## How Teachers Teach and How Students Learn

**March 22, 1999**

Students from SUNY Farmingdale in a Long Island Consortium course.

Alan C. Tucker

**Systemic change is goal for Long Island Mathematical Sciences and Their Applications Throughout the Curriculum project. **

The Long Island Consortium for Interconnected Learning in Quantitative Disciplines (LICIL), now in its third year, is a collaboration of faculty in mathematics and related quantitative disciplines at ten colleges and universities on Long Island; SUNY Stony Brook is the lead institution. As LICIL participants, we are engaged in a multifaceted project sponsored by the National Science Foundation's Division of Undergraduate Education to create and sustain instructional innovation of an interdisciplinary nature in mathematical courses and mathematically based disciplines.* In so doing, we are working toward NSF's goal of broadening and improving undergraduate education in the mathematical sciences and other disciplines and, in particular, of increasing students' appreciation of and ability to use mathe-matics. To achieve this goal, we are:

- Changing the modes of instruction and student learning to improve the educational experience of our students.
- Changing the academic culture to create better connections between instruction in mathematics and instruction in mathematically based disciplines.
- Overcoming some of the obstacles that prevent students from learning mathematics by drawing on real-world uses of mathematics in science and business to motivate the students and illustrate the value of mathematics.

In its three years, we have seen LICIL grow to involve collaborations with faculty in disciplines that use little mathematics, such as sociology, nursing, and the law.

Our strategy is to create a process that will promote change rather than specific curricular and pedagogical outcomes; one of our goals is to produce an environment conducive to continuing instructional innovation.

**Systemic Change**Systemic change in the university is the name of our game. Bringing about systemic change goes far beyond designing and changing curricula. It means changing how teachers teach and how students learn. It means that teachers must challenge their own classic teaching modes and involve their students in the thinking process, commit more time to class preparation, and exchange ideas with colleagues and faculty in other disciplines. It means that faculty should create new courses and new teaching methodologies, and use new computer-based technologies when there is something to be gained from them. It means the nurturing of a supportive administration.

Systemic change also applies to students. Students, when they start college, need to become more active learners in the classroom and the laboratory. They need to learn how to read a text, take notes, and write about what they've learned. They need to learn to organize their time and work in teams on unstructured assignments. Students also need to develop the critical thinking skills that will improve their ability to follow lectures and understand exercises in most quantitative disciplines.

Change is not easy. We believe, however, that we have had substantial success in getting hundreds of faculty and thousands of students to change their established habits of teaching and learning.

**Innovative Teaching for a Multidisciplinary Workplace**Today's scientific and business workplace is characterized by multidisciplinary thinking that draws on the paradigms and problem-solving strategies of many different disciplines. In response to the needs of such an environment, we are introducing new multidisciplinary material into our mathematics courses and creating quantitative courses in related disciplines.

We have developed several general multidisciplinary courses in quantitative reasoning. In one such course---The Mathematics of Fairness---students develop quantitative models for resolving disputes and dividing scarce resources in business, law, politics, psychology, and other settings. Another course---The Digital Revolution---examines how the shift from analog to digital information has changed the problems that can be solved and the mathematics that is used to process information in engineering, science, medicine, mathematics, and business.

Other quantitative multidisciplinary courses have been designed around particular topics, such as the weather and near-earth objects, that were the subject of popular movies last summer. In another project, instructors in mathematics, the social sciences, and business are working together to replace their respective disciplinary versions of introductory statistics with a jointly taught, unified course that illustrates the many applications of statistical analysis.

Some of our instructors have been experimenting with new pedagogical techniques, such as "cooperative learning." Motivated by a recent study from the Sloan Foundation, these faculty members decided to adopt cooperative learning and, more generally, "process-learning" approaches, including the use of computer-based technology and multimedia presentations. (In process learning, the instructor is more of a coach and less of a lecturer.)

We have found that it is difficult for one instructor to use such approaches in isolation. When groups of instructors teaching the same students in different subjects collectively implement such strategies, however, the experience is much less stressful for both instructors and students.

These new modes of teaching are spreading throughout the LICIL institutions, both in LICIL-sponsored efforts and in other quantitative courses. Last fall, for example, the instructors of the nine-credit Foundations of Technology course at SUNY Farmingdale, which features joint mathematics, physics, and technology instruction, adopted a process-learning approach. The percentage of first-semester students finishing the course with grades of C or better, formerly 30%, jumped to 84% last fall.

At Stony Brook, LICIL and the Hewlett Foundation are co-sponsoring a learning community experiment involving 150 Stony Brook freshmen, divided into five 30-student groups. Each group takes English composition, chemistry, and calculus together, along with a special multidisciplinary seminar in the philosophy of science. The three courses are closely linked, with, for instance, examples from chemistry presented in calculus and topics from mathematics included in the composition classes.

The use of computer-based technology is steadily increasing in mathematics and the other quantitative disciplines at the LICIL institutions. Experience has shown that helping faculty learn how to use new technology is far more effective than simply urging them to use the technology. Spreadsheets are now appearing in most mathematics and quantitative courses, and instructors are experimenting with other software packages.

There is also a growing use of Internet and Web pages as a source for course assignments and homework solutions and a resource for data. Some instructors are developing multimedia software for their courses. Interest in Web use has been stimulated by LICIL workshops on basic Web design.

**Building Faculty Participation**How do we generate genuine enthusiasm for reform? Telling faculty that they need to change their teaching methods is psychologically unproductive. Asking them to evaluate their own methods and courses is equally unproductive. The inertia of long-established practices prevails; some view any requirement for change as threatening. And many are discouraged by the view of some of our colleagues, at least in universities, that time spent on teaching methods is time lost from doing research and getting the next research contract.

Establishing clear and reasonable goals is fundamental to the reform process, but it's not enough. Here are some ideas that we have found effective in fostering change:

**The core group.** At the beginning of our project, about a dozen faculty in various departments at each institution had for some time been thinking about, and even experimenting with, new teaching methods and curricula. Working for the most part in isolation, they were scattered, like glowing embers in a barbecue. We brought them together as a group to build enthusiasm for the reform effort and to encourage them to share new ideas. Now they interact enthusiastically with each other and are working to encourage their colleagues to participate in the project.

**Options.** What appeals to one instructor may be of no interest to another. Accordingly, we offer a "food court" of instructional innovations in a variety of areas involving pedagogy, the development and use of computer-based technology, the development of new materials and multidisciplinary connections, and assistance to underrepresented groups. We have found that an instructor's success with an interesting project will motivate others to become involved.

**Incentives.** We encourage instructors to develop new ideas on their own and to seek LICIL Development Awards to pursue them. The awards-about 70 per year-have seeded the development of diverse new courses and modules on such topics as the mathematics of weather, mathematical models for nurses, and mathematics and the law. After starting individual grassroots efforts, awardees are offered follow-on funding if they will collaborate with faculty undertaking related activities at other LICIL institutions. Titles and other information about the numerous efforts funded by LICIL Development Awards can be found at www.licil.org.

**Professionalism.** We remind our faculty of the well-known view that "good researchers make the best teachers" and challenge them to prove it through their creativity in the classroom. In addition, administrators at all LICIL institutions are encouraging instructional professionalism. In particular, the dean of Stony Brook's College of Engineering and Applied Sciences now tells candidates for faculty positions that, along with research grants and good teaching evaluations, he expects documented evidence of instructional innovation in tenure and promotion files. The provost at SUNY Farmingdale targeted faculty who have been particularly active in LICIL for some of his pool of merit raise funds.

**Conferences and workshops.** We conduct two conferences each year for LICIL participants to share experiences and report on their progress. Attendees include both participating LICIL faculty and curious faculty not involved in the project. We also conduct workshops for faculty in the use of computer-based technology.

**Increased interaction.** While project participants have quite diverse views and interests, LICIL encourages the sharing of ideas and a cooperative, supportive spirit in all the quantitatively based disciplines. Trying to make participants feel like co-investigators rather than followers is one approach. Another is the nurturing and publicizing of grassroots efforts of faculty by project investigators.

**Encouraging Results**About 25% of the approximately 1000 faculty in the quantitative disciplines at participating institutions have been affected by LICIL. Some are expanding on efforts that existed prior to LICIL, but the vast majority are doing new things in their classes that can be traced in part or in full to LICIL activities.

While a number of single-section experimental and reworked courses have been offered, many large, multisection introductory courses have also been affected. Calculus and precalculus instruction has changed for most students at almost all the institutions, and statistics instruction has been affected for thousands of students. Students in the social sciences are using quantitative models in their courses for the first time.

Students who take introductory statistics classes in Farmingdale's mathematics department go into engineering design classes to make quality-control measurements on devices built by the engineering students. All precalculus courses at most LICIL institutions now use one of the "reformed" precalculus texts, in which the emphasis is on realistic applications, technology, and cooperative learning materials.

Finally, we are receiving wide support from administrators at all the LICIL institutions in the form of released time, summer support, equipment funds, and enlarged merit pools.

While faculty are the prime focus of LICIL's efforts to create and sustain an atmosphere for instructional motivation, the students and their learning are the ultimate targets. Student surveys and changes in some standard indices, such as dropout rates, have been encouraging: As a result of our instructional changes, students have become more proficient in using quantitative methods.

*Alan C. Tucker is project director of LICIL and associate chair of the Department of Applied Mathematics and Statistics at SUNY Stony Brook. *

* NSF awarded a total of seven grants under the initiative, Mathematical Sciences and Their Applications Throughout the Curriculum (MATC); reports on other projects have appeared in *SIAM News*.