Problem Solving

Problem Solving

1. Problem solving skills are needed to reach goals when the solution isn't immediately obvious

2. Well-defined problems have a clear correct answer: if you apply the appropriate procedures, you will arrive at the correct solution (e.g., Maths)

3. Ill-defined problems are more common in everyday life: they don't have one clear "correct" answer, and the way to arrive at a solution is unclear (e.g., ending a war, health or relationship problem)

4. Problems have 3 crucial elements: A starting state, A goal state, A set of processes (operators) that can transform the starting state into the goal state

5. Understanding the Problem

   • Understanding refers to the construction of a mental representation of the problem based on the info provided and your past experience
   • Thus to understand a problem you need to construct an accurate mental representation
   • It's important to decide which info is relevant/irrelevant to problem-solving and pay attention to that info in order to successfully understand the problem, if you don't pay attention you're unlikely to solve the problem

6. Representing the Problem

   • Symbols
     • Using symbols (e.g., algebra) can be an effective method for representing abstract problems
     • The problem with using symbols is that we often make errors when translating problems into symbols
     • Schoenfeld found that when calculus students tried to rephrase problems to make them easier to understand, 30% of the rephrased problems were incorrect
   • Effective forms of representation allow you to organise information efficiently, reducing the burden on working memory, and increasing the likelihood of successful problem solving
   • Matrices
     • Matrices are a very effective why of solving complex problems involving categorical info
     • Matrix: Chart showing all possible combinations of items
     • Scharts and colleagues' research indicates that participants who represent problems using a matrix are more likely to solve the problem than those who use other forms of problem representation
   • Diagrams
     • Hierarchical tree diagrams, Venn diagrams and graphs are all useful forms representing problems
     • Novick and Morse found that people given a step-by-step diagram in addition to verbal instructions were better at making origami objects than people relying solely on verbal instructions
     • Research shows that diagrams attract eye gaze to important information, aiding problem solving
   • Visual Images
     • Individuals vary in their preference to represent problems visually: for some, visual imagery is key to coming up with a solution
     • People who use visual thinking report that it facilitates truely creative thinking
     • Friedrich Kekule's discovery of the structure of the benzene ring: he envisioned the benzene ring as a snake biting its own tail

7. Context

   • According to the situated-cognition approach, knowing is inseparable from doing: our ability to solve a problem is tied to the specific context in which we learned to solve that problem
     • e.g., people can determine whether the 500g or the 1kg box of breakfast cereal is better value, but would not be able to solve the same problem outside the context of the supermarket
   • IQ tests, and abstract tests of intelligence, fail to assess this aspect of intelligence
   • This suggests that ecological validity and practical examples are important when teaching problem-solving in a school setting

8. Strategies

   • Analogy Approach
     • One of the most common strategies used for problem solving and involves employing a solution used for a similar problem to help solve the new problem
     • Relies on the transfer of experience from one problem to another and can be used for a broad range of problems, from maths to design
     • The trick in implementing the analogy approach is understanding the real problem
       • People tend to focus on surface features rather than the structural features
       • Research shows that participants often fail to notice the analogy between a problem they've already solved and a new problem with similar structural features
     • Dunbar and Dunbar & Blanchette recorded molecular biologists and immunologists during lab meetings, they found that the researchers used analogies 3-15 times per 1 hour meeting
   • Means-Ends Heuristic
     • Problem-solving strategy in which you identify the "ends" you need and figure out the "means" needed to reach those ends
     • Has two subcomponents: 1. Divide the problem into subproblems, 2. Reduce the distance between the initial state ad goal state for each of the subproblems
     • Sometimes we aren't always able to reduce the difference between the initial state and the goal state: sometimes we need to increase the distance (i.e., go backwards) in order to move forwards
       • People are reluctant to increase the distance between the initial and goal states, leading to poorer problem-solving
     • Used to solve problems like the Tower of Hanoi
   • Hill-Climbing Heuristic
     • Strategy requiring that every choice point in the path between initial state and goal state, you choose the option that moves you in the direction of your goal
     • Helpful strategy when you're trying to solve a problem based on limited information and you can only see your next step
     • However, because the strategy is 'short-sighted', it can lead you astray since it doesn't allow for backwards movements thus doesn't guarantee you'll end at the top
     • Better for achieving short term rather than long term goals