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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.

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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.

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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.

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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.

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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.

F10.01_ECE311

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.

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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?”

© Photodisc / Thinkstock

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

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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.

© Stockbyte / Thinkstock

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

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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.

11 one

6 six

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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)

© 2019 Bridgepoint Education, Inc. All rights reserved. Not for resale or redistribution.

Promoting Cognitive Development Chapter 10

11 one

6 six

0 55

50

45

40

35 30

25

20

15

10

5 12

6

3

4

2 1

57 8

9

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

50

45

40

35 30

25

20

15

10

5 12

6

3

4

2 1

57 8

9

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)

© 2019 Bridgepoint Education, Inc. All rights reserved. Not for resale or redistribution.

Promoting Cognitive Development Chapter 10

11 one

6 six

0 55

50

45

40

35 30

25

20

15

10

5 12

6

3

4

2 1

57 8

9

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,

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