|
|
| Home | Textbook | Newsletter | Discussion Forum | Contact |
 Textbook
|
|
[1] Reflections on Piloting the Contemporary College AlgebraCandy Hodges
Bethune-Cookman University
(The objective of the NSF and ARO funded HBCU Retreat and Follow-On program
sponsored by the U.S. Military Academy is to assist schools in refocusing
their college algebra course. The Contemporary College Algebra is an example
of a refocused college algebra course.)
As the team leader of Bethune-Cookman University's team that participated in
the 2008 HBCU Retreat and Follow-On program at the U.S. Military Academy, I
would like to share some successes from the first two semesters that
Contemporary College Algebra (Contemporary) was piloted. The Contemporary course was first piloted in Fall 2008, when traditional college algebra courses were offered simultaneously.
This refocused course resulted in 67.6% of students passing, as compared to the
traditional course passing rate of 52.3%. The Spring 2009 Contemporary course
passing rate was 63.9% passing, where the traditional passing rate was 40.4%.
No students dropped from the Contemporary sections, whereas 36 students --
nearly 7% -- dropped from the traditional college algebra sections. Students in the two sections of the Contemporary program from the Fall 2008 semester were given an anonymous survey at the end of the semester. They were asked: a. Would you recommend this class to a friend? and b. Why or why not? All but one of the students responded "Yes" and some of their reasons follow exactly as written: "I would recommend this class to someone who is a visual learner because that way they can see the lessons worked out compared to the traditional way. I believe this is a better way of
learning because you're not learning straight out of the textbook and this
class makes you think."
"This explores audio, visual, and kinesthetic learning, which means that any
kind of learner can be successful in this class." "I would recommend this class to a friend because it is very comprehensive and it's another way of learning math. The math in this class is very useful and it's not just about plugging numbers
in a formula but a given situation that has to be solved. It's sort of like
putting math into writing." "Because it helps me think outside the box sometimes. It's a great class to sharpen your rusty skills. If your class is productive the teacher doesn't have to teach all the time. The students can teach
each other and as students we sometimes learn better from our peers."
The two principal goals of Don Small's Contemporary College Algebra textbook
are (1) to aid students in developing their problem-solving abilities in the
modeling sense, in order to empower students to use mathematics to quantify
real-life situations, and (2) to empower students to become exploratory
learners, not to master a list of algebraic rules. On the first day of class,
students were divided into groups of six and tasked the problem, "A group of
six people meet and each person shakes the hand of every other person exactly
once. Determine the total number of handshakes for the group of six people."
The two principal goals were evident with this problem alone. Circulating
amongst the groups, I observed students making tally marks, drawing stick
figures, using letters of the alphabet -- using a variety of approaches to
represent the six hand shakers. Some groups were obtaining what I knew was the
correct answer, others an incorrect answer, and still others floundering.
Still, I refrained from commenting. After about 15 minutes, each group was
asked to present their method and answer. After all had presented and
discussions had taken place, I informed the curious class full of students of
the correct answer. One group, in particular, maintained that their
(incorrect) answer was correct. I asked them to come forward to model the
situation, which was one method no group in this section had used. The first
two shook hands and the moment they released their grip, every member's eyes
widened as one exclaimed, "Oh, we don't have to count those two again!" We
then discussed what the group had just accomplished and where they and others
had erred in their thinking and which groups had not. That was definitely
problem-solving by modeling (physically) and learning through exploration and
that was the beginning of a semester full of such "Ah-ha!" moments.
Another of the refocused college algebra goals is "To improve communication
skills (reading, writing, presenting, and listening). Students were
responsible for reading the text and because many of the questions and queries
throughout the text required writing, they practiced their writing skills
daily. As students worked in groups, they definitely sharpened listening
skills. Presentations were required for certain projects and activities and
most students took much pride and demonstrated creativity and organizational
skills, as well as skills in mathematics.
"To employ small group work, including in-class group activities and
out-of-class group projects" is yet another goal of the course. After a
maximum of 15 minutes per class that I spent "lecturing", students were put to
task on group activities. This way, the students were working, thinking, and
discussing -- they were actively involved in the mathematics tasks. As I would
circulate about the room, I heard wonderful discussions and students helping
each other out. The atmosphere was most conducive to learning.
Also a goal of the course is "To use technology for plotting and computation".
Students employed technology by utilizing graphing calculators virtually every
day. Students also gained experience using Microsoft Excel and PowerPoint for
some of the projects, which will be useful to the students in subsequent
classes and in the workplace.
Two remaining goals are "To develop personal confidence as a problem solver"
and "To facilitate student enjoyment of applying mathematics to meaningful
situations." Students' confidence improved throughout the semester as they
solved real-world relevant problem situations. Most come with experience only
in plugging formulas and obtaining "meaningless" answers, which is not
conducive to confidence building or to enjoyment.
I hope that more and more colleges and universities give a refocused college
algebra course a chance and believe that one day, the data will be
indisputable enough that more college algebra courses offered will be taught
using the Contemporary, as opposed to traditional, pedagogical
paradigm. [2] Fun Project: What Hourly Wage Must I Earn to be Financially Independent?
The purpose of this small-group Fun Project is to have students analyze their
financial situation after graduation. Each group forms a list of expected
expenses including, but not limited to: rent or mortgage payment, car payment,
food expenses, debt payments (credit card, college loans, etc.), clothing
expenses, social expenses. Accompanying the list is a realistic justification
of the amount for each expense category (e.g., statement from a realtor or
bank, personal interviews). Assuming that a person has a 40 hour per week
employment, determine the minimum hourly rate that the person would have to
receive in order to pay his/her expenses? [3] Finishing the Race
Running is one of the faster growing forms of exercise. In fact, the number of
people running for exercise and/or sport has more than doubled in the past
eighteen years. June 4, 2009 was celebrated as the inaugural National Running
Day. The primary purpose is to promote running as a healthy, easy, and
accessible form of exercise. USA Today published the following table (Source:
Running USA/New York Road Runners) in its June 4, 2009 edition:
a. Display this data in a scatter plot. b. Fit a linear model to this data. c. Interpret the meaning of the slope in your model. d. Approximate the number of finishers in the road races in 1970, 1980, and 2010.
e. What is a reasonable domain for your model? Explain your
reasoning. [4] Systems of EquationsCandy Hodges
Bethune-Cookman University John is investigating the long distance calling plans of three different companies, Company A, Company B, and Company C. He has obtained the long distance charge information from the three companies. Company A charges .08 per minute and has a $1.00 per month service charge. Company B charges .07 per minute and has a $2.00 monthly service charge. Company C charges .05 per minute and has a monthly service charge of $4.00. 1. For this situation, which costs are variable and which are fixed? Explain. 2. For this situation, what is the independent variable? Explain. What is the dependent variable? Explain. 3. For each of the three plans, form a table showing a month's charge under the four scenarios of long distance calling times: 20 minutes, 80 minutes, 140 minutes, and 200 minutes. 4. Using the same coordinate plane, form a scatter plot (by hand) of the data in each of the three tables (three scatter plots). Then connect the points in each scatter plot to form three line plots on the same coordinate plane. Label the axes and each of the line plots. 5. Write equations to represent the month charges for each of the 3 companies. Company A ______________ Company B ______________ Company C ______________ 6. What are the y-intercepts for each line? Company A ____ Company B ____ Company C ____ 7. Explain what the y-intercepts represent within the context of the problem. 8. Explain what the slopes represent within the context of the problem. 9. After reviewing the past year's long distance bills, John determined that he averaged 30 minutes of long distance calling per month. If his long distance calling remains similar to last year, which plan should he choose? ______ What plan should he choose if his average last year was 60 minutes? ______ What plan should he choose if his average last year was 90 minutes? ______ What plan should he choose if his average last year was 120 minutes? ______ What plan should he choose if his average last year was 150 minutes? ______ What plan should he choose if his average last year was 180 minutes? ______ 10. At what amount of minutes of long distance calls per month are the 3 plans the same price? Explain your reasoning. 11. How do the rates of the three companies compare before the amount found in #10 above? How do the rates compare after that amount?
12. Explain the comparison results found and described in #11 above. (Be
certain to address the differences in the slopes and y-intercepts in your
explanation.) [5] Notices
* Supported by the National Science Foundation and the U.S. Military Academy. |
|
| Home | Textbook | Newsletter | Discussion Forum | Contact |
