What Are Teaching Models In Mathematics?
Mathematics is not only a subject but it is the language with some different symbols and relations. Mathematics simplifies all the things easily but in different manner. Math teaching models are just like a bridge which associates mathematics with real life event or a problem. The basic purpose of those models is how to make mathematics education interesting and students enjoy doing mathematics, not only for their academic progress but discovers new tricks, methods and mainly they can be able to relate all the math problems or content of text book to real life problems.
Education defines mathematical modeling as a way of solving problems in the maths and science, if modeling is carried out taking into account the real characteristics of the processes or systems that are being modeled.
The difference is that mathematical modeling can be part of Realistic Mathematics Education (RME) is a domain-specific instruction theory for mathematics. In other words, it is hardly possible to educate mathematical modeling by itself, since it is most often associated with an understanding of processes and systems studied in other sciences (physics & etc.).
Therefore, RME is an innovative learning approach that emphasises mathematics as a human activity that must be associated with real life using real world context as the starting point of learning.
Maths teaching models or mathematical modellings are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Mathematical models can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models etc. Mathematical models are of different types:
Linear vs. nonlinear:- If all the operators in a mathematical model exhibit linearity, the resulting mathematical model is defined as linear. A model is considered to be nonlinear otherwise. The definition of linearity and nonlinearity is dependent on context, and linear models may have nonlinear expressions in them.
Static vs. dynamic:- A dynamic model accounts for time-dependent changes in the state of the system, while a static model calculates the system in equilibrium, and thus is time-invariant. Dynamic models typically are represented by differential equations or difference equations.
Explicit vs. implicit:- If all of the input parameters of the overall model are known, and the output parameters can be calculated by a finite series of computations, the model is said to be explicit. But sometimes it is the output parameters which are known, and the corresponding inputs must be solved for by an iterative procedure, such as Newton's method or Broyden's method. In such a case the model is said to be implicit.
Discrete vs. continuous:- A discrete model treats objects as discrete, such as the particles in a molecular model or the states in a statistical model; while a continuous model represents the objects in a continuous manner, such as the velocity field of fluid in pipe flows, temperatures and stresses in a solid, and electric field that applies continuously over the entire model due to a point charge.
Deterministic vs. probabilistic:- A deterministic mathematical model is meant to yield a single solution describing the outcome of some ""experiment"" given appropriate inputs. A probabilistic model is, instead, meant to give a distribution of possible outcomes.
Deductive, inductive, or floating:- A deductive model is a logical structure based on a theory. An inductive model arises from empirical findings and generalization from them. The floating model rests on neither theory nor observation, but is merely the invocation of expected structure.
The creation and use of maths teaching models can help students develop new concepts or relationships and make connections between symbols and concepts. Because different models show different aspects of the maths and science concept. Through model, students can express how they understand the mathematical concept or relationship.
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