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: email@example.com
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: firstname.lastname@example.org email@example.com
For inquiries about mentoring, contact lead mentor: Patrica Mills, firstname.lastname@example.org
For inquiries about technology, contact: David Taubenheim, email@example.com \
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 firstname.lastname@example.org 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