Mathematical modeling is a cyclical and iterative process that utilizes mathematics to analyze, interpret, and solve authentic, real-world problems or situations, thereby improving decision-making in everyday life. A core feature of mathematical modelling is the constant translation back and forth between the real world and the mathematical world. This process is complex, involving several key steps, often referred to as the mathematical modeling cycle or phases (Blum and Leiβ, 2007).

1. Understanding the real problem/situation and constructing a conceptual model of the situation (situation model)

2. Simplifying/Structuring: Consciously simplifying the situation model by identifying, introducing, and specifying variables and conditions to create a simplified real model

3. Mathematization (or Formulation): Translating the simplified real situation into a formal mathematical model (such as a term, equation, figure, or function)

4. Working Mathematically (or Employment/Investigation): Operating within the mathematical model to execute clearly described procedures, concepts, facts, and algorithms to solve the mathematically phrased problems and obtain a mathematical solution

5. Interpretation: Translating the mathematical result(s) back into the real-world context and determining whether the results are reasonable and logical in the given situation

6. Validation: Verifying the actual results against the situation model to ensure appropriateness

7. Communication: Presenting and communicating the solution, model, and reasoning process

If the solution is unsatisfactory, the modelling cycle is often repeated or refined. Mathematical modelling requires and develops critical thinking, social skills, and background knowledge as learners collaboratively create strategies for their solutions.