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4
Dimension 2
CROSSCUTTING CONCEPTS
Some important themes pervade science, mathematics, and technology and appear over
and over again, whether we are looking at an ancient civilization, the human body, or a
comet. They are ideas that transcend disciplinary boundaries and prove fruitful in expla-
nation, in theory, in observation, and in design.
—American Association for the Advancement of Science [1].
I
n this chapter, we describe concepts that bridge disciplinary boundaries, having
explanatory value throughout much of science and engineering. These crosscut-
ting concepts were selected for their value across the sciences and in engineer-
ing. These concepts help provide students with an organizational framework for
connecting knowledge from the various disciplines into a coherent and scientifi-
cally based view of the world.
Although crosscutting concepts are fundamental to an understanding of sci-
ence and engineering, students have often been expected to build such knowledge
without any explicit instructional support. Hence the purpose of highlighting them
as Dimension 2 of the framework is to elevate their role in the development of
standards, curricula, instruction, and assessments. These concepts should become
common and familiar touchstones across the disciplines and grade levels. Explicit
reference to the concepts, as well as their emergence in multiple disciplinary con-
texts, can help students develop a cumulative, coherent, and usable understanding
of science and engineering.
Although we do not specify grade band endpoints for the crosscutting
concepts, we do lay out a hypothetical progression for each. Like all learning
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in science, students’ facility with addressing these concepts and related topics at
any particular grade level depends on their prior experience and instruction. The
research base on learning and teaching the crosscutting concepts is limited. For
this reason, the progressions we describe should be treated as hypotheses that
require further empirical investigation.
SEVEN CROSSCUTTING CONCEPTS OF THE FRAMEWORK
The committee identified seven crosscutting scientific and engineering concepts:
1. Patterns. Observed patterns of forms and events guide organization and
classification, and they prompt questions about relationships and the fac-
tors that influence them.
2. Cause and effect: Mechanism and explanation. Events have causes,
sometimes simple, sometimes multifaceted. A major activity of science
is investigating and explaining causal relationships and the mechanisms
by which they are mediated. Such mechanisms can then be tested across
given contexts and used to predict and explain events in new contexts.
3. Scale, proportion, and quantity. In considering phenomena, it is critical
to recognize what is relevant at different measures of size, time, and ener-
gy and to recognize how changes in scale, proportion, or quantity affect
a system’s structure or performance.
4. Systems and system models. Defining the system under study—specify-
ing its boundaries and making explicit a model of that system—provides
tools for understanding and testing ideas that are applicable throughout
science and engineering.
5. Energy and matter: Flows, cycles, and conservation. Tracking fluxes of
energy and matter into, out of, and within systems helps one understand
the systems’ possibilities and limitations.
6. Structure and function. The way in which an object or living thing is
shaped and its substructure determine many of its properties and
functions.
7. Stability and change. For natural and built systems alike, conditions of
stability and determinants of rates of change or evolution of a system are
critical elements of study.
This set of crosscutting concepts begins with two concepts that are funda-
mental to the nature of science: that observed patterns can be explained and that
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science investigates cause-and-effect relationships by seeking the mechanisms that
underlie them.
The next concept—scale, proportion, and quantity—concerns the sizes of
things and the mathematical relationships among disparate elements.
The next four concepts—systems and system models, energy and matter
flows, structure and function, and stability and change—are interrelated in that
the first is illuminated by the other three. Each concept also stands alone as one
that occurs in virtually all areas of science and is an important consideration for
engineered systems as well.
The set of crosscutting concepts defined here is similar to those that
appear in other standards documents, in which they have been called “unifying
concepts” or “common themes” [2-4]. Regardless of the labels or organizational
schemes used in these documents, all of them stress that it is important for stu-
dents to come to recognize the concepts common to so many areas of science
and engineering.
Patterns
Patterns exist everywhere—in regularly occurring shapes or structures and in
repeating events and relationships. For example, patterns are discernible in the
symmetry of flowers and snowflakes, the cycling of the seasons, and the repeated
base pairs of DNA. Noticing patterns is often a first step to
organizing and asking scientific questions about why and
how the patterns occur.
One major use of pattern recognition is in classifica-
tion, which depends on careful observation of similarities
and differences; objects can be classified into groups on the
basis of similarities of visible or microscopic features or on
the basis of similarities of function. Such classification is
useful in codifying relationships and organizing a multitude
of objects or processes into a limited number of groups.
Patterns of similarity and difference and the resulting clas-
sifications may change, depending on the scale at which a
phenomenon is being observed. For example, isotopes of a
given element are different—they contain different numbers
of neutrons—but from the perspective of chemistry they
can be classified as equivalent because they have identical patterns of chemical
interaction. Once patterns and variations have been noted, they lead to questions;
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❚ Scientists seek explanations for observed patterns and for the
similarity and diversity within them. Engineers often look for and
❚
analyze patterns, too.
scientists seek explanations for observed patterns and for the similarity and diver-
sity within them. Engineers often look for and analyze patterns, too. For example,
they may diagnose patterns of failure of a designed system under test in order
to improve the design, or they may analyze patterns of daily and seasonal use of
power to design a system that can meet the fluctuating needs.
The ways in which data are represented can facilitate pattern recognition
and lead to the development of a mathematical representation, which can then be
used as a tool in seeking an underlying explanation for what causes the pattern to
occur. For example, biologists studying changes in population abundance of sev-
eral different species in an ecosystem can notice the correlations between increases
and decreases for different species by plotting all of them on the same graph and
can eventually find a mathematical expression of the interdependences and food-
web relationships that cause these patterns.
Progression
Human beings are good at recognizing patterns; indeed, young children begin to
recognize patterns in their own lives well before coming to school. They observe,
for example, that the sun and the moon follow different patterns of appearance
in the sky. Once they are students, it is important for them to develop ways
to recognize, classify, and record patterns in the phenomena they observe. For
example, elementary students can describe and predict the patterns in the sea-
sons of the year; they can observe and record patterns in the similarities and
differences between parents and their offspring. Similarly, they can investigate
the characteristics that allow classification of animal types (e.g., mammals, fish,
insects), of plants (e.g., trees, shrubs, grasses), or of materials (e.g., wood, rock,
metal, plastic).
These classifications will become more detailed and closer to scientific
classifications in the upper elementary grades, when students should also begin
to analyze patterns in rates of change—for example, the growth rates of plants
under different conditions. By middle school, students can begin to relate patterns
to the nature of microscopic and atomic-level structure—for example, they may
note that chemical molecules contain particular ratios of different atoms. By high
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school, students should recognize that different patterns may be observed at each
of the scales at which a system is studied. Thus classifications used at one scale
may fail or need revision when information from smaller or larger scales is intro-
duced (e.g., classifications based on DNA comparisons versus those based on vis-
ible characteristics).
Cause and Effect: Mechanism and Prediction
Many of the most compelling and productive questions in science are about why
or how something happens. Any tentative answer, or “hypothesis,” that A causes
B requires a model for the chain of interactions that connect A and B. For exam-
ple, the notion that diseases can be transmitted by a person’s touch was initially
treated with skepticism by the medical profession for lack of a plausible mecha-
nism. Today infectious diseases are well understood as being transmitted by the
passing of microscopic organisms (bacteria or viruses) between an infected person
and another. A major activity of science is to uncover such causal connections,
often with the hope that understanding the mechanisms will enable predictions
and, in the case of infectious diseases, the design of preventive measures, treat-
ments, and cures.
Repeating patterns in nature, or events that occur together with regular-
ity, are clues that scientists can use to start exploring causal, or cause-and-effect,
relationships, which pervade all the disciplines of science and at all scales. For
example, researchers investigate cause-and-effect mechanisms in the motion of
a single object, specific chemical reactions, population changes in an ecosys-
tem or a society, and the development of holes in the polar ozone layers. Any
application of science, or any engineered solution to a problem, is dependent on
understanding the cause-and-effect relationships between events; the quality of
the application or solution often can be improved as knowledge of the relevant
relationships is improved.
Identifying cause and effect may seem straightforward in simple cases, such
as a bat hitting a ball, but in complex systems causation can be difficult to tease
out. It may be conditional, so that A can cause B only if some other factors are
in place or within a certain numerical range. For example, seeds germinate and
produce plants but only when the soil is sufficiently moist and warm. Frequently,
causation can be described only in a probabilistic fashion—that is, there is some
likelihood that one event will lead to another, but a specific outcome cannot be
guaranteed. For example, one can predict the fraction of a collection of identical
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atoms that will undergo radioactive decay in a certain period but not the exact
time at which a given atom decays.
One assumption of all science and engineering is that there is a limited and
universal set of fundamental physical interactions that underlie all known forces
and hence are a root part of any causal chain, whether in natural or designed sys-
tems. Such “universality” means that the physical laws underlying all processes are
the same everywhere and at all times; they depend on gravity, electromagnetism,
or weak and strong nuclear interactions. Underlying all biological processes—the
inner workings of a cell or even of a brain—are particular physical and chemical
processes. At the larger scale of biological systems, the universality of life mani-
fests itself in a common genetic code.
Causation invoked to explain larger scale systems must be consistent with
the implications of what is known about smaller scale processes within the system,
even though new features may emerge at large scales that cannot be predicted
from knowledge of smaller scales. For example, although knowledge of atoms is
not sufficient to predict the genetic code, the replication of genes must be under-
stood as a molecular-level process. Indeed, the ability to model causal processes
in complex multipart systems arises from this fact; modern computational codes
incorporate relevant smaller scale relationships into the model of the larger sys-
tem, integrating multiple factors in a way that goes well beyond the capacity of
the human brain.
In engineering, the goal is to design a system to cause a desired effect, so
cause-and-effect relationships are as much a part of engineering as of science.
Indeed, the process of design is a good place to help students begin to think in
terms of cause and effect, because they must understand the underlying causal
relationships in order to devise and explain a design that can achieve a speci-
fied objective.
One goal of instruction about cause and effect is to encourage students to
see events in the world as having understandable causes, even when these causes
are beyond human control. The ability to distinguish between scientific causal
claims and nonscientific causal claims is also an important goal.
Progression
In the earliest grades, as students begin to look for and analyze patterns—whether
in their observations of the world or in the relationships between different quanti-
ties in data (e.g., the sizes of plants over time)—they can also begin to consider
what might be causing these patterns and relationships and design tests that gather
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more evidence to support or refute their ideas. By the upper elementary grades,
students should have developed the habit of routinely asking about cause-and-
effect relationships in the systems they are studying, particularly when something
occurs that is, for them, unexpected. The questions “How did that happen?” or
“Why did that happen?” should move toward “What mechanisms caused that to
happen?” and “What conditions were critical for that to happen?”
In middle and high school, argumentation starting from students’ own
explanations of cause and effect can help them appreciate standard scientific
theories that explain the causal mechanisms in the systems under study. Strategies
for this type of instruction include asking students to argue from evidence when
attributing an observed phenomenon to a specific cause. For example, students
exploring why the population of a given species is shrinking will look for evidence
in the ecosystem of factors that lead to food shortages, overpredation, or other
factors in the habitat related to survival; they will provide an argument for how
these and other observed changes affect the species of interest.
Scale, Proportion, and Quantity
In thinking scientifically about systems and processes, it is essential to recognize
that they vary in size (e.g., cells, whales, galaxies), in time span (e.g., nanoseconds,
hours, millennia), in the amount of energy flowing through them (e.g., lightbulbs,
power grids, the sun), and in the relationships between the scales of these differ-
ent quantities. The understanding of relative magnitude is only a starting point.
As noted in Benchmarks for Science Literacy, “The large idea is that the way in
which things work may change with scale. Different aspects of nature change at
different rates with changes in scale, and so the relationships among them change,
too” [4]. Appropriate understanding of scale relationships is critical as well to
engineering—no structure could be conceived, much less constructed, without the
engineer’s precise sense of scale.
From a human perspective, one can separate three major scales at which
to study science: (1) macroscopic scales that are directly observable—that is,
what one can see, touch, feel, or manipulate; (2) scales that are too small or fast
to observe directly; and (3) those that are too large or too slow. Objects at the
atomic scale, for example, may be described with simple models, but the size of
atoms and the number of atoms in a system involve magnitudes that are difficult
to imagine. At the other extreme, science deals in scales that are equally dif-
ficult to imagine because they are so large—continents that move, for example,
and galaxies in which the nearest star is 4 years away traveling at the speed of
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light. As size scales change, so do time scales. Thus, when considering large enti-
ties such as mountain ranges, one typically needs to consider change that occurs
over long periods. Conversely, changes in a small-scale system, such as a cell, are
viewed over much shorter times. However, it is important to recognize that pro-
cesses that occur locally and on short time scales can have long-term and large-
scale impacts as well.
In forming a concept of the very small and the very large, whether in space
or time, it is important to have a sense not only of relative scale sizes but also of
what concepts are meaningful at what scale. For example, the concept of solid
matter is meaningless at the subatomic scale, and the concept that light takes time
to travel a given distance becomes more important as one considers large distances
across the universe.
Understanding scale requires some insight into measurement and an ability
to think in terms of orders of magnitude—for example, to comprehend the dif-
ference between one in a hundred and a few parts per billion. At a basic level, in
order to identify something as bigger or smaller than something else—and how
much bigger or smaller—a student must appreciate the units used to measure it
and develop a feel for quantity.
The ideas of ratio and proportionality as used in science can extend and
challenge students’ mathematical understanding of these concepts. To appreci-
ate the relative magnitude of some properties or processes, it may be necessary to
grasp the relationships among different types of quantities—for example, speed as
the ratio of distance traveled to time taken, density as a ratio of mass to volume.
This use of ratio is quite different than a ratio of numbers describing fractions of
a pie. Recognition of such relationships among different quantities is a key step in
forming mathematical models that interpret scientific data.
Progression
The concept of scale builds from the early grades as an essential element of under-
standing phenomena. Young children can begin understanding scale with objects,
space, and time related to their world and with explicit scale models and maps.
They may discuss relative scales—the biggest and smallest, hottest and coolest,
fastest and slowest—without reference to particular units of measurement.
Typically, units of measurement are first introduced in the context of
length, in which students can recognize the need for a common unit of mea-
sure—even develop their own before being introduced to standard units—
through appropriately constructed experiences. Engineering design activities
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involving scale diagrams and models can support students in developing facility
with this important concept.
Once students become familiar with measurements of length, they can
expand their understanding of scale and of the need for units that express quanti-
ties of weight, time, temperature, and other variables. They can also develop an
understanding of estimation across scales and contexts, which is important for
making sense of data. As students become more sophisticated, the use of estima-
tion can help them not only to develop a sense of the size and time scales relevant
to various objects, systems, and processes but also to consider whether a numeri-
cal result sounds reasonable. Students acquire the ability as well to move back and
forth between models at various scales, depending on the question being consid-
ered. They should develop a sense of the powers-of-10 scales and what phenom-
ena correspond to what scale, from the size of the nucleus of an atom to the size
of the galaxy and beyond.
Well-designed instruction is needed if students are to assign meaning to the
types of ratios and proportional relationships they encounter in science. Thus the
ability to recognize mathematical relationships between quantities should begin
developing in the early grades with students’ representations of counting (e.g.,
leaves on a branch), comparisons of amounts (e.g., of flowers on different plants),
measurements (e.g., the height of a plant), and the ordering of quantities such as
number, length, and weight. Students can then explore more sophisticated math-
ematical representations, such as the use of graphs to represent data collected. The
interpretation of these graphs may be, for example, that a plant gets bigger as time
passes or that the hours of daylight decrease and increase across the months.
As students deepen their understanding of algebraic thinking, they should
be able to apply it to examine their scientific data to predict the effect of a
change in one variable on another, for example, or to appreciate the difference
between linear growth and exponential growth. As their thinking advances, so
too should their ability to recognize and apply more complex mathematical and
statistical relationships in science. A sense of numerical quantity is an important
part of the general “numeracy” (mathematics literacy) that is needed to interpret
such relationships.
Systems and System Models
As noted in the National Science Education Standards, “The natural and designed
world is complex; it is too large and complicated to investigate and comprehend all
at once. Scientists and students learn to define small portions for the convenience
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of investigation. The units of investigations can be referred to as ‘systems.’ A sys-
tem is an organized group of related objects or components that form a whole.
Systems can consist, for example, of organisms, machines, fundamental particles,
galaxies, ideas, and numbers. Systems have boundaries, components, resources,
flow, and feedback” [2].
Although any real system smaller than the entire universe interacts with and
is dependent on other (external) systems, it is often useful to conceptually isolate
a single system for study. To do this, scientists and engineers imagine an artificial
boundary between the system in question and everything else. They then exam-
ine the system in detail while treating the effects of things outside the boundary
as either forces acting on the system or flows of matter and energy across it—for
example, the gravitational force due to Earth
on a book lying on a table or the carbon diox-
ide expelled by an organism. Consideration of
flows into and out of the system is a crucial
element of system design. In the laboratory or
even in field research, the extent to which a
system under study can be physically isolated
or external conditions controlled is an impor-
tant element of the design of an investigation
and interpretation of results.
Often, the parts of a system are interde-
pendent, and each one depends on or supports
the functioning of the system’s other parts.
Yet the properties and behavior of the whole
system can be very different from those of any
of its parts, and large systems may have emergent properties, such as the shape of
a tree, that cannot be predicted in detail from knowledge about the components
and their interactions. Things viewed as subsystems at one scale may themselves
be viewed as whole systems at a smaller scale. For example, the circulatory system
can be seen as an entity in itself or as a subsystem of the entire human body; a
molecule can be studied as a stable configuration of atoms but also as a subsystem
of a cell or a gas.
An explicit model of a system under study can be a useful tool not only for
gaining understanding of the system but also for conveying it to others. Models of
a system can range in complexity from lists and simple sketches to detailed com-
puter simulations or functioning prototypes.
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Models can be valuable in predicting a system’s behaviors or in diagnosing
problems or failures in its functioning, regardless of what type of system is being
examined. A good system model for use in developing scientific explanations or
engineering designs must specify not only the parts, or subsystems, of the system
but also how they interact with one another. It must also specify the boundary of
the system being modeled, delineating what is included in the model and what is
to be treated as external. In a simple mechanical system, interactions among the
parts are describable in terms of forces among them that cause changes in motion
or physical stresses. In more complex systems, it is not always possible or useful to
consider interactions at this detailed mechanical level, yet it is equally important
to ask what interactions are occurring (e.g., predator-prey relationships in an eco-
system) and to recognize that they all involve transfers of energy, matter, and (in
some cases) information among parts of the system.
Any model of a system incorporates assumptions and approximations; the
key is to be aware of what they are and how they affect the model’s reliability and
precision. Predictions may be reliable but not precise or, worse, precise but not
reliable; the degree of reliability and precision needed depends on the use to which
the model will be put.
Progression
As science instruction progresses, so too should students’ ability to analyze and
model more complex systems and to use a broader variety of representations to
explicate what they model. Their thinking about systems in terms of component
parts and their interactions, as well as in terms of inputs, outputs, and processes,
gives students a way to organize their knowledge of a system, to generate ques-
tions that can lead to enhanced understanding, to test aspects of their model of the
system, and, eventually, to refine their model.
Starting in the earliest grades, students should be asked to express their
thinking with drawings or diagrams and with written or oral descriptions. They
should describe objects or organisms in terms of their parts and the roles those
parts play in the functioning of the object or organism, and they should note
relationships between the parts. Students should also be asked to create plans—
for example, to draw or write a set of instructions for building something—that
another child can follow. Such experiences help them develop the concept of a
model of a system and realize the importance of representing one’s ideas so that
others can understand and use them.
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As students progress, their models should move beyond simple renderings or
maps and begin to incorporate and make explicit the invisible features of a system,
such as interactions, energy flows, or matter transfers. Mathematical ideas, such
as ratios and simple graphs, should be seen as tools for making more definitive
models; eventually, students’ models should incorporate a range of mathematical
relationships among variables (at a level appropriate for grade-level mathematics)
and some analysis of the patterns of those relationships. By high school, students
should also be able to identify the assumptions and approximations that have
been built into a model and discuss how they limit the precision and reliability of
its predictions.
Instruction should also include discussion of the interactions within a sys-
tem. As understanding deepens, students can move from a vague notion of interac-
tion as one thing affecting another to more explicit realizations of a system’s phys-
ical, chemical, biological, and social interactions and of their relative importance
for the question at hand. Students’ ideas about the interactions in a system and the
explication of such interactions in their models should become more sophisticated
in parallel with their understanding of the microscopic world (atoms, molecules,
biological cells, microbes) and with their ability to interpret and use more complex
mathematical relationships.
Modeling is also a tool that students can use in gauging their own knowl-
edge and clarifying their questions about a system. Student-developed models may
reveal problems or progress in their conceptions of the system, just as scientists’
models do. Teaching students to explicitly craft and present their models in dia-
grams, words, and, eventually, in mathematical relationships serves three purpos-
es. It supports them in clarifying their ideas and explanations and in considering
any inherent contradictions; it allows other students the opportunity to critique
and suggest revisions for the model; and it offers the teacher insights into those
aspects of each student’s understanding that are well founded and those that could
benefit from further instructional attention. Likewise in engineering projects,
developing systems thinking and system models supports critical steps in develop-
ing, sharing, testing, and refining design ideas.
Energy and Matter: Flows, Cycles, and Conservation
One of the great achievements of science is the recognition that, in any system,
certain conserved quantities can change only through transfers into or out of the
system. Such laws of conservation provide limits on what can occur in a system,
whether human built or natural. This section focuses on two such quantities,
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❚ The ability to examine, characterize, and model the transfers and cycles
of matter and energy is a tool that students can use across virtually all
❚
areas of science and engineering.
matter and energy, whose conservation has important implications for the dis-
ciplines of science in this framework. The supply of energy and of each needed
chemical element restricts a system’s operation—for example, without inputs of
energy (sunlight) and matter (carbon dioxide and water), a plant cannot grow.
Hence, it is very informative to track the transfers of matter and energy within,
into, or out of any system under study.
In many systems there also are cycles of various types. In some cases, the
most readily observable cycling may be of matter—for example, water going back
and forth between Earth’s atmosphere and its surface and subsurface reservoirs.
Any such cycle of matter also involves associated energy transfers at each stage,
so to fully understand the water cycle, one must model not only how water moves
between parts of the system but also the energy transfer mechanisms that are criti-
cal for that motion.
Consideration of energy and matter inputs, outputs, and flows or transfers
within a system or process are equally important for engineering. A major goal in
design is to maximize certain types of energy output while minimizing others, in
order to minimize the energy inputs needed to achieve a desired task.
The ability to examine, characterize, and model the transfers and cycles
of matter and energy is a tool that students can use across virtually all areas
of science and engineering. And studying the interactions between matter and
energy supports students in developing increasingly sophisticated conceptions of
their role in any system. However, for this development to occur, there needs to
be a common use of language about energy and matter across the disciplines in
science instruction.
Progression
The core ideas of matter and energy and their development across the grade
bands are spelled out in detail in Chapter 5. What is added in this crosscutting
discussion is recognition that an understanding of these core ideas can be infor-
mative in examining systems in life science, earth and space science, and engineer-
ing contexts. Young children are likely to have difficulty studying the concept of
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energy in depth—everyday language surrounding energy contains many shortcuts
that lead to misunderstandings. For this reason, the concept is not developed at
all in K-2 and only very generally in grades 3-5. Instead, the elementary grades
focus on recognition of conservation of matter and of the flow of matter into,
out of, and within systems under study. The role of energy transfers in conjunc-
tion with these flows is not introduced until the middle grades and only fully
developed by high school.
Clearly, incorrect beliefs—such as the perception that food or fuel is a form
of energy—would lead to elementary grade students’ misunderstanding of the
nature of energy. Hence, although the necessity for food or fuel can be discussed,
the language of energy needs to be used with care so as not to further estab-
lish such misconceptions. By middle school, a more precise idea of energy—for
example, the understanding that food or fuel undergoes a chemical reaction with
oxygen that releases stored energy—can emerge. The common misconceptions can
be addressed with targeted instructional interventions (including student-led inves-
tigations), and appropriate terminology can be used in discussing energy across
the disciplines.
Matter transfers are less fraught in this respect, but the idea of atoms is not
introduced with any specificity until middle school. Thus, at the level of grades
3-5, matter flows and cycles can be tracked only in terms of the weight of the sub-
stances before and after a process occurs, such as sugar dissolving in water. Mass/
weight distinctions and the idea of atoms and their conservation (except in nuclear
processes) are taught in grades 6-8, with nuclear substructure and the related con-
servation laws for nuclear processes introduced in grades 9-12.
Structure and Function
As expressed by the National Research Council in 1996 and reiterated by the
College Board in 2009, “Form and function are complementary aspects of objects,
organisms, and systems in the natural and designed world. . . . Understanding
of form and function applies to different levels of organization. Function can be
explained in terms of form and form can be explained in terms of function” [2, 3].
The functioning of natural and built systems alike depends on the shapes and
relationships of certain key parts as well as on the properties of the materials from
which they are made. A sense of scale is necessary in order to know what proper-
ties and what aspects of shape or material are relevant at a particular magnitude or
in investigating particular phenomena—that is, the selection of an appropriate scale
depends on the question being asked. For example, the substructures of molecules
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are not particularly important in understanding the phenomenon of pressure, but
they are relevant to understanding why the ratio between temperature and pressure
at constant volume is different for different substances.
Similarly, understanding how a bicycle works is best addressed by examin-
ing the structures and their functions at the scale of, say, the frame, wheels, and
pedals. However, building a lighter bicycle may require knowledge of the proper-
ties (such as rigidity and hardness) of the materials needed for specific parts of
the bicycle. In that way, the builder can seek less dense materials with appropriate
properties; this pursuit may lead in turn to an examination of the atomic-scale
structure of candidate materials. As a result, new parts with the desired properties,
possibly made of new materials, can be designed and fabricated.
Progression
Exploration of the relationship between structure and function can begin in
the early grades through investigations of accessible and visible systems in the
natural and human-built world. For example, children explore how shape and
stability are related for a variety of structures (e.g., a bridge’s diagonal brace)
or purposes (e.g., different animals get their food using different parts of their
bodies). As children move through the elementary grades, they progress to
understanding the relationships of structure and
mechanical function (e.g., wheels and axles,
gears). For upper-elementary students, the con-
cept of matter having a substructure at a scale
too small to see is related to properties of mate-
rials; for example, a model of a gas as a collec-
tion of moving particles (not further defined)
may be related to observed properties of gases.
Upper-elementary students can also examine
more complex structures, such as subsystems of
the human body, and consider the relationship
of the shapes of the parts to their functions. By
the middle grades, students begin to visualize,
model, and apply their understanding of structure and function to more complex
or less easily observable systems and processes (e.g., the structure of water and
salt molecules and solubility, Earth’s plate tectonics). For students in the middle
grades, the concept of matter having a submicroscopic structure is related to
properties of materials; for example, a model based on atoms and/or molecules
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and their motions may be used to explain the properties of solids, liquids, and
gases or the evaporation and condensation of water.
As students develop their understanding of the relationships between struc-
ture and function, they should begin to apply this knowledge when investigating
phenomena that are unfamiliar to them. They recognize that often the first step
in deciphering how a system works is to examine in detail what it is made of
and the shapes of its parts. In building something—say, a mechanical system—
they likewise apply relationships of structure and function as critical elements of
successful designs.
Stability and Change
“Much of science and mathematics has to do with understanding how change
occurs in nature and in social and technological systems, and much of technol-
ogy has to do with creating and controlling change,” according to the American
Association for the Advancement of Science. “Constancy, often in the midst of
change, is also the subject of intense study in science” [4].
Stability denotes a condition in which some aspects of a system are unchang-
ing, at least at the scale of observation. Stability means that a small disturbance
will fade away—that is, the system will stay in, or return to, the stable condition.
Such stability can take different forms, with the simplest being a static equilib-
rium, such as a ladder leaning on a wall. By contrast, a system with steady inflows
and outflows (i.e., constant conditions) is said to be in dynamic equilibrium. For
example, a dam may be at a constant level with steady quantities of water com-
ing in and out. Increase the inflow, and a new equilibrium level will eventually be
reached if the outflow increases as well. At extreme flows, other factors may cause
disequilibrium; for example, at a low-enough inflow, evaporation may cause the
level of the water to continually drop. Likewise, a fluid at a constant temperature
can be in a steady state with constant chemical composition even though chemi-
cal reactions that change the composition in two opposite directions are occurring
within it; change the temperature and it will reach a new steady state with a dif-
ferent composition.
A repeating pattern of cyclic change—such as the moon orbiting Earth—can
also be seen as a stable situation, even though it is clearly not static. Such a system
has constant aspects, however, such as the distance from Earth to the moon, the
period of its orbit, and the pattern of phases seen over time.
In designing systems for stable operation, the mechanisms of external con-
trols and internal “feedback” loops are important design elements; feedback is
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important to understanding natural systems as well. A feedback loop is any mech-
anism in which a condition triggers some action that causes a change in that same
condition, such as the temperature of a room triggering the thermostatic control
that turns the room’s heater on or off. Feedback can stabilize a system (negative
feedback—a thermostat in a cooling room triggers heating, but only until a par-
ticular temperature range is reached) or destabilize a system (positive feedback—a
fire releases heat, which triggers the burning of more fuel, which causes the fire to
continue to grow).
A system can be stable on a small time scale, but on a larger time scale it
may be seen to be changing. For example, when looking at a living organism over
the course of an hour or a day, it may maintain stability; over longer periods, the
organism grows, ages, and eventually dies. For the development of larger systems,
such as the variety of living species inhabiting Earth or the formation of a galaxy,
the relevant time scales may be very long indeed; such processes occur over mil-
lions or even billions of years.
When studying a system’s patterns of change over time, it is also important
to examine what is unchanging. Understanding the feedback mechanisms that
regulate the system’s stability or that drive its instability provides insight into
how the system may operate under various conditions. These mechanisms are
important to evaluate when comparing different design options that address a
particular problem.
Any system has a range of conditions under which it can operate in a stable
fashion, as well as conditions under which it cannot function. For example, a par-
ticular living organism can survive only within a certain range of temperatures,
and outside that span it will die. Thus elucidating what range of conditions can
lead to a system’s stable operation and what changes would destabilize it (and in
what ways) is an important goal.
Note that stability is always a balance of competing effects; a small change
in conditions or in a single component of the system can lead to runaway changes
in the system if compensatory mechanisms are absent. Nevertheless, students typi-
cally begin with an idea of equilibrium as a static situation, and they interpret a
lack of change in the system as an indication that nothing is happening. Thus they
need guidance to begin to appreciate that stability can be the result of multiple
opposing forces; they should be taught to identify the invisible forces—to appreci-
ate the dynamic equilibrium—in a seemingly static situation, even one as simple as
a book lying on a table.
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An understanding of dynamic equilibrium is crucial to understanding the
major issues in any complex system—for example, population dynamics in an
ecosystem or the relationship between the level of atmospheric carbon dioxide and
Earth’s average temperature. Dynamic equilibrium is an equally important concept
for understanding the physical forces in matter. Stable matter is a system of atoms
in dynamic equilibrium.
For example, the stability of the book lying on the table depends on the fact
that minute distortions of the table caused by the book’s downward push on the
table in turn cause changes in the positions of the table’s atoms. These changes
then alter the forces between those atoms, which lead to changes in the upward
force on the book exerted by the table. The book continues to distort the table
until the table’s upward force on the book exactly balances the downward pull of
gravity on the book. Place a heavy enough item on the table, however, and stabil-
ity is not possible; the distortions of matter within the table continue to the mac-
roscopic scale, and it collapses under the weight. Such seemingly simple, explicit,
and visible examples of how change in some factor produces changes in the sys-
tem can help to establish a mental model of dynamic equilibrium useful for think-
ing about more complex systems.
Understanding long-term changes—for example, the evolution of the diver-
sity of species, the surface of Earth, or the structure of the universe—requires a
sense of the requisite time scales for such changes to develop. Long time scales
can be difficult for students to grasp, however. Part of their understanding should
grow from an appreciation of how scientists investigate the nature of these
processes—through the interplay of evidence and system modeling. Student-
developed models that use comparative time scales can also be helpful; for exam-
ple, if the history of Earth is scaled to 1 year (instead of the absolute measures in
eons), students gain a more intuitive understanding of the relative durations of
periods in the planet’s evolution.
Progression
Even very young children begin to explore stability (as they build objects with
blocks or climb on a wall) and change (as they note their own growth or that
of a plant). The role of instruction in the early grades is to help students to
develop some language for these concepts and apply it appropriately across
multiple examples, so that they can ask such questions as “What could I change
to make this balance better?” or “How fast did the plants grow?” One of the
goals of discussion of stability and change in the elementary grades should
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be the recognition that it can be as important to ask why something does not
change as why it does.
Likewise, students should come to recognize that both the regularities of
a pattern over time and its variability are issues for which explanations can be
sought. Examining these questions in different contexts (e.g., a model ecosystem
such as a terrarium, the local weather, a design for a bridge) broadens students’
understanding that stability and change are related and that a good model for a
system must be able to offer explanations for both.
In middle school, as student’s understanding of matter progresses to the
atomic scale, so too should their models and their explanations of stability and
change. Furthermore, they can begin to appreciate more subtle or conditional situ-
ations and the need for feedback to maintain stability. At the high school level,
students can model more complex systems and comprehend more subtle issues of
stability or of sudden or gradual change over time. Students at this level should
also recognize that much of science deals with constructing historical explanations
of how things evolved to be the way they are today, which involves modeling rates
of change and conditions under which the system is stable or changes gradually, as
well as explanations of any sudden change.
I NTERCONNECTIONS BETWEEN CROSSCUTTING CONCEPTS
AND DISCIPLINARY CORE IDEAS
Students’ understanding of these crosscutting concepts should be reinforced by
repeated use of them in the context of instruction in the disciplinary core ideas
presented in Chapters 5-8. In turn, the crosscutting concepts can provide a con-
nective structure that supports students’ understanding of sciences as disciplines
and that facilitates students’ comprehension of the phenomena under study in
particular disciplines. Thus these crosscutting concepts should not be taught in
isolation from the examples provided in the disciplinary context. Moreover, use of
a common language for these concepts across disciplines will help students to rec-
ognize that the same concept is relevant across different contexts.
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REFERENCES
1. American Association for the Advancement of Science. (1989). Science for All
Americans. Project 2061. New York: Oxford University Press. Available: http://www.
project2061.org/publications/sfaa/online/sfaatoc.htm [March 2011].
2. National Research Council. (1996). National Science Education Standards. National
Committee for Science Education Standards and Assessment. Washington, DC:
National Academy Press.
3. College Board. (2009). Science College Board Standards for College Success.
Available: http://professionals.collegeboard.com/profdownload/cbscs-science-
standards-2009.pdf [June 2011].
4. American Association for the Advancement of Science. (2009). Benchmarks for
Science Literacy. Project 2061. Available: http://www.project2061.org/publications/
bsl/online/index.php?txtRef=http%3A%2F%2Fwww%2Eproject2061%2Eorg%2
Fpublications%2Fbsl%2Fdefault%2Ehtm%3FtxtRef%3D%26txtURIOld%3D%252
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Fonline%2Fbolintro%2Ehtm [June 2011].
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Print copies of the Next Generation Science Standards are available for pre-order now or you can view the online version at nextgenscience.org
The standards are based largely on the 2011 National Research Council report A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas.
