Lesson from Galileo

galileoscopeHow will I incorporate what I have learned into my classroom:

My unit outline on Connections with Galileo consists of four experiments related to the discoveries of Galileo.  My teaching method will focus on serving as a guide for my students as they conduct their research.  I will focus on the processes of problem-solving, communication, reasoning and proof, representation, and connection within the classroom.  I will help my students make connections with the math that we study to other disciplines such as physics, astronomy, and history.

Falling Objects Experiment

Up until Galileo’s time people had accepted the Aristotle’s belief that the heavier an object is, the faster it will fall.  Galileo challenged that belief with his falling objects experiment in which he reputedly dropped iron balls of unequal weights from the leaning tower of Pisa.

Goals: To determine if the weight of an object affects its rate of fall (acceleration)

Student Activities:

  • Students will go to the computer lab to simulate Galileo’s Falling Objects Experiment in which two cannonballs of unequal weights are dropped
  • The students will predict which simulated cannonball will fall first and then actually conduct the simulated experiment to determine the results.
  • The students will watch a video on the same experiment conducted by a physics professor from the University of Pisa who dropped bottles of water with the same shape but containing different amounts of water from the top of the Leaning Tower of Pisa.
  • The students will then conduct the same experiment live dropping containers of water and then a bowling ball and a soccer ball at the same time from the top of the stadium to determine if weight actually affects the rate of fall.
  • The students will write a mini-lab report on the experiments they conducted.
  • The students will discuss the Law of Falling Bodies. From HOWSTUFFWORKS.com : “A falling body in a vacuum accelerates at the rate of 32 feet, per second (9.8 m/s) during each second that it falls. This acceleration is called the acceleration of gravity, which is expressed mathematically as g.”
  • The students will solve math problems to determine the velocity, acceleration, and position of falling bodies on the earth, the moon, Jupiter, and other planets.

Assessments:

  • Lab-report on experiment
  • Quiz on velocity, acceleration, and position of falling bodies

The Pendulum Experiment

Galileo claimed that one day he became bored during a service at the Cathedral of Pisa and began to watch a swinging chandelier.  This led him to experiment with pendulums to determine if the weight of the bob, the height of the release, and/or the length of the string affected the period of the pendulum(the time it take to make one full swing)

Goal:  To determine if the weight of the bob, the height of the release, and/or the length of the string affects the period of the pendulum.

Student Activities:

  • Students will go to the computer lab to simulate Galileo’s Pendulum Experiment using pendulums of different weights, angles, and lengths.
  • Teams of students will use the following items to conduct their own pendulum experiment outside to conduct their own experiments: string, cup or small pail with a handle, sand, for weight, a tree limb, stop watch
  • Students will write a mini-lab report on the results of their experiments.
  • After a discussion about the fact that the square of a pendulum’s period varies directly with its length, students will solve problems related to the pendulum with varying lengths and cycles.

Assessments:

  • Lab-report on experiment
  • Quiz on the mathematics related to the movement of a pendulum

The Inclined Plane Experiment

Goals:

  • To measure short time intervals with a water clock
  • To calculate the acceleration of a rolling ball

Student Activities:

  • Students will watch the reenactment by an Italian professor of Galileo’s inclined plane experiment on a video
  • Student teams will assemble inclined planes and water clocks from materials ordered
  • Student teams will pour water into the top of the water clocks that they created
  • Student teams will time the ball’s motion down the plane by turning the water clock’s valve on and off
  • Student teams will record the time it took for the ball to travel starting at different heights along the inclined plane on a data sheet and then compute the ball’s acceleration from each height using the equation for distance, time, and acceleration ( d = ½ a t2 ).
  • Student teams will create posters showing the data they collected and the results of their experiments. This will include graphs related to the experiment. All teams will display their work and a class discussion of the results will be held.

Assessment:  Rubric for Students’ Posters for project Grade

 

Galileo’s Telescope

In 1609 Galileo first heard of the invention of the telescope and immediately began to make improvements upon it.  He used it to make major astronomical discoveries from the mountains of the moon to the moons of Jupiter.   His discoveries led him to believe in the Copernican model of the solar system in which the sun rather than the earth was the center of the solar system with all of the planets rotating about it.  This led Galileo into serious trouble with the church and eventual house arrest for his beliefs.

Goals:

  • Describe how a reflecting telescope produces an image
  • Examine the history of the telescope from Galileo to Hubble
  • To build a replica of Galileo’s telescope
  • To use the telescopes to examine the planets and stars at night
  • To learn more about the development of the telescope by visiting a planetarium

Student Activities:

  • Students will watch the video 400 Years of the Telescope and answer questions related to the design of a telescope, Galileo’s contribution to the development of the telescope, and the designs and contributions of later telescopes.
  • Teams of students will build their own Galileoscopes.
  • Students will meet at night with the local astronomy club in order to use their Galileoscopes.
  • Students will go to the planetarium in Montgomery to learn more about astronomy
  • Students will compute the eccentricity of the elliptical orbit of each of the planets

Assessments:

  • Rubric developed for building of Galileoscope
  • Journal articles from meeting with astronomy club and from trip to planetarium
  • Quiz on ellipses and eccentricity
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Galileo and Apollo 15

This is a reenactment of Galileo’s famous experiment on falling bodies conducted on the moon by our astronauts.

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Galileo Quote

Galileo's Tomb in Florence

Galileo’s Tomb in Florence

“You cannot teach a man anything, you can only help him find it within himself.”
Galileo Galilei

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Thank You to Fund for Teachers

Every child grows up hearing the story of Galileo dropping weights from the Leaning Tower of Pisa in an experiment to determine the truth about falling objects.   Over the years I continued reading more about this Renaissance mathematician, physicist, engineer, and astronomer whom Einstein would later call the “father of modern science.”   As a high school mathematics teacher I was intrigued with Galileo’s belief that the universe like a book is written in the language of mathematics with the words represented by “triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it.”  I wanted to know more about his work and his desire to know the truth at any cost.  Fund for Teachers gave me the opportunity to spend 10 days in Italy researching the details of his complex and at times turbulent life, actually seeing and studying his inventions up close, and discovering how the culture of the Renaissance dramatically affected his life.    I came back learning so much more than I had expected and am now eager to share what I learned with my students and with other teachers.  Posts from this blog give some of the information I learned from each of the sites from my trip.

Stanmding in front of the bell tower at the Duomo in Venice where Galileo first displayed his telescope to the Venetian leaders.

Stanmding in front of the bell tower at the Duomo in Venice where Galileo first displayed his telescope to the Venetian leaders.

I want to thank the Fund for Teachers for giving me this wonderful professional development opportunity.  As the Italians say, “Mille grazie!”

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Galileo’s Children

Sister Maria Celeste, one of Galileo's children

Sister Maria Celeste, one of Galileo’s children

On one of Galileo’s trips to Venice, he met Marina Gamba.  Galileo moved her to Padua, but they lived in separate homes. Many historians believe that Galileo did not feel that Marina’s family was of the same social standing as his own so there could be no marriage. Between 1600 and 1606, Marina bore Galileo three children Virginia, Livia, and Vincenzo.  When Galileo left Padua for Florence he took Virginia and Livia with him leaving the 4 year old Vincenzo with his mother.  Because the two girls were listed as illegitimate, there was little hope of their being married so Galileo arranged for them to enter the convent for life. Upon becoming a nun Virginia took the name Sister Maria Celeste in honor of the Virgin Mary and of her father’s love of astronomy.  Livia chose the name Sister Arcangela.   Maria Celeste served as the apothecary of the San Matteo Convent and often sent herbal treatments to Galileo for his illnesses.  She and her father exchanged letters throughout her life.  Galileo once remarked that his oldest daughter was “a woman of exquisite mind, singular goodness, and most tenderly attached to me”.  Galileo even bought a home near the convent later in life so he could be near his daughters.  However, convent life was extremely harsh at that time, and Maria Celeste died from dysentery a the age of 34. Vincenzo would also move to Florence as a child to live with his father.  Galileo fought to have his son’s birth legitimized by the Grand Duke of Tuscany and was eventually successful  There were conflicts between the father and son over the years, but it was said that they had reconciled and actually worked together before Galileo died.

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Visiting the University of Padua

Standing in the courtyard where Galileo taught at the University of Padua

Standing in the courtyard where Galileo taught at the University of Padua

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The University of Padua

Anatomical theater at the University of Padua

Anatomical theater at the University of Padua

Galileo was a professor at the University of Padua for 18 years.  The university began in 1222 when a group of approximately 1,000 students and teachers left the University of Bologna.  The school was initially a student run organization with the students choosing the professors and paying their salaries.  For many years the school specialized in law, medicine, philosophy, and theology.  It is famous for being the site of the oldest permanent anatomical theater and the location of the first university botanical gardens along with being the first university in the world to award a university degree to a woman (Elena Lucrezia Cornaro Piscopia – Doctor of Philosophy in 1678)

Galileo taught inside these walls of the University of Padua.

Galileo taught inside these walls of the University of Padua.

On this trip I was actually able to sit in the hall where Galileo lectured, touch the podium from which he taught, and explore the famous anatomical theater of the University of Padua.  It was an amazing experience that I will always remember.

 

 

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