being able to sort a group of objects on the basis of one criterion. All of the green things or all of the round things go together, but not all of the green and round objects go together in a group. · Creating groupings on the basis of two or more properties, putting all of the green and round objects together in a group. · Sorting objects or events according to function, use, or on the basis of a negative concept, such as all of the things that are not used in the kitchen. Before children can classify and sort, they need to understand concepts such as “belongingness,” “put together,” “alike,” and “belong together.” These concepts are acquired over time as children have varied hands-on experiences in the early childhood program. Your role as teacher is to help children gain these ideas through many experiences with a wide variety of materials selected specifically for classifying and sorting activities. Activity suggestions for classifying and sorting are found at the end of this chapter. Materials for children’s classifying and sorting may be kept together on a shelf in the manipulative toy or game area of your room. Boxes or sorting trays (common plastic dishpans and muffin tins work well) are kept with the materials. Sorting trays can be constructed by either attaching a series of metal jar lids to a board or piece of cardboard; mounting a number of clear plastic cups on a board; dividing a board or tray into sections with colored pieces of tape; or by mounting small, clear plastic boxes on a board. Egg cartons, plastic sewing boxes, tool boxes (such as those for storing nuts and bolts), and fishing tackle boxes are also useful for sorting trays and stimulate children to use materials mathematically. Brain Research Says Mathematics, Music, and Math Difficulty Everyday learning experiences, such as listening to music, are especially important in supporting developing mathematics concepts in children from infancy to  old (Linder, Powers-Costello, & Stegelin, 2011). Music is made up of rhythmic patterns and can be structured to make the patterning simple or complex, depending on the activity. Zentner and Eerole (2010) suggest that infants and toddlers have an innate capacity to not only see patterns but also hear them in music. Reinforcing these capabilities by teaching patterns through music at an early age may benefit children’s cognitive abilities (Bell et al., 2009; Meltzoff et al., 2009). Teaching patterns to very young children is also a key to the concept of emergent mathematics, which parallels the idea of emergent literacy. As with literacy, emergent mathematics suggest the following: · Mathematical learning begins very early in life. · Mathematics is related to many other developmental milestones. · Mathematics develops from real-life situations in which the child is an active participant (Geist, Geist, & Kuznik, 2012). Neuropsychological case studies have provided support for the involvement of key brain regions in tasks involving number processing and calculations in adults (bilateral posterior superior parietal lobe, bilateral horizontal segment of the intraparietal sulcus, and left angular gyrus) (van Eimeren et al., 2010). Children appear to engage a similar network of brain regions in simple number processing (Ansari & Dhital, 2006). However, children also use the inferior frontal cortex to a greater extent than adults (Cantlon et al., 2008). Did You Get It? · Children progress through developmental steps as they learn the skill of classification. A child who groups together toy cars, buses, bicycles, and trains because they are all modes of transportation has reached the  level. · a. second · b. first · c. last · d. third Take the full quiz on CourseMate. Comparing LO 6   The skill of  comparing  seems to come easily and naturally, especially when it is a personal comparison: “My shoes are newer than yours.” “I’ve got the biggest.” “My sister is little.” “You’ve got more.” When children build with blocks, they may be asked to make additional comparisons: “Which tower is the tallest?” “Pick up the heaviest blocks first.” “Build something as tall as this.” Have children identify parts of their buildings using the vocabulary of comparison. When different size and shape containers are used in sand and water play, children can make comparisons based on volume. In the early childhood program, these are informal and related to children’s actual experiences. “How many blue cups of water will it take to fill this bucket?” “How many are red?” “Which is the heaviest?” “This doesn’t hold as much.” Stories and poems, often the folk tales children are already familiar with, offer other opportunities for informal comparisons. The Three Billy Goats Gruff, Goldilocks and the Three Bears, and others offer comparisons on the basis of differing attributes. Throughout the preschool years, ask children to observe and note differences in the objects of their environment, to name them, and to discuss them with one another. Did You Get It? · A preschool teacher takes a few dolls from a basket and instructs her student to choose some dolls as well. She then asks her student to figure out who has more dolls, the teacher or the students. Which mathematical skill is the teacher nurturing in her students? · a. seriation · b. classification · c. rational counting · d. comparing Take the full quiz on CourseMate. Ordering (Seriation) LO 7 Another mathematical idea that is a vital part of a complete number concept formation is the idea of  ordering (seriation) . Ordering the environment into series begins when children are very young and continues throughout adult life. The child begins by perceiving opposite ends of a series: big—–———little heavy———light cold——–—–hot long——–—–short The intervention of an adult, suitable materials, and appropriate language lead to refinement of these early basic concepts. The comparison of the height of two children is the beginning of ordering, as is the comparison of two sets of things as more or less. Ordering sticks, blocks, or nesting cups in a sequence that leads gradually from the smallest to the biggest helps children see ordered size relations (see Photo 20-3). Photo 20-3 Nesting blocks teach about size, shapes, seriation, and ordering. © 2015 Cengage Learning When children line up to go outdoors, they meet another idea of order: Juan stands in front of Ne’Andrea, and Yvonne stands in back of Drew. They may use their understanding of sequence when they say, “I want to be first,” or “Jimmy is last.” After listening to the story of Goldilocks and the Three Bears, their observations may become more refined as they discuss the story. The story contains big–little and one-to-one relationships in addition to its many other enjoyable qualities. The idea of ordering in size also appears naturally in other classroom areas. The teacher can make ordering a part of natural discussions in relation to the children’s play and activities: sets of cans, bottles, and books can also be used for practicing ordering of size. With younger children, only two objects are compared at first; this will be extended to three or more objects for older children. Children enjoy ordering and do so spontaneously. Many table toys provide ordering experiences, as do ordinary objects such as measuring spoons and cups. Your role is to provide materials and sufficient time. When children find the existing materials too easy, you can awaken their interest by encouraging them to use the toys differently, by asking them questions, and by providing additional materials. Ordering activities can include length (sticks), height (bottles), total size (bowls and shoes), weight (stones), color (from light to dark), and other endless possibilities. Suggestions for ordering activities are found at the end of this chapter. Did You Get It? · A young child expresses understanding of the opposite terms “tall” and “short.” She is beginning to grasp the mathematical concept of · a. classification. · b. ordering. · c. comparing. · d. nonrational counting. Take the full quiz on CourseMate. Shape and Form LO 8   Young children need many experiences with shapes and making comparisons between shapes before they focus on naming shapes. Usually, it is enough to introduce one new shape at a time. As the new shape is understood, other shapes may be added, thus building new learning on previous learning (see Photo 20-4). Photo 20-4 Children need many experiences with shapes. © Cengage Learning Think about It Numerical Matching Abilities in Young Children Using a Touchscreen Computer This study presents the first evidence that preschool children perform more accurately in a numerical matching task when given multisensory rather than single sense (unisensory) information about numbers using a touchscreen computer. Participants were  children:  girls and  boys, mean age ; eight -year-olds, eight -year olds, and eight -year-olds (Jordan & Baker, 2011). Children learned to play a numerical matching game on a touchscreen computer, which asked them to match a sample number with a numerically equivalent choice. To begin a trial, children were required to press a picture of a puppy located in the lower-right corner of the screen; this ensured that children were attending as each trial was initiated. For trials that contained an auditory sample, the sample tones were played sequentially from the speaker; for trials that contained visual sample elements, these elements appeared sequentially in the center of the screen. Immediately after the last sample element, two choice stimuli appeared. If the child correctly chose the numerical match, a green border flashed around the match, a positive sound occurred (clapping and people cheering), and the child was given a sticker in their cup. In contrast, if the child touched the incorrect choice, the screen turned black, a negative sound was emitted (single, brief tone), and no sticker was provided. Each session contained  trials, with approximately one-third of trials visual, one-third of trials auditory, and one-third of trials audiovisual. Children performed significantly better when provided with multisensory samples. Also there was no speed-accuracy trade-off between single sense and multisensory trial types. Thus, the researchers suggested that multisensory numerical stimuli enabled the preschool children to more precisely match representations of number. They concluded that this is an important finding for our knowledge of the development of numerical processing in typically developing children (Jordan & Baker, 2011). Based on this study’s results, activities using more than one sense in teaching number concepts would seem an appropriate approach in the early childhood mathematics curriculum. In teaching young children about shape and form, it is important to include more shapes than the common geometric shapes of a circle, triangle, rectangle, and square. Because shapes aid in, or are sources of, identification, limiting instruction to the “basic shapes” excludes from the learning environment important aspects of recognition of shapes in general. Yet familiar shapes must be taught before uncommon ones. Most of these unfamiliar shapes depend on previous shape identification and recognition. From the basis of understanding simple shapes, the child is able to build more complex structures. Shapes of various kinds can be found throughout the child’s environment. Words defining shapes should be used often. For example, everyday language should include such statements as “That is a square box,” rather than “That is square”; “The clock is round,” rather than “This is round”; “Put the book on the square table,” rather than “Put it over there.” With these phrases, the object and its characteristic shape are made clear to the child. Later on, characteristics such as color, size, texture, and number may be added. When unfamiliar shapes are introduced, a review of already familiar ones should precede the new introduction. Then children’s thinking can be stimulated with such questions as “How is this new shape the same as …?” or “How is this new shape not the same as (or different from) …?” Such comparisons reinforce and review shapes already learned. Did You Get It? · A teacher decides to introduce shapes to her four-year-old students by teaching recognition of hexagons and oval shapes. Developmentally speaking, her technique is · a. correct, as beginning with complex shapes will challenge the children and aid in their learning. · b. correct, as children understand those shapes more readily than they understand squares and circles. · c. incorrect, as children can understand uncommon shapes on the basis of their understanding of simple shapes. · d. incorrect, as children cannot understand uncommon shapes before they reach grade school age. Take the full quiz on CourseMate. Mathematics: Grades 3–5 LO 9 Mathematics is a subject most students in grade 3 through 5 like. Students in grade 3 through 5 see mathematics as practical, are challenged with many new ideas, and believe that what they are learning is important. However, sometime between grade 4 and , students’ interest in mathematics begins to wane. Although they continue to view mathematics as important, students are less likely to characterize it as interesting or to consider themselves good at math by grade 8 (Charlesworth, 2011). It is crucial that mathematics education in the upper-elementary and early middle grades be challenging, relevant, and engaging for students. The curriculum materials and instructional approaches a teacher uses help students connect mathematical ideas and provide a basis for making them meaningful. Because the amount of content in grade 3 through 5 expands greatly from that of the earlier grades, students need help in building connections and managing the many new concepts and procedures they are encountering. Students in grade 3 through 5 must also understand and bear responsibility for their learning. In math, this means learning how to examine, ask questions, and consider different strategies—all with the goal of making sense of mathematical ideas and fitting them to other, related areas. While the  standards of the National Council of Mathematics Teachers apply to all grade levels, the instructional emphases for grade 3 through 5 build on those outlined for grades pre- and extend well beyond them. Although number and operation continue to be cornerstones of the curriculum in grade 3 through 5, each of the content standards (number, data, measurement, algebra, and geometry) is essential for building student knowledge at this level. Several “big ideas” or central mathematical themes for this grade span are woven through these areas, including multiplication, equivalence, and the notion of unit. Likewise, knowledge and use of mathematical processes should be deepened and expanded in these grades. Students in grade 3 through 5 are capable of sophisticated reasoning and should be challenged and supported in their learning (see Photo 20-5). In grade 3 through 5, extending understanding from whole numbers to fractions and decimals is a key dimension of the mathematics curriculum. Students need many and varied experiences in order to understand what fractions and decimals represent, how they are related to each other, and how they are different from whole numbers. Suggestions for fraction and decimal activities are found at the end of this chapter. Photo 20-5 Older elementary students are capable of more sophisticated reasoning and mathematical concepts. Casper Holroyd 20-9aCalculators: Grades 3–5 Appropriate use of calculators is an important part of a balanced mathematics education at all levels, including elementary. The National Council of Teachers of Mathematics has elaborated this position in a public statement, Principles and Standards for School Mathematics (NCTM, 2000). Thus, the calculator and a variety of computer software should be considered legitimate tools for learning math concepts and performing math computations and should be available to students in grade 3 through 5. Students need access to calculators, but they also need pencil-and-paper skills. Balancing these two is an important part of an elementary teacher’s work. Research has shown that students who use calculators are better at understanding mathematical concepts and solving problems (Roschelle, & Singleton, 2008). The same studies confirm that calculator use does not interfere with students’ development of computational skills, and in many of these studies, students’ pencil-and-paper skills increased when they also had the opportunity to use calculators. Calculators are tools and, as such, are only as effective as the person pushing the buttons. Just as a hammer does not build a house, a calculator does not think or solve problems. This is a job for people, and a job that students can learn early on. Also, just as a hammer does not choose where to put a nail or prevent a nail from going into the wrong board, a calculator does not know what operation to use and cannot keep a person from forgetting a decimal point. These are also jobs for people, and they involve exactly the kinds of skills that teachers can help students learn. Sometimes a calculator is the right tool for a job, and sometimes it is not. Knowing when to use a calculator and when not to use one is a skill teachers can help children develop (Charlesworth, 2011). One of the most important ways in which students can use calculators is to solve problems that they would not be able to solve otherwise. With a calculator, all children can deal with problems involving numbers that are seemingly unmanageable and that arise from their everyday experience. Whenever the teacher has a class working on developing problem-solving skills, and computational procedures are not the main point of the lesson, calculator use might be appropriate. Students can develop their decision-making and problem-solving skills far beyond what they would be able to do if they were limited to numbers that they could handle quickly using pencil and paper (Charlesworth, 2011). Teachers need to create opportunities and make judgments about when and how math tools are used to support learning. They can arrange activities requiring students to use calculators and spreadsheets to solve problems. Students in grade 3 through 5 can use graphing and geometry software and calculators to explore, experiment, verify, and visualize mathematical ideas. For example, these children might explore geometric relationships using software to create, modify, and examine shapes. They might create graphs and consider how some presentations of data highlight or distort certain trends. They might use calculators to explore the relationship between decimals and whole numbers and between negative numbers and positive numbers. Students in this age group should also have the opportunity to learn how to search the Internet to gather information needed to solve mathematical problems. The calculator is an important tool in teaching mathematics in grade 3 through 5. However, calculators do not circumvent the need for rapid recall of basic facts, a basic understanding of math concepts, or the ability to formulate and use strategies for computing. Rather, the calculator should support these goals by enhancing and stimulating student learning. As students solve problems involving many complex computations, the calculator should be used to perform calculations. The calculator serves as a tool for enabling the problem solver to focus on the big picture rather than become entangled in the calculating details. (See the end of this chapter for some suggested activities for grade 3 through 5.) Did You Get It? · A fourth-grade teacher forbids the use of calculators, contending that they interfere with children’s grasp of mathematical concepts. Developmentally speaking, this teacher’s approach is · a. incorrect, as math instruction for fourth graders should incorporate calculators and pencil and paper. · b. incorrect, as fourth graders should be permitted calculator use to complete homework assignments, but not to assist with classroom assignments. · c. correct, as research has shown that children who use calculators have a poor understanding of math. · d. correct, as calculators distract children from the task at hand. Take the full quiz on CourseMate.