May 1997 // Case Studies
The Calculus Consortium Project:
Technology in Math Education
by Rebecca Montgomery
Note: This article was originally published in The Technology Source (http://ts.mivu.org/) as: Rebecca Montgomery "The Calculus Consortium Project:
Technology in Math Education" The Technology Source, May 1997. Available online at http://ts.mivu.org/default.asp?show=article&id=1034. The article is reprinted here with permission of the publisher.

The problem is this, at the same time legislators are pushing for more and better use of technology, and the costs of building labs and classrooms goes up, the voters are pushing even harder for limits to government spending. Legislatures never seem to find enough money for colleges to keep both academic and administrative computing current, let alone to fully explore the uses of other technologies. Schools cut corners, delaying upgrades. They eliminate budgets for training and technical support. This financial issue is easy to see and understand its component dilemmas familiar to anyone whose ever tried to adhere to a budget.

Money, money, money

The problem is this, at the same time legislators are pushing for more and better use of technology, and the costs of building labs and classrooms goes up, the voters are pushing even harder for limits to government spending. Legislatures never seem to find enough money for colleges to keep both academic and administrative computing current, let alone to fully explore the uses of other technologies. Schools cut corners, delaying upgrades. They eliminate budgets for training and technical support. This financial issue is easy to see and understand its component dilemmas familiar to anyone whose ever tried to adhere to a budget.

The nature of the beast

But there is another problem at work, one not so visible to those on the outside of the academic world. Faculty, by and large, represent their respective fields. They jointly hold the responsibility for exploring and discovering the new knowledge, which forms the lifeblood, of whatever discipline for which they are members. They study their own fields constantly, keeping abreast of new work being done and its implications. Surveys of college faculty show that they average a 55-60 hour work week when they aggregate their interactions with students, their on-going learning and their other duties. In the context of this typical work pattern, learning about ways technology might fit into their daily agendas seems less urgent. They have their hands full now.

The government moves in

It is issues like these that granting agencies like the National Science Foundation (NSF) try to address by the careful allocation of money to faculty whose proposals seem most likely to bear fruit. Often, these focus more on developing the core ideas and essential research avenues of a given field than on things like the integration of technology, but occasionally these agendas overlap. In mathematics during the late 1980s, for example, NSF chose to fund research on the teaching and curriculum of calculus. NSF reasoned that calculus was a common requirement in nearly every degree in a scientific discipline. Calculus classes, therefore, could be seen to act as a critical filter into scientific careers: indeed, some discipline faculty advocated adding a class like calculus to degree requirements specifically to filter students out. Additionally, even among the disciplines where the skills gained in these classes were desired, there had long been complaints from the "client" departments that today's calculus classes were not producing students who could readily do good problem solving. Add to this the fact that mathematics classes across the nation rarely used the available technologies with students prior to graduate school, and you have the basis for the flood of grant money NSF allocated to the development of a new calculus curriculum.

Several remarkable achievements came out of this initiative. Two projects particularly interested those of us watching here in Washington State: a course written by a consortium of faculty at Harvard and another put together at Duke. Both made extensive use of similar core guidelines, and both made extensive use of technology. At this stage, the NSF found itself at much the same place as the visionaries mentioned at the beginning of this article. Here on the one hand were all the exciting opportunities they had spent millions to develop and over there were the faculty and students they had been intended for. The next step had to be dissemination of these new ideas and materials throughout the colleges in the United States.

A local miracle

Good methods for spreading new ideas across campuses were well established in Washington. Early in the 1980's, an organization formed here which had that as its sole purpose, the Washington Center for the Improvement of Undergraduate Education, the Washington Center for short. Faculty from every institution of higher education in the state were already actively participating, teaching one another new ways to address old problems in the college classroom. At the beginning, most of the efforts centered new methods of teaching, but the challenge of finding a way to bring many of the math faculty across the state up to speed all at once proved irresistible. The leaders of the Washington Center made a proposal to NSF. They proposed that a "core" group of 50 faculty be brought together for intensive workshops during the terms breaks, requiring them to produce enhancements to what they had been taught in their own classrooms and provide ample follow-up assistance and support while the enhancements were "growing".

It worked. Over the 4-year duration of the grant, some 278 faculty across the state began to use the new information, some with and some without modifications. In the process, some unexpected results occurred, one of which was particularly important to the NSF: the number of students who continued on to study more math and science after taking one of the "new" calculus courses increased by half again the previous rates. Students reported feeling somehow connected to the new material, finding themselves so interested and involved in the process of learning that they wanted to continue it.

Parenthetically, as a long-time math teacher, the idea that students would chose to learn more math, felt a connection to the subject and reported that they found math interesting -- well, I have to say it took my breath away. This had to be a miracle.

One teacher's experience

The NSF initiative fascinated me from the beginning because it was so intently focused on a specific discipline, in this case math. New techniques and tools were incorporated only when they served the core goals of learning math. Technology was integral to this, but appropriate technology. For example, one of the things mathematicians want students to know and understand is the concept of a function. We go to a great deal of work to make this happen. We have our favorite categories of functions, and traditionally make students roll their eyes in wonder that we think such things are important. Providing connections to their own experiences has been very difficult, if for no other reason than the interesting cases have been too hard or too complex to do in a classroom setting. The new approaches we learned from the Washington Center's training program mandated that any topic be approached from as many different angles as possible; problems were to be solved graphically, numerically, algebraically, verbally and any other activity we could devise. A specific example may be beneficial.

I gave my students a project to describe the progress of the AIDS epidemic in the United States, and make predications about its course across the near future. We gathered data from public health offices at the city, county and state levels and from the national Center for Disease Control. The students struggled with organizing the information in ways that made sense, but this struggle was made viable by the use of computers in the classroom. The classroom was laid out with in a network of PC's running the Windows NT operating system, Office and several good math software packages (DERIVE, MathCad, Geometer's Sketchpad). Students were grouped four to a table, and each table had two computers. The project was deliberately much too difficult for any one student to accomplish. In addition, it was close enough to their knowledge of the current world to engage them deeply. Over the period of several weeks, they developed equations to represent the various stages of the epidemic progress, graphs and presentation materials tied to such intervening events as the Surgeon General's mass informational mailing, written reports and predictions for the future. We invited public health officials and colleagues to watch the students present their findings. All in all, they learned a lot about functions and I learned a lot about the importance of giving students meaningful work to do.

Conclusions

The success of the calculus curriculum revision has many lessons for those who want to expedite the integration of technology in higher education.

  • First, the initiative was based solidly in a specific discipline, the formative ideas put together by highly respected members of the faculty and funded by an overarching agency. This is important in higher education.
  • Second, a core group of faculty was intensively trained in the use of the materials and the technology, again, funded by an outside agency. These faculty then became the trainers for the second and third waves of faculty. This both increased the number of trained faculty and increased the critical mass of people involved.
  • Third, ample initial support was available to the core group.
  • Last, the students themselves were required to present their work to outside visitors. This pushed them to both learn far more about the available software and to research their facts carefully. It also gave them enormous feelings of accomplishment at the completion of the project. The students' reactions to the overall effort are critical to the success of any academic project: teachers want students to learn more than they want anything else.

The ideas mentioned above, establishing a core group of experts to carry on the work, basing any initiative solidly in a discipline and never forgetting that students are of foremost importance to teachers can be used in almost any college environment. The essential concept is that academics are devoted to teaching and learning. Any time you want them to change, you must ensure that these core values are visibly addressed. Today, in math departments across the state, computers are commonplace, integrated into the fabric of every day. Faculty are enthusiastic and excited to see what might come next. It is indeed a success story of technology being integrated into the fabric of higher education.

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