Report for the TiME Committee

by Jerry Kissick

jkissick@pcc,edu

The TiME committee has been busy working on the issue of equal access to technology for all students.  The final result of our discussions was a motion to the AMATYC board at their spring meeting to modify our current position paper dealing with the instructional uses of technology by adding an additional bullet to the position paper.  The board approved the additional bullet during the meeting.  The statement is:

Students should have access to calculators and computers to facilitate learning with technology.  Whenever possible, mathematics departments should endeavor to provide access to the technology both in the college and at home.

Since the publication of our last newsletter, our newsletter editor Joyce Oster has been forced to resign as newsletter editor because of her increased work load associated with doing on-line courses.  I wish to express my thanks to Joyce for all she did to help get the newsletter put together during the last year and a half.  We have been fortunate to find Renae Weber of Treasure Valley Community College in Ontario, OR who has agreed to help with putting this newsletter together.  I am very thankful to Renae for agreeing to do this work.

I also want to thank the people who are continuing to contribute articles for our newsletter.  In this issue are articles from Brian Smith summarizing the results of the session from the AMS/MAA conference dealing with Innovative Uses of the World Wide Web in Teaching Mathematics and a  second article from Wayne Mackey about Uniform Standards for Evaluating Student Learning.

The process of asking for volunteers at the annual conference is working out well.  Since we are a paperless newsletter, length is not a problem, so anyone wishing to contribute a technology related article, report on a technology event/workshop, etc attended, or announce an upcoming technology event/workshop, etc please e–mail your information to myself at

            jkissick@pcc.edu

The MATHEDCC internet discussion list is continuing to function well and there have not been any problems since Brian Smith re-hosted the list to the Math Forum.

During the Chicago conference, the AMATYC board established a new Distance Learning Committee.  Karen Estes agreed to be the TiME committee representative to this committee.  Since that time she has experience an overwhelming teaching load and has asked to be relieved of this duty.  We are currently looking for a volunteer to act as our committee representative.  As far as I know, the only responsibility for this position is to attend their committee meetings at the annual conference and report items of interest to the TiME committee.  If you have an interest in distance learning and would be willing to attend their meetings, please contact me and I will forward your name to AMATYC as our committee representative.

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Uniform Standards for Evaluating Student Learning

by Wayne F. Mackey

Director, Math Resource & Tutoring Center

University of Arkansas, Fayetteville

wmackey@mail.uark.edu

http://MRTC.uark.edu

Despite much effort, many new textbooks, new standards from AMATYC, NCTM, AMS and the MAA, as well as new educational techniques, very little progress has been made in bringing American mathematics students to higher rankings in relation to other countries.  Some things that I believe very firmly after being involved for over thirty years are as follows.

i)                                            Most teachers are doing an excellent job of teaching, perhaps better than ever before.

ii)                                          Students are just as bright as ever.

iii)                                        Textbooks are just as good as they ever were and probably better.

iv)                                        Students are learning just as much as ever before.

The last assertion might need a bit of exposition in light of the opening paragraph.  I believe that students at the high school and up levels have always been bright enough in general to arrange their schedules and focus their efforts to achieve their goals as efficiently as possible.  I believe they still do.  The only conclusion I can come to is that students today can achieve their goals with less effort and less time put into learning.  In other words, a high school student can graduate most efficiently by learning less now than the parents or grandparents did.  Even though there are more opportunities for learning and understanding now, less of it is required.  Students are still learning just as much as they must to achieve their goals but no more.   Look at these figures.

Consider the percentage of entering college freshmen that say they averaged studying six or more hours per week during their last year in high school.

            1987 - 47.0%                                     Now - 36.0%

Consider the percentage of entering college freshmen that had an A average during their last year in high school.

            1968 - 17.6%                                     Now - 42.9%

Consider the percentage of entering college freshmen that had a C average during their last year in high school.

            1968 - 23.1%                                     Now - 6.6%

The above figures were taken from http://www.gseis.ucla.edu/heri/heri.html.

What about that first year in college?  Do things change there?  We can consider two students from different colleges who both got grades of A in college algebra.  What does this tell society and us?  In many colleges grades are sometimes not intended to reflect the amount of mathematical knowledge, skill, or understanding gained.  Instead the grade rates the amount of work done (or at least handed in), the amount of time spent, or various other even more nebulous criteria such as how hard the student is trying or how badly the grade is needed by the student.

Even if both grades are based exclusively on tests that are well designed to determine the mathematics learned, the grades can still have different meanings.  In an orientation session for new teaching assistants I did a very quick experiment.  I gave these new graduate students a typical math test problem along with several typical incorrect student answers, asking them to assign partial credit out of 5 points for each correct answer.

The test problem was to find the equation of the directrix of a parabola.  The correct answer was x = 4 and these were the incorrect student answers.

                           4

                   y = 4

                   x = 8/2

                   x = 8

Those inexperienced teaching assistants gave the incorrect or incomplete answers partial credit ranging form 0 points to 5 points on each one.  Now imagine a test with 25 problems.  If one such test paper is graded by 50 different teachers independently, the probability that any two scores would be the same approaches zero.

In an attempt to rectify this situation or at least bring it to light, more and more "standardized tests" are given at various points along the educational road.  President Bush has proposed giving these tests every year but hasn't said anything about what should happen to students who fail the tests.  In California next year it is proposed that students who don't pass standardized tests given in the senior year not be allowed to graduate.  There is a great hue and cry in protest with many California teachers quite forthrightly saying that very few high school students will graduate if this policy is enforced.  It is obvious that this approach is not going to help at all.  Students who haven't learned enough in 12 years to pass that test are not going to learn anything by being told they can't graduate.

Fortunately, with the advent of modern technology (computers, not calculators), we can actually begin to try realistic approaches to solving the problem.  It is possible now to have unique but equivalent tests for each student at each level and over each topic.  Furthermore the tests can be graded according to strictly uniform standards for partial and full credit on each question or problem.  Obviously the typical standardized test with all multiple-choice questions has many difficulties so these can all be eliminated or at least reduced in number and importance.  Since all tests are different but equivalent it is not necessary that all students take a test at the same time so students can proceed at their own pace rather than having to wait for the rest of the class to catch up with them or having to move ahead with the class without any understanding of the previous lesson.  A student who fails a test can simply repeat the lesson or try a different approach without falling behind a class.

If this system were in place two students who had gone through school with the same grades could be safely assumed to be at the same level of knowledge, understanding, and skills even if they attended different schools with different teachers.  This is of course a pipe dream but we could begin implementing such a system in the first two years of college anytime.

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Report on the MAA Contributed Paper Session on Innovative Uses of the World Wide Web in Teaching Mathematics

Brian Smith

For the second consecutive year, the CCIME (Committee on Computers in Mathematics Education) of the Mathematical Association of America organized a contributed paper session titled Innovative Uses of the World Wide Web in Teaching Mathematics. The session was presented at the Joint Mathematics Meetings in New Orleans in January 2001, and was organized by Marcelle Bessman of Jacksonville University, Florida, and Brian Smith of McGill University in Montreal.

With approximately thirty contributions, this session was well attended and proved to be a great success.  The quality and variety of the presentations was outstanding and the sessions, spread over three days, proved to be a great source of innovative and exciting new ideas for anyone currently teaching, or planning to teach, courses involving web-based materials.

While the sessions were not of a commercial nature, nevertheless several of the presentations dealt with applications of popular software packages, and participants were able to see how various types of software could be used effectively to present and manipulate mathematical material on the web.   Among the software based presentations were Interactive Web-Based Materials for Calculus Using LiveMath by Brian Gill of Seattle Pacific University, WebCT Quizzes in Precalculus and Calculus by Jeffrey Hirst of Appalachian State University, Group Writing Using Blackboard CourseInfo by Kris Green of St. John Fisher College, Online Mathematics Courses at the Mathsoft Learning Site  by William Mueller of Mathsoft Inc., and Visual Calculus – a Report, by Lawrence Husch of the University of Tennessee, Knoxville.

Other presentations covered many aspects of teaching mathematics using World Wide Web resources.  Topics included the use of Applets, Web-based simulations, Activities from the Mathwright Library and Project WELCOME, a National Library of Web-based interactive manipulatives, Statistical data on the Internet, using Java, animated GIFs and Shockwave movies, and on and on it goes!

The presentation Stuck in Traffic in Chicago: A WWW Project by Elyn Rykken and Maureen Carroll demonstrated a very original application employing Chicago’s on-line traffic information system. Students were asked to help solve a crime by estimating the time required by a suspect to commute from one district of the city to another.  Another very creative presentation was entitled Learning Trigonometry through a Virtual Mathematics Learning System – Infomath.  This talk featured dazzling graphics and a little help from the Pokemon character Pikachu!  The presenters, Yuan Yuan and Ming-Jang Chen  were visiting professors from Taiwan.

Overall the session was very popular and, though the attendance waxed and waned throughout the fairly lengthy time-blocks, it was gratifying to see that both the early morning and late afternoon sessions maintained a good turnout.  Owing to the popularity of the session it has already been approved for next year for the San Diego Joint Mathematics Meetings, January 6-9, 2002.  If you are planning to attend the meetings look out for some lively and informative talks at the third MAA contributed paper session on Innovative Uses of the World Wide Web