Week 9 : Problem-solving and Creativity Flashcards
Well defined problem
A well-defined problem is a problem that is clear, specific, and has a defined goal or outcome. It is a problem that has a precise description of what needs to be solved, the scope of the problem, and the criteria for a satisfactory solution. A well-defined problem is crucial in problem-solving because it helps to focus efforts and resources, and to avoid confusion and wasted time. It also helps to ensure that everyone involved in solving the problem understands what needs to be done, and what success looks like.
- These problems have a clear answer (Example: Math’s problems)
Ill-defined problems
Ill-defined problems are problems that lack clear goals, constraints, or a specific solution approach. These problems are often vague, open-ended, and complex, and there may be multiple interpretations of the problem. Ill-defined problems may also have incomplete or contradictory information, making it challenging to determine the best solution.
Examples of ill-defined problems include global warming, poverty, and social inequality. These problems are complex and multifaceted and require a nuanced understanding of different perspectives, values, and trade-offs.
Solving ill-defined problems requires creativity, critical thinking, and collaboration. It involves identifying and framing the problem, exploring different solutions, and evaluating the effectiveness of the chosen solution. Unlike well-defined problems, there is no single correct solution to an ill-defined problem, and the best solution may vary depending on the context and stakeholders involved.
Symbols role in problem solving
Symbols can play a critical role in problem-solving by helping us to represent and manipulate information in a meaningful and concise way. Symbols are abstract representations of concepts, ideas, or objects that can be used to convey information and relationships between elements. They can be visual, such as diagrams and graphs, or linguistic, such as mathematical equations and programming code.
Symbols are particularly useful in problem-solving because they can help us to:
Clarify the problem: Symbols can help to represent the problem in a clear and concise way, making it easier to understand the relationships between different elements.
Generate ideas: Symbols can inspire new ideas and approaches to solving the problem, by highlighting connections and patterns that may not be immediately apparent.
Test solutions: Symbols can be used to simulate and test different solutions to the problem, allowing us to evaluate their effectiveness and identify potential issues before implementing them in the real world.
Communicate solutions: Symbols can be used to communicate solutions to others, making it easier to share ideas and collaborate on solving the problem.
Examples of symbols that are commonly used in problem-solving include flowcharts, diagrams, matrices, mathematical equations, and programming code. By using symbols effectively, we can improve our ability to solve problems, think critically, and communicate our ideas to others.
Matrices role in problem solving
Matrices play an important role in problem-solving, particularly in fields such as mathematics, physics, engineering, and computer science. A matrix is a rectangular array of numbers, symbols, or expressions that can be used to represent a wide range of mathematical and physical concepts.
Matrices are useful in problem-solving for several reasons:
Matrix operations: Matrices can be used to perform a variety of mathematical operations, including addition, subtraction, multiplication, and inversion. These operations can be used to solve a wide range of problems, including systems of linear equations, optimization problems, and data analysis.
Transformations: Matrices can be used to represent and perform a wide range of transformations, including rotations, scaling, and shearing. These transformations are essential in many applications, including computer graphics, robotics, and physics.
Data analysis: Matrices can be used to represent and manipulate large data sets, making it easier to analyze and visualize complex relationships between different variables.
Probability and statistics: Matrices can be used to represent and calculate probabilities, making them useful in fields such as finance, economics, and risk analysis.
Overall, matrices are a powerful tool for problem-solving, and their versatility and flexibility make them suitable for a wide range of applications. By understanding how to use matrices effectively, we can improve our ability to solve complex problems, and make better decisions in many different contexts.
Diagrams role in problem solving
Diagrams play an essential role in problem-solving as they provide a visual representation of the problem, making it easier to understand, analyze and solve. Diagrams can help to:
Clarify the problem: Diagrams can help to visualize complex problems, making it easier to identify patterns, relationships, and dependencies between different elements.
Generate ideas: Diagrams can be used to brainstorm and generate ideas, by representing information and concepts in a visual and structured way.
Analyze data: Diagrams can be used to organize and analyze data, making it easier to identify trends, patterns, and outliers.
Communicate solutions: Diagrams can be used to communicate solutions to others, making it easier to share ideas and collaborate on solving the problem.
There are many different types of diagrams that can be used in problem-solving, depending on the nature of the problem and the information that needs to be represented. Some common types of diagrams include flowcharts, Gantt charts, Venn diagrams, cause-and-effect diagrams, and mind maps.
Using diagrams in problem-solving can help to improve our ability to think creatively, identify solutions, and communicate our ideas to others. By learning how to use diagrams effectively, we can become more proficient problem-solvers and make better decisions in a wide range of contexts.
Visual imagery role in problem solving
Individuals vary in their preference to represent problems visually: for some, visual imagery is key to coming up with a solution
e.g., Friedrich Kekule’s discovery of the structure of the benzene ring: he envisioned the benzene ring as a snake biting its own tail.
“The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought”, (Einstein, 1949, cited in Miller, 1992, p.409). Einstein’s theory of relativity was based on visual imagery of moving boxcars and riding on light beams
Einstein was very much a visual learner
Context in problem-solving
Context in problem-solving refers to the situational or environmental factors that can impact the nature and scope of a problem.
- People can solve maths problems in the real world (Example 20% of a $60 pair of shoes) Some people can solve this in that context but when its on paper as a maths question they may not be able to.
- Given this puting problems into different contexts can determine if the person can solve it or not.
What are some strategies of problem solving
Analogy approach
Means-Ends heuristic
Hill-Climbing heuristic
Analogy approach
The analogy approach is a problem-solving technique that involves using analogies or similarities between two or more situations to find a solution to a problem. In this approach, the problem-solver identifies a problem that is similar in some way to the current problem and uses the solution to that problem as a basis for solving the current problem.
The analogy approach can be a useful problem-solving technique because it allows problem-solvers to draw on their past experiences and knowledge to find solutions to new problems. By identifying the analogous relationships between two or more situations, problem-solvers can apply solutions that have been successful in the past to new and unfamiliar situations.
- Applying a similar problem to the problem at hand
- Applying feedback from assignments to future assignments is an analogy approach.
- People use analogy approach in work meetings a lot (3 to 15 times with a 1 hour meeting)
- Medicine use this – example – this medicine is similar to …
Means-Ends heuristic
The Means-Ends heuristic is a problem-solving strategy that involves breaking down a larger problem into smaller, more manageable sub-problems, and then identifying actions or “means” that can be taken to move closer to the desired end goal. This strategy involves several steps:
Hill-Climbing heuristic
Hill-Climbing heuristic is a problem-solving strategy that involves choosing the option that appears to bring the problem solver closer to the goal state, even if that option is not guaranteed to be the best or optimal solution. This strategy is called “hill-climbing” because it is similar to climbing a hill, where the goal is to reach the highest point on the hill, and each step is taken to bring the climber closer to the top, even if it is not the best step in every possible way.
In Hill-Climbing heuristic, the problem solver evaluates possible actions or moves and chooses the action that brings them closer to the goal state. This approach may not always lead to the optimal solution, as the problem solver may get stuck in a suboptimal solution, unable to move to a better solution. Hill-climbing can also be biased towards local optima, as it tends to favour moves that improve the current state without considering the possibility of larger improvements in a different direction.
Despite its limitations, Hill-Climbing heuristic can be a useful strategy for solving simple problems with limited possibilities. In more complex problems, Hill-Climbing heuristic is often combined with other strategies, such as randomization or backtracking, to explore a wider range of possibilities and avoid getting stuck in suboptimal solutions.
