What are the advantages of mathematical modelling in the teaching and learning of mathematics? (2023)

What are the advantages and disadvantages of mathematical Modelling?

Mathematical modeling has many benefits related to real-world problems, but the main disadvantages are process simplification, specific rules of the model, and lack of information or data monitoring.

The purpose of the mathematical models is to have students develop the mathematics from a problem context so they can make sense of the situation and make sense of the mathematics at the same time.

- Mathematical models can help managers to make decisions quickly and more accurately as they can be used for predictions and scenario analysis. - Mathematical models are typically more convenient and cheap (more cost-effective) than other kinds of models, such as physical models.

Mathematical modeling is one of the bases of mathematics education. Mathematical modeling is described as conversion activity of a real problem in a mathematical form. Modeling involves to formulate the real-life situations or to convert the problems in mathematical explanations to a real or believable situation.

Models use familiar objects to represent unfamiliar things. Models can help you visualize, or picture in your mind, something that is difficult to see or understand. Models can help scientists communicate their ideas, understand processes, and make predictions.

Mathematical population models can be used to describe and simulate common patterns of population growth. The exponential growth model describes how a population grows when it has unlimited resources. In this model, the population continues growing larger and faster over time.

Models are useful tools in learning science which can be used to improve explanations, generate discussion, make predictions, provide visual representations of abstract concepts and generate mental models (Treagust, Chittleborough and Mamiala, 2003).

With "Modeling", the teacher engages students by showing them how to perform a skill while describing each step with a rationale. This provides students with both a visual and verbal example of what they will be expected to do.

In its broadest sense, mathematical modeling is the process of a problem solving by the mathematical expression of real life event or a problem. This process enables learners to relate mathematics to real life and to learn it more meaningfully and permanently.

How does mathematical modeling help solve problems?

Mathematical modelling is a problem solving process including rich cognitive and metacognitive activities that enables the understanding of the relations within the nature of the problems from real world, the assumptions and the relations among assumptions are explained with mathematical models by discovering the ...

Mathematical models allow researchers to investigate how complex regulatory processes are connected and how disruptions of these processes may contribute to the development of disease.

Mathematical models are now used to help understand changing animal populations, the evolution of biological patterns, the spread of disease and the functioning of the nervous system.

Mathematical models 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).

The advantage of using a model is that it allows prediction and simplification of complex systems. On the other hand, the disadvantage of a model is that they could be misleading and can be misinterpreted in a different way.

Making a model allows designers to visualise and test how a product looks and performs in 3D and is a great way of checking a product's viability .

First, that process modelling is useful, primarily for understanding and documenting business processes, but also for planning implementation projects. The major downside of process modelling is the risk of over analysis.

By studying math you develop analytical skills and an analytical attitude. You learn to pay attention to all the assumptions involved in a given problem or situation, and you learn to break down a complicated problem into a series of tractable steps.

A mathematical model of the economy is a formal description of certain relationships between quantities, such as prices, production, employment, saving, investment, etc., with the purpose to analyze their logical implications.

Modeling is an extremely useful teaching tool that should be used as often as possible. Modeling is a teaching strategy where a teacher explicitly shows the students how to complete an activity or assignment before the students begin. Modeling is also an excellent class management technique.

How does modeling improve student learning?

Model Thinking:

By having students become a part of the process, they begin to understand the concept quicker because they are able to explain and communicate the learning concept. It helps students to become critical thinkers and to be able to express themselves and their learning.

Example: An ice cream company keeps track of how many ice creams get sold on different days. By comparing this to the weather on each day they can make a mathematical model of sales versus weather. They can then predict future sales based on the weather forecast, and decide how many ice creams they need to make ...

These are usually used in case of new product launch, change in strategy, investment needs, expansion projects, etc. In such cases, predictive mathematical models are used that analyze historical data and use probability distribution as input for predicting the future values.

Mathematical models are often used by historians to study historical events, such as the rise and fall of civilizations and empires or cycles of war and peace. These models give insights into the causes and impacts of such events.

It gives us a way to understand patterns, to quantify relationships, and to predict the future.

Mathematical Modeling

In engineering and technology it provides the analytical basis for design and control in which predictions can be confidently made without spending valuable resources of money and effort.

improves the quality of design, improves visualization, and has potential for functional automation and integration. Geometric Modeling is a fundamental CAD technique. The capability of various CAD tools in geometric modeling is usually used as a crucial factor in tool selection.

the ubiquity of mathematical theory in economics also has serious downsides: it creates a high barrier to entry for those who want to participate in the professional dialogue, and makes checking someone's work excessively laborious.

What are the advantages of modelling in the design process?

Making a model allows designers to visualise and test how a product looks and performs in 3D and is a great way of checking a product's viability .

-It is not that much affected by fluctuations of sampling. -It is suitable for further mathematical analysis and observations. Disadvantages of Geometric Mean: -Due to the complex numerical character and abstract behaviour it is not friendly for non-mathematical people.

Pros of Surface modelling

Surface modelling allows to create more free-form shapes. It is more definitive in nature. There is no unnecessary ambiguity in this modelling technique. Creation of complex surfaces is easier in comparison with other modelling techniques.

The geometric mean is an average or average that gives the central tendency or typical value of a series of numbers by taking the product of the numbers. The main advantage of the geometric mean are : The calculation is based on all the terms of the sequence. Suitable for further mathematical analysis.

As nouns, the difference between disadvantage and advantage is that disadvantage is a weakness or undesirable characteristic; a con while the advantage is any condition, circumstance, opportunity, or means, particularly favorable to success, or any desired end.

It develops our reasoning, helps us to have analytical thinking, quickens our mind, generates practicality and also its use can be applied in the day to day. The mathematics is present in our daily lives.

Understanding basic business math is necessary for profitable operations and accurate record keeping. Knowing how to add, subtract, multiply, divide, round and use percentages and fractions is the minimum you need to price your product and meet your budget.

Mathematica is a symbolic mathematical computation program, sometimes called a computer algebra program, used in many scientific, engineering, mathematical, and computing fields.

Wolfram Mathematica (or simply Mathematica) is one of the best software that exists for scientific computations and multitasking. With Mathematica one essentially can perform all scientific calculations including Machine Learning (ML).

Models are useful tools in learning science which can be used to improve explanations, generate discussion, make predictions, provide visual representations of abstract concepts and generate mental models (Treagust, Chittleborough and Mamiala, 2003).

What are the benefits of modelling in teaching?

Modelling can be used in all stages to help learn a new skill, undertake a task more effectively in terms of the success criteria, develop thinking skills, and thought processes etc. Task modelling occurs when the teacher demonstrates a task students will be expected to do on their own.

It helps them identify the importance of the task and employ self-regulating skills as well. Modeling empowers students to begin their tasks with the confidence to proceed. It then allows teachers to monitor students who may need extra support as they struggle to implement the new concept or skill.