Problem solving is a type of complex cognitive processes.
Why Problem Solving is Considered “Complex”
- Beyond Memory: It moves past basic mental activities like attention and recall to involve higher-level stages of thinking such as understanding, analyzing, and evaluating.
- Application of Knowledge: It requires using or transforming previously acquired skills to navigate from an initial state to a desired outcome.
- Higher-Order Thinking: It is a core component of Higher Order Thinking Skills (HOTS/KBAT).
- Strategic Requirement: It involves selecting and implementing specific strategies—such as algorithms or heuristics which requires conscious effort and mental flexibility.
1. Types of Problems
The document distinguishes between two main categories of problems:
- Well-defined problems: These are highly structured and provide all the information necessary to reach a solution (e.g., a math equation like x + 3 = 9).
- Ill-defined problems: These are more complex, lack a clear structure, and often have multiple acceptable solutions or strategies (e.g., community development projects).
2. The 5-Step Problem-Solving Model
Problem solving is described as a cyclical process involving five key steps:
- Identify the problem: Recognizing that a goal needs to be reached.
- Represent the problem: Defining or visualizing the nature of the challenge.
- Select a strategy: Choosing the best approach to find a solution.
- Implement the strategy: Carrying out the chosen plan.
- Evaluate the results: Reflecting on whether the solution was effective.
3. Problem-Solving Strategies
There are several ways to approach a problem, ranging from rigid rules to flexible “shortcuts”:
a) Algorithm
An algorithm consists of a set of clearly defined steps that lead to a guaranteed solution for a specific problem.
- Example: Following a specific recipe to bake a cake or using a mathematical formula.
b) Heuristics (Informal “Rules of Thumb”)
Heuristics are mental shortcuts that may solve a problem but do not guarantee a solution. They are useful for complex tasks where an algorithm is not available:
- Means-ends analysis: Breaking down a large, complex problem into smaller, manageable sub-problems.
- Working-back strategy: Starting at the desired end goal and moving backward to the initial state to determine the necessary steps.
- Analogical reasoning: Using successful solutions from past, similar problems to address a new situation (though this can sometimes lead to wrong solutions).
- Trial and error: Trying various alternative solutions in a non-systematic way until one works.
c) Incubation
This involves temporarily halting or postponing attempts to solve a problem after a period of deep reflection. It allows the learner to “take a breather” and avoid despair, often leading to fresh insights later. Incubation is not procrastination.
4. Factors Affecting Problem Solving Success
- Hindrances: Problem-solving can be blocked by cognitive rigidity, functional fixedness (only seeing an object for its usual use), or affective factors like anxiety.
- Expertise: Unlike novices, expert problem solvers spend more time planning and identifying the problem, have a larger repertoire of strategies, and possess superior metacognitive skills.
5. Relationship with Other Processes
Problem solving does not exist in a vacuum. It is deeply interconnected with other complex cognitive processes:
- Metacognition: Solving problems effectively requires “knowing about knowing,” such as monitoring whether a chosen strategy is working or needs to be changed.
- Reasoning: It is the process of deriving conclusions. Its primary goal is to determine what is true or what follows logically from certain information. Reasoning is a specific mental process that falls under the broader category of thinking. While it is distinct from problem solving in its goal, it serves as a critical cognitive tool used to navigate and resolve problems.
- Transfer of Learning: Successful problem solving often depends on the student’s ability to transfer past knowledge to a new, different context.
