## Even Our Puzzles Are Outdated … Mathematics for 2025 (and today)

Earlier this month, the Conference Board of Mathematical Sciences (CBMS) held a forum on mathematics in the first two years; many of the presentations are available on the web site (http://cbmsweb.org/Forum5/)

As part of one of the first plenary sessions, Eric Friedlander commented … Students in the Biological Sciences now outnumber those in the Physical Sciences in the standard calculus 1 course. (David Bressoud shared some specific data on those enrollment patterns.)

Historically, the developmental mathematics curriculum was all about getting students ready for pre-calculus. Our “applications” tended to be puzzles created with physical sciences in mind — bridges, satellites, pendulums, and the like. Few problems in our developmental courses draw the attention of those in biologically-oriented fields (including nursing).

We could include:

- Surge functions to model drug levels
- Functions to estimate the proportion of a population needed to be immunized to prevent epidemics (P_sub_c = 1 – R_sub_0)
- Models for spread of cancer … and for treatments
- Pollution prediction (simplified for closed systems)

This list is a ‘bad list’ because there is no common property (except being related to biology) … and because I do not know enough to provide a better list. Take a look at books in applied calculus for the biological sciences; you will see applications that are perhaps better than those above.

There is a trend in the new models for developmental mathematics (AMATYC New Life, Dana Center New Mathways, and Carnegie Foundation Pathways) to include a balance of applications — including more from biology. We need to bring in more of these applications throughout our curriculum (from the first developmental course up to calculus).

Most of us realize that the ‘applications’ in our courses and textbooks are puzzles created by somebody who knew the answer; generally, these problems do not represent the use of mathematics to solve problems and answer questions in the world around us. Sometimes, we are not able to provide enough non-mathematical information to provide representative problems … in those cases, some reduction to the ‘puzzle state’ is acceptable.

Our puzzles should represent the diversity in the uses of mathematics, with a significant portion of applications being realistic in nature.

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