Problem Solving: Computational Methods

I. Conceptual Understanding:

Understanding of the problem: This initial stage requires clear comprehension of the problem at hand, the goals to be achieved, and the constraints within which the solution needs to be implemented.
Importance of creativity: Creativity and innovation are vital in conceptualising distinctive and robust answers to complicated problems.

II. Approach to Problem Solving:

Problem decomposition: The practise of breaking a complex problem down into smaller, manageable components.
Abstraction: The process of eliminating unnecessary detail to focus on pertinent aspects of the problem, simplifying its complexity.
Pattern recognition: Identifying commonalities or patterns within a problem to simplify the process of solving it.
Generalisation: Applying a solution to a broad set of similar problems.

III. Algorithms:

Algorithm design: Crafting a sequence of instructions to solve a specific problem.
Algorithm efficiency: Understanding the importance of optimising code for execution speed and resources utilisation.

IV. Coding and Programming:

Programming constructs: Understanding the use and function of constructs like sequence, iteration, selection, and recursion.
Programming paradigms: Understanding different styles of programming such as procedural, object-oriented and event-driven, and their applications.
Data types and structures: Understanding and using various data types and data structures appropriate for different tasks.
Validation and verification: Ensuring that both the programme as a whole and individual components work as intended.
Testing and debugging: Carrying out systematic tests to spot and fix errors in code. Utilising debugging tools to help track down and rectify problems.

V. Evaluation and Reflection:

Evaluation of solutions: Critically analysing a programme’s effectiveness in solving the problem. This might include considering, among other factors, speed, accuracy and maintainability.
Reflective practises: Reflecting on the development process and learning from successes and problems encountered in programming.
Adapting solutions: Making necessary changes to initial solutions to reflect assessment and feedback, ensuring continuous improvement and refinement.

Important to remember: These are not discrete stages, but are often iterative and interact with each other, so don’t hesitate to re-visit and revise aspects as you work through problems.