Bernoulli’s
Principle
Science as a
Human Endeavor
by Deborah McCarthy
W
hat do the ideas of Daniel Bernoulli—
an 18th-centur y Swiss mathematician,
physicist, natural scientist, and professor—and your students’ next landing
of the space shuttle via computer simulation have in
common? Because of his contribution, referred to
in physical science as Bernoulli’s principle, modern
flight is possible. The mini learning cycle described
here explores Bernoulli’s principle with several
simple activities, and highlights its application in
our lives. The learning-cycle method of instruction
has taken on many forms since its introduction, with
some versions including steps in addition to the four
that I prefer to implement: the elicitation phase, the
exploration phase, the invention phase, and the application phase (Martin et al. 2005).
Through this constructivist instructional strategy,
students experience scientific inquiry as a process of
discovery shared by humans, during which various
explanations of observed phenomena are exchanged
among team members. To underscore the human side
of this most important scientist and place his life in historical context, I wrote a biography of Daniel Bernoulli
(see Figure 1) that further emphasizes science as a human endeavor, thus tapping into the affective domain
and evoking the empathy of my students toward those
who work in science.
The elicitation phase
I begin the mini learning cycle with a quick review of
atoms, molecules, and pressure expressed as pressure
equals force divided by area, relating the information
generated by my seventh-grade students on all three
topics back to previous activities to tap into their prior
knowledge. Previous activities included representing
the structure of the atom with models, drawing molecules, and applying their understanding of the concept
of pressure to explain why it is more comfortable to
stand in sneakers than high heels.
I distribute a penny, ruler, and sugar cube to each
student. They trace the penny, draw a line 1-centimeter long, and sketch the sugar cube in their notebooks. Then I ask them to estimate how many atoms
could fit single file on that 1-centimeter line (10 million atoms) and the face of the penny (200 million atoms). Finally, we estimate the number of molecules
that could occupy a cubic centimeter of space as
they obser ve their sugar cube, which is roughly one
cubic centimeter in volume (3 billion molecules).
After the predictions are made, I share the correct
estimates. We then imagine the classroom filled with
sugar cubes stacked like bricks from ceiling to floor
bernoulli’s principle: science as a human endeavor
and wall to wall. We ponder the enormity of such an
amount and the almost impossible task of expressing it as a number. I then ask students to explain the
purpose of this simple exercise. Without much hesitation, they reply that atoms and molecules are extremely small and numerous, filling the classroom.
To complete the elicitation phase of the cycle, I
present the following discrepant event (Beisenherz
and Dantonio 1996). On my cart, I place a large,
empty food container, a container of water, an empty
glass jar, and several index cards. I explain to my
students that I am going to fill the empty jar with water, place the index card on the mouth of the jar, and
turn the jar upside down over the food container.
Before performing the demonstration, I ask students
to record in their notebooks a
prediction of what will happen to
the water. They are working in
groups of three or four and able
to discuss their ideas, but students are encouraged to predict
on their own. When I ask students what they predict will happen, their hypotheses always include that the card will “stick” to
the mouth of the jar or the water
will fall into the food container.
Some students will also predict
that the water will remain in the
jar. As I perform the activity, students’ eyes are wide as saucers
and the room becomes silent as
the water remains in the jar. They
record their obser vations in their notebooks and infer reasons for this phenomenon together. When
asked to explain what they saw, students usually
begin by saying the card “sticks” to the jar because
the water creates “suction” or that the water is pulling the card to the mouth of the jar. Inevitably the
term suction must be defined. After many attempts
at student-generated definitions, I ask one student to
locate the word in the dictionar y. The formal definition usually includes the term vacuum, so we discuss
what constitutes a vacuum. Someone explains that it
means that the air is gone. At this point, I reach
for the suction cup that is holding an ornamental
stained-glass red bird to the classroom window. My
question becomes, “How do you make this work?” A
student explains that you must push the cup against
the surface so that all the air goes out and it sticks. I
allow students to think about what could be pushing
the suction cup to the surface. Then, as a class, we
return to the demonstration and examine the setup
again. Several students realize that only water occupies the jar; there is no air! I remind students of the
rows and columns of sugar cubes that could fill the
classroom and the number of molecules each contains, at which point their explanations as to why the
water remained in the jar begin to fall apart. Finally,
one student will exclaim that it must be the air molecules in the room that are pushing on the index card
to keep it in its place, not that the card is sticking
to the jar. If the connection is not made, each group
presents their explanation to the class. As I listen to
the inferences, I jot down key words or phrases from
each report on the whiteboard; these can be combined to compose our final explanation. In groups,
students then arrange the items
on the whiteboard and construct
a likely description. Depending on
time, students may simply vote on
what they surmise is the best account and refine it. The one chosen is recorded in their notebooks
and boxed to eliminate any confusion in identifying the correct
explanation. The best explanation
is that pressure from the force exerted by air molecules on the area
of the index card keeps the card
in place. I introduce the term air
pressure and we identify the force
as the air molecules, and the area
of the index card as being where
the pressure occurs. Of course,
we must then investigate the phenomenon using different-sized jars and var ying amounts of water. The
same results occur regardless of the dif ferences.
During this class discussion, we compare the different-sized columns of air created in the partially filled
jars with the columns of air in the room, reemphasizing the effect of the force exerted by the enormous
amount of air molecules present in the classroom, as
opposed to those trapped in the jars. I then explain
that we will be investigating how air pressure can be
influenced, and begin the exploration phase of the
learning cycle.
As I perform the activity,
students’ eyes are wide
as saucers and the
room becomes silent
as the water remains
in the jar. They record
their observations in
their notebooks and
infer reasons for this
phenomenon together.
The exploration phase
I designed the exploration phase (Figure 3) to engage students in a sequence of activities that builds
an understanding of Bernoulli’s principle as one way
to influence air pressure. Before students begin to
work in their groups of three or four, I walk them
S e p t e m b e r 2 008
19
bernoulli’s principle: science as a human endeavor
through each procedure and demonstrate how to
set up the materials. They approach the activities
as if they were a team of scientists obser ving and
developing explanations for what they see. Students
only know that these activities will probably have
something to do with air pressure. The procedures
are clear, but the questions that follow are purposely
worded to be ver y vague, asking only for predictions, obser vations, and explanations of what the
group obser ved (see Figure 3). Students have little
idea of what to expect and are often amazed at the
outcomes, performing the activities several times in
order to verify what they are actually seeing.
The exploration phase begins with the Hanging Paper activity. Students blow air between two pieces of paper, which clash together. In the second activity, There
She Blows! (Part 1), students blow air under a piece
of paper placed on two books separated by several
centimeters, observing that the paper caves in. When
they blow over a piece of paper held under their chin in
the third activity, There She Blows! (Part 2), students
observe that the paper flips up. In each of the three
activities, students show surprise that the paper acts in
the opposite manner from their initial predictions. Each
group discusses the observations they have recorded
FIGURE 1
The invention phase
During the invention phase (see Figure 4), I bring
the class together as a group of student scientists
to share obser vations and explanations of the three
activities, The Hanging Paper, There She Blows!
(Part 1), and There She Blows! (Part 2), that they
performed in the exploration phase. Again, I evoke
the image of our classroom filled with sugar cubes.
After much discussion, students infer that the two
pieces of paper clash together because there is less
air pressure in the area between the two pieces of
paper: The air pressure in the room on the outer
sides of the pieces of paper is greater and forces the
two pieces together. They surmise that the paper sitting on the two textbooks caves in when air is blown
through the opening under the paper because the
air pressure must be less below the paper and the
air pressure in the room above the paper is greater,
forcing it to cave in. To explain why the paper flips
up when they blow air across the top of it as they
hold it under their chins, students presume that air
Biography of Daniel Bernoulli
Daniel Bernoulli (1700–1782) was a Swiss mathematician
and physicist, born in Basel, Switzerland, to Johann
Bernoulli and Dorothea Faulkner. He had an older brother,
Nicolaus II, who passed away in 1725, and a younger
brother, Johann II.
Daniel Bernoulli made significant contributions to
calculus, probability, medicine, physiology, mechanics, and
atomic theory. He wrote on problems of acoustics and fluid
flow and earned a medical degree in 1721. Daniel was a
professor of experimental philosophy, anatomy, and botany
at the universities of Groningen in the Netherlands and
Basel in Switzerland. He was called to teach botany and
physiology at the most ambitious Enlightenment scientific
institution in the Baltic states, the St. Petersburg Academy
of Science. Later in his academic career he obtained the
chair of physics, which he kept for 30 years. St. Petersburg
Academy offered mathematics, physics, anatomy, chemistry,
and botany courses. Its buildings included an observatory, a
physics cabinet, a museum, a botanical garden, an anatomy
theater, and an instrument-making workshop. His most important publication, Hydrodynamica,
discussed many topics, but most importantly, it advanced
20
in their notebooks and prepares their explanations. The
key question they must address is “How are the three
activities similar?”
SCIENCE SCOPE
the kinetic molecular theory of gases
and fluids in which Bernoulli used
the new concepts of atomic structure
and atomic behavior. He explained
gas pressure in terms of atoms
flying into the walls of the containing
vessel, laying the groundwork for the
kinetic theory. His ideas contradicted
the theory accepted by many of
his contemporar ies, including
Newton’s explanation of pressure Daniel Ber noulli
published in Principia Mathematica. (1700–1782)
Newton thought that particles at
rest could cause pressure because they repelled each
other. Because of the brilliance of Newton’s numerous
discoveries, it was assumed by most scientists of the
time that his explanation was correct, even though it was
inaccurate. Although Bernoulli disagreed with Newton’s
theory, Bernoulli supported the physics of Isaac Newton,
as did his female contemporary, Emilie du Châtelet, who
translated Newton’s work into French in the late 1740s. In
Section X of his book, Bernoulli also offered his explanation
bernoulli’s principle: science as a human endeavor
pressure must be less on top, allowing the greater
air pressure under the paper to force the paper upward. During the explanations, we diagram and label
each activity, indicating with arrows where the air
pressure is greater and where it is less. Now it is
appropriate to report the similarities obser ved in all
three activities, which is fundamental to explaining
the change in air pressure occurring in each. As a
group of scientists would operate, all responses are
initially accepted. Some students reply that whatever
they predicted, the reverse happened, or whenever
they blew the air over one surface, the opposite surface was affected. Now I ask students to describe
what happens to air when they blow it. The middle
schoolers respond that it becomes disturbed, or it
goes faster, or the speed changes, and in due course,
that it moves.
Finally, we agree on what we consider the best
explanation for the changes in air pressure, and
students define Bernoulli’s principle in their own
words. In my opinion, and that of Munby (1976), using common language rather than scientific jargon
presents an instrumentalist view of the discipline.
The instrumentalist values theories as inferences
or explanations of phenomena. Using common lan-
guage also allows students to better understand the
human origin of scientific knowledge. Students decide that air moving rapidly over a surface reduces
the air pressure on that surface: Moving air influences air pressure.
At this point, I identify their statement as Bernoulli’s principle, and distribute the biography of the
scientist, complete with a picture and questions on
which to reflect, to each student. For homework, I
ask students to read the biography (Figure 1), respond to the questions that follow (Figure 2), and
of pressure measured with a new instrument named by
Boyle, the barometer. In Hydrodynamica, Bernoulli took on the task of solving
difficult mechanical problems mentioned in Newton’s Principia
Mathematica. In the 10th chapter, Bernoulli imagines that
gases, which he called “elastic fluid,” were composed of
particles in constant motion and describes the behavior of the
particles trapped in a cylinder. As he depressed the moveable
piston, he calculated the increase in pressure, deducing
Boyle’s law. Then he described how a rise in temperature
increases pressure, as well as the speed of the atomic
particles of the gas, a relationship that would later become a
scientific law.
He attributed the change in atmospheric pressure to gases
being heated in the cavities of the Earth’s crust that would rush
out and rise, increasing barometric pressure. The pressure
dropped when the internal heat of the Earth decreased and
the air contracted.
Bernoulli not only used his mathematical expertise to
contribute to physical science. He attempted to statistically
predict the difference in the number of deaths from
smallpox that would occur in the population if people
were properly inoculated against the horrible disease.
But in modern physical science textbooks, Daniel
Bernoulli is best recognized for Bernoulli’s principle, or the
Bernoulli effect, which describes the inverse relationship
between the speed of air and pressure. In 1738, Bernoulli
stated his famous principle in Section XII of Hydrodynamica,
where he described the relationship between the speed of a
fluid and pressure. He deduced this relationship by observing
water flowing through tubes of various diameters. Bernoulli
proposed that the total energy in a flowing fluid system is a
constant along the flow path. Therefore if the speed of flow
increases, the pressure must decrease to keep the energy
of flow at that constant. Today we apply this relationship to
the flow of air over a surface, as well. Because of Daniel
Bernoulli, we are able to build aircraft, fly helicopters, water
the lawn, and even pitch a curve ball.
Daniel Bernoulli, physicist, mathematician, natural
scientist, and professor, died in his native Basel, Switzerland,
on March 17, 1782, and fittingly, was buried in the Peterskirche,
meaning St. Peter’s Church, in Vienna. It is believed that the
location of St. Peter’s Church has supported a place of
worship since the second half of the fourth century.
FIGURE 2
Questions for reflection
• From your reading, tell me what you remember about Daniel
Bernoulli’s great discoveries and accomplishments.
• After reading Bernoulli’s ideas about the kinetic molecular
theory, why do you think scientific explanations remain
the same even if they should be changed?
• How did reading Daniel Bernoulli’s explanation of changes
in air pressure affect your opinion of him as a scientist?
• How do Bernoulli’s discoveries affect you today?
S e p t e m b e r 2 008
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bernoulli’s principle: science as a human endeavor
FIGURE 3
The exploration phase
The Hanging Paper
There She Blows! (Part 1)
There She Blows! (Part 2)
2 books
Paper
1 piece of paper
Materials
2 pieces of paper
2 clothespins or clips
Procedure
1.Clip the clothespins to the top of each
piece of paper.
2.Hold them by the clothespins about 4
cm apart in front of you so that the two
pieces of paper are facing each other.
3.In your notebook, predict what will
happen when you blow air between
the pieces of paper.
4.Try it, then observe your group
members as they try it.
5.Observe and record.
6.Using what you know about air
pressure, explain your observations.
1.Place two books side by side about
4 cm apart.
2.Place a piece of paper on top of the
two books.
3.In your notebook, predict what will
happen when you blow air through
the opening under the paper.
4.Try it, then observe your group
members as they try it.
5.Observe and record.
6.Using what you know about air
pressure, explain your observations.
1.Take a sheet of paper and hold it near
the top with your thumbs.
2.Place it directly under your chin.
3.In your notebook, predict what will
happen when you blow air across the
top of the paper.
4.Do this several times. Let everyone
in the group try.
5.Observe and record.
6.Using what you know about air pressure, explain your observations.
How are the three activities similar? Be prepared to discuss your ideas and explanations with the class.
FIGURE 4
The invention phase
11. As a class, we are now prepared to discuss the three
activities completed in the exploration phase.
12.What did you observe in the Hanging Paper activity?
13.Explain your observations.
14.What did you observe in There She Blows! (Part 1)?
15.Explain your observations.
16.What did you observe in There She Blows! (Part 2)?
17. Explain your observations.
18.How are the explanations of these activities similar?
19.We can use these similarities to give reasons for the
change in air pressure.
(Student responses are then combined to write a clear
statement of explanation.)
10. We call this explanation of changing air pressure Bernoulli’s principle.
11. Think of examples where Bernoulli’s principle is used
every day.
be prepared for a discussion of Daniel Bernoulli’s
life. I use responses to the questions and the discussion as informal assessments. To close the invention
phase, I ask students to think of examples where
22
SCIENCE SCOPE
Bernoulli’s principle is used ever y day. “Airplane” is
usually the first response, but then I hear examples
like birds, helicopters, Frisbees, and boomerangs.
We then discuss the art of pitching a cur ve ball and
how some water sprinklers feed the grass. I so enjoy
the signs of revelation that I see on students’ faces
as they leave the room. They appreciate the significance of Bernoulli’s principle, developed over 200
years ago, as it applies to their lives today.
The human side of Bernoulli
The following day, the classroom is set up for the
final activities of the learning cycle, but as students
enter the room, they notice that there is a large area
of empty floor. I ask them to bring Bernoulli’s biography, sit, and form a circle. Many students have
highlighted sections of the biography that address
the corresponding questions, or have recorded the
answers in their notebooks. We discuss any sections
in the reading that they found difficult to understand
and relate the era of Bernoulli’s life to events happening in other parts of the world, in particular the
American Revolution. For those students who have
reading difficulties, a CD or audiotape of the biography would be helpful. A colorful PowerPoint presentation of the information or a short play created
bernoulli’s principle: science as a human endeavor
FIGURE 5
Liftoff
The application phase
A Wing That Works
Materials
2 Styrofoam cups
Rulers
Tape
Index cards
A pivot such as a prism,
clay, or large pencil on
which the ruler can rest in
a seesaw fashion
FIGURE 6
Laboratory report
Laboratory reports are generally written as students
complete the activities in the application phase.
Group Number_______
Names _________________________
Statement of the problem or question
(Students compose a question that is related directly to the
objective or purpose of the activity.)
Procedure
Procedure
Hypothesis/Prediction
1.Gently place one cup 1.Using the index card,
inside the other.
create a wing that when
taped correctly will lift
2.Using Bernoulli’s prinone end of the ruler from
ciple, attempt to cause
resting on the table.
the inner cup to pop out
of the outside cup with- 2.Use Bernoulli’s principle
by blowing across the top
out using your hands or
of the index card.
feet.
3.Illustrate
your design
3.Record the procedure
when
it
appears
successthat was successful.
ful.
4.Explain why your proce4.Explain why your design
dure works.
works.
Observations
by students depicting an event in Bernoulli’s life
could also accompany the written biography. (For an
animated demonstration of Bernoulli’s principle, see
http://home.earthlink.net/~mmc1919/venturi.html.)
Then we discuss the corresponding questions
for reflection (Figure 2), which ser ve several
purposes. The first question (From your reading,
tell me what you remember about Daniel Bernoulli’s great discoveries and accomplishments) is
designed to help students recollect facts about
Bernoulli from their reading. They respond with
answers such as the following: He was the author of books, he was a teacher, he worked on the
kinetic theor y, he knew a lot about atoms, and,
of course, he developed his own principle.
The intention of question two (After reading Bernoulli’s ideas about the kinetic molecular theory, why
do you think scientific explanations remain the same
even if they should be changed?) is to help students
understand why scientific explanations are revised
at a slow pace. Political and social factors often
influence the formation and dissemination of scien-
Conclusions (inference)
tific knowledge, according to the Nature of Science
Benchmark “Scientific Worldview” (AAAS 1993) and
the National Science Education Standard “The Nature of Science” (NRC 1996). Students propose that
perhaps Bernoulli was afraid of losing his friends or
his job. Maybe he feared being ridiculed since his
ideas were different from Newton’s, who was such a
powerful figure at that time. We then recall misconceptions such as the Earth being the center of the
solar system and the world being flat, believed to be
true for centuries by ver y intelligent people.
To raise awareness that scientific knowledge is
tentative and often the best explanation of a phenomenon available at the time, we discuss question three
(How did reading about Daniel Bernoulli’s explanation of changes in air pressure af fect your opinion of
him as a scientist?). The question also addresses
a willingness to discard or revise information, as
expressed in the Nature of Science Benchmark “Scientific Worldview” (AAAS 1993), and the National
Science Education Standard “The Nature of Science”
(NRC 1996). Years before national benchmarks, in
his lecture to the John Dewey Society, Professor
Abraham Maslow proposed that the roots of science should be presented, rather than science at its
technical peak (Maslow 1966). My students generally convey to me that Bernoulli’s explanation of the
internal heat of the Earth determining atmospheric
pressure was only a small part of the many brilliant
ideas and contributions he made. They still consider
him a ver y smart scientist.
The fourth question (How do Bernoulli’s discover-
S e p t e m b e r 2 008
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bernoulli’s principle: science as a human endeavor
ies af fect you today?) is aimed at students’ feelings
toward the positive and negative effects of science
on members of society. The Nature of Science
Benchmark “Scientific Worldview” (AAAS 1993) and
the National Science Education Standard “The Histor y of Science” (NRC 1996) investigate and stress
the relevancy of science. To answer question four,
students always refer to the second-to-last paragraph of the biography, which enumerates several
applications, and those applications we generated
earlier in class.
What is most rewarding about our discussion is
that students see Daniel Bernoulli from a dif ferent perspective. They remark that he had a family,
friends, and a job, and in some instances, proposed
theories that were more accurate than his contemporar y Sir Isaac Newton’s. I also point out that he lived
for 82 years, a ver y long life during the 18th centur y.
After the discussion, students engage in the final
phase of this learning cycle, the application phase,
in which the principle they articulated in the invention phase is used to solve new but similar problems,
helping them to make the connection between science and technology.
The application phase
In the application phase (Figure 5), I present students with two challenges, again walking them
through and demonstrating each procedure. The
first challenge is to place one Styrofoam cup into another and cause the inner cup to pop out of the outer
cup by applying Bernoulli’s principle, without using their hands, feet, etc. After just a few moments,
someone in the group shows the other members
that blowing across the mouth of the cups achieves
liftoff. Soon, cups are popping up all over the room.
Students quickly surmise that blowing air over the
mouths of the two cups moves the air and reduces
the air pressure above and between the outside walls
of the two cups. The air pressure in the small space
between the bottoms of the two is greater, so the inner cup is forced upward.
The second challenge is to use a ruler, tape, index
card, and wedge to build a wing that allows one side
of the ruler to rise on its pivot when students move
the air across the top of the index card. This requires
more time and thought, and students ask questions
like “Can we fold it?” and “Can we cut it?” Eventually,
a group will simply bend the index card into a curved
surface and tape it to the ruler. This group of student
scientists has designed a crude wing that lifts one end
of the ruler on its pivot when they move the air over
24
SCIENCE SCOPE
FIGURE 7
Formal assessment of
Bernoulli’s principle
Use Bernoulli’s principle to explain the following events.
Illustrate your explanations.
1. A roof is removed from a house by strong winds during a
severe thunderstorm.
[Answer: Applying Bernoulli’s principle exclusively, the
moving air over the curved roof of the house causes a
decrease in air pressure. The air pressure inside of the
house is greater because it is moving very little and is also
somewhat confined (Boyle’s law). The greater air pressure
in the house causes the roof to be pushed up, similar to the
two Styrofoam cups.]
2. When a large truck speeds past a small car, the car moves
closer to the truck as it passes.
[Answer: Applying Bernoulli’s principle exclusively, the
moving air between the truck and car as the truck speeds
by causes a decrease in air pressure between the car and
truck. The air pressure on the opposite side of the car is
greater, which pushes it toward the truck, similar to the
hanging pieces of paper.]
3. Leaves lift off the road as a car passes over them.
[Answer: Applying Bernoulli’s principle exclusively, the
passing car causes the air to move rapidly above the road
where the leaves are resting, causing a decrease in air
pressure on top of the leaves. The greater air pressure below
the leaves pushes them upward, similar to the piece of paper
students held under their chin.]
4. An airplane lifts off the ground when it reaches the proper
speed.
[Answer: Applying Bernoulli’s principle exclusively,
an airplane’s wing is curved on the top and straighter
underneath the wing. As air hits the wing, it moves over and
under the wing. Since the top of the wing is more curved
than the bottom of the wing, the air moving over the top of
the wing has further to travel: It must move faster than the air
moving underneath the wing. This faster-moving air on top
causes a decrease in air pressure. The greater air pressure
creates lift similar to the index card on its pivot.]
it. The groups share their design with the rest of the
class, although it is usually difficult for them to arrive
at an explanation of why bending the index card made
their wing work. Finally someone recalls an answer
to a homework question on flight and the discussion
we had in class during the invention phase. Curving
bernoulli’s principle: science as a human endeavor
the card causes the air to move more quickly over the
top of the card, reducing air pressure. The air pressure below the card on its pivot is greater, forcing
it upward and allowing it to lift one end of the ruler.
Students realize that both activities are comparable to
what they observed when they blew air across the top
of the piece of paper held under their chin in the exploration phase. During each activity and the writing
of laboratory reports (Figure 6), which usually occurs
as students complete the application phase, I observe
students’ cooperative learning skills. The repor ts
completed during the application phase and my anecdotal remarks serve as informal assessments for each
student group, in addition to the questions for reflection accompanying Bernoulli’s biography (Figure 2).
At the conclusion of the learning cycle, each student
completes an individual formal assessment consisting
of four related scenarios (Figure 7). The assessment
is used to evaluate students’ understanding of the
principle and its application.
Reflections
This mini learning cycle on Bernoulli’s principle
provides students with the opportunity to obser ve
a phenomenon investigated over 220 years ago that
has impacted modern society. They approach the
investigation in the same manner as scientists do,
by obser ving, making inferences together to explain what they have obser ved, and applying their
understanding to solve a problem. They realize that
because of Daniel Bernoulli, men and women can
return from space or rescue people from their rooftops. After completing the learning cycle, students
understand why the shower curtain moves toward
them while the water is streaming past, or the reason the car shakes when a large truck passes by.
They understand the danger of standing close to a
moving train and how birds soar. Equally important,
students experience the nature of science as inquir y
and begin to look at scientists like Bernoulli as real
people who are passionate about understanding the
natural phenomena around them. n
References
American Association for the Advancement of Science
(AAAS). 1993. Benchmarks for science literacy. New
York: Oxford University Press.
American Council of Learned Societies. 1991. Biographical dictionary of mathematics (s.v. “Bernoulli”). New
York: Scribner.
Asimov, I. 1982. Asimov’s biographical encyclopedia of
science and technology. New York: Doubleday.
Bacon, F. 1915. The advancement of learning. Ed. G.W.
Kitchin. London: J.M. Dent.
Beisenherz, P., and M. Dantonio. 1996. Using the
learning cycle to teach physical science: A handson approach for middle grades. Portsmouth, NH:
Heinemann.
Clark, W., J. Golinski, and S. Schaffer, eds. 1999. The
sciences in enlightened Europe. Chicago: University
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Deborah McCarthy ([email protected]) is
an assistant professor in the College of Education and
Human Development, Department of Teaching and
Learning, at Southeastern University in Hammond,
Louisiana.
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