David M. Bressoud June, 2007
Access pdf files of the CUPM Curriculum Guide 2004. |
Purchase a hard copy of the CUPM Curriculum Guide 2004. |
Access html files of the CUPM Illustrative Resources Find other Launchings columns. |
Beginning in 1990, the Conference Board of the Mathematical Sciences (CBMS) has been tracking some of the approaches to teaching that were then being promoted by the Calculus Reform movement. These are use of graphing calculators, use of computer assignments, use of writing assignments, and use of group projects. I often hear complaints funneled via their high school teachers that students who used graphing calculators while in high school as a means of supporting their understanding of calculus concepts find, when they get to college, that they are not allowed to use them. I initially went to the CBMS data to determine the use of graphing calculators in colleges and universities, but as I was drawn into the data, I discovered some disturbing trends.
The 2005 National Assessment of Educational Progress [1] (NAEP) confirms that graphing calculators are ubiquitous in the high schools. Among all 12th graders, 84% use calculators at least once a week in math class, 62% use calculators daily. For 64% of those with calculators, it is usually a graphing calculator. For 81%, it is at least sometimes a graphing calculator.
The CBMS data [2] is broken down by type of school, and this is very illuminating as shown in the following graph of the percentage of sections that used graphing calculators (the extent or nature of use is not specified) in mainstream Calculus I in the fall term of 2005.
Use of graphing calculators in colleges clearly peaked in 2000. Except for PhD granting universities, at least 50% of all sections still used graphing calculators in 2005. But PhD granting institutions account for the largest group of Calculus I students. In 2005, of the 251,000 students who took mainstream Calculus I in college in the fall term, 105,000 were at PhD institutions, 30,000 at universities offering an MA as the highest degree in mathematics, 65,000 at BA colleges, and 51,000 at 2-year colleges. Also, the 40% of sections at PhD universities is deceptive because large lecture sections are the least likely to allow use of graphing calculators (only 37%), and they account for well over half of the students at PhD institutions.
I was curious about the decline since 2000. A natural hypothesis is that graphing calculators are being replaced by computers. I next looked at the number of sections using computer assignments. Again, this is the percentage of sections of mainstream Calculus I in the fall term that require computer assignments. The decline since 2000 is remarkable.
I should not have been surprised. I had been hearing a lot of anecdotal evidence that colleges were pulling back from the use of computer labs in Calculus instruction. This is not because they do not work, but because they are so time- and energy-intensive if they are to be done right. Those who had initially developed computer labs were moving on to other things, and these labs were proving difficult to sustain. I think that there is some cause for optimism, that the steady state will prove to be above the level of 1990. But it is clear that the intensive push for the incorporation of computer assignments that occurred in the 1990s has not been sustainable.
What I found in the use of computer assignments was echoed in writing assignments and group projects.
We are ahead of where we were, but we are not consolidating and building on
our gains. The answer is not to rally the troops to roll that particular boulder
back up that particular hill. Again anecdotally, I hear from many mathematicians
that there are continual pressures to teach larger sections, to teach with
more adjunct faculty, to spread ourselves ever thinner. Innovative and effective
but time-consuming approaches are not sustainable over a span of much more
than a decade.
But we also now have 15 years of experimentation across a broad spectrum of
institutions. There are places where these changes have taken root and flourished.
I believe that we can build on those successes, that we can identify the adjustments
and changes that produce the most gain for the least additional effort. That
is where we now must focus our attention.
[1] US Department of Education, The Nation’s Report Card: Mathematics Results for Grade 12. http://nationsreportcard.gov/reading_math_grade12_2005/s0301.asp
[2] CBMS data is taken from
• Albers, Donald J., Don O. Loftsgaarden, Donald C. Rung, Ann E. Watkins,
Statistical Abstract of Undergraduate Programs in the Mathematical Sciences
and Computer Science in the United States, 1990–91 CBMS Survey, MAA
Notes Number 23.
• Loftsgaarden, Don O., Donald C. Rung, Ann E. Watkins, Statistical
Abstract of Undergraduate Programs in the Mathematical Sciences in the United
States, Fall 1995 CBMS Survey, MAA Reports Number 2
• Lutzer, David J., James W. Maxwell, and Stephen B. Rodi, Statistical
Abstract of Undergraduate Programs in the Mathematical Sciences in the United
States, Fall 2000 CBMS Survey, American Mathematical Society
• CBMS Survey, Fall 2005, preliminary tables www.math.wm.edu/~lutzer/cbms2005/.
Do you know of programs, projects, or ideas that should be included in the CUPM Illustrative Resources?
Submit resources at www.maa.org/cupm/cupm_ir_submit.cfm.
We would appreciate more examples that document experiences with the use of
technology as well as examples of interdisciplinary cooperation.
David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, he was one of the writers for the Curriculum Guide, and he currently serves as Chair of the CUPM. He wrote this column with help from his colleagues in CUPM, but it does not reflect an official position of the committee. You can reach him at bressoud@macalester.edu. |