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Calculus&Mathematica Internet Distance Education Program
Posted:
Apr 24, 1995 11:03 PM
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University of Illinois at Urbana-Champaign
Calculus&Mathematica
Distance Education Program
The University of Illinois at Urbana-Chamgaign Calculus&Mathematica
Distance Education Program (C&M DEP) runs on the electronic highway to
bring top rural and inner city high school students to the university and
to send top university undegraduates to rural and inner city high schools
to form a human, electronic community devoted to mathematics learning.
Below are answers to frequently asked questions about the program.
At what students is the Calculus&Mathematica Distance Education Program
(C&M DEP) targeted?
C&M DEP is targeted at motivated high school students who need a calculus
course not offered by their own high schools. For example, many rural and
inner city schools do not have sufficient demand to devote a teacher to a
calculus class. C&M DEP exists to provide these students with the
opportunity to take calculus. Similarly, other motivated high school
students are ready for Calculus2 or Calculus3 not offered by their high
schools. These students are also targets of C&M DEP. In the future, C&M
DEP will also target non-traditional students working in homes or offices.
What kind of student is likely to do well in C&M DEP?
Any student with a firm commitment to a career involving scientific
calculation and measurement. This includes students with ambitions in
engineering, physical sciences, life sciences (including pre-med), and
mathematics. Students who want just to go through the motions cannot be
expected to do well in C&M DEP.
Is University of Illinois credit available for these students in C&M DEP?
Are the courses in C&M DEP the same as the Calculus&Mathematica courses
offered on the Urbana campus?
A student who passes the a course offered in C&M DEP is entitled to
University of Illinois credit. This credit is transferable. These courses
are the same as Calculus&Mathematica sections offered at the University
of Illinois at Urbana-Champaign and at other leading universities like Ohio
State University, University of Missouri, Michigan Tech, University of
Pittsburgh, Illinois Weslyan, Air Force Academy, Louisiana State, etc. The
following University of Illinois at Urbana-Champaign courses are currently
offered through C&M DEP: Calculus1 (Math 120), Calculus2 (Math 130),
Calculus3 (Math 242), Advanced Calculus (Math 280), and Differential
Equations (Math 285).
What financial advantage do students and parents of students in C&M DEP get?
Engineering students who enter universities having to take Calculus 1
frequently have to spend five years to get their undergraduate engineering
degree.Taking as much calculus as possible through C&M DEP allows a student
a reasonable shot at getting an engineering degree in four years. Thus
success in C&M DEP can pay off in big financial dividends for both students
and parents.
Who is involved in the Calculus&Mathematica Distance Education Team?
The Calculus&Mathematica Distance Education Team is an electronic and
human community all geared at making advanced mathematics courses available
to students who want them. It consists of:
-> High school students who want to learn mathematics beyond the level of
math taught at their schools.
-> Coordinators who are high school teachers who sponsor students from
their schools.
-> University of Illinois undergraduate engineering, science and
mathematics students who act as mentors and role models for the high school
students. This group of outstanding undergraduate students is the driving
force behind the program. C&M DEP alumni constitute about one half of the
mentor team.
-> University of Illinois mathematics faculty members who oversee the
course, make up and grade all tests and issue final grades.
How does learning take place in C&M DEP?
C&M DEP exploits a blend of mathematics, graphics, technology and writing
to give the student a mathematical and technological experience that has
been impossible in the past. Here are some highlights:
Students use professional tools (hefty computers running the Mathematica
System). Believing that the ability to use professional tools is part of
their overall education, C&M DEP students typically throw themselves into
the course. The students understand what vistas these professional tools
open up. Two C&M DEP student reactions:
" The overall technology of the program impressed and amazed me."
" I wasn't aware of what exactly the Internet was or what could be had on
there... and now, I know how to get files, call other systems, and perform
searches, and I wouldn't have known about any of this if it weren't for
Calculus & Mathematica."
Students use the computer and the interactive text to learn math visually.
The course is driven by well-chosen re-executable, interactive computer
graphics and student-produced graphics inviting the students to experiment,
to construct for themselves,to describe, and to explain what's happening in
their own words. A C&M DEP student reaction:
"[The] whole idea of being able to work on a computer and plot functions
and stuff is a great concept. It's nice to be able to see what a function
actually does rather than have to try and draw a mental image - or even
worse, plot it out by hand - or even much worse, just accept the idea that
something works just because some thick math book says so."
Students are given work whose importance they can recognize. "What's this
stuff good for?" is a student question often heard from students in
ordinary math courses but seldom heard from C&M DEP students. The reason is
that the mix of student problems in C&M puts students in a position to try
calculus out and to see what calculus can do for them in terms of their own
lives and in terms of their own planned professional futures in
measurement, calculation and science. A C&M DEP student reaction:
"Most of all, [the course] is great because it applies EVERYTHING to real
situations. I feel that traditional math courses that I have taken have
fallen short in this area. I have always loved math, but for those who
didn't, they needed a reason to "force" themselves to do the math. This
course is showing me how math is everywhere in the real world. I can't
wait to get out there and put it to the test that really counts!!"
Students are given the opportunity to organize their thoughts by explaining
themselves in writing. When a student explains a mathematical fact, the
student becomes committed to what he or she writes because it is written as
a result of the student's own experience. A C&M DEP student reaction:
" This course has taught me how to use logical thinking, writing skills,
and math all at once. I never once thought a math course would deal with
this amount of writing."
Students are given the experience of taking a University of Illinois at
Urbana-Champaign course before they leave high school. A C&M DEP student
reaction:
"[This course] has given me the confidence that I needed to believe that I
can succeed in college. . . . I believe this has been one of the most
interesting and advantageous experiences I could have possibly had in high
school."
Students are given pencil and paper Literacy Quizzes and Literacy Tests. A
C&M DEP student reaction:
"I was also pleased to see that the DEP did not entirely rely on the
computer to teach the class but provided written literacy sheets and tests.
I believe that this helped bridge the gap between a computerized calculus
class and a traditional calculus class. "
What do the undergraduate mentors do?
Students are given weekly computer assignments. When a student gets stuck,
the student uses the telephone to call a mentor at the university. If the
problem can be fixed over the telephone, the session is over. If not, then
the mentor activates screen-sharing software which displays the student's
actual screen on a DEP computer in Urbana. The student and the mentor work
together until the difficulty is resolved. In addition, mentors grade and
comment on the weekly assignments. In short, the mentors drive the
program.
What about the internet?
Eventually, the telephone communications will be replaced by internet
comminications. In fact, all courses in C&M DEP can now be offered over
the internet to students at schools with an internet connection.
Are the courses self-paced?
The courses are paced by weekly assignments. Ambitious students are free to
go at their own faster pace. As a result, some students take both
Calculus1 and Calculus 2 in one year, while others take only Calculus 1.
What funds back the program?
The program is backed by a grant from the National Science Foundation's
Calculus Reform Initiative and by a grant from the State of Illinois
Scientific Literacy Board.
The Scientific Literacy Board grant is administered by Robert Rogers,
Superintendent of the Scott-Morgan School District, Bluffs, Illinois.
Telephone: 217-754-3351, email: rogers@archimedes.math.uiuc.edu
Where does one get more information about the Calculus&Mathematica
Distance Education Program?
Contact:
J.J. Uhl or Debra Woods
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 West Green Street
Urbana,Illinois 61801
Telephone: 217 - 333- 3350
e-mail: juhl@ncsa.uiuc.edu
dwoods@ux1.cso.uiuc.edu
For inquiries about mentoring, contact lead mentor:
Patrica Mills, p-mills@ux4.cso.uiuc.edu
For inquiries about technology, contact:
David Taubenheim, dbt@uiuc.edu
\
University of Illinois at Urbana-Champaign
Calculus&Mathematica High School
Distance Education Program
1993-94 Student Comments
-> "As a whole, I thought that the course was well worth the time invested.
I would definitely like to take another one in the future, and I am
planning on doing so next year."
-> "Calculus and Mathematica has been very good to me this year. There
was nothing I did not like about the course; the work was hard, but it was
nothing I could not handle. . . "
-> "The five hours of credit I may earn from this class may be just enough
for me to get through my chemical engineering curriculum at the University
of Illinois in 4 years rather than 4 1/2 years."
-> "Calculus and Mathematica has opened many new doors and opportunities
for me. Not only has it helped me learn how to work problems and become
familiar with a computer, it has helped me with getting . . . credits for
college. I would definitely recommend this program to any high school
student with the capability for the course."
-> "The technology put into the program was outstanding. I would really
like to meet some of the people who devised the program because I would
just like to get a glimpse of how their minds work."
-> "This course has taught me many new things; it made calculus more fun
and exciting. I would definitely take another Calculus and Mathematica
course, and I would recommend it to any person I think has the capability."
-> "The Calculus and Mathematica course has been a very good experience
for me this year. The course has helped me to understand how computers
will be used in college and to give me some experience with using the
computer. . . This course has taught me a lot about calculus and was very
beneficial to me."
-> "Next year I'll be at U of I studying physics. I'm in the
college of engineering, so this course should give me a good start."
-> "I'm glad I took this course although I really had my doubts at first."
-> "I have become very interested in advanced mathematics, so I decided to
take Calculus and Mathematica . I really enjoyed this program because of
my fondness of computers and problem solving, and because of the
independence I had from a direct teacher. This is what drew me towards
Calculus and Mathematica . I was very pleased with this program."
-> "I believe that the most important factors in the course are the
communications, the program, the lessons, and the guidance of the students.
The amount that I learned from the course was affected directly by these
things."
-> "At first I just planned on using Calculus and Mathematica to prepare
me for advanced mathematics, but as I progressed through the material I
realized that I was getting a lot more out of the program than I had
planned."
-> "[This course] has given me the confidence that I needed to believe
that I can succeed in college. . . The challenge of understanding is what
kept me looking forward to [it] , and that is what is the best thing about
this class. . . I believe this has been one of the most interesting and
advantageous experiences I could have possibly had in high school."
-> "[The] whole idea of being able to work on a computer and plot functions
and stuff is a great concept. It's nice to be able to see what a function
actually does rather than have to try and draw a mental image - or even
worse, plot it out by hand - or even much worse, just accept the idea that
something works just because some thick math book says so."
-> "Every day, it seemed, I would learn something new on my own I did not
know or understand before."
-> "C&M, I feel, will be a great help to me as I enter the University this
fall as a computer science major in the College of Engineering. I've heard
stories about the math one needs in order to be a computer science major,
so I literally jumped at the chance to take calculus here in high school
AND earn credit for the U of I. I think this will help me -- not only
credit-wise, but in terms of understanding the material, I feel I now have
an advantage in understanding calculus."
-> "Calculus was cool. (I NEVER thought I'd say that!)"
-> "I wasn't aware of what exactly the Internet was or what could be had on
there... and now, I know how to get files, call other systems, and perform
searches, and I wouldn't have known about any of this if it weren't for
Calculus & Mathematica."
-> " I feel that I've gained a great deal from C&M and I plan on taking
more when I come down to the U of I in the fall."
-> "I have greatly enjoyed the U of I's Mathematica version of calculus.
I believe that this course is assuredly helping all of us along the
information superhighway. I will be attending the University of Illinois
at Urbana-Champaign this fall, majoring in Chemistry. This course not only
provided a start for my "college work", but has given me an idea of where I
stand in comparision to my future classmates."
-> " I liked that I am getting college credit for the course and will
have a jump on my math courses for next year."
-> "Being involved in Calculus & Mathematica and the Distance Education
Program was a great learning experience for me. I will be attending the
University of Illinois next year and will be majoring in Pre-Medicine in
the field of Chemistry. The overall technology of the program impressed
and amazed me."
-> "TheMathematica software was extraordinary and created a wonderful
working environment. I am thankful to have experience the phenonmenal work
done by computers with theMathematica software. Although taking this
course was a great opportunity for college experience and a college credit,
immediately with the homework or just mathematical concepts. Even though
this class was very time consuming, I have greatly enjoyed taking it. I
was impressed with Mathematica and the University of Illinois Faculty, whom
I am looking forward to meeting next year at the University of Illinois."
-> "I feel that this year has been a great experience for me. I must
admit that when I first heard about the idea of taking Calculus as a Senior
I was kind of leary, scared, and not really interested. I mean as a Senior
I was hoping to kick back, lounge around, and as the Eagles would say "Take
It Easy." Anyway I thought about it for awhile, conferred with some
friends, and finally decided to be daring and take the class... Well
now two semester later I'm sitting here typing away at the computer
finishing up one year of Calculus. It feels pretty good too. I feel that
I have learned a lot this year. It's not only like I was taking a Calculus
class but it was like I was taking a computer class too. I've learned a
lot about Macintosh computers this year. Like how to use E-Mail and all of
that computer stuff. I thought the Calculus part went pretty well too."
-> "I am very happy to have been able to participate in the Calculus and
Mathematica Distance Education Program. I believe I have been very well
exposed to the level of work and time required of a college course. Next
fall, I plan to attend the Univeristy of Illinois, majoring in Computer
Science in the College of Engineering. I hope to broaden my exposure to
the Mathematica language by taking further classes of Calculus and
Mathematica . I very much liked using the software and found it to be a
different, but enjoyable, way to do calculus."
-> "Overall, I think I most enjoyed the technology of the program. Before
this course, I had never been involved in anything using e-mail, modems, or
the Internet, but since then I have developed a strong interest in the many
possibilities which become available to people with increased technology.
In fact, I became so interested in these possibilities that I had to
purchase a modem near the beginning of the year for my computer at home so
that I could explore a few of the many facets of e-mail and the Internet.
-> " I have really enjoyed working on it this year. This math course has
challenged my mind and has given me an idea of what college classes will be
like. This course has taught me how to use logical thinking, writing
skills, and math all at once. I never once thought a math course would
deal with this amount of writing."
-> "Calculus&Mathematica has not been easy for me. I am not the type of
person who does not have to study. Every day I spend several hours looking
at the computer, sometimes not knowing what to do next. This classs has
shown me that if I try hard enough, I can accomplish anything I set my mind
to do."
-> "This class has been one of the most interesting and fun math classes I
have ever taken. I believe that the Calculus & Mathematica program as well
as the distance education program are very effective."
-> "I found the problems used in the Calculus &Mathematica lessons to be
very interesting because of their relevance to real life problems. It is
much more interesting and worthwhile to solve an engineering or physics
problem using the calculus concepts that have been learned than to memorize
how to take derivatives and integrals the whole year as would be done in a
traditional calculus class."
-> "The use of the Mathematica program also provides a good way to see how
changing formulas and constants affects the outcome of some interesting
problems. This "playing around" with calculus helps bring out some of the
subtler concepts of calculus that would probably not even be mentioned in a
traditional calculus course."
-> "I was also pleased to see that the DEP did not entirely rely on the
computer to teach the class but provided written literacy sheets and tests.
I believe that this helped bridge the gap between a computerized calculus
class and a traditional calculus class. I am very pleased with the way the
course is set up and for the opportunity to receive college credit for this
class. "
-> "I think C&M taught me alot about responsibility and the pressures of
college life."
-> "This course sparked enough of a new interest in Mathematics that I may
be Minoring in the subject as well."
This program could be very successful
in the years to come. It allows a high school student to take a glimpse at
the work required at the college level and at the same time utilize one of
the most powerful tools for math in the world, the computer. The software
technology is on the leading edge, as is the hardware which is required by
the memory demanding programs.
-> "I would definitely consider taking another C & M course. It makes
learning easier but challenges you more because of the added problem
solving power of the computer."
-> "Calculus as defined by Webster's Seventh New Collegiate Dictionary is
a concentration of mineral salts around organic material. This definition
represent the way calculus builds on a person. Webster's definition may
not pertain to mathamatical calculus, never the less it is a true
deinition. My experiences with Calculus and Mathematica have been an ever
building experience.. . I am the organic substance as defined by Webster's
Dictionary and calculus is the mineral salt that has been deposited upon
me. I will never forget this experience. . . "
-> "I couldn't pass up this opportunity, I knew that it would only happen
once in my lifetime. Throughout the year, my thoughts have only been
reinforced."
-> "Another building aspect of this program was how it was centered around
self-teaching."
-> "I am thankful that this program exists. I am the only student in our
school on this program. This separates me from the crowd. I have studied
integrals, derivatives, and limits. This is more mathematics than many of
the people in my class will ever do. I have a better knowledge of the
world around me, and the way fundamental mathematics works, all because of
the Calculus and Mathematica program. The knowledge that this course has
bestowed upon me is the best factor of this program."
-> "This course was a great thing for me. Before this year, I had no idea
as to what my college major would be. I had always been interested in math
but thought that there was nothing to it but simple formulas and the
plugging in of numbers. But this course has proven that silly notion
wrong. It has shown me that math is a wonderful subject that can never be
truly mastered. One aspect of this course that I came to relish was the
proving of a formula. Being able to say that one function's derivative is
"x" and then being able to show why is a remarkable thing to me. Having
the knowledge and the power to show and prove things in a mathematical
sense is a great ability."
-> "The Mathematica program itself was amazing. Whatever you told it to
do, it would. Not only did I use it for this calculus class, but I also
used it for my advanced math and physics classes here at Wethersfield."
-> "In retrospect, I am very glad that I decided to take this class. It
has been extremely worthwhile and has made me open my eyes to the sheer
beauty of calculus and further mathematics. No other course I have ever
taken has made me want to spend a majority of time working and thinking
about it. I would like to say thanks for offering this course and allowing
me to catch the mathematical bug."
-> "[The course] gave me a good idea of what to expect academically in
college next year. Also, this is the first course of my high school career
that has challenged me, and I always feel good about myself after
successfully completing a problem.
-> " The technology amazed me. One of the best things that I have
gotten from this course is a better understanding of computers. In
addition, the software amazed me. I felt very advanced compared to the
students in my class who are taking traditional math courses; I felt like
I belonged in the twenty-first century."
-> " Our mentor, Tricia Mills, was OUTSTANDING!!!!! I cannot stress how
much she helped. She graded fairly and used explanations. In addition,
she made a strong effort to regularly communicate with us, even going so
far as to schedule phone review sessions before exams (which helped
tremendously). I really appreciate all the time she has taken to help us."
-> "I think [that the course] makes calculus more tangible, more
imaginative and just plain more interesting compared to the traditional
pencil-and-paper courses. Also, I feel that Calculus&Mathematica is the
wave of the future and that soon all courses will be taught via computer."
----------------------------------------------------------------------
Jerry Uhl juhl@ncsa.uiuc.edu
Professor of Mathematics 1409 West Green Street
University of Illinois Urbana,Illinois 61801
Calculus&Mathematica Development Team
http://binkley.math.uiuc.edu
"The axiomization and algebraization of mathematics, after more than fifty
years, has led to the illegibility of such a large number of mathematical
texts that the threat of complete loss of contact with physics and the
natural sciences has been realized." . . . V. I. Arnold
"Students should be become insiders in the culture of mathematics as soon
as possible. I don't know why teachers protect them from exposure to what
real mathematicians say to each other and what they do in practice. Do
mathematicians go home and think - first I will do a little basic math and
give myself a quiz.Then I will do the algebra part and have a little quiz"
.....Hubert Hohn
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