5. Project Activities

Upstate New York involvement in the following activities will lag about two years behind Long Island efforts.

5.A. Systemic change in faculty instruction and student learning in quantitative disciplines

i) Energizing Faculty to Rethink Modes of Instruction and Student Learning. Numerous small projects, as well as more comprehensive efforts, have been funded by NSF, FIPSE and other sources to promote alternative modes of instruction in quantitative disciplines. There are several such efforts on Long Island. The 1000-student general introductory chemistry course at Stony Brook has added a one-hour workshop of cooperative learning-based projects. Calculus reform classes throughout Long Island are using cooperative learning, open-ended questions, and increased writing. Across the nation there are many exciting developments: Harvard physicist Eric Mazur's innovative introductory physics course and the open-ended group projects in the new thematic chemistry courses of a midwest consortium centered at Beloit, to name just two. Moreover, a number of articles have appeared in educational research journals about the benefits of less structured, more exploratory approaches to classroom learning, such as group learning, open-ended questions and extensive writing.

As noted earlier, this project will bring together faculty from several disciplines and several institutions who are interested in changing modes of instruction and will tie these changes with new curricular materials and educational technology. An immediate challenge is to help faculty and students become comfortable and effective with new modes of instruction and learning. With the support of campus deans and departmental chairs, the local disciplinary groups will encourage and support faculty efforts to rethink their instructional practices in the larger interconnected framework of this initiative. The consortium planning effort has identified scores of faculty on Long Island already experimenting with instructional reform. The actions of the committed will help engage those who are interested which will in turn motivate those standing on the sidelines to become involved. (See Section 7 for further discussion of administrative support and faculty recruitment.)

Implementation: There will be a consortium-wide task force on modes of instruction. Faculty will be introduced to new modes of instruction and project activities that build on these new modes of instruction through: (i) informational departmental meetings organized by the local disciplinary groups; (ii) institution-wide meetings organized by the local organizing committee (such meetings would have a featured outside speaker); (iii) consortium-wide training sessions organized by the task force on modes of instruction; (iv) videotapes of classrooms with innovative instruction, prepared by the instruction task force; (iv) electronic interest group forums on instruction; and (v) the consortium newsletter. Special attention will be given to assessing student learning in courses with alternative instructional styles. Faculty will be invited to visit classes taught by colleagues using new instructional styles. When faculty begin instructional changes, support will be available from project personnel and more experienced faculty who will visit their classes and provide constructive advice. Twice-a-month luncheons will give faculty trying instructional reform a chance to share their experiences with colleagues in other disciplines.

Local disciplinary groups will keep files on the involvement of faculty in their departments. Each semester, the groups will record activities that interest each of the faculty, and his/her level of participation, as well as plans for further involvement through workshops, etc. Faculty members implementing instructional reform will have their classes visited at least twice during the semester, with an assessment report prepared for the faculty member (and for project records). Each semester, participating faculty will be asked for self-assessment of progress and feedback on the organization and effectiveness of consortium efforts.

Outcomes: After two years, we seek to have several faculty in every quantitative department at the ten Long Island institutions using new modes of instruction, in conjunction with other project activities mentioned below; they should be reporting positive experiences in evaluation surveys. After four years, most faculty in quantitative disciplines on Long Island will have become active.

Post-reform versus pre-reform student self-evaluation of their confidence in using mathematics in quantitative disciplines should increase. Other measures of success in reformed courses include improved student performance in mathematical reasoning and more students continuing into advanced S.M.E. courses, as compared with students not in reformed courses.

ii) Promoting Day-to-Day Coordination of Instruction in Mathematical Sciences and Their Uses Throughout the Curriculum. Engineering departments at Stony Brook, New York Institute of Technology and elsewhere are now offering freshman design courses that are closely coordinated with the science and mathematics that beginning engineering students take (rather than the past practice of delaying engineering courses until the sophomore year). The junior-level physical chemistry course at Stony Brook has just added an extra hour each week to allow more time to discuss the associated mathematics; there will be half a dozen guest lectures by mathematics faculty. At SUNY-Old Westbury, a finance professor has regularly taught a section of calculus.

With reform calculus courses now using realistic examples from the natural and social sciences, it is a natural next step for these examples to come directly from course material in other departments; similarly for linear algebra, statistics and finite mathematics. Freshman physics instructors and calculus instructors will coordinate, where appropriate, weekly syllabi and key examples from each other's courses. Mathematics faculty can coordinate with instructors of calculus�related courses in a number of diverse departments. These coordination efforts will enable faculty in those calculus�related courses to connect better with prerequisite mathematics material instead of, as often happens, developing much of the needed mathematics from scratch. There will also be exchange class lectures where faculty in, say, mathematics and electrical engineering guest teach in each other's class. We want students to be reminded constantly of the two-way link between mathematics and other quantitative disciplines.

Implementation: Responsibility for this activity will reside with the local disciplinary groups and local organizing committees. This activity will be closely linked to efforts in activity (i) above on modes of instruction. Following departmental and general campus meetings to discuss the goals and methods for coordination, the local disciplinary groups will arrange meetings between one or two faculty in their discipline and one or two mathematics faculty to plan concrete steps for coordinating syllabi and sharing examples, including visiting each other's classes. In the first year, math/physics coordination will be a primary focus; in the second year, math/chemistry&biology. There will also be coordination among science and engineering courses which use common mathematics. Effective use of exchange lectures will be developed.

Outcomes: After one year, we seek moderate levels of day-to-day coordination and exchange lectures among half a dozen pairs of faculty in quantitative courses at each participating Long Island institution. After four years, all faculty in S.M.E. departments will be involved in substantial coordination efforts. Evaluation forms mentioned in activity (i) will also assess coordination efforts. In particular, student questionnaires before and after new coordination efforts should show an increased appreciation of the usefulness of mathematics.

iii) Educational Technology Across the Curriculum. The State University of New York recently announced a $100,000,000, 8-year initiative to purchase computers and related equipment, rehab classrooms, and hire support staff to make educational technology pervasive in SUNY classrooms and laboratories and to foster innovative, technology-based instruction. The level of expenditures in this initiative in the near future is in doubt, although the SUNY leadership remains strongly committed to this initiative. The SUNY Provost wants this project to help provide an intellectual framework for the SUNY initiative in quantitative disciplines, both to nurture the development and use of educational technology and to ensure inter-discipline, inter-campus cooperation and dissemination of efforts funded by this initiative (see his letter of support).

Among large-scale efforts on Long Island worthy of note are the use of the Michigan State's Computer Assisted Personalized Assessment software to create individualized quizzes for each student in Stony Brook freshman chemistry and physics courses; and the use of PC-Solve-based simulation laboratories in a set of introductory and advanced Stony Brook economics courses. Some consortium faculty in the sciences have already developed extensive state-of-the-art multimedia presentations for their courses. Stony Brook's Computer Science and Psychology Departments have an NSF grant to create courses on developing multimedia software (the only grant of its kind).

Over the period of the proposal, we plan to transport the coordination efforts in activity (ii) to hypertext on the World Wide Web. Hypertext is an ideal medium for making connections between courses in a wide range of disciplines, and the web provides a reliable underlying technology. The World Lecture Hall at "http://wwwhost.cc.utexas.edu/world/instruction/index.html #Computer" is already starting to collect course materials from around the world. With course materials on the web, links to examples in other disciplines are easy to make and easy for students to follow. For example, when discussing derivatives in a calculus course, the hypertext lesson would have links to numerous examples from courses in physics, economics, engineering, etc. These examples could come from courses at other institutions in the project or could have been developed across the country. Going the other way, hypertext for physics, economics, engineering courses, etc. would have links to a readable discussion of the underlying concept/theory of derivatives in the calculus hypertext lessons. All this software will be immediately available nationally through the Internet.

Implementation: There will be a guiding task force on educational technology, with many teams working on individual software efforts. Co-PIs Dawes (Economics), Ferguson (Engineering) and Henderson (Computer Science) will oversee these efforts. Adapting existing educational software packages� and in some cases, designing their own-- task force teams will develop computer-based assignments for use in multiple disciplines, such as graphing the behavior of second-order differential equations with different forcing functions which, in courses in different departments, could model an economic system or a chemical reaction or the response of a car with different types of shock absorbers. Software development efforts will be assisted by undergraduate and Master's computer science students at consortium institutions. We anticipate that costs for equipment and software purchases should be covered by the SUNY initiative. Some additional federal funding may be sought for the hypertext effort.

The educational technology task force will organize regional and campus workshops about: (i) mathematical software, both general purpose systems like Maple and MATLAB and problem-solving software like PC-Solve; (ii) special propose educational software developed locally and nationally; (iii) technology-based pedagogical innovation; and (iv) multimedia authoring systems. Workshops will emphasize the integration of technology with instructional and curricular reform.

Outcomes: We seek to have 100 Long Island faculty become new users of educational technology in their courses by the second year. The number of new users will grow each successive year until after five years the vast majority of quantitative faculty on Long Island will be using educational technology extensively. Software and associated written material will be developed for about four multidisciplinary computer projects each year. After five years, over a dozen courses will be transported to hypertext format with the links mentioned above. Student and faculty satisfaction with educational technology efforts will be monitored through assessment methods similar to those mentioned for previous activities.

5.B. Creation of new courses and curricular materials

iv) Developing New Multidisciplinary Courses. The project will have a task force to develop a number of courses in subjects that draw upon two or more disciplines. One planned multi-disciplinary course is Digital Information and its Mathematics, which would involve computer science, engineering, the natural sciences, and mathematics. It would cover topics such as DNA sequencing, high definition television, compact discs, wireless communication, image compression, and two-dimensional bar codes. Another is the Mathematics of Fairness and Equity, which involves mathematics, computer science, business, and social and behavioral sciences. It would cover topics such as elections and ranking schemes, cost allocation and taxing schemes, game theory, fair division, and bargaining and arbitration. Outlines for these two courses are given in the Appendix 5. These courses will advance the project goals of interconnectivity by drawing upon modes of reasoning and concepts from several disciplines.

There are many new courses being planned involving one quantitative department and mathematics, such as game theory (economics), applied number theory (computer science), and quality control (engineering). Some are mathematics courses for particular majors; for example, a course entitled Mathematical Modeling in Biological Systems is being developed at Stony Brook under a Howard Hughes Medical Institute educational grant. Some are liberal arts courses, such as a proposed lower-division core curriculum course in mathematical modeling and a Computer Mathematics course, surveying topics such as the principles of magnetic resonance imaging and error correcting codes. At two-year colleges, TechPrep courses integrating mathematics, science and technology will be developed, following SUNY-Farmingdale�s model. Some of the new course development will build on course materials developed elsewhere under NSF grants.

The consortium includes several faculty with experience in innovative curriculum development: Malkevitch's For All Practical Purposes, Henderson's Foundations of Computer Science (which integrates mathematical and computer science problem-solving paradigms), Gordon's Functioning in the Real World, and Beltrami's Mathematics for Dynamic Modeling.

Implementation: Joe Malkevitch (York College) will head the task force developing multidisciplinary courses. He will be team leader for courses in digital mathematics, applied geometry and mathematics of fairness. The computer mathematics courses will be overseen by Peter Henderson (Stony Brook). Teams of faculty from several institutions will be involved in writing textual material (including exercises) and support software and hypertext linkages for each of the cross-disciplinary courses. There are many good sources for parts of the new texts, although such material is written from the perspective of one discipline. In the early development stages of new courses, material will be used as modules in selected existing courses in consortium institutions.

Outcomes: One new multidisciplinary course will be ready for class testing in several consortium schools every three semesters; 3 courses over 5 years. Modules for one new CS/math course (initially to supplement existing texts) will be available each year starting in the second year. Slightly slower development schedules are anticipated in other cross-disciplinary efforts.

Academia has a tendency to promote insular instruction in which, say, psychology majors are taught statistics solely from the point of view of what is needed in certain psychology courses, with little thought of students' broader career needs. Groups of departments which are each currently offering their own customized versions of some mathematics subject, such as statistics or numerical methods, will develop new unified (cross-listed) versions of the course, with most discipline-specific issues relegated to sequel courses.

While this is a politically sensitive issue, we are encouraged by the fact that faculty at some Long Island institutions are already working to implement it. Moreover, we have very strong support from campus administrators to make this happen. Discussions are now underway at Dowling College and at St. Joseph's College among faculty in biology, psychology, business and mathematics to develop a common introduction to statistics. Besides covering the core material of the subject from a standard general purpose statistics text, these courses would have supplementary material written to explain why different disciplines focus on different types of statistical analysis. For example, explaining why behavioral sciences have extensive categorical data, while engineers have very little; why economics is naturally interested in regression and time series, while psychology is interested in analysis of variance and hypothesis testing (and regression). Such courses would be cross-listed in several departments and staffed by faculty from different departments (in a fashion to keep workload the same as existed in the previous disciplinary courses). When the total enrollment is small, such a course would be taught on a rotating basis among departments.

Implementation: The local organizing committees, with strong administrative backing, will coordinate efforts to bring together faculty in departments teaching duplicative courses to find ways to cooperate and develop such unified courses.

Outcomes: After one year, discussions will be started at all Long Island consortium institutions to re-think instruction in statistics (and other courses with multiple offerings) in a less discipline-focused fashion. New unified courses will be developed and taught at all Long Island institutions after three years. Success of this activity for students will only be truly measurable many years after graduation. We will rely on faculty assessment of students' general appreciation of these unified approaches.

vi) Calculus Reform and its Implications Across the Curriculum. Calculus reform, primarily with the Harvard Consortium calculus text, is well advanced on Long Island. Consortium personnel are leaders in the Harvard Consortium effort: Sheldon Gordon (Suffolk C. C.) is a text co-author and Phil Cheifetz (Nassau C.C.) is co-author of the Instructor's Manual. Stony Brook's Anthony Phillips has an NSF calculus reform implementation grant, which includes a 'reformed' version of a year-long, integrated precalculus/calculus course. Sandy Monteferrante of Dowling College has NSF support for implementing calculus reform with Dubinsky's 'more radical' reform text. Dowling and C. W. Post faculty are enhancing calculus reform by developing associated computer laboratories involving problems from students' major disciplines. Suffolk Community College is developing an integrated approach to multivariable calculus and physics II.

However, the implications for calculus reform for user disciplines here and across the nation are only beginning to be considered. The pervasive use of graphing calculators (now required on the AP calculus exam) and computers to visualize complex functions and evaluate definite integrals which lack close-form solutions is not yet reflected in calculus-based problems in science and engineering courses. Also, reform materials for multivariable calculus and differential equations are still evolving and lack good associated software.

Implementation: A task force on implementing calculus reform will run reform workshops for all four courses of the standard calculus/DE sequence to assist faculty in adopting calculus reform. The workshops will be largely text-independent. The local disciplinary groups together with the calculus reform task force will organize campus workshops to explain to faculty in quantitative disciplines how to take advantage of calculus reform and associated technology and pedagogy in their instruction; for example, assigning parametric types of problems where students numerically evaluate a complicated integral with a variety of values of some parameter and form a graph of the solution as a function of the parameter.

Outcomes: After two years, most sections of calculus will be reformed at all Long Island consortium institutions. Comparison of pre- and post-reform tests should show the improved conceptual and problem-solving skills claimed for calculus reform in the MAA Assessing Calculus Reform Efforts report. After three years, the majority of faculty teaching courses requiring calculus will be basing their instruction on new student capabilities arising from calculus reform. This change will be assessed by student and faculty questionnaires.

vii) Precalculus Reform and Its Implications Across the Curriculum. Precalculus reform efforts are just beginning across the country. One problem is clarifying what the real purpose of precalculus is, since only a small fraction of students taking precalculus ever complete a calculus course and few other courses have precalculus as a formal prerequisite. A complicating factor in precalculus reform is that precalculus students usually have substantial weaknesses in their mathematical skills. One of the furthest developed reform efforts is led by Sheldon Gordon, whose preliminary text Functioning In the Real World is currently being class-tested by about 40 instructors across the country (several of whom learned about it at the consortium's Albany conference). Phil Cheifetz is co-author of the precalculus text under development by the Harvard Bridge Consortium. Sandra Monteferrante has a NSF grant to extend the approach of Dubinsky's calculus reform to precalculus. These reform courses include new mathematical topics, such as difference equation modeling, which have extensive applications in the natural and social sciences and business. Developing such application linkages will be part of coordination efforts discussed in activity (ii). Precalculus reform will involve new modes of instruction and learning mentioned in activity (i) and will use educational technology extensively.

Implementation: Sheldon Gordon and Phil Cheifetz will lead a task force for precalculus reform. The task force will give formal workshops on using precalculus reform materials. The task force will work with local disciplinary groups to promote the use of reform precalculus ideas in appropriate quantitative courses.

Outcomes: After two years, at least one reformed precalculus section will be taught at all Long Island consortium institutions. In five years, almost all precalculus instruction on Long Island will be reformed. Student performance on common exam questions in reformed and unreformed precalculus should show a statistically significant improvement in the reform group. More reform precalculus students should take and pass a semester of calculus. Questionnaires to faculty should show that they perceive an improved learning environment in reform precalculus classes.

5.C. Developing Human Resources

viii) Assisting Groups that are Underrepresented in Quantitative Disciplines. Throughout quantitative disciplines, workshops for minorities and women in the spirit of Uri Treisman�s Berkeley PDP program have been shown to help underrepresented groups succeed in SME majors. There are several initiatives underway on Long Island that are succeeding in increasing participation and performance of women and underrepresented minorities in S.M.E. disciplines. Stony Brook has major NSF funding for its Project WISE (Women in Science and Engineering- and mathematics) whose programs include hands-on research experiences, a speakers series, special research-oriented courses, informal social activities, a strong mentoring system as well as extensive outreach to girls in the schools. SUNY-Old Westbury and Stony Brook both have SUNY Science/Technology Entry programs for incoming minority freshmen (including outreach to minorities in local schools). There are two NSF Research Careers for Minority Scholars grants� Old Westbury's centered in science, Stony Brook's in mathematics. Stony Brook's large Howard Hughes Medical Institute educational grant has a substantial minority support component. Note that underrepresented minorities at Stony Brook, Old Westbury, and CUNY-York constitute 25%, 40%, and 80%, respectively, of the student populations.

A consortium of SUNY two-year and four-year colleges has an NSF grant to run workshops to train faculty in minority support efforts. David Ferguson (Stony Brook), who formerly assisted Treisman in the Berkeley PDP program, is director of a pending SUNY-wide Alliance of Minorities in Engineering proposal to NSF. To enhance the impact of these activities for underrepresented groups, sessions for faculty are planned to make them more sensitive to the particular problems and concerns these students face in quantitative disciplines. The project activities in section 5.A, such as cooperative learning, have been shown to be especially helpful for underrepresented groups.

Implementation: The task force on assisting underrepresented groups will coordinate and extend existing efforts for developing support programs for minority and female students in all disciplines on Long Island. Outreach efforts to women and minorities in local schools will be expanded. We have a good idea what needs to be done and experience in doing it on a small scale. The challenge is to get wide-spread adoption of these efforts as regular campus activities, rather than as special efforts funded by a state or federal grant.

Outcomes: In the first year, all consortium institutions will hold annual faculty sensitivity training sessions (mentioned above). After two years, mentoring systems, utilizing both faculty and 'big brothers' and 'big sisters', will be in place to serve all minority or female S.M.E. majors. After three years, Treisman-type workshops will be underway at all institutions in introductory college math and science courses having critical masses (6 or more) of minority students.

ix) Preparing Future Teachers. The preparation of future school mathematics and science teachers needs to be reworked to reflect the values of the NCTM Mathematics Standards and the forthcoming NRC Science Standards. (For the immediate future, this effort faces the hurdle of needing simultaneously to prepare teachers to follow the NY State Regents mathematics and science curricula.) Since teachers tend to teach the way they were taught, all aspects of this project impact directly on the preparation of future teachers. In turn, students entering college who were taught in the environment proposed here will help move our reforms even further.

Special efforts are needed to overcome the "math phobia" of most prospective elementary school teachers. At the doctoral level, there is a growing awareness that future faculty need solid training in effective instructional techniques as well as a familiarity with emerging trends in instructional reform and curriculum development.

All Bachelors-granting institutions in the consortium have secondary mathematics and science teacher preparation programs. Jong Lee at Old Westbury and other consortium members have developed a successful array of continuing education and Saturday enrichment courses for school teachers and students. These courses will be used as forums to develop dialogues with secondary and primary school teachers about new pedagogical and curricular developments. Stony Brook's Graduate School has an extensive series of workshops on instructional methods for graduate students. The four SUNY University Centers have a FIPSE proposal to place doctoral students for one year in nearby four-year and two-year institutions to expand their teaching experience.

Implementation: Building on recommendations from professional societies for Standards-based pre-service training for mathematics teachers, a task force on teaching training will rethink the pre-service curriculum for secondary mathematics teachers. Local school mathematics teacher organizations will be involved. While it is not in the purview of the Mathematical Sciences Across the Curriculum initiative to rework preservice science teacher training, consortium members will work with science educators on individual campuses and regionally to assist efforts to revise science teacher training with an eye on the quantitative component.

Encouraging efforts have begun at St. Joseph's College for a course for pre-service elementary school teachers that uses familiar applications to help overcome their math anxiety. To improve the training of undergraduate teachers, doctoral seminars on instructional strategies will be started in quantitative disciplines at Stony Brook.

Outcomes: After three years, pre-service curricula for secondary mathematics teachers at Long Island institutions will be reworked to reflect the NCTM Standards. This will include changes in disciplinary courses taken by preservice students as well as the teaching methods courses. Surveys of prospective mathematics teachers should indicate that they believe they have been well prepared to implement the NCTM Standards in their teaching. By the second year, the new mathematics course for elementary school teachers will be refined and tested at several schools. By the second year, graduate instructional seminars will be running in all quantitative doctoral programs. Surveys of doctoral students before and after the seminars will be expected to show a significant change in students' awareness of, competence in, and appreciation for instructional matters.

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The Long Island Consortium is sponsored by the NSF Initiative: Mathematical Sciences and Their Application Throughout the Curriculum, DUE #9555142. The original NSF proposal can be accessed by clicking here.