STEM and Early Childhood Education

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Cognitive Development, Mathematics, and Science

Learning Objectives

After reading this chapter, you should be able to:

1. Define and explain the concept and components of cognitive development.

2. Explain how early learning standards for cognitive development relate to mathematical and scientific thinking.

3. Describe early childhood curriculum activities that support the development of math- ematical concepts and processes.

4. Describe early childhood curriculum activities that support development of scientific concepts and processes.

10 Pretest 1. Infants are not capable of learning before

the age of 1. T/F

2. Bloom’s taxonomy is a tool teachers can use to help promote higher-order thinking. T/F

3. Mathematics and science standards for PreK-2 focus on the development of abstract reasoning. T/F

4. The best way to teach mathematics concepts is with paper-and-pencil activities. T/F

5. Scientific thinking involves the application of curiosity and reasoning to answer questions. T/F

Answers can be found at end of the chapter.

Cognitive Development and General Knowledge Chapter 10

So far, so good! The children are beginning to form friendships and you are paying careful attention to the emotional challenges some of them are facing. Your focus on strategies to promote self-regulation seems to be paying off, and you have been successful in helping the children develop some confidence in problem solving and conflict resolution. You’ve launched a study of the neighborhood, using the social studies standards as a guide. James’s mother and Eduardo’s grandfather have been able to accompany you on excursions, and that seems to be helping James and Eduardo with their feelings of insecurity. Your children have enjoyed meeting some of the nearby merchants, and they are starting to play “store” in the dramatic play center.

You enjoy listening to the children’s conversations and have noticed that they have many questions and theories about how things work. You’ve observed that every day, Alonzo takes out a bin of plastic animals and arranges them in different ways. Yesterday, Monique and Destiny came to you and asked how they could make paper dresses that would be the same size as the doll babies. You recognize that, in your role as an early childhood educator, you want to support the children’s interests, but you also need to cultivate their cognitive develop- ment, in part by providing intentional activities that teach important concepts.

Cognitive development occurs as children acquire and process different kinds of knowledge. Mathematics and the sciences for children share a focus on inquiry, problem solving, and the development of critical thinking skills through processes and practices that engage them in hands-on explorations. This chapter focuses on the early learning standards for cognitive development and experiences that build a good foundation for math and science standards and curricula.

10.1 Cognitive Development and General Knowledge Cognitive development is the process that occurs as thinking and reasoning develop and become more complex over time. Early learning standards for cognitive development are based on the broad assumption put forth by the National Education Goals Panel (NEGP) that “cognition and general knowledge represent the accumulation and reorganization of expe- riences that result from participating in a rich learning setting with skilled and appropriate adult intervention. From these experiences children construct knowledge of patterns and rela- tions, cause and effect, and methods of solving problems in everyday life” (Kagan, Moore, & Bredekamp, 1995, p. 4). In other words, cognition includes the various ways in which humans know and represent their understanding of the world.

According to cognitive psychologists, there are three different kinds of interrelated knowledge:

1. Physical knowledge consists of concepts about physical properties observed through first-hand experience. Examples of how children might gain physical knowledge include learning about colors by mixing paints or using an ice cube tray and freezer to learn that water can change from a liquid to a solid and back again.

2. Logicomathematical knowledge consists of mentally constructed relationships about comparisons and associations between and among objects, people, and events. This is the least understood and most complicated cognitive process. Examples include a child sorting a group of small cars, who must apply criteria that make sense to him, such as color, to separate them into logical groups. He may then put them back into a pile and resort them according to size, while another child might divide them into groups of cars of different sizes or by which cars go fast or slow.

Cognitive Development and General Knowledge Chapter 10

3. Social-conventional knowledge consists of arbitrarily agreed upon conventions that provide a means for representing or expressing physical and logicomathematical knowl- edge (Piaget & Inhelder, 1969). The conventions may vary by culture or group; examples include the names of numbers or letters.

Accommodation and Assimilation

Regardless of type, all knowledge ultimately consists of basic concepts, or schema, a term originally coined by psychologist Jean Piaget. Examples of individual schema include concepts about colors, such as the ideas of “blue,” “red,” and “green,” or the idea that a rubber ball is round and smooth and rolls when pushed. Piaget (1969) described how children acquire and modify concepts through the assimilation and accommodation of experiences.

When a child encounters something new, the brain tries to process it in terms of concepts already stored. That is, the brain assimilates or integrates the new object or experience if it conforms to schema already formed. Using the ball example above, if you give the child similar balls that are smooth, round, and roll when pushed, the existing concept is confirmed and the child moves on to exploring other things.

If, however, you structure a discrepant event, by giving the child a different kind of ball that he has not previously encountered, disequilibrium (cog- nitive conflict) arises owing to tension between the child’s concept of “ball” and the new unfamiliar ball. Because humans are wired to prefer equilib- rium, the child will be motivated to expend men- tal effort to make sense of the new balls. He will thus accommodate the new information by modi- fying or expanding the original schema to include the characteristics of the new balls (e.g., whether the ball is knobby or made of leather or wood, or much larger or smaller than those he encountered before).

Accommodation is a more complex process than assimilation, affected by the quantity and kinds of experiences a child encounters. As one concept builds upon another, children develop more com- plex thinking. This is one of the reasons early child- hood experiences are considered so critical to future intellectual and academic functioning and one of the premises of early intervention programs such as Head Start.

Early childhood educators foster accommodation as well as the three kinds of knowledge, by introducing a variety of familiar and new materials as children are ready for them and using language to help them expand and create new schema. In the early childhood years, children progress through two of Piaget’s four stages of cognitive development, sensorimotor (birth to age 2) and preoperational (ages 2 to 7). Thereafter they begin the transition to concrete operations (ages 7 to 11). Teachers must therefore adapt the experiences and materials they use to complement the different ways in which children think during each of these develop- mental periods, as the next two sections illustrate.

A discrepant event is a previously unencoun- tered experience or object that induces a state of mental disequilibrium; this motivates the child to adapt existing schemas in order to regain intellectual balance.

Cognitive Development and General Knowledge Chapter 10

Sensorimotor Stage Infants and toddlers begin to acquire tentative concepts through their senses simply by explor- ing their world (hence they are in the sensorimotor stage, per Piaget’s description). Giving an infant a new ball and saying “this is a squishy ball,” or “here is a blue ball,” provides the child with the new terms squishy and blue as characteristics that apply to balls. The child can also apply these concepts to things that are not balls. The teacher has thus introduced an oppor- tunity to develop new physical knowledge (a different kind of ball that can be handled and observed), logicomathematical knowledge (making mental connections with other kinds of balls), and social-conventional knowledge (giving names to the characteristics of the new ball).

The Preoperational and Concrete Operations Stages of Development Children in the preoperational stage are beginning to expand logicomathematical knowledge, but the process is hampered by their tendency to center or focus on one characteristic or fea- ture of what they observe to the exclusion of others. For example, if a child looks at a picture of five dogs and two cats and the teacher asks, “are there more animals or dogs?” the child is likely to say, “more dogs.”

Further, they are egocentric, which means they tend to consider the appearance of objects from only their perspective. So if a teacher held a puppet with its face toward a child, the child would assume that the teacher also saw the puppet’s face rather than its back. Third, preoper- ational children are easily deceived by appearances and unable to mentally conserve or retain the idea of fixed quantities. For example, if eight ounces of water is poured from a short, wide container into a tall, narrow one, the child is not likely to recognize that the amount of liquid remains the same; instead, he may think that the taller glass holds more (Figure 10.1).

During the concrete operations stage of cognitive development, children gradually acquire the ability to conserve, but they still need objects such as counters to model and solve com- putational problems. This shift from concrete to abstract thinking is best facilitated through repeated direct hands-on trial-and-error explorations, such as pouring water back and forth into different sized containers in the water table.

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Number: Non-conserving child will say there are more objects in bottom line

Volume: Non-conserving child will think that the same amount of water distributed into different sized containers changes the amount of water—“blue has the most”

Length: Non-conserving child will say that rods on the left are equal, but of the 2 on the right, the rod on the left is “taller”

Figure 10.1: Conservation

The cognitive concepts of centration, conservation, and reversibility are key for shifting from con- crete to abstract thinking.

Cognitive Development and General Knowledge Chapter 10

Knowledge of Patterns and Relationships

As young children encounter repeating patterns in daily life, they begin to under- stand that the natural world is organized. As their thinking becomes more sophisti- cated, they apply knowledge of concrete patterns to more abstract concepts and ideas—the essence of understanding the predictability and rhythms of phenom- ena, social interactions, and behavior. For instance, the idea of taking turns repre- sents a simple pattern—first I use the red marker, then I give it to you, then you give it back to me.

In the absence of an internalized sense of predictability and patterns, the child would not know what to expect next—a chaotic existence to be sure. Decisions teachers make about materials, routines, schedules, and how to organize a classroom reinforce con- cepts of patterns and relationships. Teachers promote an understanding of patterns and rela- tionships in many kinds of activities, as discussed later in this chapter.

Cause and Effect

Young children frequently display magical thinking, proposing preposterous or clearly unre- alistic explanations (often humorous to adults) for why something happens because they have not yet discerned the relationship between cause and effect (Catron & Allen, 2003; Hendrick & Weissman, 2007). Determining why something happens and predicting what might happen when certain conditions are present or constructed represents a complex hierarchy of increas- ingly analytical concepts.

Logical reasoning develops slowly, gradually replacing magical thinking and animism, children’s tendency to attribute human qualities to inanimate objects or animals (Copple & Bredekamp, 2009). Children’s explanations may be “intuitively reasonable” and therefore hard to change; thus the importance of a constructivist approach that aims to facilitate reconstructing miscon- ceptions through exploring, questioning, predicting, and testing (Landry & Forman, 1999).

Understanding the relationship between cause and effect is also fundamental to many aspects of behavior—one of the reasons teachers and adults strive to be clear about consequences. Children begin learning about cause and effect intuitively from birth: when I am wet someone changes me, when I am hungry someone feeds me, when I smile, my mommy smiles back, etc. They learn intentionally through informal trial and error during play when they exert force on an object or mix colors of paint, for example.

After repeated trials with identical results, they begin to understand causality and develop confidence in their predictions. Teachers help children learn about cause and effect when they ask questions like “What happened when you put yellow paint on top of the blue paint?” or “What do you think will happen if you put water in the bucket of sand?” or even “What hap- pened the last time you took the baby doll away from Steven?”

Children begin to form an understanding of auditory patterns as rhythm when they take turns clapping or clap along to music or a rhyme.

Promoting Cognitive Development Chapter 10

Problem Solving

Problem solving is a part of daily life for children and is fostered in a flexible environment that promotes explora- tion and experimentation (Catron & Allen, 2003; Seefeldt & Galper, 2004). Children are naturally curious and moti- vated to pursue questions and solve problems about why things happen and how things work, first through sensory exploration and gradually by using mathematics and science tools and logic to represent their thinking.

Children’s problem solving parallels the development of their thinking, proceeding from concrete to abstract. At first, they model solutions to problems with concrete objects and then proceed to relying less on objects and more on recall and reasoning (Campbell, 1999; Charlesworth, 2005).

10.2 Promoting Cognitive Development To create an environment that promotes the three types of cognitive knowledge—as well as learning about cause and effect, patterns, and problem solving—teach- ers should aim to:

• Provide a wide variety of interesting and challenging materials and experiences for children.

• Foster cognitive conflict by introducing discrepant events or information that motivate children to experiment and test their theories.

• Document the way children solve problems to make their thinking visible, and provide opportunities for metacognition (thinking about their thinking).

• Promote conversation about problem solving; social debate about ideas, theories, and inferences leads to powerful learning (Landry & Forman, 1999).

Physical Knowledge

Mathematics and science are subject areas that help children make connections between concrete materials and abstract concepts. The preschool classroom should have interest areas designated for mathematics materials and science/discovery investigations. The materials in these centers provide children with opportunities to develop the three kinds of cognitive knowledge. They acquire physical knowledge through handling and manipulating materials and making observations about their properties. Block play and sensory activities were dis- cussed in detail in Chapter 7, and many of the materials listed in Chapter 8 that support fine motor development (manipulatives) are also used for mathematics.

Figure 10.2 displays examples of materials commonly used to support important mathematics concepts. Figure 10.3 displays examples of basic equipment for science explorations.

Teachers foster problem solving by giving children the freedom to select materi- als and explore them through hands-on manipulation.

Promoting Cognitive Development Chapter 10

Figure 10.2: Mathematics Materials

Most mathematics materials for young children foster the development of multiple concepts. But since con- cepts are typically developed in a predictable sequence, certain materials such as matching activities and counters are more appropriate for younger children than number tracing boards or base-ten cubes.

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Picture lotto boards and games

Matching, one-to-one correpondence

Memory matching games

Matching, one-to-one correspondence, developing recall

Counters: small objects of di�erent colors and shapes (animals, boats, planes, etc.)

Counting, sorting, grouping, making patterns, non-standard measuring

Plastic links, paper clips, etc.

Counting, sorting, grouping, making patterns, non-standard measuring

Interlocking cubes

Counting, sorting, grouping, making patterns, modeling operations, 3-D data display

Cuisenaire rods Sorting, grouping, sets, base ten operations

Abacus Counting, sets, grouping, modeling base ten operations

Base ten blocks (Montessori golden beads)

Counting, sets, grouping, modeling base ten operations

Dominoes Matching, counting, sorting, grouping, measuring

Dice Matching, counting, modeling problems, shape

Tactile numbers (rubber, Montessori sandpaper, magnetic)

Numeral recognition, writing numbers

Number puzzles Numeral recognition, matching, shape

Pegboards Numeral recognition, quantity, matching, counting

Matching numeral and quantity cards

Numeral recognition, counting

Number stamps Writing numerals

Magnetic numerals

Numeral recognition, counting

Pegboards Shape, spatial sense

Beads Sorting, patterns, shape

Nesting toys Shapes, spatial relations

Shape sorters Shape, sorting, spatial relations, patterns

Attribute blocks Shape, classi�cation, patterns

3-D shapes Shape, spatial relations, sorting

Shape puzzles Sorting, matching, shape

Pattern blocks Sorting, shape, patterns, spatial relations

Tangrams Shape, spatial relations, patterns, sorting

Plastic coins Currency, sorting, classi�cation

Sand timers Measuring time Digital timer Numeral recognition, measuring clock time

Analog clock Measuring clock time, numeral recognition

Teaching clock (movable hands)

Analog time measurement, numeral recognition

Bucket balance Measurement (weighing), comparing

Graphing chart Displaying data

Measurement containers

Measuring volume, comparing, conservation

Calculator Numeral recognition, operations, technology

Material Sample Applications Material Sample Applications

(continued)

Promoting Cognitive Development Chapter 10

11 one

6 six

0 55

35 30

5 12

2 1

57 8

10 11

Picture lotto boards and games

Matching, one-to-one correpondence

Memory matching games

Matching, one-to-one correspondence, developing recall

Counters: small objects of different colors and shapes (animals, boats, planes, etc)

Counting, sorting, grouping, making patterns, non-standard measuring

Plastic links, paper clips, etc.

Counting, sorting, grouping, making patterns, non-standard measuring

Interlocking cubes

Counting, sorting, grouping, making patterns, modeling operations, 3-D data display

Cuisenaire rods Sorting, grouping, sets, base ten operations

Abacus Counting, sets, groupong, modeling base ten operations

Base ten blocks (Montessori golden beads)

Counting, sets, grouping, modeling base ten operations

Dominoes Matching, counting, sorting, grouping, measuring

Dice Matching, counting, modeling problems, shape

Tactile numbers (rubber, Montessori sandpaper, magnetic)

Numeral recognition, writing numbers

Number puzzles Numeral recognition, matching, shape

Pegboards Numeral recognition, quantity, matching, counting

Matching numeral and quantity cards

Numeral recognition, counting

Number stamps Writing numerals

Magnetic numerals

Numeral recognition, counting

Pegboards Shape, spatial sense

Beads Sorting, patterns, shape

Nesting toys Shapes, spatial relations

Shape sorters Shape, sorting, spatial relations, patterns

Attribute blocks Shape, classification, patterns

3-D shapes Shape, spatial relations, sorting

Shape puzzles Sorting, matching, shape

Pattern blocks Sorting, shape, patterns, spatial relations

Tangrams Shape, spatial relations, patterns, sorting

Plastic coins Currency, sorting, classification

Sand timers Measuring time Digital timer Numeral recognition, measuring clock time

Analog clock Measuring clock time, numeral recognition

Teaching clock (movable hands)

Analog time measurement, numeral recognition

Bucket balance Measurement (weighing), comparing

Graphing chart Displaying data

Measurement containers

Measuring volume, comparing, conservation

Calculator Numeral recognition, operations, technology

Material Sample Applications Material Sample Applications

11 one

6 six

0 55

35 30

5 12

2 1

57 8

10 11

Picture lotto boards and games

Matching, one-to-one correpondence

Memory matching games

Matching, one-to-one correspondence, developing recall

Counters: small objects of different colors and shapes (animals, boats, planes, etc)

Counting, sorting, grouping, making patterns, non-standard measuring

Plastic links, paper clips, etc.

Counting, sorting, grouping, making patterns, non-standard measuring

Interlocking cubes

Counting, sorting, grouping, making patterns, modeling operations, 3-D data display

Cuisenaire rods Sorting, grouping, sets, base ten operations

Abacus Counting, sets, groupong, modeling base ten operations

Base ten blocks (Montessori golden beads)

Counting, sets, grouping, modeling base ten operations

Dominoes Matching, counting, sorting, grouping, measuring

Dice Matching, counting, modeling problems, shape

Tactile numbers (rubber, Montessori sandpaper, magnetic)

Numeral recognition, writing numbers

Number puzzles Numeral recognition, matching, shape

Pegboards Numeral recognition, quantity, matching, counting

Matching numeral and quantity cards

Numeral recognition, counting

Number stamps Writing numerals

Magnetic numerals

Numeral recognition, counting

Pegboards Shape, spatial sense

Beads Sorting, patterns, shape

Nesting toys Shapes, spatial relations

Shape sorters Shape, sorting, spatial relations, patterns

Attribute blocks Shape, classification, patterns

3-D shapes Shape, spatial relations, sorting

Shape puzzles Sorting, matching, shape

Pattern blocks Sorting, shape, patterns, spatial relations

Tangrams Shape, spatial relations, patterns, sorting

Plastic coins Currency, sorting, classification

Sand timers Measuring time Digital timer Numeral recognition, measuring clock time

Analog clock Measuring clock time, numeral recognition

Teaching clock (movable hands)

Analog time measurement, numeral recognition

Bucket balance Measurement (weighing), comparing

Graphing chart Displaying data

Measurement containers

Measuring volume, comparing, conservation

Calculator Numeral recognition, operations, technology

Material Sample Applications Material Sample Applications

(continued)

Promoting Cognitive Development Chapter 10

11 one

6 six

0 55

35 30

5 12

2 1

57 8

10 11

Picture lotto boards and games

Matching, one-to-one correpondence

Memory matching games

Matching, one-to-one correspondence, developing recall

Counters: small objects of different colors and shapes (animals, boats, planes, etc)

Counting, sorting, grouping, making patterns, non-standard measuring

Plastic links, paper clips, etc.

Counting, sorting, grouping, making patterns, non-standard measuring

Interlocking cubes

Counting, sorting, grouping, making patterns, modeling operations, 3-D data display

Cuisenaire rods Sorting, grouping, sets, base ten operations

Abacus Counting, sets, groupong, modeling base ten operations

Base ten blocks (Montessori golden beads)

Counting, sets, grouping, modeling base ten operations

Dominoes Matching, counting, sorting, grouping, measuring

Dice Matching, counting, modeling problems, shape

Tactile numbers (rubber, Montessori sandpaper, magnetic)

Numeral recognition, writing numbers

Number puzzles Numeral recognition, matching, shape

Pegboards Numeral recognition, quantity, matching, counting

Matching numeral and quantity cards

Numeral recognition, counting

Number stamps Writing numerals

Magnetic numerals

Numeral recognition, counting

Pegboards Shape, spatial sense

Beads Sorting, patterns, shape

Nesting toys Shapes, spatial relations

Shape sorters Shape, sorting, spatial relations, patterns

Attribute blocks Shape, classification, patterns

3-D shapes Shape, spatial relations, sorting

Shape puzzles Sorting, matching, shape

Pattern blocks Sorting, shape, patterns, spatial relations

Tangrams Shape, spatial relations, patterns, sorting

Plastic coins Currency, sorting, classification

Sand timers Measuring time Digital timer Numeral recognition, measuring clock time

Analog clock Measuring clock time, numeral recognition

Teaching clock (movable hands)

Analog time measurement, numeral recognition

Bucket balance Measurement (weighing), comparing

Graphing chart Displaying data

Measurement containers

Measuring volume, comparing, conservation

Calculator Numeral recognition, operations, technology

Material Sample Applications Material Sample Applications

11 one

6 six

0 55

35 30

5 12

2 1

57 8

10 11

Picture lotto boards and games

Matching, one-to-one correpondence

Memory matching games

Matching, one-to-one correspondence, developing recall

Counters: small objects of different colors and shapes (animals, boats, planes, etc)

Counting, sorting, grouping, making patterns, non-standard measuring

Plastic links, paper clips, etc.

Counting, sorting, grouping, making patterns, non-standard measuring

Interlocking cubes

Counting, sorting, grouping, making patterns, modeling operations, 3-D data display

Cuisenaire rods Sorting, grouping, sets, base ten operations

Abacus Counting, sets, groupong, modeling base ten operations

Base ten blocks (Montessori golden beads)

Counting, sets, grouping, modeling base ten operations

Dominoes Matching, counting, sorting, grouping, measuring

Dice Matching, counting, modeling problems, shape

Tactile numbers (rubber, Montessori sandpaper, magnetic)

Numeral recognition, writing numbers

Number puzzles Numeral recognition, matching, shape

Pegboards Numeral recognition, quantity, matching, counting

Matching numeral and quantity cards

Numeral recognition, counting

Number stamps Writing numerals

Magnetic numerals

Numeral recognition, counting

Pegboards Shape, spatial sense

Beads Sorting, patterns, shape

Nesting toys Shapes, spatial relations

Shape sorters Shape, sorting, spatial relations, patterns

Attribute blocks Shape, classification, patterns

3-D shapes Shape, spatial relations, sorting

Shape puzzles Sorting, matching, shape

Pattern blocks Sorting, shape, patterns, spatial relations

Tangrams Shape, spatial relations, patterns, sorting

Plastic coins Currency, sorting, classification

Sand timers Measuring time Digital timer Numeral recognition, measuring clock time

Analog clock Measuring clock time, numeral recognition

Teaching clock (movable hands)

Analog time measurement, numeral recognition

Bucket balance Measurement (weighing), comparing

Graphing chart Displaying data

Measurement containers

Measuring volume, comparing, conservation

Calculator Numeral recognition, operations, technology

Material Sample Applications Material Sample Applications

Promoting Cognitive Development Chapter 10

A mathematics area should have ample space on the floor or tabletop for children to spread out materials and work in small groups. The science/discovery area should be located as close to a water source as possible. As with other classroom interest areas, materials should be organized and labeled for easy access and cleanup. Clear storage containers or open baskets make it easy for children to choose items and also provide sorting and classification practice when they are being put away.

Logicomathematical Knowledge

From infancy, children start to notice relationships, and any time you introduce additional complexity, unfamiliar materials, or a problem to solve, you encourage children to construct and refine concepts and discern relationships between materials and ideas. For instance, because infants are developing object permanence (knowing that someone or something is

Observing: Prisms, magnify- ing glasses, magni�er stand, butter�y cage

Classi�cation: Sea animals, rocks, insects, shells

Sensory Exploration and Discrimination: Montessori color tiles, Montessori baric (weight) tablets, feely box, Montessori smelling jars

Ecology: Planting equipment, composting box, rain gauge, thermometer

Physical Science: Gears/pulleys, balance scale, ramps, balls, magnetic wands

Figure 10.3: Basic Science Equipment for Early Childhood

Basic science/discovery materials promote observation of the natural world, data collection, and the conduc- tion of experiments.

Promoting Cognitive Development Chapter 10

present even when not visible), any action that involves hiding an object creates a problem for the baby to solve. Further, putting a favorite rattle inside a bag where it can still be heard is very puzzling to an infant because the sound is familiar and recognized but the child is not sure where it is coming from (the bag). The child will be motivated to find the rattle and thus to make progress towards object permanence.

Table 10.1 provides examples of simple things babies and toddlers do that educators can facili- tate to encourage and extend their explorations (Geist, 2003, pp. 10–12).

Table 10.1: Facilitating Logicomathematical Knowledge with Infants and Toddlers

Behavior/Activity Concept(s) Teacher Strategies

Sorting objects Discerning similarities and differences among objects

Offer a wide variety of toys in different shapes, colors, etc., such as large colored beads with containers or compart- mentalized trays for sorting.

Shaking, striking, beating instruments

Counting beats and rhythm

Provide objects that make sounds and help children to use in different ways; count out rhythms during use.

Nesting objects Comparing relative size Use “comparing” words that describe what they are doing (such as big, bigger, biggest).

Putting toys away Matching Provide picture or shape labels on containers so children can match an item they are holding with the corre- sponding picture on a storage container.

Crawling, finding places to sit/hide

Spatial relationships Set up a collapsible tunnel, large cardboard boxes, or stack of mats or pillows to climb on.

Filling/pouring Conservation Set up a sand/water table with containers, funnels, etc., of various sizes.

Stringing beads Patterns, shapes Point out and name patterns.

Social-Conventional Knowledge

Conversations are part of teachers’ daily interactions with children. These exchanges provide numerous opportunities to help them develop socio-conventional knowledge by modeling the language and vocabulary of mathematics and the sciences. As you describe and label what they do, you also ask them questions that prompt thinking. As an educator, you will want to formulate your questions so that they maximize the thinking required to answer them.

One effective strategy is to use the categories provided in Bloom’s taxonomy to guide your questions. This is a model introduced in 1956 by cognitive psychologist Benjamin Bloom that illustrates the increasing complexity of intellectual behavior. Revised during the 1990s, the current model (Figure 10.4) provides guidance for teachers about how to promote cognitive development (Anderson & Cruikshank, 2001).

For instance, suppose you posed this question to older preschoolers: “How many ways can we make a boat that will float in the water table?” As you observe them in action and talk with them about their boat-building activities, you can apply the taxonomy to questioning them about their work. If you ask “Did the paper boat float or sink?” children only have to recall what happened to respond, the lowest level on Bloom’s taxonomy. But if you ask, “Can you use your words to tell us what happened to the paper boat?” the responses would reflect the next higher level, “understanding.”

Promoting Cognitive Development Chapter 10

Extending this example, other questions of increasing complexity could be:

• Applying: “Since we know that crumpling the paper in a ball makes the paper float, is there another material we might also try crumpling?”

• Analyzing: “How can we organize testing our boats so we can find out what makes them sink or float?”

• Evaluating: “LaShawn, I heard you say that any boat made of aluminum foil will float; why do you think that is the case?”

• Creating: “Let’s look at all the boats you made and give each of you a chance to tell the story of how you made it.”

Documenting Children’s Thinking

Using different strategies to document children’s work makes their thinking visible. Documentation gives teachers a means of reflecting on children’s cognitive growth to inform ongoing decisions about curricular materials, activities, and instructional strategies. For exam- ple, taking pictures and writing down children’s words or ideas as they work on a prob- lem or inquiry provides data that can later be used for assessment, gives children a visible record of their progress, and establishes concrete reference points for conversations about problem solving.

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Creating

Evaluating

Analyzing

Applying

Understanding

Remembering

Figure 10.4: Bloom’s Taxonomy

Bloom’s Taxonomy can help teachers plan activities and use interactions with children to promote higher-level critical thinking.

Mathematics and Science Standards Chapter 10

Table 10.2 represents children’s words and thoughts a teacher might record about the boat- building activity described above. The teacher could use the chart with children to help them remember what they did and talk through what to do next.

Table 10.2: Documentation of Boat-Building Observations

Ideas for Materials Things We Tried That Work Problems We Had So Far

Paper Crumpling up paper in a ball keeps it from sinking.

If paper stays in the water too long, it gets wet and collapses.

Plastic lids We can use a lump of clay on the lid to hold up the sail mast, so it doesn’t make a hole in the boat.

If water gets on top of a lid, it sinks.

Sponges The sponge will float with the green side up but not with the sponge side up.

Marshmallows Marshmallows float at first, then they melt.

Wood Wood definitely floats. We can’t figure out how to attach a sail.

Other Ideas for Materials

Other Things We Tried That Work

Other Problems We’ve Had So Far

Foil

Bottle caps

Sticks

Clay

Cork

Trying the materials in the water first to see if they float before we make the rest of the boat.

Making the bottom of the boat bigger than the sail keeps it from sinking.

If we put a toothpick and paper sail in a cork, it falls over.

Opportunities for routine documentation of a work in progress could include:

• Block constructions

• Different ways children sorted a collection of objects

• Progress of planted seeds as they sprout and grow

• Children using bubble wands

• Different strategies children use to finger paint and the resulting visual effects

• An easel painting from start to finish

• Children putting a puzzle together

• Figures constructed with pattern blocks

• Distances measured with plastic chain links

10.3 Mathematics and Science Standards Fundamental concepts and their application to problem solving in mathematics and the sci- ences are interrelated. This idea is reflected in the current national standards for mathemat- ics and emerging new standards for science that integrate knowledge and process skills in mathematics and practice skills in science and engineering while also placing increasing emphasis on technology in both disciplines.

Mathematics and Science Standards Chapter 10

In the early childhood classroom, the rela- tionship between mathematics and science is evident in highly integrated activities and investigations. Suppose that children are helping the teacher make a snack mix. They may look for recipes in cookbooks or on the Internet to choose one they want to try. They may hypothesize or predict how well they think they will like it or what it might taste like.

They will apply math concepts as they set up and count their equipment (“We need one big spoon, two bowls, three measur- ing cups.”), sort/group ingredients (crack- ers, dried fruits, cereal, seeds), and follow ordinal (sequential) directions in determin- ing what to do first, second, and so on and in using different size cups to measure. They apply operations to divide items (mix in one big bowl and divide into smaller bowls for serving) and one-to-one corre- spondence for serving (one napkin/scoop for each child).

They will also use science skills as they observe the process (“Look at all the colors we have in the bowl!”). They will decide when ingredients are fully mixed, and ask questions (“Why are the raisins and cranberries all wrinkly?”) that could lead to further investigation (drying fruits). They will evaluate the results of their recipe trial, perhaps graphing the preferences of children in the group.

Mathematics Standards

The national mathematics and science standards differ in content and the ways in which strat- egies are applied and used for problem solving and inquiry. The National Council of Teachers of Mathematics (NCTM) developed the standards (2000) for math education from pre-K through high school. The NCTM describes principles on which math education should be based, content knowledge, and processes for development of mathematical competence. The 2010 revised joint position statement by the National Association for the Education of Young Children (NAEYC) and NCTM also stresses that high quality mathematics for young children is grounded in their natural interests, daily experiences, and opportunities for play. Children acquire informal mathematical knowledge and skills needed for understanding formal mathematics from daily life (Baroody, Lai, & Mix, 2006; Charlesworth, 2005; Sypek, 2017; van Hoorn, Nourot, Scales, & Alward, 2011). Common Core Standards (CCSS) for education from kindergarten through high school were finalized in 2010. Although CCSS for mathematics are being used in 35 states, the standards do not address pre-K education (Ujifusa, 2017).

The development of mathematical concepts is cumulative, so informal knowledge is very impor- tant as a basis for intentional and systematic mathematics instruction. But because children’s

Cooking is an example of an activity that integrates both mathematics and science skills.

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experiences can vary significantly by socioeconomic con- text, the early childhood years provide opportunities for both informal and planned experiences with mathematics, which occur and develop concurrently. Research supports an approach to mathematics instruction that focuses nei- ther on direct instruction nor unguided discovery but on guided discovery that includes both:

• Adult-initiated experiences, such as games, tasks, and projects

• Child-initiated activity with guided adult responses, such as building upon a child’s questions during play (Baroody, Lai, & Mix, 2006; Campbell, 1999; Charlesworth, 2005; Rice, 2014)

The content standards identify what children should know and be able to do in five strands within mathematics:

1. Numbers and operations

2. Algebra

3. Geometry

4. Measurement

5. Data analysis and probability

Emphasis on each of the strands varies over time, depend- ing on where the children are developmentally and what they’ve already learned. But one thing is sure: future suc- cess in mathematics is based on sound foundations of conceptual and procedural understanding in the early years (Campbell, 1999; Linder, 2017; NAEYC/NCTM, 2010; Seefeldt, 1999; Witzel, Ferguson, & Mink, 2012).

Science Standards

The Next Generation Science Standards for K–12 reflect and are guided by A Framework for K-12 Science Education: Practices, crosscutting concepts, and core ideas, published by the National Research Council in July 2011. The framework emphasizes an approach for stan- dards development that integrates three dimensions: science/engineering practices (the methods used in science and engineering), cross-cutting concepts (integrated understandings across the science disciplines), and core ideas within each of the four science disciplines— physical science; life science; earth science; and engineering, technology and applications.

Doing Math and Science

The process standards for mathematics and practices for science focus on how children learn and apply concepts. Common to the disciplines is an emphasis on using concrete materials (Witzel, Ferguson, & Mink, 2012) for inquiry and problem solving, active involvement in the processes and practices used in mathematics and the sciences, developing and using critical thinking skills, and communication. Early childhood educators understand that developing dispositions and skills through first-hand experiences is essential to a firm foundation for mathematical and scientific thinking (NAEYC/NCTM, 2010).

In guiding instruction, the teacher doesn’t use directed instruction or take a completely hands-off approach but carefully facilitates play and scaffolds activities.

http://www.nextgenscience.org/

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Table 10.3 displays the interrelated nature of the mathematics process skills and the sci- ence/engineering practices. You can see how they reflect the different levels of Bloom’s taxonomy.

Table 10.3: Mathematics Process Skills and Science/Engineering Practices

Mathematics Process Skills Science/Engineering Practices

Inquiry and problem solving

Reasoning and proof

Communication

Connections

Representations

Asking questions (for science) and defining problems (for engineering)

Developing and using models

Planning and carrying out investigations

Analyzing and interpreting data

Using mathematics and computational thinking

Constructing explanations (for science) and designing solutions (for engineering)

Engaging in argument from evidence

Obtaining, evaluating, and communicating information

Processes focus on analysis of patterns, structures, and the testing of hypotheses or pre- dictions. Learning to make inferences and predictions and to justify data-based conclusions helps children begin to make sense of the physical world. Through active listening to others’ explanations and communicating their own results and reasoning, they begin to appreciate multiple perspectives to problem solving and also learn to use communication as an effective means for sharing ideas.

Teachers apply knowledge of children’s general and individual characteristics and learning styles to encourage them to represent ideas in a variety of ways. Mathematics and science for young children are no longer primarily paper-and-pencil activity, as our understanding of children as concrete learners now stresses representation of thinking with words, pictures, materials, graphic organizers, and symbols (Campbell, 1999).

10.4 Mathematics Concepts and Curricular Activities Content standards and mathematics concepts are heavily emphasized in preschool and pri- mary grades curricula and classrooms. It is important for early educators to understand the hierarchical nature of how mathematical thinking grows and children’s need for concrete materials and hands-on experiences to eventually develop abstract reasoning. Each of the following sections describes mathematical concepts, materials, strategies, and activities that support the goals and expectations expressed in the national mathematics standards for PreK–2 children.

Number and Operations

The primary goal for numbers and operations is developing number sense, or “intuition” about the meaning of numbers in relation to other numbers (Charlesworth, 2005; Campbell, 1999; Witzel, Ferguson, & Mink, 2012). For example, a child who knows that 4 represents 1 more than 3 (2 + 2, 3 + 1), and 1 less than 5 understands that numbers are more than a matter of simple counting (Campbell, 1999, p. 113). Number sense links to future success

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in mathematics much as phonological awareness (recognizing and using language sounds) relates to achievement in reading (Witzel, Ferguson, & Mink, 2012).

One-to-One Correspondence The most fundamental concept of number is one-to-one correspondence, which is basic to understanding equivalence and conservation and necessary for counting. Children dem- onstrate one-to-one correspondence when they distribute items saying, “one for me, one for you,” or match materials to silhouette or picture labels on shelves and baskets during cleanup time. When you label each child’s cubby with a photograph, they associate these spaces with their belongings. Likewise, providing a sign-in sheet where each child has a preprinted line with his or her name and an adjacent blank space for signing in reinforces one-to-one correspondence.

Matching and one-to-one correspondence activities and materials include:

• Lotto boards and matching games (see Figure 10.2)

• Tossing rings of different colors onto matching-colored posts

• Musical chairs

• Repeating hand-clap patterns or clapping once for each word in a rhyme

• Solving puzzles that have one space for each matching piece (see Figure 10.2)

• Place mats with outlines for plate and utensils that children use to set their table

• Using tweezers or tongs to remove one item at a time from a full bowl and transfer it to an empty bowl

• Shadowing games—children repeat/mimic the motions of a leader

• Making puzzle cards (such as the ones Ms. Phyllis made for her insect unit in Chapter 6 (Figure 6.8)

Counting A child’s ability to recite numbers, or count by rote, doesn’t necessarily mean that he or she associates the name of a number with quantity or the name of the number with its numerical symbol. To rote count, children memorize number sequences, and it is not unusual for them to skip a number or group of numbers, as in “one, two, three, six, eight, nine, ten.”

Once past ten, they also sometimes have difficulty mastering the number names as they are expressed in English and may say “eleventeen” or “twelvety.” Children gradually move from rote counting to rational counting, correctly associating the name of a number with objects in a group (Charlesworth, 2005).

It is important to work with children at their level of understanding, so a teacher would not, for example, lead rote-counting practice or use finger plays that count in descending (backwards) order before children had mastered ascending order. Rote counting is reinforced

One-to-one correspondence develops as the child learns to match one object with a corresponding space or item.

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through the use of rhymes/finger plays such as, “one, two buckle my shoe, three four, shut the door. . . ,” or counting songs, like “one little, two little, three little monkeys, four little, five little . . . .” These are reinforced by regular practice and routines like “Let’s count to ten before I open the door—repeat after me: one, two . . . .”

You promote rational counting to associate number with discrete quantities by pointing to each object as children count; also by asking children to count groups of objects and then saying, “How many did we count in this pile?” Daily opportunities abound for rational count- ing, including:

• Counting different numbers of sticks or straws and putting them in a can with a cor- responding number of dots.

• Counting the number of children in a group seated at a table and then counting the correct number of red crayons needed so that each child has one.

• Counting the number of steps to “4” as they step on each number of a number line taped to the floor.

• Counting the number of fish in the aquarium.

• Counting off while standing in line waiting to go outside.

• Counting the number of stacking blocks needed for a construction in groups of one, two, three, etc.

Operations Understanding numbers as parts of other numbers is the basis for the operations of addition and subtraction. Once children have achieved rational counting, whether they can represent numbers in writing or not, they can begin to perform operations. The child who takes three bears from a bin and puts them on the table, counting “one, two, three, I have three bears,” and then takes two more bears from the bin and counts, “four, five—first I had three and now I have five,” is beginning to perform the simple operation of combining or adding sets of objects. The child with five bears who announces separating them into two separate piles of 3 and 2, is demonstrating understanding of the concept of assigning referent numbers to sub- sets (Campbell, 1999). There is some evidence to suggest that in early education, emphasizing parts and wholes over direct teaching of computation steps and base 10 operations promotes a more flexible understanding of algorithms (multiple-step problem solving) (Campbell, 1999; Witzel et al., 2012). Thus if you use an open-ended question to ask a child to partition 12 Unifix cubes in as many ways as possible, the child might construct sets of 1 + 11, 2 + 10, 3 + 9, etc., but subsets of 1 + 4 + 5 + 2 would also be correct. Later on, that approach may lead to computation strategies that do not necessarily have to match the “one right way” you might remember from your own experiences with math instruction.

Understanding the relationship between parts and wholes is also the beginning of fractions. Children learn that parts may be of either equivalent or nonequivalent size. Eventually they learn that fractions represent equally divided subparts that can be combined and expressed in different ways (Charlesworth, 2005). Children should be encouraged to combine and divide whole objects and groups of objects in different ways, such as cutting or tearing paper, separating piles of objects into multiple containers, putting interlocking puzzles together, or counting the number of slices in a pizza.

Children need manipulatives to work out operations and the symbols for addition, subtraction, and equivalence before representing them abstractly with their number symbols. You help them make this transition by modeling with objects and gradually moving to two-dimensional

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representations (flannel board, overhead projector, paper and pencil).

Symbolic Representation Like counting, learning to represent numbers with the corresponding numeral is developmentally sequenced. A child who counts correctly does not necessarily associate the number with its matching symbol. Thus many materials that support learning to count—such as an abacus, Unifix cubes, or domi- noes—do not feature numerals. Conversely, being able to trace or write a number may not mean that the child understands the connection between the numeral and the quantity it represents. In order for that to happen, children need to recognize the sym- bol, be able to identify and associate it with the cor- rect number of objects in a set, and then represent the number in writing legibly (Charlesworth, 2005, p. 218; Witzel, Ferguson, & Mink, 2012).

Typical examples of materials that focus on one or more of these three tasks are included in Figure 10.2; they should be accessible and used in both preschool and primary classrooms (Witzel, Ferguson, & Mink, 2012). Because of individual variations in the develop- ment of this concept, teachers can best help children to acquire symbolic representation through one-on- one and small-group activities such as:

• Making number books with stickers or stamps (Seefeldt & Galper, 2004)

• Writing numerals on sequence picture charts

• Using magnetic letters to represent numbers

• Using calendars with blank spaces and modeling writing in the numbers

• Making numbers out of pipe cleaners, play dough, or wire

Algebra

The foundations for algebra begin with understanding classification, ordering, and patterns (Taylor-Cox, 2003). Classification (sorting and grouping) activities help children begin to dis- tinguish, compare, and categorize concrete objects by characteristics or attributes (such as color, shape, or size) and reinforce the concept of sets. Applying comparison skills leads to identification of simple color, shape, or sound patterns in the environment necessary for alge- braic reasoning.

Classification Classification includes sorting and grouping. When children sort, they separate (subtract) objects into categories; when they group, they combine (add) by noting the characteristics that items have in common, thus making and rearranging sets according to different criteria.

Writing numbers correctly represents a long developmental sequence—rote count- ing, rational counting, recognizing numer- als, identifying numerals, associating each numeral with the correct quantity, and finally learning to write numerals legibly.

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Children begin classifying by a single obvious attri- bute, such as color or shape (red bears, blue bears, yellow bears; squares, circles, triangles). At first they don’t necessarily know or express what the criteria are, but they do demonstrate observation about how the items are alike or different.

Gradually they begin to classify by less obvious cri- teria such as material (hard/soft), pattern (striped/ checked), texture (rough/smooth), or function (moves/ doesn’t move) and more sophisticated characteristics such as animal type (sea/land animals or reptiles/ birds). They also move to classifying objects by more than one attribute, such as color and size (big blue cars, small blue cars, big red cars, small red cars). A child’s approach to classification reflects his or her growing sense of logic. It is important to understand, however, that children represent logical thinking in different ways; what seems an obvious attribute to one child might not be apparent to another. You can learn a lot about how children think by asking them to explain the way they sorted a particular group of objects.

Teachers promote classification indirectly with activi- ties such as lining up by shirt color or by boys vs. girls or by listing foods that children like/dislike. They also provide intentional sorting activities with materi- als such as buttons or beads. Children can also be encouraged to place different toys and props—such as blocks, play foods, and cars—into appropriately labeled bins during cleanup time.

Teachers facilitate classification skills by introducing and modeling different ways to sort or group and suggesting more challenging criteria. Using effective language will also help. The directions teachers give to children:

• Reflect recognition of what they observe, such as “It looks like you are sorting the ani- mals according to where they live. Is that right?”

• Add to the child’s repertoire of criteria, such as “I see you have sorted the buttons into color groups. Can you sort them again by how big they are?”

• Encourage application of multiple criteria as a child’s ability to sort by a variety of sin- gle attributes develops, as by saying, for example, “Hmmm we have all these turtles. Some are big, some are small, and they are yellow, brown, and green. Do you think you could sort them into big/green, small/green, big/yellow?”

• Encourage children to describe and label the criteria they are using.

Classification activities provide a natural segue to graphing and representing data, as dis- cussed a bit later in this section.

How many ways can you sort buttons? A box of buttons and any kind of container with compartments offers the child opportunities to sort by many different attributes, includ- ing color, shape, size, number of holes, mate- rial (plastic/wood/fabric), and pattern (solid, printed, striped).

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Ordering At first children compare pairs of objects and later each additional item to the selected crite- ria. Ordering, or putting items into series—also called seriation—represents the graduated comparison of more than two things or sets in a larger group. This procedure is more complex than making comparisons in pairs (Charlesworth, 2005).

Seriation activities focus on ordering according to any applicable attribute, by size in ascend- ing or descending order, or temporal ordering of events from first to last (Hendrick, 2007), or ordering by graduated differences such as color shades, sound, or weight.

Any activities that involve paired comparisons can be extended to ordering and seriation sim- ply by addition of materials such as:

• Graduated paper shapes

• Sticks, straws, or rods of different lengths (e.g., Cuisenaire rods)

• Nesting items such as measuring cups and spoons

• Arranging different shades of a single color in order from lightest to darkest

• Storing pots and pans in dramatic play on hooks from smallest to largest

• Arranging pictures of children in order of birthday from January to December

• Lining up by size

• Time lines

• Sequencing picture cards or flannel-board cutouts for familiar stories such as Goldilocks, The Three Little Pigs, or If You Give a Mouse a Cookie

• Playing/singing a favorite song several times, varying the volume from soft to loud

• Using pictures to represent the daily routine and having children put them in order

Note that because of preschoolers’ egocentrism, they often represent people or objects in their drawings and paintings by relative importance rather than by actual size/proportion. Thus, in a picture of mom’s flower garden, mom and the flowers might be bigger than the house! Comparing, seriation, and ordering activities with real objects help children gradually move from psychological to more accurate concrete representations.

Patterns and Patterning In mathematics, a pattern represents a repeating series of any kind. We want to help children learn to recognize, replicate, represent, and extend visual, sound, and motor pat- terns. Many of the typical materials in Figure 10.2 are useful for learning about, copying, and creating patterns. To identify a pattern, children apply classification, comparison, and ordering concepts to establish where a pattern starts, ends, and repeats. Teachers help chil- dren “read” patterns by encouraging them to name the items in sequence, as in “blue, red, green, blue, red, green,” etc. (Taylor-Cox, 2003). Teachers label different kinds of patterns to indicate the level of complexity in a repeating segment, such as a/a, a/b, a/b/c, or ab/ac/ bc, and so on.

A growing pattern increases the number of repetitions in each sequence, such as jump, squat, jump 1x/jump, squat , jump 2x/jump, squat, jump 3x . . . (Taylor-Cox, 2003). Many children find the inherent rhythm of patterns soothing. Some children may find it easier to identify one type of pattern than another. Patterns presented to children for identification should

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represent at least one repeat to help them determine what comes next (i.e., square, circle, rectangle/square, circle, rectangle/ square, circle . . . ) (Taylor-Cox, 2003).

Learning to recognize patterns is impor- tant not just for mathematics but for inter- preting text in reading as well. Teachers can foster learning about patterns by:

• Displaying photographs of patterns in nature, such as a pine cone or nautilus shell

• Pointing out a pattern in the brick- work of a building

• Having a “pattern hunt” in the class- room or on the playground

• Clapping out the rhythm patterns in songs

• Making up motor games with actions that represent a pattern

• Decorating cupcakes with cutout patterns

• Filling in the days and weeks on a calendar

• Making patterns on paper with stamps or stickers

Geometry

“If mathematics is perceived as the search for order, pattern, and relationships to characterize ideas and experiences, then geometry and spatial sense should be central topics in a math- ematics curriculum for young children,” (Campbell, 1999, p. 124). Young children can begin to learn about geometry as they encounter a variety of shapes in play and daily life. Children play with and often recognize objects and symbols (including letters and words) by shape. As with other developmental sequences, children first match, then identify, name, and finally represent shapes (Charlesworth, 2005).

Spatial awareness develops as children learn prepositional and directional words such as on top of, below, next to, and so on. Teachers can help children learn the vocabulary of geom- etry, to develop a sense of two- and three-dimensional shapes and their respective character- istics as well as to think in terms of spatial relationships (Seefeldt & Galper, 2004).

Shapes Concepts about shape include the ideas that:

• There are different kinds of shapes

• Shapes can be found everywhere in different kinds of objects

• A single item can have different shapes (e.g., cookie or rock)

• A shape can be modified (made bigger or smaller, etc.)

• Combining shapes can create new or different shapes

Recognizing and constructing repeating patterns is fun- damental to algebraic thinking. Children begin with simple a/b/a/b patterns and advance to patterns of increasing complexity.

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Activities that promote learning about shapes include:

• Holding and feeling the edges of cutouts or models of different flat and three- dimensional shapes

• Tracing shapes

• Matching shapes with cutouts

• Making shapes with their bodies

• Using shape cookie cutters with play dough and for baking

• Making and cutting foods like a tray of brownies or pancakes into different shapes

• Folding paper to make simple origami

• Having a “shape hunt”

• Making mobiles with straight-sided shapes from objects like straws or toothpicks or making curved shapes with yarn or pipe cleaners

• Making silhouette cutouts of objects and matching them or having guessing games

• Making collections based on different shapes

• Using geoboards to make shapes with rubber bands

• Staking out “giant” shapes on the playground with crepe paper or string

Spatial Relationships Activities that promote spatial relationships focus on encouraging children to locate bodies or objects in space, use their knowledge of spatial relationships to describe where something is located, interpret representations of spatial relationships (mapping), and represent spatial rela- tionships with symbols (mapping). Active games such as hide and seek, duck-duck goose, or building an obstacle course build spatial awareness.

Measurement

Children learn to measure first by nonstandard means such as pacing off distances and later with uniform but nonstandard measurement tools (e.g., measuring the width of a tabletop with paper clips) and later still with conventional measurement tools. As they do so, they develop a sense of the kinds of things that are measured. Concepts related to measurement include measuring to represent comparisons, using a variety of different tools to measure, and seeing estimation as useful but not the same thing as accurate measurement. We encourage children to think about measurement with questions that start with “How far,” How much,” How long,” and so on.

Linear Measures, Weight, and Volume Examples of standard measures—such as a growth chart, weight scale, or masking tape on the floor to mark off distances in inches or feet—should be displayed and used to build

As children explore spatial relation- ships, they learn to use vocabulary that describes positions in space, relative size, and directionality.

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awareness of linear measures (length, width, height). Children should be encouraged dur- ing play to describe nonstandard measurements, such as “How many blocks long/high is your castle?” (Charlesworth 2005).

Activities for linear measurement can include:

• Using any long object (crayon, paper clip, straws, pipe cleaners, string) to measure objects or distances (classroom dimensions, rugs, furniture, height of children, etc.)

• Filling up cups, quart/liter/gallon containers with liquids or sand

• Counting the number of marbles it takes to fill different-sized jars

• Comparing measurements of objects in terms of longer, shorter, wider, narrower, etc.

• Cooking activities

• Using a balance to compare the weights of different objects and combinations of objects

• Pacing off longer distances such as the length of a hallway, sidewalk, or rows in the garden

• Using standard measurement tools such as rulers, yardsticks, or a tape measure

Temperature Understanding that temperature is something that can be measured is abstract and difficult for young children other than in general terms such as hot, cold, and warm. The classroom should include different tools for measuring temperature with displays in both analog and digital format, including oral, candy, meat, and refrigerator thermometers and outdoor digital and clock-style thermometers. Children can be encouraged to observe and record tempera- tures and engage in activities that involve materials that they can heat, melt, or freeze.

Children can also be encouraged to monitor the movement of mercury or dials as temperature changes. For example, many states’ licensing laws prohibit play outdoors when the tempera- ture exceeds 90 degrees Fahrenheit; in applicable climates, if you mark the window thermom- eter at the 90 degree mark and children can be on the lookout for when the mercury or dial handle reaches that mark to announce “It’s 90!”

Time Children confuse general use of the word time in the context of nap time, time to go, and so on with actual measurement of time. The various dimensions of time—clock, calendar, and historical time—are also abstract and take time to develop. Charlesworth (2005) describes three kinds of time: personal experience (past, present, future), social activity (routines/order), and cultural (fixed by clocks and calendar measurements).

You can promote basic concepts, such as that:

• Time is relative and cyclical

• Time can be represented as sequence or by duration

• Time always goes forward but we can talk about time that has passed.

• We measure time by equal intervals of different kinds (e.g., seconds, hours, days, years)

It is also important to develop a “time vocabulary”—words like time, age, morning, after- noon, soon, tomorrow, yesterday, early, and late. Concrete tools for measuring time can be very helpful. For example, setting a kitchen timer or using a small sand hourglass while

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The Twenty-Four Foot Python: A Teachable Moment about Measurement

Ms. Deanna was working her way through Shel Silverstein’s book Light in the Attic (1981, p. 44) with her preschool/kindergarten class when she came to “Snake Problem”:

It’s not that I don’t care for snakes, But oh what do you do

When a 24-foot python says . . .

I love you.

The poem prompted an animated discussion about how long a twenty-four-foot python would be. Many ideas were suggested, but they could not agree on a single answer. Ms. Deanna decided to follow up, asking what they could do to find out. The children said they wanted to make a twenty- four-foot-long paper python model. It became evi- dent that the focus of the investigation was going to be accuracy—exactly twenty-four feet, not an inch shorter or longer! Ms. Deanna produced a ruler, introducing it as a standard unit of measure for one foot. Using the ruler, the children quickly realized the classroom floor tiles all measured exactly one foot square. They spent several hours measuring off distances in the classroom in floor tiles but found that no matter how they measured, there was no twenty-four-foot space in which they could build their model.

Betty, in a flash of insight during a conversation about the problem said, “I know! The hallway is really long. What if we build it in the hallway?” They used masking tape to mark off the begin- ning and end of twenty-four feet and commenced building the python out of white mural paper, stuffing it with crumpled newspaper. They pored over books and online pictures of pythons to get an idea of how big the head should be in relation to the body. They “amputated” the first head they made when they realized it was too large proportionally and made a smaller one that was “just right.” They painted the python to repli- cate the coloring patterns they found in their pictures.

The children carried the python to show it to their friends in another classroom, and it lived a long life in their classroom, since Ms. Deanna hung it from the ceiling, where it became a frequent source of reference in other conversations about measurement and snakes.

▶ Stop and Reflect 1. How did this project involve children in mathematics and science processes reflected in the

standards?

2. How might you have documented the work children were doing to encourage ongoing discus- sion and problem solving?

As children painted the model, they tried to replicate patterns they had observed in many photographs of pythons.

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children are engaged in an activity helps them gain a sense of how clock time passes. This is particularly useful for helping impulsive children learn to wait for “just a minute” or “two minutes.” Other things you can do include:

• Counting days until birthdays, holidays, or an anticipated special event

• Talking about what children did over the weekend on Mondays

• Displaying the daily routine in a linear sequence of pictures

• Emphasizing what came before and what comes next in sequenced activities, such as following a recipe

• Gardening activities that offer opportunities to count days and measure growth over time

• “How many things can we do in a minute” games

• Installing a sundial outdoors

Currency Children find American currency challenging because of centration—they assume bigger means more and that therefore a nickel should be worth more than a dime or penny. They also have trouble with paper vs. coin. As with the representation of number as quantity in

general, it takes time for them to understand the symbol- ism behind currency—that the nickel represents 5 cents, the dime 10 cents, the dollar 100 cents, and so on.

Children do learn about the value of money and its con- crete uses (buying things) and can be engaged in using real money judiciously. For example, children in Mr. Dick’s 4-year-old class decided to use the outdoor playhouse to set up a store for selling snacks. They made juice pop- sicles, secured a “loan” to buy a big box of Goldfish crack- ers, and determined that each item would cost a penny to buy. They made signs for the store and dictated a note for home, asking parents to send their friends with pennies to spend in the store. They also “hired” children in the 2-year-old class to do jobs for them they didn’t want to do (such as sweeping out the playhouse) for a penny!

While the value placed on work and their product was not realistic in terms of the real world, it definitely showed their understanding of how money is used and critical to the exchange of goods and services. They carefully tracked their revenues over a week and were able to determine when they had enough pennies to pay back their loan. They were also ecstatic to find, at the end of the week, that they had made a profit of $3.34!

Data Analysis and Probability

Through daily experiences, children learn to answer questions of practical value by organiz- ing, interpreting, and representing information with graphs and charts, pictures, and words. Graphing activities should move from concrete to abstract, starting with three-dimensional

Children learn to count change in mean- ingful activities that they can relate to real-life transactions.

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graphs using beads on a string, stacking rings on dowel rods, or interlocking Unifix cubes to represent each unit of data (Charlesworth, 2005). Two-dimensional charts, wipe-off boards, or lines, paper squares or circles taped on the floor or wall can be used to represent many different kinds of information as children’s understanding grows.

Whitin and Whitin (2003) suggest developmentally appropriate guidelines for using graphs with young children, pointing out that they can:

• Tie to a social context (favorite story, group activities)

• Represent the same data set in multiple ways

• Lead to open-ended discussion questions

• Encourage children to name/title graphs

• Revisit data during/after discussions

• Model/demonstrate throughout process of data collection and creating graphs (p. 39)

Graphs should represent data meaningful to children, such as shoe colors, birthdays, tracking the number of children present per day for a week, or preferences. Very simple graphs can be done with children as young as two or three. For example, Ms. Stephanie conducted a unit on babies with her older 2-year-old class, including sampling baby foods. She made a picture graph with the different jar labels across the top and each child put their fingerprint under- neath the picture of the food he or she liked the best.

Graphs can be effectively used to represent the cycle of prediction, testing, and results in an investigation of any kind. For example, if you plan to plant seeds, children can predict how many days it will take for them to sprout and compare predictions with observations. Any activity with an either/or outcome, such as sinking/floating can be graphed in terms of predic- tions/outcomes. Likewise, any unknown future activity can be graphed by possible outcomes children suggest. Suppose you are reading a new story with a problem to solve. Before getting

Figure 10.5 Three-Dimensional Graph

Three-dimensional graphs are a good way to begin using graphs with young children, since they involve the use of concrete objects that children can manipulate to represent data. This graph rep- resents animals on land, on sea, and in the air.

Science Concepts and Curriculum Activities Chapter 10

to the end of the book, children can suggest several possible endings and then you can graph their preferences and compare with the actual ending.

10.5 Science Concepts and Curriculum Activities Science content and curriculum are currently not emphasized in early learning standards and primary grades curriculum to the same extent as mathematics. But teachers should facilitate science learning and scientific inquiry through both informal and structured or facilitated investigations (Hamlin & Wisneski, 2012).

Informal science learning occurs daily as children explore their surroundings during play. They apply science concepts and skills as they make observations about practically everything, from the temperature of soup to whether their parent is driving fast or slowly to classifying the rocks they have collected for study. Their perennial question “why” reflects the natural human drive to make sense of the world.

Scientific thinking involves the application of curiosity and reasoning to answering ques- tions, and teachers promote systematic investigation by helping children focus on ques- tions like “What’s wrong here? What happened here?” and “What proof do you have?”

(Campbell, 1999, p. 134). As documented in the study of power, force, and motion in Chapter 6, teachers support informal science inquiry during exploratory play by choosing provocative materi- als, posing questions, and furthering learning with additional activities (Hamlin & Wisneski, 2012; Stoll, Hamilton, Oxley, Eastman, & Brent, 2012).

Physical science describes and explains the prop- erties of objects and phenomena. Life science is the study of living things and their habitats. Earth science focuses on learning about the forces of nature and studying problems that affect the health of our planet.

This part of the chapter will focus on general ideas for planning activities and units and facilitat- ing transformation of everyday concepts acquired through play to science concepts that represent structured thinking and logic using the language of science (Hamlin & Wisneski, 2012, p. 85).

Physical Science

Everyday concepts about physical science are acquired as children do such things as paint in the art center, build with magnetic translucent tiles on the light table, see their shadows while running outdoors, or try to push a heavy truck up a wooden ramp in the block center. As they manipulate and

Children are natural scientists as they explore their world and all of its mysteries.

Science Concepts and Curriculum Activities Chapter 10

observe everyday objects, they learn about natural forces such as gravity, magnetism, light, and speed. Sensory play (Chapter 7) allows children to exert force on pliable materials, develop conservation in water play, and compare stimuli such as the difference between the way an onion and a flower smells.

Physical science inquiries appropriate for young children focus on explorations, building mod- els, and using simple machines (Cur, 2011). Children investigate phenomena that they can reproduce on their own, allow for variations, are observable, and produce immediate results (Devries, Zan, Hidelbrandt, Edmiaston, & Sales, 2002). The sections below provide suggestions for topics that are both interesting and appropriate for young children about:

• Light/shadow

• Color

• Magnetism

• Solids, liquids, and gases

• Weight, force, and motion

• Static electricity

Light and Shadow Young children are highly intrigued by the interplay of light and shadow and the ways light can be manipu- lated to achieve different kinds of effects. Young children can under- stand and use terms such as light, shadow, reflection, filter, rainbow, image, transparent, translucent, and magnify.

Concepts that can be acquired by young children include the ideas that:

• Light comes from the sun and stars

• Light appears invisible but contains colors

• Blocking light creates shadows

• Some materials allow light to pass through (transparency)

• Light bounces off of shiny objects (reflection)

• Light passes through objects (refraction), changing the way they look by magnification and reduction

The topic of light and shadow lends itself well to both indoor and outdoor activities. To explore transparency, children can sort objects that allow or block light, make sunglasses or put different colors of cellophane over a flashlight to filter light. Children can watch as you make a kaleidoscope using household materials and online directions (requires use of cutting tool not appropriate for young children).

Viewing objects in water or using different types of glass containers and magnifying glasses or other curved glass objects such as marbles reveals the effects of refracted light. To explore

Experiences with objects such as a kaleidoscope provide oppor- tunities for children to explore the qualities of light and its effects on different kinds of materials.

Science Concepts and Curriculum Activities Chapter 10

how shadows are made and change, children can make a shadow-puppet theater or panto- mime stage or they can measure or draw shadows outside. They can also make shadow prints by placing objects on photo-sensitive or construction paper and exposing it to light.

Observing prisms in different locations and at different times of day, using a water hose in the sunshine to make rainbows, or adding oil to a water puddle outdoors in the sunshine allow children to see the light spectrum as a rainbow. They are naturally intrigued by images in mir- rors, and setting up several mirrors so that images are reflected in multiple ways provides a fascinating challenge for them.

Color Color is all around us, providing a context for informal learning and intentional activities to help children learn concepts such as that:

• There are many different colors.

• A single color can have different shades/tints.

• Colors have names.

• Color is not an object but a means to describe objects.

• Colors can be combined.

• Sometimes colors can change.

• Objects can be classified by color.

• An object of one color can be changed to another color.

As with the difference between rote counting and number sense in mathematics, children may be able to recite the names of colors without being able to identify the corresponding color correctly; likewise, they may match and sort colors before being able to name them. Also, just as there are variations in the ways numerals are represented or written in different fonts, color tints or shades such as lemon, light, or gold may be difficult for a child to all cate- gorize as being in the yellow family. Therefore as children play informally with colored objects and engage in activities such as drawing with crayons or markers or using paints, teachers can help them learn the names of colors and distinguish between them. Children should learn words such as shade, tint, dark, light, primary colors, and secondary colors.

Many materials are useful for explorations with color, including food coloring, water, different colors and kinds of paints, eggs, crayons, markers, colored pencils, colored cellophane, con- tainers, eyedroppers, ice cube trays, paint-chip sample cards, and color sticker dots.

Activities that promote learning about colors include these:

• Sorting and/or matching paint-chip cards (from hardware or paint store) within color groups

• Having a color scavenger hunt

• Making a set of colored water bottles that represent the three primary (red, blue, yel- low) and three secondary (orange, green, purple) colors

• Using paints, crayons, or markers to combine colors and mix them together

• Mixing multicultural paints to match exact skin tones among children

• Dyeing eggs

Science Concepts and Curriculum Activities Chapter 10

Magnetism Children are naturally attracted to the unique qualities of magnets and the invisible power they represent for attracting and repelling some objects but not others. Terminology appropri- ate for young children includes words such as force, magnet, repel, attract, pole, and metal (iron). Materials to include in the classroom for exploring magnets can be made available in interest centers for informal exploration as well as intentional activities with an experimen- tal approach to distinguish magnetic from nonmagnetic objects, note strength of magnetic force, and so on.

As children use magnets and metal and nonmetal objects of different kinds, concepts such as the following are supported:

• Magnets exert force and cause objects to move

• Only metal is magnetic

• Only certain kinds of metal are magnetic

• Magnets both attract and repel

• The earth has magnetic force

Discovery activities focus on providing assorted objects and different kinds of magnets; chil- dren can subsequently classify, graph, or label magnetic/nonmagnetic materials. Informal play with magnets can be set up, for example, by attaching magnets to the fronts of small metal cars and pulling them along a premade or improvised racetrack or attaching paper clips to cut- out paper fish and fishing with a magnet attached to the end of a string or line. Children could also use a magnet wand to move floating corks with an inserted straight pin in the water table. Although a bit on the abstract side as far as making symbolic geographic connections, young children can easily learn how to tell where “north” is with a compass and understand that magnetism is what makes the compass work.

Solids, Liquids, and Gases Basic concepts related to states of matter appropriate for young children include the following:

• Liquids assume the shape of their container

• Solids retain their shape

• Some solids dissolve in liquid; some do not

• Water changes form when frozen or boiled

• Liquids move at different speeds (viscosity)

• Air is a gas

• Adding liquid to a solid changes its properties

• Some objects float in water; some sink

Corresponding terminology includes the words liquid, solid, gas, volume, dissolve, and solu- tion. Different liquids (milk, juice, syrup, water), cornstarch, bubble wands, glycerin, dish soap, straws, blender, and empty soda bottles are all materials that can be kept on hand for explo- rations with solids, liquids, and gases. These activities should encourage children to do things like dropping marbles into different fluids to see how long they take to sink to the bottom or observing ice cubes as they melt in water.

Teachers can enlist children in mixing equal parts cornstarch and water, which confounds them as it exhibits properties of both solids and liquids at the same time. Making bubble

Science Concepts and Curriculum Activities Chapter 10

solution with glycerin and dishwashing liquid and then blowing bubbles with wands fasci- nates them, and the teacher can help them to understand that the air inside the bubble is trapped by a liquid “shell.” Children can also blow bubbles through a straw into milk, water, and syrup or pour these kinds of liquids back and forth to explore viscosity.

Making fruit smoothies demonstrates the principle of a suspension. Children can classify and label objects in the classroom as liquids or solids or have a liquid lunch, and they will certainly spend a great deal of time at the water table exploring the concepts of sinking and floating.

Weight, Force, and Motion Applying force to an object makes it move—a concept children employ every day as they push cars or blocks across the floor, draw with a crayon, or pedal a tricycle on the playground. Simple machines such as pulleys, gears, ramps, and levers are endlessly fascinating to children in their efforts to figure out what makes things work, as illustrated by the emergent investiga- tion example in Chapter 6.

Other important ideas are the concepts that moving air is called wind, friction occurs when one object moves over another and produces heat, objects fall down, moving water has force, and machines help people work in different ways. Vocabulary for young chil- dren includes pulley, cause/effect, push/ pull, force, motion (and names of motions such as roll, glide, fly, bounce), weight, balance, friction, and incline.

Many materials for learning about this ele- ment of physics are easily found in pre- school classrooms, such as wood planks in the block area, train track, marbles, wheeled toys, straws, and heavy paper. Other materials can include a balance, pulleys, pendulum, scooters, oscillating fan, rope, plunger or suction cups, clear plastic tubing, and cove molding.

Activities that help children learn about weight, force, and motion include:

• Using blocks and different types of materials to build ramps of different heights/ lengths; timing the speed of different kinds of objects rolled down and categorizing/ graphing them as fast/slow

• Setting up a clothesline pulley on the playground and using it to move objects

• Going on a ramp hunt throughout a building or neighborhood

• Building a marble maze with tubing

• Setting up an obstacle course for scooter races

• Using magnets to move objects underneath paper

• Tracking shadows over the course of a day on the playground

• Blowing objects across a flat surface with straws

• Tying crepe paper streamers to a fan

Many routine activities children engage in during the course of the day involve principles of physics, such as the push-pull forces at work during a game of tug of war.

Science Concepts and Curriculum Activities Chapter 10

• Having a tug of war

• Making paper airplanes and measuring how far they fly

• Applying suction cups to different surfaces

• Placing a cardboard box outside in the sun and drawing different colored chalk lines around its shadow at different hours during the day

Static Electricity Activities with static electricity help children learn that electricity has force and makes light. Children can easily produce a static electricity charge by rubbing a balloon on their hair, socks on a carpet, or a comb through their hair and then on a piece of wool. When they take a charged object such as a balloon and place it next to something very light, such as crisped rice cereal, they can observe the cereal pieces stick to the balloon. While we want children to be wary of the power of electricity so they don’t do things like putting an object into an electrical outlet, learning about static electricity can be both fun and harmless.

Life Science

Life science investigations focus on the study of living things and their habitats. It makes the most sense, in terms of concrete learning and consideration of prior experience, to begin the study of living things with those that are most relevant and in closest proximity to your set- ting. So, for example, if you live in a rural area, you might study farm animals and local crops; if you live on the coast, you might study ocean animals, reptiles, and beach grasses.

Important life science concepts for young children to learn include the facts that:

• All living things grow and change over time.

• Living things need food.

• When living things die, they decompose.

• Fossils are the remains of living things.

• Living organisms have systems that make them work.

• Living things inhabit and interact with different kinds of environments.

Plants Children learn about plants of different kinds with first-hand experience by growing, examin- ing, and observing them and using them for different purposes. Even in programs without enough outdoor space for a traditional garden, vegetables and flowers can be grown in containers or a terrarium, in window boxes, or from seed or bulbs in pots or trays in the class- room. Some plants grow in soil, others in sand, and some even in water. Children can observe the stages of growth from germination through the plant’s life cycle.

They can learn about how plants distribute nutrients by putting celery in water with food coloring and watching as the color moves through the stalk and leaves. They can measure growth, care for, draw, and photograph plants as they grow. In short, gardening provides many opportunities for learning. For example, Ms. Mary’s preschool class has a garden receiving varying amounts of sun/shade during the day; children wondered if all their bean plants would grow to the same height. This question led to a controlled experiment that continued over two months as children tracked the growth of plants mostly shaded and those mainly in the sun. These same children went to a nearby park and harvested bamboo

Science Concepts and Curriculum Activities Chapter 10

stalks which their teachers helped them fashion into trellises of different kinds to train their (pole) bean plants, eventually growing a “bean house” big enough to put a small table and chairs inside.

At the end of the school year, the children wondered aloud how big the weeds would become over the summer, so they were left unattended; to the children’s delight, when they returned in the fall they had a “forest” of weeds, through which they trampled paths. They made “houses” and “forts” in this forest and enjoyed it for several weeks before pulling it out

to begin a new garden. Finally, these children wondered what would happen to a pumpkin they had carved if they left it in the garden. Over the entire winter they documented its decomposition until it eventually hardened into a petrified, shrunken shell.

Children love flowers and can collect, press, dissect, and classify them by color, petal type, etc. They can sort and classify seeds, pods, and leaves; make collages or rubbings of dif- ferent kinds of plants; cut or slice vegetables and fruits; and make prints to compare shapes and characteristics.

Similarly, to learn about trees, a “tree cookie” (cross-sectional slice of a tree trunk) provides opportunities to measure circumference and count rings. Planting or adopting a tree in a city park or finding and photographing the oldest tree in the community helps children begin to understand the long-term invest- ment that trees represent. If there is a tree on the playground, to help them learn how trees experience changes over time, children can collect all the twigs that fall from it for a month; they can press leaves between sheets of wax paper or assemble photographs of the tree taken at different times of the year.

Animals One organized approach to the study of ani-

mals is by habitat—sea, farm, jungle, desert, mountains, etc. As with plants, learning about animals can be a hands-on experience. Indoors, activities such as incubating eggs; taking care of a class pet, aquarium, or ant farm; and dissecting owl pellets all offer opportunities for children to observe the life cycle. There are also many activities for the outdoors, such as planting milkweed to attract monarch butterflies, installing a bird feeder on the playground, or doing a pond study to observe the stages of life. National Geographic offers crittercams at different global locations that enable children to observe wild animals in their natural sur- roundings in real time.

Gardening activities are intrinsically satisfying to chil- dren and a means to help them connect to the earth and learn many concepts related to plants, seasons, the life cycle, and sustainability.

Science Concepts and Curriculum Activities Chapter 10

Children can practice close observation skills by examining insect specimens or making them with bugs they catch or find themselves. They can apply what they learn to sort and classify plastic toy animals and construct habitats for them; they can also make collections of animal pictures and then match them in different ways, such as baby and adult animals.

The Human Body Young children should certainly begin learning about the human body and can begin acquir- ing names for its various parts when they are toddlers, while they learn other words. Children can paint or trace their feet and hands and draw outlines of the body, or they can play games that involve the identification of body parts, such as “pin the body part,” with cutouts and a life-size paper figure. The light table or overhead projector can serve as a means for viewing x-rays, and a shadow box will enable children to draw silhouettes. Many teachers measure, weigh, and photograph children regularly and keep a growth chart or book in the classroom as well as a record of lost teeth.

Earth Science

Children need go no farther than outside the classroom door to encounter earth science. As natural collectors, they love to pick up, examine, collect, and sort rocks. They dig and play in the dirt. They are fascinated by weather, seasonal changes and by clouds, the stars, the sun, and the moon. Children who live near or visit the Great Lakes, the Gulf of Mexico, or the Atlantic or Pacific Oceans see the effects of tides and waves. Children who live near the great American deserts watch the sand blow and explore dunes and rock formations. They see the effects of earthquakes, volcanoes, hurricanes, and tornadoes on television.

Earth science represents all the mysterious and enormous forces that affect the rhythm of life. Children fall in love with the earth and want to take care of it, so recycling and efforts to solve environmental problems make sense to them.

One of the challenges of earth science is that some topics, like astronomy, are very difficult for adults, let alone children, to grasp. Some earth science tools, such as the satellite imagery that guides our weather forecasting, also require an understanding of a bird’s-eye perspec- tive, which children have not yet acquired. Thus learning about the solar system, for example, outside of the heavenly bodies that are directly observable, is really not developmentally appropriate for young children. What we can do is focus children’s curiosity on observation, hands-on investigation of the elements of earth that are accessible, and work on the develop- ment of environmentally responsible attitudes and dispositions.

Basic concepts important to earth science for young children include the following:

• Earth is the place where all living things (that we know about) reside

• The earth is very big

• The earth is constantly changing

• The earth is made of different kinds of materials, including dirt, rocks, minerals, air, and water

• The sun and moon affect the earth in different ways

Experts and researchers are placing increasing emphasis on creating outdoor environments that connect children to the natural world. (Bronson & Merryman, 2009; Wirth & Rosenow, 2012). While some educators assume they don’t have the time or resources to do so, there

Science Concepts and Curriculum Activities Chapter 10

are many ways to add opportunities for access to nature to an existing playground, such as raised-bed or container planters, a rain barrel, composting bin, weather observation tools, and natural materials (e.g., dirt, logs, etc.). In addition, a growing number of print and online resources are available to teachers who want to promote learning about the natural world (see the reference list at the end of this chapter).

Dirt, Earth, and Rocks Concepts and terminology about dirt, earth, and rocks include soil, composition, erosion, hardness, and variety. Children can learn what is in dirt by digging up a square foot of soil, screening it, and examining everything they find. They can collect samples from different areas on the playground or in the neighbor- hood and compare them with their original sample. Creating a worm bed or allowing children to run a hose in the sandbox or sand table to create water channels allows them to see the effects of erosion.

Children should be encouraged to collect, sort, weigh, measure, and label rocks and stones. They can examine them in different

ways, including putting them between layers of heavy paper or canvas and breaking them apart with a hammer (using safety goggles). Children also enjoy creating displays; they can fill jars with rocks, lay them out in trays or on shelves, or place them in a display case.

At the program where the author works, the children helped dig out and create a rock pond which we filled with rocks instead of water. It provides endless hours of fascination as the children enjoy bringing new ones to add to the pond, washing the rocks, wetting them with squirt guns or the hose to see them change colors, and taking them out and rearranging them periodically.

Air, Wind, and Weather As children experience the natural elements daily, concepts about air, wind, and weather are very relevant and real to them. Terms that represent concepts young children can learn and use include wind, evaporation, condensation, conditions, cloud, fog, rain, snow, sleet, hail, change, season (spring, summer, fall, winter), and prediction.

To explore the effects of wind, children can make pinwheels or observe a windsock or stream- ers on the playground to determine its direction and strength. To investigate evaporation, they can dissolve salt in water and use squirt bottles to spray on paper, leave outside or overnight and observe residue. They also enjoy painting with water on the walls or sidewalks and watch- ing the water disappear as it dries. Putting a mirror or other objects in the freezer and then taking them out is a way to observe condensation.

Children seem naturally drawn to rocks and fasci- nated by their individual characteristics, weight, hardness, colors, and textures.

Science Concepts and Curriculum Activities Chapter 10

Daily monitoring and weather reporting with children should focus on applying observa- tions to meaningful applications, such as decisions about appropriate clothing for outdoor play, when the garden needs watering, interpreting signals such as gathering dark clouds or a drop in temperature to predict how the weather might be changing, and observing sea- sonal changes. A simple clear plastic rain gauge and outdoor thermometer can provide data that children will be able to track on a calendar or chart. They can also choose a spot on the playground or in the neighborhood and photograph it monthly to observe seasonal changes over time.

Many communities have TV weather personnel willing to visit or host children and interactive materials to promote interest in weather reporting and forecasting. Many teachers plan sea- sonal units or explorations that focus on clothing, activities, foods, holidays, and weather to help children understand the influence of these annual cycles on our daily lives.

Environmental Stewardship Recycling is a concrete activity that develops math and science concepts such as sorting, classifying, and identifying different kinds of materials. It is difficult, however, for children to understand the more abstract concept about how recycling and other kinds of conservation efforts represent responsible environmental stewardship, sustainability, and reducing waste. Therefore it is helpful to establish routines and do activities with children that begin to build those connections.

For example, in the program directed by the author, children have been engaged in recycling classroom materials for many years. Children in each class take turns bringing a small con- tainer to the recycling center at the end of the day and sorting its contents to the bins for paper, cardboard, plastic, and metal. In the past year, we decided to reduce the number of consumable cups used by providing an individual water bottle for each child and installing a drinking fountain on the playground.

In addition to the composting bin in the garden, a rainwater collection system with two fifty- gallon barrels was also established. To help children understand how these measures would reduce waste, we involved them in:

• Counting all the paper cups recycled in a week on the playground before installation of the drinking fountain.

• Collecting and measuring water used as the teacher brushed her teeth with the water running and brushed them again with the faucet turned off to estimate how much water could be saved (several gallons per person!). Counting how many watering cans we were able to fill and use for daily watering before needing the garden hose after the first rainstorm filled the water barrels.

Many American educators are inspired by the Reggio Emilia concept of remida—using recy- cled materials for aesthetic purposes (Ferrari & Giacopino, 2005). There are many online and print resources with ideas for using recycled materials for arts, crafts, and other activities. Teachers in the program described above have, for instance, saved soda can pop tops and then used them to make holiday wreaths and jewelry. They have also permanently installed a wooden frame on the playground on which children hang painted or decorated found items such as pine cones, cast-off puzzle pieces, old compact discs, and festival beads. Children learned how to make paper from recycled cardboard and constructed a large permanent painted sculpture from cast-off boxes and packing containers.

Posttest Chapter 10

Chapter Summary • Cognitive development occurs as children accumulate and reorganize experiences and

begin to apply logical reasoning to solve problems through application of their under- standing of patterns, relationships, and cause and effect.

• Children develop and adapt concepts in a continual cycle of assimilation and accom- modation in response to experiences and interactions.

• Teachers promote cognitive development by facilitating the acquisition and processing of physical, logicomathematical, and social-conventional knowledge.

• Teachers support knowledge acquisition by providing interesting materials, fostering cognitive conflict, encouraging children to think about their thinking, and modeling collaborative problem solving.

• Mathematics and the sciences for children share a focus on inquiry, problem solving, and the development of critical thinking skills through processes and practices that engage them in hands-on explorations.

• Mathematics and science standards differ in the specific content and ways strategies are applied to solve problems.

• Mathematics standards focus on number and operations, algebra, geometry, measure- ment, and data/probability. Each strand of the standards emphasizes important con- cepts that build on one another.

• Teachers apply their knowledge of how mathematical thinking develops and direct observations of children to facilitate informal learning through play and planning appropriate mathematics activities as children are ready for them.

• Science standards address physical, life, earth science, and technology. Science activi- ties for young children engage them in observation of and interaction with the natural world and phenomena that they can experience at first hand through their senses.

• Teachers promote scientific thinking by involving children in systematic investigations of phenomena and objects with questions that focus on questions like “What’s wrong here?” “What happened here?” “What proof do you have?”

Posttest

1. The preoperational stage of cognitive development is characterized by:

a. Abstract reasoning, problem solving, and symbolic representation.

b. The ability to solve abstract problems but only with concrete materials.

c. Purely reflexive response to tactile and visual stimulation.

d. Egocentrism and the inability to conserve mentally.

2. The relationship between the mental processes of assimilation and accommodation is best described by the following:

a. Assimilation and accommodation are equally complex.

b. Assimilation is a more complex process than accommodation.

c. Accommodation is a more complex process than assimilation.

d. Assimilation must occur before accommodation can take place.

3. Three kinds of interrelated cognitive knowledge include:

Posttest Chapter 10

a. Physical, social, and psychological knowledge.

b. Social, logicomathematical, and scientific knowledge.

c. Mathematical, verbal, and scientific knowledge.

d. Physical, logicomathematical, and social knowledge.

4. Teachers foster cognitive conflict when they:

a. Introduce a discrepant event that challenges children’s current level of thinking and motivates them to experiment and test their theories.

b. Put children in situations where they are likely to begin quarreling or fighting.

c. Provide children with the answers to their questions in language they can’t understand.

d. Refuse to provide children with any answers to their questions, so they have to find out everything for themselves.

5. Mathematical processes and scientific practices represent:

a. Concepts articulated in the national standards that are discrete, highly specific to each subject, and thus not integrated.

b. Skills articulated in the national standards that are interrelated across both disciplines.

c. Concepts that become increasingly complex as children grow older and gain more experience.

d. Skills not developmentally appropriate for preschoolers or children in the primary grades.

6. Mathematical processes and scientific practices focus on how children:

a. Learn and apply concepts.

b. Learn to be responsible.

c. Learn to memorize large amounts of material.

d. Learn to solve social conflicts.

7. The growth of mathematical thinking is best described as:

a. The ability to recite numbers from 1 to 100 before the age of 4.

b. Acquisition of concepts in no particular order but synthesized in very particular and distinct ways.

c. The integration and application of increasingly complex concepts to solve problems.

d. A process that does not occur until children have progressed to the concrete opera- tional stage of thinking.

8. Which of the following sequences best represents acquisition of number sense?

a. Rote counting, operations, rational counting.

b. Rote counting, rational counting, operations.

c. Operations, rational counting, rote counting.

d. Rational counting, rote counting, operations.

9. Informal science learning occurs daily as children:

Science Resources Chapter 10

a. Create controlled experiments with the help of the teacher.

b. Methodically record observations during circle time about plants growing in the classroom.

c. Explore, observe, and pose questions about their surroundings during play.

d. Correctly order a sequence of pictures displaying the steps of an investigation.

10. Experiences with physical science for young children help them learn about:

a. The observable characteristics of organisms.

b. Natural forces such as gravity, magnetism, light, and speed.

c. Air, wind, and weather.

d. Environmental sustainability.

Answers: 1 (d); 2 (c); 3 (d); 4 (a); 5 (b); 6 (a); 7 (c); 8 (b); 9 (c); 10 (b)

Discussion Questions

1. Identify and explain three examples of things toddlers might do that indicate they are assimilating or accommodating new information.

2. Many adults have “math phobia” due to negative experiences with learning mathemat- ics as children. How will you use the information in this chapter to promote enthusiasm and a love for mathematics with young children?

3. Time devoted specifically to a science curriculum is often limited in primary classrooms. What are some examples of ways you might integrate science learning across the curriculum?

Answers and Rejoinders to Chapter Pretest

1. False. Infants begin learning at (or prior to) birth.

2. True. Bloom’s taxonomy describes everyday terminology that characterizes increasingly higher levels of thinking.

3. False. PreK-2 children are in the preoperational stages of thinking and mathematics focuses on foundational concepts that eventually lead to abstract reasoning.

4. False. Young children need hands-on experiences with concrete materials, objects, and processes to develop mathematics and science concepts.

5. True. Science focuses on the art of asking questions and structuring investigations to find answers.

Science Resources

The Exploratorium in San Francisco: https://www.exploratorium.edu/

EPA site for recycle city: https://www3.epa.gov/recyclecity/

Science for Preschoolers: http://scienceforpreschoolers.com/

PBS Learning Media, Science and Engineering: https://pbslearningmedia.org/science/

Teach Preschool Science: http://www.teachpreschoolscience.com/index.html

https://www.exploratorium.edu/

https://www3.epa.gov/recyclecity/

http://scienceforpreschoolers.com/

https://pbslearningmedia.org/science/

http://www.teachpreschoolscience.com/index.html

Key Terms Chapter 10

NASA Kids' Club: https://www.nasa.gov/kidsclub/index.html

Geography4kids: http://www.geography4kids.com/

Geography and Geology for Kids: http://www.kidsgeo.com/

Earth for Kids: http://www.sciencekids.co.nz/earth.html

NWS: http://www.weather.gov/

The Science Spot, Kid Zone: http://sciencespot.net/Pages/kidzone.html

Key Terms

Accommodation Adapting existing schema

Algorithm In algebra, a formula, or series of steps for problem solving

Animism Tendency to attribute human characteristics to animals

Assimilation Accepting new stimuli as consistent with existing schema

Bloom’s taxonomy Benjamin Bloom’s 1956 hierarchy of critical thinking skills

Centering Focusing on one attribute of an object to the exclusion of others

Concrete operations Stage of development (from ages 7 to 11) when children can per- form abstract operations with the assistance of concrete objects

Conservation Understanding that changing the arrangement of objects does not change the quantity (number, length) or that changing the size of a container does not affect the volume

Discrepant event An experience that causes disequilibrium, prompting the brain to adapt existing schema to accommodate to the new experience

Discrete quantities Amounts that are counted

Disequilibrium A state of mental imbalance when existing schema do not match a new experience

Egocentric Cognitive characteristic of children in the preoperational period who are not yet able to understand the concept of multiple perspectives

Equilibrium State of intellectual balance between the self and world

Guided discovery Providing scaffolding rather than direct instruction to promote learning

Informal mathematical knowledge Learning that takes place through daily experience and play

Linear measure Measuring length, width, distance

Logicomathematical knowledge Mentally constructed relationships

Magical thinking Irrational beliefs about why things occur

https://www.nasa.gov/kidsclub/index.html

http://www.geography4kids.com/

http://www.kidsgeo.com/

http://www.sciencekids.co.nz/earth.html

http://www.weather.gov/

http://sciencespot.net/Pages/kidzone.html

References Chapter 10

Nonstandard measurement Using unconventional means for measuring, such as paper clips or string

Number The idea or concept of quantity

Numeral The graphic symbol for a discrete quantity

Number sense Intuitive sense about quantity

One-to-one correspondence Understanding that each number represents one and only one quantity

Operations Processes used for solving mathematical problems

Order irrelevance The fact that counting in any order does not change quantity

Ordering Putting items into a series

Ordinal numbers Numbers expressed in terms of sequence, as first, second, third

Pattern Repeating series

Physical knowledge Concepts based on observable properties of objects and phenomena

Practice skills Specific activities defined in science standards that are associated with scien- tific inquiry

Process skills Skills used in mathematics to solve problems and think mathematically

Rational counting In counting, associating each number with the corresponding quantity

Rote counting Reciting numbers without knowing what they represent

Schema Mental construct of a single idea

Science/engineering practices Comparable to math process skills; methods and pro- cesses used for science inquiry

Social-conventional knowledge Concepts based on arbitrary understandings determined by groups of people, societies, or cultures

Seriation Comparing multiple items in a set and ordering them by logical sequence

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