In last week's Math News, a research report demonstrated that even scientists (in this case, biologists) tended to overlook (i.e. ignore) "their colleagues' research if it is packed full of mathematical equations." So, the real trouble now has been identified, comparing this research with prior claims.
A report in 2009 made this claim: "As mathematics continues to become an increasingly important component in undergraduate biology programs, a more comprehensive understanding of the use of algebraic models is needed by the next generation of biologists to facilitate new advances in the life sciences." But, will they even use or read about these models?
In 2009, the researchers added: "Future generations of biologists will routinely use mathematical and computational approaches to develop and frame hypotheses, design experiments, and analyze results. Sound mathematical models are essential for this purpose and are currently used in the field of systems biology to understand complex biological networks. Two types of mathematical models, in particular, have been successfully used in biology to reproduce network structure and dynamics: Continuous-time models derived from differential equations (DE models) focus on the kinetics of biochemical reactions, while discrete-time algebraic models built from functions of finite-state variables focus on the logic of the connections of network variables."
Biology students need to be exposed to both Differential Equation models and Discrete-Time Algebraic models (e.g. Boolean networks), as the latter are "increasingly being used to model a variety of biochemical networks, including metabolic, gene regulatory, and signal transduction networks."
Virginia Tech researcher Reinhard Laubenbacher. "Often, researchers do not have enough of the information required to build detailed quantitative models. Algebraic models need less information about the system to be modeled, making them useful for instances where quantitative information may be missing. All the work that goes into building them can then be used to construct detailed kinetic models, when additional information becomes available. In addition, algebraic models are much more intuitive than differential equations models, which makes them more easily accessible to life scientists."
According to Sweet Briar College's Raina Robeva, "The exciting thing about algebraic models from an educational perspective is that they highlight aspects of modern-day biology and can easily fit in both the biology and mathematics curricula. At the introductory level, they provide a quick path for introducing biology students to constructing and using mathematical models in the context of contemporary problems such as gene regulation. At the more advanced level, the general study and analysis of such models often require sophisticated mathematical theories. This makes them perfect for inclusion into mathematics courses, where the biology can provide a meaningful framework for many of the abstract structures. As educators, we should actively be looking for the best ways to seize this opportunity for advancing mathematical biology."
So what to do...to educate...or to hide the mathematics in an Appendix? My suspicions or predictions are...
Source: ScienceDaily, July 30, 2009