To underscore the human side of this most important scientist and place his life in his-torical context, I wrote a biography of Daniel Bernoulli see Figure 1 that further emphasizes scie
Trang 1by Deborah McCarthy
Bernoulli’s
Science as a
Human Endeavor
What do the ideas of Daniel Bernoulli—
an 18th-century Swiss mathematician, physicist, natural scientist, and profes-sor—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 ap-plication 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 his-torical context, I wrote a biography of Daniel Bernoulli (see Figure 1) that further emphasizes science as a hu-man 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 mol-ecules, 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-centi-meter long, and sketch the sugar cube in their note-books Then I ask them to estimate how many atoms could fit single file on that 1-centimeter line (10 mil-lion atoms) and the face of the penny (200 milmil-lion at-oms) Finally, we estimate the number of molecules that could occupy a cubic centimeter of space as they observe 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
Trang 2and wall to wall We ponder the enormity of such an
amount and the almost impossible task of
express-ing it as a number I then ask students to explain the
purpose of this simple exercise Without much
hesi-tation, they reply that atoms and molecules are
ex-tremely 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
wa-ter, 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
stu-dents are encouraged to predict
on their own When I ask
stu-dents what they predict will
hap-pen, their hypotheses always
in-clude 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,
stu-dents’ 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
in-fer 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
pull-ing 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 dictionary The formal
defini-tion 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 occu-pies 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 con-tains, 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 mole-cules 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 com-bined 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 ac-count and refine it The one cho-sen is recorded in their notebooks and boxed to eliminate any con-fusion in identifying the correct explanation The best explanation
is that pressure from the force ex-erted 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 dif-ferent-sized jars and varying amounts of water The same results occur regardless of the differences During this class discussion, we compare the differ-ent-sized columns of air created in the partially filled jars with the columns of air in the room, reemphasiz-ing 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
The exploration phase
I designed the exploration phase (Figure 3) to en-gage 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
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
Trang 3bernoulli’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 observing 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 very vague, asking only for
predic-tions, observapredic-tions, and explanations of what the
group observed (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
Pa-per activity Students blow air between two pieces of
pa-per, 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
Biography of Daniel Bernoulli
FIGURE 1
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
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 contemporaries, including Newton’s explanation of pressure
published in Principia Mathematica
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
Daniel Bernoulli (1700–1782)
in their notebooks and prepares their explanations The key question they must address is “How are the three activities similar?”
The invention phase
During the invention phase (see Figure 4), I bring the class together as a group of student scientists
to share observations 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 sit-ting 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
Trang 4guage also allows students to better understand the human origin of scientific knowledge Students de-cide that air moving rapidly over a surface reduces the air pressure on that surface: Moving air influ-ences air pressure
At this point, I identify their statement as Ber-noulli’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), re-spond to the questions that follow (Figure 2), and
Biography of Daniel Bernoulli
Questions for reflection
FIGURE 2
• 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?
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
pressure must be less on top, allowing the greater air pressure under the paper to force the paper up-ward 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 observed 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 sur-face 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), us-ing 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
Trang 5lan-bernoulli’s principle: science as a human endeavor
be prepared for a discussion of Daniel Bernoulli’s
life I use responses to the questions and the
discus-sion as informal assessments To close the invention
phase, I ask students to think of examples where
Bernoulli’s principle is used every 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 curve 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 sig-nificance 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 bi-ography, 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 hap-pening in other parts of the world, in particular the American Revolution For those students who have reading difficulties, a CD or audiotape of the biog-raphy would be helpful A colorful PowerPoint pre-sentation of the information or a short play created
The exploration phase
FIGURE 3
The hanging paper There she blows! (part 1) There she blows! (part 2)
materials
2 pieces of paper
2 clothespins or clips 2 booksPaper 1 piece of paper
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 pres-sure, explain your observations.
How are the three activities similar? Be prepared to discuss your ideas and explanations with the class.
The invention phase
FIGURE 4
1 1 As a class, we are now prepared to discuss the three
activities completed in the exploration phase.
1 2 What did you observe in the Hanging Paper activity?
1 3 Explain your observations.
14 What did you observe in There She Blows! (Part 1)?
1 5 Explain your observations.
1 6 What did you observe in There She Blows! (Part 2)?
1 7 Explain your observations.
1 8 How are the explanations of these activities similar?
1 9 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
Ber-noulli’s principle.
11 Think of examples where Bernoulli’s principle is used
every day.
Trang 6by 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 Ber-noulli’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 au-thor 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
Ber-noulli’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-The application phase
FIGURE 5
liftoff 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
procedure
1 Gently place one cup inside the other.
2 Using Bernoulli’s prin-ciple, attempt to cause the inner cup to pop out
of the outside cup with-out using your hands or feet.
3 Record the procedure that was successful.
4 Explain why your proce-dure works.
1 Using the index card, create a wing that when taped correctly will lift one end of the ruler from resting on the table
2 Use Bernoulli’s principle
by blowing across the top
of the index card.
3 Illustrate your design when it appears success-ful.
4 Explain why your design works.
Laboratory report
FIGURE 6 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 Hypothesis/Prediction Observations Conclusions (inference)
tific knowledge, according to the Nature of Science
Benchmark “Scientific Worldview” (AAAS 1993) and
the National Science Education Standard “The Na-ture 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 miscon-ceptions such as the Earth being the center of the solar system and the world being flat, believed to be true for centuries by very intelligent people
To raise awareness that scientific knowledge is tentative and often the best explanation of a phenom-enon available at the time, we discuss question three
(How did reading about Daniel Bernoulli’s
explana-tion of changes in air pressure affect 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
“Sci-entific 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
sci-ence should be presented, rather than scisci-ence at its technical peak (Maslow 1966) My students gener-ally 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 very smart scientist
The fourth question (How do Bernoulli’s
Trang 7discover-bernoulli’s principle: science as a human endeavor
ies affect 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
His-tory of Science” (NRC 1996) investigate and stress
the relevancy of science To answer question four,
students always refer to the second-to-last
para-graph of the biopara-graphy, 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
differ-ent perspective They remark that he had a family,
friends, and a job, and in some instances, proposed
theories that were more accurate than his
contempo-rary Sir Isaac Newton’s I also point out that he lived
for 82 years, a very long life during the 18th century
After the discussion, students engage in the final
phase of this learning cycle, the application phase,
in which the principle they articulated in the
inven-tion phase is used to solve new but similar problems,
helping them to make the connection between
sci-ence and technology
The application phase
In the application phase (Figure 5), I present
stu-dents with two challenges, again walking them
through and demonstrating each procedure The
first challenge is to place one Styrofoam cup into
an-other and cause the inner cup to pop out of the outer
cup by applying Bernoulli’s principle, without
us-ing 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
in-ner 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
Formal assessment of Bernoulli’s principle
FIGURE 7 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
Trang 8the card causes the air to move more quickly over the top of the card, reducing air pressure The air pres-sure 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 ex-ploration 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 reports completed during the application phase and my anec-dotal remarks serve as informal assessments for each student group, in addition to the questions for reflec-tion 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 observe
a phenomenon investigated over 220 years ago that has impacted modern society They approach the investigation in the same manner as scientists do,
by observing, making inferences together to ex-plain what they have observed, 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 roof-tops After completing the learning cycle, students understand why the shower curtain moves toward them while the water is streaming past, or the rea-son 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 inquiry and begin to look at scientists like Bernoulli as real people who are passionate about understanding the natural phenomena around them. n
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Deborah McCarthy (deborah.mccarthy@selu.edu) is
an assistant professor in the College of Education and Human Development, Department of Teaching and Learning, at Southeastern University in Hammond, Louisiana