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Published in Trends &
Issues: The Publication of the Florida Council for the Social Studies,
Volume 12 (Fall 2000), pp. 12-14.
Exploring
World History Along the Silk Route:
A Social Studies Investigation Through Mathematics
Richard A. Austin
Denisse R. Thompson
University of South Florida
College of Education, EDU 162
4202 E. Fowler Ave.
Tampa, FL 33620
813-974-2852 (Austin)
813-974-2687 (Thompson)
austin (or thompson)@tempest.coedu.usf.edu
Both
Dr. Austin and Dr. Thompson are associate professors of mathematics education
at the University of South Florida. They are working together on several
activities relating the teaching of mathematics to literature. Some of
their previous publications or presentations have explored teaching both
science and math through literature written for elementary school children.
Exploring World History Along the Silk Route:
A Social Studies Investigation Through Mathematics
The study of world history provides a natural
opportunity to integrate social studies and mathematics. Map skills, the
study of cultures, and looking at modes of travel are all social studies
concepts that are natural venues for exploring mathematics. In this article,
we discuss how the use of the book, The Silk Route: 7,000 Miles of
History (John S. Major, 1995), serves as the context for this integration.
The activities are appropriate for upper elementary or middle grades students;
they are also easily adaptable for use with other levels.
Summary of the Book
The Silk Route: 7,000 Miles of History takes the reader on a caravan
trip from central China to Tyre and then onto Byzantium in the year 700
AD. This is a period of great changes in world history. The silk route
described here illustrates contact between various cultures because of
the desire for trade. In addition to material goods being traded the author
points out that various religions were also being exchanged and their
influences felt across the world. The author’s concluding paragraph
provides a wonderful overview on the process of trade.
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The garments
worn by the wealthy people of Byzantium are made of silk cloth brought
from China, more than 6,000 miles away. Few people in Byzantium
have more than a vague idea of where China is or what its people
are like, just as few Chinese know anything about the Eastern Roman
Empire. Yet Chinese silk is sold in Byzantium, and Byzantine gold
coins circulate in the markets of China. The two empires are linked
together by trade, thanks to the brave and enterprising merchants
of the Silk Route. (p. 28 - 29)
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Exploring Map Skills
The ability to read and use maps is an important
area within the social studies curriculum. Working with maps provides
a mathematical opportunity to discuss the use of legends or keys and to
discuss the difference in distance as the “crow flies” versus
distance along a road.
The very beginning of the The Silk Route
features a map of The Silk Route. This map is a simple form that
is not cluttered with extra information that would be provided in most
general maps of the region. The route winds from city to city like a red
and gold snake. In finding the distance between cities, students might
be tempted simply to count the number of red and gold segments on the
route. However, on a closer inspection they will find that the segments
are not of equal size across the entire map; thus, they need to use the
distance key provided. It is interesting to note that distance is provided
in both kilometers and miles.
After reading The Silk Route to a
class, the teacher might challenge students to check the distance from
Chang’an in China to Byzantium. If students are going to check the
claim of the author then they need to be sure to use the miles key. (Note:
the scale is 500 miles per inch.)
Upper elementary students could place a
string on the map to closely follow the silk route indicated on the map,
measure the length of the string, and then multiply their length in inches
by 500 miles per inch. Such an activity is great for small groups because
it helps to have several fingers to place the string on the route on the
map. (We found the total distance to be about 7700 miles.)
Students may also want to find the distance
between each of the cities mentioned in the story.
| From |
To |
Distance Between
the cities in inches |
Distance in
Miles |
|
| Answers: |
|
|
|
|
| Chang'an |
Dunhuang |
____________________________ |
___________________ |
(1300) [1200] |
| Dunhuang |
Kashgar |
____________________________ |
___________________ |
(1500) |
| [1300] |
|
|
|
|
| Kashgar |
Tashkent |
____________________________ |
___________________ |
(800) [700] |
| Tashkent |
Heret |
____________________________ |
___________________ |
(900) [800] |
| Heret |
Baghdad |
____________________________ |
___________________ |
(1300) |
| [1100] |
|
|
|
|
| Baghdad |
Damascus |
____________________________ |
___________________ |
(400) [400] |
| Damascus |
Tyre |
____________________________ |
___________________ |
(200) [200] |
| Tyre |
Byzantium |
____________________________ |
___________________ |
(1400) |
| [1400] |
|
|
|
|
|
TOTAL |
____________________________ |
____________________ |
(8000) |
| [7000] |
|
|
|
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(Note: the distance between cities varies depending on the measured distance
along the route on the map or the straight-line distance between the mentioned
cities. Our estimates for actual map or curved paths are indicated in
parentheses and the corresponding straight-line distances are enclosed
in brackets. Which do you suppose the author used? How can you support
that claim?)
Modes and Speed of Travel
Considering the differences in modes and
speeds of travel provides another opportunity to integrate discussion
of cultural differences and history and computational work in mathematics.
The following activities suggest some ways to integrate social studies
and mathematics. These activities are appropriate for upper elementary
or middle grades students, depending on their mathematical background;
teachers can easily adapt activities by modifying the numbers used.
At the end of the story, the author provided
additional information about the places and modes of travel. He indicated
that a caravan might travel as few as 10 miles per day or as many as 50
miles per day, depending on the terrain and weather conditions.
Example 1. Suppose you are a private
Chinese merchant who is making the trip as far as Kashgar. It is important
to get to Kashgar and back as far as Dunhuang before the summer heat makes
crossing the Taklamakan Desert too dangerous. To be safe you decide that
the trip must be completed by June 1. If the reliable guides claim that
you can average 30 miles per day, when would be the latest that you could
leave Chang’an with confidence that you would make it according to
your ideal time schedule? (Answer: 143 days before June 1)
Explain
how you decided on the date on which to leave with the caravan.
Example
2. Suppose that you are traveling west with a load of fine silk. At
Dunhuang, your caravan guide informs you that you must pack at least 8
liters of water per day for the trip across the desert. Your camel can
carry an additional 70 kilograms. Will you have to get an additional camel
to transport the needed water? Explain your answer.
(Answer:
YES!! – at 1500 miles a rate of 30 miles per day means 50 days. 50
days x 8 liters is 400 liters of water. Each liter weighs one kilogram
so that’s 400 kilograms -- a lot more than the 70 your camel could
carry. To convert kilograms to pounds multiply by 2.2 to get 880 pounds
of water.)
Example 3. After carefully listening
to stories from older merchants you have determined that the value of
fine silk increases by 50% for each 1000 miles it is moved to the west.
Further you determine that fine rugs from Baghdad increase the same amount
for each 1000 miles they are transported to the east. You determine to
make the trip from Chang’an to Baghdad with a load of silk. After
arriving in Baghdad you plan to trade the silk for Persian rugs, which
you will sell back in China. If you leave with $1000 worth of silk, what
value should you have upon trading in Baghdad? (Answer: about $11,000
) Now, if all of that money is put back into Persian rugs that are transported
back to Chang’an what will be the value of the rugs at the end of
the trip? (Answer: about $125,300)
[ Hint: use the miles between cities figured earlier (about 6000 miles).]
Example
4. A rival merchant from Chang’an also has plans to trade silk
for Persian rugs, but the rival is only going as far as Kashgar. There
the rival will sell the silk and buy the rugs for later sale in Chang’an.
The rival will not make as much money, but believes that he can make two
such trips while you make only one. If the rival actually can make the
two trips to your longer one, who will have the greater profit from the
business (assume the expenses of caravan travel are the same for your
one trip and for the rival’s two trips)?
(Answer: Rival will make about $18,000 for the two trips; you make $125,000
if the bandits don’t get you or your stuff!)
Changes Over Time
Students often fail to realize that cities
may change names over time, depending on various historical actions such
as war and occupation by other countries. Exploring such changes provides
another opportunity to integrate mathematics and social studies, along
with technology through exploration via reference books or the Internet.
For the next exercise students investigate
which cities mentioned in the Silk Route have had name changes since 700
AD. For example, Byzantium changed to Constantinople and is now Istanbul.
However, Damascus, Baghdad, Tyre and Dunhung are still called by the same
names. What kind of reference book could be investigated to check on city
names?
Example 5. Using a current map, plot
a route that passes through the cities mentioned in the story from Chang’an
(now Xi’an) to Tyre. Then approximate how long it would take to travel
that route by truck if the driver actually drives for 10 hours per day
and can average 50 miles per hour (assume that there are no problems passing
from one country to another). (Answer: 12 days) How much would it cost
if you hire a truck driver at a rate of 55 cents per mile? The driver
pays for the fuel at a rate of 75 cents per liter. If the truck can average
8 miles per liter of fuel how much will the driver make for the entire
trip? (Answer: about $2700, using 6000 miles for the trip.)
Example 6. If the truck driver had
to have his/her passport stamped at each border crossing how many times
would the truck driver have had his/her passport stamped?
Conclusion
The ideas discussed here are just a few
of the ideas that can tie mathematics with a story of early commerce between
two major civilizations, Chinese and Persian of the late first millennium,
that are not often featured in the social studies curriculum. The focus
here was on mathematical tasks, but we believe that teachers who read
The Silk Route will find a treasure of other possible activities and investigations
that are appropriate for the students that they teach.
References
Major, John S. The Silk Route: 7,000 Miles of History. (1995) Harper
Collins Publishers.
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