Explanation

Definition

An explanation is a statement or account that makes something clear or understandable by detailing the reasons or causes behind it. In mathematical modeling, explanations help bridge the gap between abstract mathematical concepts and their real-world applications, providing insight into how models operate and what they represent.

5 Must Know Facts For Your Next Test

1. Explanations in mathematical modeling help clarify how specific assumptions lead to particular outcomes in a model.
2. An effective explanation can reveal the underlying mechanisms of a model, which is essential for understanding its behavior and limitations.
3. Explanations can take various forms, including verbal descriptions, visual diagrams, or mathematical derivations.
4. Clear explanations enhance communication among stakeholders, such as researchers, policymakers, and practitioners, making the implications of the model more accessible.
5. A well-structured explanation not only conveys information but also aids in identifying areas for further investigation or improvement within the model.

Review Questions

• How does providing an explanation enhance the understanding of a mathematical model's assumptions and outcomes?
  • Providing an explanation enhances understanding by clearly outlining how specific assumptions influence the model's outcomes. This clarity allows users to see the logical connections between inputs, processes, and results. Without a good explanation, users might misinterpret results or fail to grasp how changing assumptions could impact the model's predictions.
• Discuss the role of explanations in the validation process of mathematical models.
  • Explanations play a crucial role in validating mathematical models by outlining the rationale behind chosen assumptions and methodologies. A comprehensive explanation allows for better comparison between model outputs and real-world data, helping to assess whether the model accurately captures the dynamics of the system being studied. The more robust the explanation, the easier it is to defend the validity of the model against scrutiny from peers or stakeholders.
• Evaluate how effective explanations can influence decision-making processes in real-world applications of mathematical modeling.
  • Effective explanations can significantly influence decision-making by providing stakeholders with clear insights into model outputs and their implications. When decision-makers understand not just what the model predicts but also why it predicts those outcomes, they are better equipped to make informed choices based on the model's results. This deeper understanding fosters trust in the model, encourages stakeholder engagement, and can lead to more successful implementation of solutions derived from modeling efforts.

Related terms

Modeling Assumptions: The foundational beliefs or simplifications made in a mathematical model that influence its design and outcomes.

Validation:

The process of checking if a mathematical model accurately represents the real-world system it aims to simulate.

Output Interpretation: The analysis of results produced by a mathematical model to draw conclusions or inform decisions based on those results.