7.2. Theories of Thinking and Problem Solving

The information processing model suggests that thinking is a process of receiving input, organizing it, and processing it to reach a conclusion or solution.

The process is divided into several stages:

1. Encoding: Gathering and organizing information.
2. Storage: Holding the information for future use.
3. Retrieval: Accessing and applying the stored information when needed.

The Information Processing Model describes how we think as a series of steps much like a computer processes data. It starts with encoding, where we gather and organize new information. Next, we store this information, keeping it safe until we need it again. Finally, when we need to use this information, we retrieve it, pulling it from our memory to help us think or solve problems. This model emphasizes that thinking is active and systematic, involving multiple stages that help refine our understanding and conclusions.

Imagine you are preparing for a trivia quiz. First, you gather information from books and websites (encoding). Then you memorize the facts you think will be important for the quiz (storage). Lastly, when the quiz starts, you remember and use that stored information to answer questions (retrieval). This whole process mirrors what the Information Processing Model describes.

An algorithm is a step-by-step procedure that guarantees a correct solution to a problem. It is thorough and exhaustive but can be time-consuming.

Example: Solving a math problem using a formula or method.

An algorithm is a clearly defined set of steps to solve a problem. It's like following a recipe in cooking: if you follow it correctly, you'll get the intended dish. For example, in a math class, you might use an algorithm to solve equations by applying specific rules and formulas. However, because algorithms can involve many steps, they may take longer to use than other approaches.

Think of building furniture with a manual. If you follow each step in order, you will successfully create the furniture piece. This method, like an algorithm, ensures you won't miss any important steps, although it may require more time than just trying to figure it out on your own.

A heuristic is a mental shortcut or rule of thumb used to make decisions or solve problems quickly, but it does not guarantee a correct solution.

Example: Using "trial and error" or "working backwards" to solve a problem.

Heuristics are strategies that allow us to make quick judgments or decisions based on limited information. Unlike algorithms, which guarantee a correct solution, heuristics rely on our experience and intuition to find a solution faster, but they can sometimes lead us astray. For example, if you're trying to find your way in a new city, you might try getting to know it by recognizing landmarks instead of studying a map exhaustively.

When looking for your lost keys, you might first check the last place you remember having them instead of searching every possible location. This is an example of using a heuristic, where you use past experiences to guide your search.

1. Well-Defined Problems:

• Problems with clear goals, defined steps, and known solutions (e.g., mathematical problems or puzzles).
• Example: Solving an equation in mathematics.

2. Ill-Defined Problems:

• Problems that do not have clear solutions or defined steps, and often involve ambiguity or uncertainty (e.g., personal decisions or ethical dilemmas).
• Example: Deciding on a career path or resolving a moral conflict.

Problem-solving can be classified into two main types: well-defined and ill-defined problems. Well-defined problems have clear parameters; you know what the goal is and the steps needed to reach that goal, like a math problem where you have a specific answer to find. On the other hand, ill-defined problems lack clear solutions or steps, requiring deeper thinking and more subjective evaluation, like choosing a career path where many factors are involved and uncertain.

Imagine preparing for a multiple-choice exam; that's a well-defined problem, as you can study specific materials and practice questions. Conversely, deciding which college to attend represents an ill-defined problem; many factors to consider might include location, cost, academic programs, and your personal interests, with no straightforward answer.

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