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[1] Reflection
Reflecting and acting on reflection are key components in becoming an
exploratory learner. As teachers, we need to model reflection practices in
helping our students learn how to reflect. Here are some
suggestions:
a. Share with students an experience of a reflection that led to an action.
For example, how a reflection on a class led to changes in the lesson plan for
the next day. The example needs to be specific and related to the
students.
b. Periodically hold a reflection time during class. Call on students to
reflect on a particular topic. Ask them to discuss implications and
ramifications based on their reflections.
c. Call on students to discuss last night's homework. What was it about? What
did you learn from it? This should be done frequently so that students learn
to anticipate (and hopefully prepare) being asked about their homework. This type of reflection provides a measure of a student's
development over the course of a semester.
d. After a test, hold a class reflection on the preparation for the
test.
e. Hold a Peer Reflection related to group work. Create a matrix with
favorable characteristics (e.g., shows leadership, dependable, contributes,
etc.) listed as row headings. Hand out a copy to each student with
instructions to list the names of their group members as column headings and
then fill in the matrix, rating each group member on a scale of one to five
with five being the best rating. Encourage students to include additional
comments. Create a scatter plot of the results (categories on the horizontal
axis and ratings on the vertical axis) to display to the class. Results for an
individual student could be discussed during individual counseling sessions.
Holding three or four or more Peer Reflections provides the teacher with an
insight to student development that is not necessarily shown in the normal
assessment. Readers, please send me your thoughts and suggestions on how reflection leads to student growth. I will include them in future issues of this Newsletter so that all may benefit from your experience and insight.
[2] Growth Rates
The economic historian, Simon Kuznets, called the period 1,800 to 2,000 the
time of modern economic growth. The world's population had grown from
roughly 230 million in 1 A.D. to 900 million 1800 years later. (Today, the
world's population is approximately 6.3 billion, a 7-fold increase in a little
over 100 years.)
A comparison of the Gross Domestic Product (GDP) of the United States and
Western Europe over the period 1820 to 1998 illustrates the power of compound
interest. In 1820, the GDP of the United States and Western Europe was
approximately the same at $1,200 per person. The average annual growth rates
in GDP over the period 1820 to 1998 was approximately 1.9 percent for the
United States and 1.5 percent for Western Europe. Although the difference in
these rates do not seem to be great, they lead to radically different results
when applied over a 178 year span. The United States had approximately a 20
-fold increase in its GDP over that time compared to a 14-fold increase for
Western Europe.
By contrast, the approximate GDP of Africa was $400 per person in 1820 and its
average annual growth rate has been approximately 0.7 percent over the time
span from 1820 to 1998. Over this 178 year span, Africa's GDP had increased
from approximately $400 to $1,384 per person, slightly more than a 3-fold
increase. Over this time span, a comparison of the GDP between the United
States and Africa grew from 3-fold gap to almost six times that
amount. Compute the following: a. The annual growth rate of the world's population from 1 A.D. to 1800 A.D. b. The annual growth rate of the GDP in the United States from 1998 to 2007. [3] Interpreting Population Pyramids
Learning how to interpret graphs and draw inferences from graphs is an
important objective of a refocused college algebra course. Population pyramids
offer nice opportunities for this type of analysis. A population pyramid
represent a country's population by age. Each level represents a five year age
interval, with the bottom level being 0-to-4, the second level being 5-to-9,
etc. The left-hand side represents the male population and the right-hand side
the female population. The horizontal lengths of the bars denote the size of
the population. Because the horizontal scales are different for different
countries, comparisons and interpretations need to be based on the shapes of
the pyramids. Discuss the patterns of growth for each of the countries as suggested by their population pyramids. Consider such things as birth rates, death rates, immigration (emigration), government encouragement or discouragement of couples having children, etc. Predict the corresponding pyramids for 2025 and then check your prediction against those found at www.IDB Population Pyramids.
[4] Skill Work
Although mastering skill work is not an objective of a refocused college
algebra course, an occasional accountability session is appropriate. Such a
session might include pairing students into groups of two and presenting them
with the following list of statements. After five minutes begin calling on
different groups to state whether a given statement is True or False. If a
group says that the statement is True, ask them to give an example
illustrating the statement. If they say the statement is False, ask them to
give a counterexample (i.e., an example showing that the statement is
false).
a.
b.
c.
d.
e.
f.
g.
h.
[5] Queries
a. Margaret and Don stopped at Cooks Crossing in Searsport, Maine to buy two
crab rolls. On the menu, crab rolls were listed at $9.00 each. The bill,
including sales tax, was $19.26. What is Maine's sales tax rate?
b. The L.L. Bean outlet store in Ellsworth, Maine advertised a sale of 30% off
on all items in the store. In addition, over Labor
Day weekend the store had a sign at the check-out counter that read 50% off
the sale price on selected items. If you purchased one of the selected items,
what would be the sale percentage off? c. The price including an 8% sale tax for a cheeseburger and a cup of coffee at Alexis Diner in Newburgh, NY is $6.92. What is the menu charge for a cheeseburger and cup of coffee? 
[6] Notices
* Supported by the National Science Foundation and the U.S. Military Academy. |
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