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TIME-TRAVEL DAYS HOW FAR CAN IMAGINATION 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. 3 6 4 8 10 5 5 7 11 21 19 9 11 13 17 19 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 to make. 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. RECOMMENDED RESOURCES 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. General background 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 Publications 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. London, Wayland. 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: Scholastic Press, Europe (Dark Ages) Neuschwander, Cindy. (1997). Sir Cumference and the First Round Table : A Math Adventure. Watertown, Ma.: Charlesbridge Publishing, Europe (Renaissance) Wroble, L. A. (2001). Kids During the Renaissance. New York: Powerkids Press Sís, P. (1996). Starry Messenger. New York: Farrar Straus & Giroux Visconti, G. (2000). The Genius of Leonardo. Bath, England: Barefoot books. Women in Math 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: |
