Virginia Commonwealth University\u27s Program for K-6 and 6-8 Teachers: The Interdisciplinary B.S. in Science

Virginia Commonwealth University (VCU) has very recently revised its requirements for the K-6 Certification to include a total of 21 hours in mathematics and science as well as a three credit hour methods course in mathematics and science. This requirement includes a physical science and a biological science course, each with a laboratory component, a contemporary mathematics course with extensive student projects, collaborative work and applications, a statistics course and interdisciplinary science and mathematics course. We believe that as students complete these requirements they will meet the new State K-6 licensure requirements in all areas, with the exception of geometry. We are developing a new geometry course that we hope will be required of all future teachers. The challenge of preparing middle school teachers to teach mathematics and/or science is much more difficult. VCU has been preparing very few middle school teachers of mathematics and science. We typically averaged less than one middle school science teacher and less than one middle school mathematics teacher per year. This paper provides a description of our interdisciplinary degree in mathematics and science that appears to be attracting significant numbers of students with an interest in teaching mathematics and/or science at the middle school level

Mathematics as a tool in the Life Sciences

Teaching mathematics to students in the biological sciences is often fraught with difficulty. Students often discover mathematics to be a very 'dry' subject in which it is difficult to see the motivation of learning it given its often abstract application. In this paper I advocate the use of mathematical modelling as a method for engaging students in understanding the use of mathematics in helping to solve problems in the Biological Sciences. The concept of mathematics as a laboratory tool is introduced and the importance of presenting students with relevant, real-world examples of applying mathematics in the Biological Sciences is discussed

Biological and aerodynamic problems with the flight of animals

Biological and aerodynamic considerations related to birds and insects are discussed. A wide field is open for comparative biological, physiological, and aerodynamic investigations. Considerable mathematics related to the flight of animals is presented, including 20 equations. The 15 figures included depict the design of bird and insect wings, diagrams of propulsion efficiency, thrust, lift, and angles of attack and photographs of flapping wing free flying wing only models which were built and flown

Measurement in biological systems from the self-organisation point of view

Measurement in biological systems became a subject of concern as a consequence of numerous reports on limited reproducibility of experimental results. To reveal origins of this inconsistency, we have examined general features of biological systems as dynamical systems far from not only their chemical equilibrium, but, in most cases, also of their Lyapunov stable states. Thus, in biological experiments, we do not observe states, but distinct trajectories followed by the examined organism. If one of the possible sequences is selected, a minute sub-section of the whole problem is obtained, sometimes in a seemingly highly reproducible manner. But the state of the organism is known only if a complete set of possible trajectories is known. And this is often practically impossible. Therefore, we propose a different framework for reporting and analysis of biological experiments, respecting the view of non-linear mathematics. This view should be used to avoid overoptimistic results, which have to be consequently retracted or largely complemented. An increase of specification of experimental procedures is the way for better understanding of the scope of paths, which the biological system may be evolving. And it is hidden in the evolution of experimental protocols.Comment: 13 pages, 5 figure

A new process foundation for the applied topos

The world is in turmoil for want of sound reasoning. Economics and the environment are but two of many areas of human endeavour badly betrayed through a failed combination of physical and information science and the rule of law. Logic is the fabric of pure mathematics as the foundation of applied mathematics on which all science is based from the physical through biological and medical to the social sciences. However the symbolic logic of today seems of scarce more use than the syllogisms of Aristotle as observed by Francis Bacon nearly 400 years ago: The logic now in use serves rather to fix and give stability to the errors which have their foundation in commonly received notions than to help the search after truth. So it does more harm than good [Novum Organon Aphorism XII, 1620]