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 The Importance of Seeking Out Hidden Treasures of Support
Like many schools, Husson University runs a tutoring center where students can
get help for a variety of their classes. To support our new Contemporary
Algebra program, we have an adjunct instructor who teaches one section of the
course and tutors in our Learning Center. Our tutors are vital to the success
of many of our classes, especially Contemporary Algebra. We encourage students
to use the center, but it's not always easy to convince them to actually take
advantage of this valuable service. It's particularly difficult to get
freshmen into the Learning Center. The majority of our students are from
Maine. They come from hardworking and proud families who don't like to ask for
help. Over and above that, many students erroneously associate the Learning
Center with the "Special Education" rooms from their high schools. Usually, once we get students in the
door and they understand what the Learning Center offers and how it can help
them, they keep coming. Sadly, there's still a good number of students who
really need some extra support, but don't seek help. For some of those
students, Husson has a hidden treasure, in the form of one Julie Perkins.
Julie is in charge of purchasing and information services for Husson's
in-house and retail dining services. She's a local with a strong Down East
dialect, whom the students can easily identify with. Julie has bachelor's
degrees in Business and Computer Science, a MSB (Master of Business) and is
working towards a Juris Doctorate. Additionally, Julie teaches classes for
Husson in Ethics and Economics. She could be working a lot of other places,
but stays at Husson for the students.
What Julie does for our students is provide several hours of her own time
every week tutoring them in economics, business and math. Even though Julie's
degrees are not in math, she has always had a knack for it and more
importantly a knack for teaching others how to learn math. She tutors students
in classes from basic college math to algebra, finite math and calculus. Julie
volunteers several nights a week in the Learning Center, but she also tutors
several hours a week in the dining hall. Many of the dining hall work study
employees are "at risk" students and Julie helps them after their shifts are
over. But, it's not just dining services students who come to the dining hall
to meet with Julie. Students who are uncomfortable in the Learning Center will
come to the dining hall instead. She also gets numerous students through word
of mouth and from referrals from other dining services staff.
When Husson University adopted a Contemporary Algebra program, we
inadvertently bypassed bringing Julie on board with the changes. This was an
easy omission to make, because she works behind the scenes and doesn't draw
attention to herself or seek acknowledgement for what she does. I knew of
Julie and that she was tutoring students in math, but didn't realize the
extent of her help. When the Contemporary Algebra program was being developed,
a great deal of information was given to faculty throughout Husson. We had two
pilot courses in the spring of 2009, but it wasn't until June or July that I
realized the importance of bringing Julie up to speed with what we were doing
with our Contemporary Algebra program.
I had a "special summer edition" of Contemporary Algebra for five Husson
employees. Two of those employees were from dining services and Julie was
helping one of them. Through that student, I heard that Julie wasn't sure
where we were going with this class. Like many of us, Julie loves computations
and calculations. Contemporary Algebra takes a lot of those computations away
and focuses instead on concepts and context. No one had told Julie that we had
dramatically changed Husson's College Algebra course, a course in which she
had tutored students for many years. This situation needed to be remedied! I
set up a meeting with Julie and brought her some of the articles about the
need to refocus college algebra and the MAA/CRAFTY College Guidelines. I
explained why Science and Humanities had made the changes to the algebra
program and where we were heading. Julie was eager to hear about the new
program and quickly came to understand and appreciate why the change was made.
Since then, I've made sure to keep Julie in the loop. She was given her own
copy of Don Small's Contemporary College Algebra text and when I put together
binders of information for each of the Contemporary Algebra instructors, Julie
got a copy too. Julie has a copy of the revised teacher's guide that Husson is
using and I make sure she gets copies of all the activities, worksheets,
quizzes and exams used in my classes. That gives her an arsenal of problems to
use with the students she's tutoring. In return, Julie keeps me informed on
which topics the students seem to be having the most problems with. She's also
been an invaluable resource to get ideas and techniques from. Julie has been
invited to our workshops, but unfortunately hasn't been able to attend one due
to scheduling conflicts. She'll also be invited to meet with Don Small when he
visits Husson on his way to spending Thanksgiving with his family in Maine
Julie has become part of Husson's Contemporary Algebra program team and that greatly benefits our students. Because she doesn't brag about all the time she spends helping students, it would have been easy to miss her even longer. I urge others to find out if you have a hidden treasure like Julie. If you do, then make sure you bring them into the fold by keeping them informed of program changes and sharing class material to support their efforts. The same goes for those working with students and staff in tutoring centers. The more they are informed of what we're doing in classes, the more our students benefit. After all, all of us have an impact on the success of our students.
The purpose of this exercise is to let students discover the relationships
between the roots and coefficients of a quadratic polynomial equation. It is
assumed that students understand the terms factor and root
and their relation to one another.
Begin by computing the following:
a. Determine the quadratic equation whose roots are 2 and 3.
b. Determine the quadratic equation whose roots are and .
c. Determine the quadratic equation whose roots are 2 and 3.
d. Determine the quadratic equation whose roots are 2 and 3.
e. Determine the quadratic equation whose roots are 0 and 2.
f. Determine the cubic equation whose roots are 0, 2, and 3.
Based on the results for parts a, b, c, and d, conjecture the relationship
between the coefficients in the quadratic polynomial equation
and the roots of the equation. Prove or disprove your conjecture by denoting
and forming the corresponding quadratic polynomial equation.
Follow-on exercise: Experiment, conjecture, and verify the relationships between the roots and the coefficients of a cubic polynomial equation.
 The Better Fit
The following table showing the increase in the number of runners who finish
road races appeared in the September issue of the Vision-Potential
Determine which of the following two linear models gives the best fit to this
data and explain your reasoning.
 Fire Hose Mathematics
The driver/operator of a fire truck needs to be adept in using mathematics.
For instance, the required pressure (pounds per square inch, PSI) on a fire
hose is a function of size of the hose, length of the hose, desired nozzle
pressure, change in elevation from the pumper truck or hydrant, appliance
(wye, siamese, ladder pipe) loss, and the flow rate (gallons per minute, GPM).
Too much pressure could cause the nozzle end of the hose to "snake"
endangering the fire fighters holding the nozzle. Too little pressure would
reduce the nozzle pressure and thus shorten the carrying distance of the
stream of water.
Answer the following questions to gain a sense of the relations between friction, flow rate, and the size and length of hose. The following data are from the Waterville, ME (Fire) Pump School.
A. Friction Loss for 100 Feet of Fire Hose
Does the friction of the water against the inside of a fire hose increase or
decrease as the rate of flow (GPM) increases? Using the data in the following
table, develop a suitable model for the friction loss (PSI) for a 1 1/2" fire
hose and then predict the loss for a flow rate of 175 GPM. Repeat the exercise
for a 2" hose.
B. Flow Rate, Hose Size, Friction Loss
Is there a relationship between the size of a fire hose and the friction loss
(PSI) for a given flow rate (GPM)? If so, develop both an exponential and a
polynomial model for the relationship based on a flow rate of 100 GPM. Present
an argument for which is the better model? Check your reasoning by developing
similar models for flow rates of 150 and 200 GPM.
Approximate Friction Loss (PSI) for 100 feet of Fire Hose.
* Supported by the National Science Foundation and the U.S. Military Academy.
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