When undertaking Mathematics Education, one will in the end view mathematics as an enigmatic field of research. Studies involved in Mathematics Education are fields of research in their own rights. Here, fundamental mathematical studies are undertaken without any particular applications in mind. On the other hand, mathematics is the language used in the construction of abstract models of the real world that underpin D and R other fields, including applications in industry. Mathematics in Mathematics Education is used to help understand reality and help change parts of it for the benefit of Man. It is used in many fields, including chemistry, engineering, physics, economics, biology, political studies, environmental studies, and medicine. Business Training in Kenya has more information.
Steps Involved in Mathematics Education
The first step when undertaking Mathematics Education is often the construction of a mathematical model i.e. a description of a problem using mathematical terms. The model is then studied by analytical or numerical methods to obtain an exact or approximate solution. Eventually, the conclusions made after analysis are interpreted in the language of the original problem to make them more familiar to a client or user. Many a times the model is altered to conform or include more features of the problem. Thus, the modeling process may involve false starts, simplifications and modifications.
Serious mathematics in Mathematics Education enters in the second stage, where the solution of mathematical problems, and the analysis and development of the underlying theory are done. This stage will include numerical or analytical methods. The approach will range from formal methods and specific algorithms to abstract but general theories. It is never clear which mathematical skills will be more useful in the study of a new problem in Mathematics Education; thus the introduction of applied mathematics. A mathematical scientist must not only be a good mathematician but also knowledgeable in the area to which mathematics is to be applied.
Thus, a student undertaking Mathematics Education must be concerned with the construction and interpretation of appropriate models. The art of developing models requires that the modeler (who is the student) makes decisions about which factors to include and which to exclude. The overall aim is to produce a model that is realistic enough. It should reflect on the aspects of the phenomena being modeled, and also be simple enough to be treated mathematically.
Many a times a model is formulated to answer a specific question. Sometimes thou, the modeler must either simplify the model to allow for analysis, or devise a new mathematical method that will be employed in the analysis of the model. Often combinations of numerical and analytical methods are used. The modeling process in the Mathematics Education program may sometimes involve a sequence of models of increasing complexity. Problems sometimes lead to the development of new mathematical methods, and mathematical methods in existence often lead to new insights into the problems. Any successful Mathematics Education student must be comfortable, competent and confident in both mathematics and its fields of application.
The question of what applied mathematics is does not answer to logical classification so much as to the sociology of those who use mathematics. In Mathematics Education, applied mathematics is a branch of mathematics that deals with the application of mathematical methods to other domains. Such applications include: -
- Optimization and operations research,
- Numerical analysis,
- Mathematics of engineering,
- Continuous modeling,
- Linear programming,
- Mathematical biology and bioinformatics,
- Information theory,
- Financial mathematics,
- Probability and statistics,
- Actuarial science,
- Game theory,
- Cryptography and hence combinatory,
- Finite geometry to some extent,
- Graph theory as applied to network analysis, and
- A great deal of computer science.
The mathematical methods listed are usually applied to specific problems fielded by means of a mathematical model of the phenomena. Engineering mathematics in Mathematics Education describes physical processes, and so is often not easy to distinguish from theoretical physics. Important subdivisions include acoustic theory, fluid dynamics, mechanics, Maxwell’s equations of electromagnetism, and numerical relativity.
Conclusion on Mathematics Education
In the past, applied and pure mathematicians have argued over which endeavor is nobler. There is not so much conflict along those lines to date. It is certainly the case that mathematics is much wider in scope than the portions of it which are traditionally of highest interests to physicists. Physics is just one area of applications. That is a short description of Mathematics Education.