III. CRITERIA FOR ASSESSMENT
At the same time, assessing the value of mathematics by measuring the return
on public investment cannot be done by simply comparing the amount of
expenditure on mathematics with the amount of wealth created. The
"effects" of mathematics may not be immediate, or direct, or
attributable to a single funded program. A more accurate assessment of the
field requires one to accept the consensus view of all branches of science and
technology -- that support for mathematics is essential -- and to ask whether
that support is producing health within mathematics and a valued impact outside
it.
The Panel concluded that the most accurate way to measure the impact of
academic mathematics is to examine the three primary activities of
mathematicians:
We assessed each of these activities separately, by different criteria.
1. Criteria for Assessing Contributions to Fundamental Mathematics.
We believe that it is the mathematicians themselves who are best qualified to
assess the intellectual impact of U.S. mathematics. We asked mathematicians to
use the following benchmarks in their assessment: (i) academic recognition of
the accomplishments of mathematical scientists, as measured by publications,
awards, and presentations at major conferences; (ii) judgments of mathematical
scientists not resident in the United States; (iii) the attractiveness of the
U.S. mathematics community to foreign mathematical scientists; and (iv) the
speed with which U.S. mathematical scientists can respond to discoveries
occurring both within and outside the United States, as well as to discoveries
by other scientists and engineers, and incorporate these discoveries into their
own work. We used these measures to benchmark the standing of U.S. academic
mathematical sciences in relation to other nations.
2. Criteria for Assessing Interactions Between Mathematicians and Users of
Mathematics. Evaluating the effectiveness of interactions between academic
mathematics and the users of mathematics is necessarily more subjective. As one
measure, we used the levels of employment of mathematicians in different
segments of society. As the SIAM report(see Endnote
10) demonstrates, these levels are difficult to ascertain. As a second
measure, we used three types of subjective judgments, based on both surveys and
personal information: (i) the perceived importance of mathematics to other
areas; (ii) the effectiveness of the academic mathematical sciences in solving
the problems of these areas; and (iii) the speed with which new mathematical
ideas are transmitted to other areas and to the private sector.
3.Criteria for Assessing Undergraduate, Graduate, and Post-Doctoral
Education. Four measures are used for this assessment: (i) the flow of
students (both U.S. national and foreign) into degree programs in U.S.
universities; (ii) the quality of the research performed by university
alumni/ae; (iii) the ability of students trained in U.S. departments to find
rewarding jobs that make good use of their training; and (iv) the nature of the
work that mathematicians perform when employed.
We have not explicitly examined the influence of university research and
teaching on education at the K-12 level. U.S. universities teach those who
become the teachers of K-12 mathematics, so university instruction in
mathematics is essential to the teaching of arithmetic and mathematics in grade
school and high school. The challenges of assessing K-12 teaching and of
proposing strategies for curriculum reform are, however, beyond the scope of
this report and are being addressed by others. We do, however, wish to stress
the importance of these challenges. The health of the U.S. mathematical
sciences, and the economic well-being of the United States, are both directly
related to the quality of K-12 mathematics education.
In addition, we have not examined post-professional or continuing education
for mathematical scientists or for the teachers and users of the mathematical
sciences. We anticipate that education at these levels will become increasingly
important in the future.
