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TIME-TRAVEL DAYS HOW FAR CANIMAGINATION TAKE YOU?
A workshop presented at the
|This workshop introduced the imaginative teaching concept of “Time Travel Days”
developed by Carol Pettigrew, a grade 3 teacher in North Vancouver. Carol designed this
set of ten Days as an assignment for a Post Baccalaureate Diploma (PBD) course taught by
the presenter. However, unlike many course assignments, this one did not get left on the
shelf, and Carol has implemented her ideas for the past three years. The PBD course dealt
with historical and multicultural aspects of mathematics, and this focus is reflected in many
of the activities selected: however the Days presented a cross-curricular approach to
learning, and also included science, art, social studies and language arts. Carol designed
ten Days, ranging from a trip to Stone Age to a look at “Math of the Future”, and the
children “travelled” to a different location at the end of each month.
Before the students’ first trip, they drew pictures to show how they imagined timetravel.
The concepts of spinning around and stretching endlessly backwards were popular,
as illustrated by the pictures shown on the previous page. The students’ first trip back in
time was to the Stone Ages. They sat in two circles on the floor, holding hands (“so that
the machine won’t break”) with their eyes tightly closed (“so you won’t get dizzy”). Carol
explained that they might hear some strange sounds as they travelled, and as she announced
that the trip was starting, she switched on a tape of electronic music. As this played she led
the children back through time:
Back to the time when you were born, only 8 short years ago. ... Further back to the
time when your parents were born, ... back to the second World War, the first World
War, ... We’re spinning through the age of exploration when North America was
discovered ... back to the birth of Christ – and we’re only gone back 2000 years, my
goodness, we have a long ways to go. ... Now we’re going further and further. People
are living in little grass or wooden huts, ... and now we’re going back to caves, and
times when there was no TV, nothing that you know exists in the place we’re at.
The children really entered into the spirit of this imaginative journey. They swayed
back and forth, and as they “arrived” they opened their eyes and commented on what they
could see, hear, touch, taste and smell – including the unwashed bodies of the cavemen. At
recess time, Carol warned them to be careful, noting that “the Stone Age can be a
dangerous place”. One boy returned holding his face, which had been hit by a soccer ball,
but he explained that he had been “attacked by a sabre-toothed tiger” – the Stone Age had
certainly captured his imagination!
While in the Stone Age, the students played the role of archeologists, and were given
sets of bones to investigate (dissected Halloween skeletons). Carol had drawn marks on
these to imitate the Ishango Bone, a twenty thousand year-old bone with what appear to be
tally marks upon it. However, the children ignored these markings and concentrated on
reconstructing the skeletons, which led to a useful lesson in human anatomy. Later in the
day Carol showed them pictures of the Ishango Bone, and they were challenged to imagine
the significance of the markings. The doubling pattern was recognized by most students,
and a few even identified the sequence of prime numbers. This led to an interesting
discussion as to how much mathematics would have been known so long ago.
The second Day, the children visited ancient Mesopotamia. This time they started by
role-playing the inhabitants of four villages who used the services of a trader (Carol) to
exchange their goods. By purposely cheating the “villagers”, Carol was able to help her
students understand why writing had developed, and they explored how it had first arisen
from the use of “number tokens”, such as have been discovered in the geographic area of
ancient Sumeria. These tokens used a base sixty system (from which the modern minutes
and seconds are derived), and using replicas of
these small clay objects, the children were able to
construct numbers in this base, quite an advanced
task for grade 3 students. Later in the day, the
children became students in a Babylonian scribe
school. The class had seen the Babylonian
number symbols displayed on their class
calendar, and having identified the symbols for
one and ten, they then created their own
Babylonian tablets, using clay and stylus (a
suitably carved chop-stick). These were then
fired in a kiln to provide a permanent record of
their visit to ancient Babylon.
Egypt was the third destination, and the
children were full of information about
pyramids, tombs and mummies. However,
although they could all tell Carol the mathematical definition of a square pyramid, when
presented with a set of blocks, their constructions often showed that they had not really
internalized this definition: some “pyramids” were simply triangles, whereas others had
bases in which the “square” had unequal sides. The children had also heard of papyrus, and
were intrigued by stems of this plant (which Carol had brought from her garden), as it has a
most unusual triangular cross-section.
Carol also showed them a sheet of
papyrus, and the children constructed
their own “papyrus” by tearing strips
of newsprint and then gluing them
together in the cross-wise fashion used
by the Egyptians. Later in the day,
they solved a puzzle to determine the
number symbols used by the
Egyptians. Even though they did not
know the origin of these symbols, the
children still referred to the various
signs as “birds”, “people” and
“flowers”. They were interested to
learn why these symbols had been chosen for specific numbers, and were also delighted by
the “walking legs” symbol, which
represents addition or subtraction
according to which way the legs are
walking!. They were then able to
write equations on the papyrus they
had created earlier, as well as including the hieroglyphic symbols representing the syllables
of their names.
The trip to Ancient Greece
was notable for its use of costume:
a few days beforehand, Carol had
given her class instructions for
turning a sheet into a Greek toga,
(reading from right to left)
“Three” “two” “is added” “five” “is the answer”
and both teacher and students spent the day dressed in Greek fashion. For this day, the
students were divided into groups, each of which investigated the life and work of a
different Greek mathematician. Most of the information and activities were taken from
two series of books by Wilbert and Luetta Reimer: Historical Connections in Mathematics
and Mathematicians are People Too! The students enjoyed reading the short biographies,
and also liked exploring the different approach to mathematics, such as the Greek concept
of the shapes of numbers.
The next Time-Travel Day was planned to coincide with the Chinese New Year.
Carol organized a
Chinese Tea Ceremony
for her students, and
they discussed the terracotta
warriors and other
aspects of Chinese
history while they
sipped their tea. Later in
the day, Carol told them the legend of “Lo Shu” and the children competed to be the “child
that had saved the village” by determining the significance of the numbers. After
THE LEGEND OF “LO SHU”
In ancient times, there was a huge flood
in China, and the people offered
sacrifices to the River God. Each time, a
turtle came out of the river and looked at
their offering, but the God was not
satisfied and the floods continued. Then
a child noticed the curious markings on
the turtle shell, and was able to tell the
villagers the correct amount of sacrifice
discovering this, mathematical imagination took over as
they searched for different versions of the square.
There were many other activities in the Days
described so far, and in the remaining five Time-Travel
trips to Rome and India, the Middle Ages, Renaissance,
Women in Math and Math of the Future: unfortunately
this workshop was too short to encompass more than a
tiny fraction of what was covered during these ten
exciting school days. However, one imaginative activity
which had to be mentioned was the staging of skits taken
from the book Historical Connections in Mathematics.
The children spent their lunchtimes rehearsing these little shows, and both the actors and
the audience enjoyed these episodes from the lives of famous mathematicians.
Carol spends many hours collecting material for the students to explore, and the
following list shows some of the resources she uses.
Books of math activities (with teacher’s guides)
Irons, Calvin and James Burnett. (1995). Mathematics from Many Cultures (six ‘packs’).
San Francisco, Ca.: Mimosa Publications Pty. Limited.
Reimer, L., & Reimer, W. (1992, 1993, 1995). Historical connections in mathematics,
Vols. 1,2 & 3. Aurora, ON: Spectrum Educational Supplies Ltd.
Zaslavsky, C. (1994). Multicultural math: hands-on activities from around the world. New York:
Scholastic Professional Books.
Ganeri, A. (1996). Story of Numbers & Counting. London: Evans Brothers Ltd.
Millard, A. (1998). A Street Through Time. New York: DK Publishing.
Orlando, L. (1999) Multicultural Game Book. New York: Scholastic
Osborne, M. P. (2001). Magic Tree House Series. London: Random House
Pappas, T. (1999). Math a day. San Carlos, Ca.: Wide World Publishing/Tetra, 1997
Pappas, T. (1997). Mathematical scandals. San Carlos, CA: World Wide Publishing/Tetra
Pappas, T. (1989). The joy of mathematics: Discovering mathematics all around you. San Carlos,
CA: World Wide Publishing/Tetra.
Reimer, L. & W. Reimer (1990, 1995). Mathematicians are people, too: Stories from the
lives of great mathematicians, Vols. 1 & 2). Palo Alto, CA: Dale Seymour
Schmandt-Besserat, D. (1999) The history of counting. New York: Scholastic Inc.
Books specific to particular time-travel days
Stone Age: Scieszka, J. (1995). Your Mother was a Neanderthal. London: Puffin.
Mesopotamia: Rowland-Entwistle, T. (1986). Nebuchadnezzar and the Babylonians.
Egypt: Burnett, J., & Irons, C. (1996). Egyptian genius. San Francisco, CA: Mimosa
Publications Pty. Limited.
Greece: Leon, V. (1997). Outrageous Women of Ancient Times. New York:
John Wiley & Sons:
China: Bouchard, D. (1997). The Great Race. Brookfield, CT: Millbrook Press.
Rome: Pappas, T. (1997). Math for Kids & Other People Too! San Carlos, Ca.:
Wide World Publishing/Tetra.
India: Demi. (1997). One Grain of Rice: A Mathematical Folktale. New York:
Neuschwander, Cindy. (1997). Sir Cumference and the First Round
Table : A Math Adventure. Watertown, Ma.: Charlesbridge Publishing,
Wroble, L. A. (2001). Kids During the Renaissance. New York:
Sís, P. (1996). Starry Messenger. New York: Farrar Straus & Giroux
Visconti, G. (2000). The Genius of Leonardo. Bath, England: Barefoot
Leon, V. (1997). Outrageous Women of the Middle Ages. New York:
John Wiley & Sons:
Leon, V. (1997). Outrageous Women of the Renaissance . New York:
John Wiley & Sons: