Cognitive Development, Mathematics, and Science Learnin

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

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.
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.
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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50
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35
30
25
20
15
10
5
12
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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
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)
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40
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30
25
20
15
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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
grouping, sets,
base ten
operations
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
recognition,
matching, shape
Pegboards Numeral
recognition,
quantity,
matching,
counting
Matching

numeral and
quantity cards
Numeral
recognition,
counting
numerals
Magnetic
numerals
Numeral
recognition,
counting
sense
Beads Sorting,
patterns, shape
relations
spatial relations,
patterns
classification,
patterns
relations, sorting

matching, shape
patterns, spatial
relations
relations,
patterns, sorting
sorting,
classification
recognition,
measuring clock
time
time, numeral
recognition
Teaching clock
(movable hands)
Analog time
measurement,
numeral
recognition
(weighing),
comparing

Measurement
containers
Measuring
volume,
comparing,
conservation
Calculator Numeral
recognition,
operations,
technology
11
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six
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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
grouping, sets,
base ten
operations
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
recognition,
matching, shape
Pegboards Numeral
recognition,
quantity,
matching,
counting
Matching
numeral and
quantity cards
Numeral
recognition,
counting
numerals
Magnetic
numerals

Numeral
recognition,
counting
sense
Beads Sorting,
patterns, shape
relations
spatial relations,
patterns
classification,
patterns
relations, sorting
matching, shape
patterns, spatial
relations
relations,
patterns, sorting

sorting,
classification
recognition,
measuring clock
time
time, numeral
recognition
Teaching clock
(movable hands)
Analog time
measurement,
numeral
recognition
(weighing),
comparing
Measurement
containers
Measuring
volume,
comparing,
conservation
Calculator Numeral
recognition,

operations,
technology
(continued)
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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
grouping, sets,
base ten
operations
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
recognition,
matching, shape
Pegboards Numeral
recognition,
quantity,
matching,
counting
Matching
numeral and
quantity cards
Numeral
recognition,
counting
numerals
Magnetic
numerals
Numeral
recognition,
counting

sense
Beads Sorting,
patterns, shape
relations
spatial relations,
patterns
classification,
patterns
relations, sorting
matching, shape
patterns, spatial
relations
relations,
patterns, sorting
sorting,
classification

recognition,
measuring clock
time
time, numeral
recognition
Teaching clock
(movable hands)
Analog time
measurement,
numeral
recognition
(weighing),
comparing
Measurement
containers
Measuring
volume,
comparing,
conservation
Calculator Numeral
recognition,
operations,
technology

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
grouping, sets,
base ten
operations
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
recognition,
matching, shape
Pegboards Numeral

recognition,
quantity,
matching,
counting
Matching
numeral and
quantity cards
Numeral
recognition,
counting
numerals
Magnetic
numerals
Numeral
recognition,
counting
sense
Beads Sorting,
patterns, shape
relations
spatial relations,
patterns

classification,
patterns
relations, sorting
matching, shape
patterns, spatial
relations
relations,
patterns, sorting
sorting,
classification
recognition,
measuring clock
time
time, numeral
recognition
Teaching clock
(movable hands)
Analog time
measurement,

numeral
recognition
(weighing),
comparing
Measurement
containers
Measuring
volume,
comparing,
conservation
Calculator Numeral
recognition,
operations,
technology
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.
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.”
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.
F10.04_ECE311
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.

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
© Photodisc / Thinkstock

Cooking is an example of an activity that integrates
both mathematics and science skills.
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).
© Getty Images / Thinkstock
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/
Mathematics Concepts and Curricular Activities Chapter 10
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
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.

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 cor rect.
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 al so

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
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.
© Monkey Business / Thinkstock
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.
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.
© Imagebroker.net / SuperStock
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).

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
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.

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

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

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?
© N.E. Miles Early Childhood Development Center /
College of Charleston
As children painted the model, they

tried to replicate patterns they had
observed in many photographs of
pythons.
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
© iStockphoto / Thinsktock
Children learn to count change in mean-
ingful activities that they can relate to
real-life transactions.
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 possi ble
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 investigatio n 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.
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 sugges tions
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
© Design Pics / SuperStock
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.
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
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 nonma gnetic 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 liqui ds at the
same time. Making bubble
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

© Goodshoot / Thinkstock
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.
• 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
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.

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
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.

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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There are several early childhood curriculum activities that
support the development of cognitive processes, science
knowledge, and math knowledge. In Chapter 10 of your text,
Jaruszewicz (2019) offers an explanation of these areas of
development and ideas for educators and families to support
these areas. You will use the knowledge you have gained from
Chapter 10 and this week’s required readings to further
elaborate on the ideal classroom you created in Week 2 of this
course. Your elaboration will focus specifically on the subjects
of science, technology, engineering, and math (STEM).
To prepare for this discussion,

· Read Chapter 10: Cognitive Development, Mathematics, and
Science.
· Review the resources Why Is STEM Education so
Important? (Links to an external site.), Kids in STEM: Science,
Technology, Engineering, and Math (Links to an external site.),
and Preschool STEM Activities (Links to an external site.).
Review the classroom you designed in Week 2 of class,
considering the feedback you received from your instructor.
For your initial post:
· Explain your ideal STEM classroom. Your description must
include:
· A list of specific materials your STEM classroom will have.
· A specific activity that teaches/reinforces each STEM
component:
· One activity that incorporates science
· One activity that incorporates technology
· One activity that incorporates engineering and
· One activity that incorporates math
· A description of how your activities and/or classroom is
aligned to standards (these can be your state standards and/or
NAEYC standards previously covered in Week 1 of class).

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