The Middle Atlantic Consortium for Mathematics and its Applications Throughout the Curriculum is comprised of the University of Pennsylvania, Villanova University, Polytechnic University, Community College of Philadelphia, two Philadelphia public high sch ools and the Society for Industrial and Applied Mathematics. The primary goals of the consortium are to

The over-riding goal of this initiative is to promote a climate in which faculty across all disciplines view themselves as being jointly responsible for the (technical) education of undergraduates, rather than as clients and servants. We intend to achieve this first within our own institutions and then promote the use and development of such materials and methodologies at other institutions using our results as models.

The approaches being taken are based in part on the experience accumulated at Penn and elsewhere in developing and promoting large-scale calculus reform. Our initiative consists of four projects:

  1. Creation of multi-media applications modules for mathematics courses and mathematics modules for other-disciplinary courses.
  2. Development of basic and advanced interdisciplinary courses that integrate mathematics with specific applications areas.
  3. Development of applications and laboratory-oriented courses for mathematics majors.
  4. Development of materials for non-mathematically oriented students in consideration of mathematical literacy issues.
Consortium courses and materials in various stages of development at this time include: Other projects under development include course and module materials on the mathematics of Financial Derivatives, the Analysis of Image Data, International Economics and Monetary Policy, Applications-oriented Precalculus, and various other modules concern ing engineering applications.

SIAM is assisting with administration and dissemination for the project (articles have already appeared in SIAM News, for example). Evaluation of project materials and results is to be carried out at Penn by a group led by Robert Baruch of the Graduate Sc hool of Education, at Villanova by its Human Organization Science Institute and by CCP's Office of Institutional Reseach.

Evaluation

The Evaluation team works under the direction of Prof Robert Boruch of Penn's Graduate School of Education, and organizes itself around the following Evaluative Core Questions:

Question 1: What is the nature, severity, and scope of the problem and how do we know?

In the MATC context, this includes, for example, generating good evidence about why and how students fail to reason properly in attempting to solve word problems. It includes generating evidence on students' difficulties in educing a mathematical concep t or model from a narrative description of a physical phenomenon. It includes trying to understand the order of magnitude of the difficulty and how the magnitude can be measured or observed.

Understanding stereotypical problems that students have in learning seems basic to addressing other questions. If the problem is ill-defined, not severe, or is easily controllable, then inventing solutions and testing them seems ill advised.

At the micro (bench) level, the approach to generating evidence will be based on achievement testing and other tactics in the interest of diagnosing when and how students go wrong. It will be based on cognitive processing approaches to understanding ste reotypical mistakes, e.g., "think aloud" approaches to learning how students think. And it will be based on small surveys, on students' perceptions (or misperceptions) of their skills and abilities are and about MATC products.

Across institutions in the Consortium, we will develop a mechanism for routinely synthesizing information obtained at the subcourse and course level. This can result, for instance, in meta-analyses of the nature and distribution of students' problems or perceptions.

Question 2: How and how well are MATC products developed and emplaced?

We recognize that no program, project, or practice is ever delivered as advertised. Patients may not comply with the drug or diet regimen prescribed. Educators who have a mandate to deliver one kind of instruction, one syllabus, one module and so forth , will vary in their delivery.

This evaluation question bears primarily on process rather than product. It is apropos within sites, such as a course or institution, where a particular module might be the target of evaluation in two or three sites. It is pertinent at the consortium l evel where, for instance, the level of communication or cooperation on a module across all sites needs to be understood.

In the vernacular of the evaluation industry, the question implies "formative" evaluation, "monitoring," and "troubleshooting." When routinized well, the activity takes the form of quality assurance.

The approach we will take to this evaluative question involves direct independent observation of students' and faculty engaged in MATC activity. This can include, for example, taking time samples of student laboratory work to understand whether and how the activity accords with MATC themes. It can include periodic direct observation of out of class engagement in team work on assignments. We expect to use videotape to augment direct observations to augment direct observation of what happens, when, amon g whom, and to what end.

Other simple indicators of integration activity will be exploited where possible. Monitoring and counting the frequency or duration of exchanges between mathematics faculty and faculty in other disciplines, the frequency of joint courses, and so on is f easible, for example, based on logs maintained by faculty.

At the multi-institution, and cross course level, meta-analyses of the subcourse and out of course activity are possible. Regardless of measurement within a course or module, it seems sensible to monitor and record the simple frequency of attempts to us e MATC inventions across faculty and schools. This is a crude indicator of process and a potential indicator of ultimate exportability of MATC products.

Question 3: Does the innovation work? Relative to what standard? Based on what evidence?

The question, of course, is basic in the MATC setting. More generally, it has not often been addressed in higher education (Bok, 1986) on account of its difficulty.

Evaluating the effects of a major change in curriculum requires, for example, that we know (or guess) what would have happened to students in the absence of the particular change. This, in turn, requires good forecast or, more likely, a fair comparison group, or making an untestable assumption.

This question is misleadingly simple but crucial. It will be unbundled so as to cover four questions.

Question 4: What are the costs and cost/effectiveness of alternatives? And how do we know?

Addressing this question depends heavily on one's having addressed the preceding questions well. If the program is not properly emplaced, for instance, it does not make much sense to do a cost/effectiveness analysis.