Problem Solving and Creativity (word)

Problem solving

• mentally working to overcome obstacles to reach a goal.

• mentally working to overcome obstacles that stand in the way of reaching a goal.

Initial state

• start

• the situation at the outset in which the problem is not yet solved

Goal state

• we strive to reach the _________

• condition in which the problem has been solved.

Obstacle

• block the way

• factors that prevent us from solving our problem

Problem Identification

Do we actually have a problem?
👉 Example: You notice your grades are low.

Problem definition and representation

What exactly is the problem?
👉 Example: You realize you don’t understand the lessons.

Strategy formulation/construction

• How can we solve it?

  • Analysis

  • Synthesis

  • Divergent thinking

  • Convergent thinking

Analysis

• breaking down the whole of a complex problem into manageable elements

• Break problem into parts

Synthesis

• putting together various elements to arrange them into something useful.

• Combine ideas.

Divergent thinking

• you try to generate a diverse assortment of possible alternative solutions to a problem

Convergent thinking

• narrow down the multiple possibilities to converge on a single best answer.

• choose the best one
  👉 Example: Study more, ask help, watch videos → then choose the best method.

Organization of information

• How do the various pieces of information in the problem fit together?

• How do the pieces fit together?

• 👉 Example: Arrange your notes and topics to study.

Resource allocation

• How much time, effort, and money should I put into this problem?

Studies show that expert problem solvers (and better students) tend to devote more of their mental resources to global (big-picture) planning than do novice problem solvers.

`Novices (and poorer students) tend to allocate more time to local (detail-oriented) planning than do experts

Monitoring

• Am I on track as I proceed to solve the problem?

• Am I on track?

  👉 Example: Check if your quiz scores are improving.

Evaluation

• Did I solve the problem correctly?
  👉 Example: Your grades improve → problem solved.

Well-structured problems

• Problems with clear paths to the solution (often using a formula).
  👉 Example: Math problem in exams.

• Even if the path is clear, it can still be difficult to follow.

Problem space

• all possible actions/strategies to solve it

• the universe of all possible actions that can be applied to solving a problem, given any constraints that apply to the solution of the problem.

Algorithms

• A set of procedures repeated until the solution is reached

• Guarantees a correct answer (if applicable), but can be slow/tedious

👉 Example: Solving step-by-step math equation

• are sets of procedures (in a problem space) that may be repeated over and over again and that, in theory, guarantee the solution to a problem.

Heuristics

• Mental shortcuts

• informal, intuitive, speculative strategies that sometimes lead to an effective solution and sometimes do not.

Humans use heuristics because:

• We cannot process too many possibilities at once (limits of memory)

Computers

________ are likely to use algorithmic problem-solving strategies.

Humans

__________ are more likely to use rather informal heuristics

4 Heuristics

• Means-ends analysis

• Working forward

• Working backward

• Generate and test

Means-ends Analysis

• Solving the problem by decreasing the distance between the current position in the problem space and the end goal in that space

• Solve by decreasing the distance between current state and goal
  👉 Example: If your goal is to pass, you focus on improving weak subjects first

Working forward

• Start at the beginning and attempt to solve the problem from the start to finish

• Start at the beginning → go step by step to the end
  👉 Example: Solve a math problem from given data until final answer

Working backward

• Start at the end and attempt to work back-wards from there

• Start at the goal → work back to the beginning
  👉 Example: Think of the final answer, then figure out what steps lead to it

Generate and test

• generate alternative courses of action not necessarily in a systematic way, and note whether each course of action will work

• Generate many possible solutions, then test each
  👉 Example: Try different answers until one works

Isomorphic Problems

• Sometimes, two problems are _______—that is, their formal structure is the same, and only their content differs

• 👉 Example:

  • Scrabble and Boggle → both involve forming words from scrambled letters

Justification skills

_________ are important because ill-structured problems can be represented in different ways and often have alternative solutions.

Ill-Structured Problems

• there are no clear, readily available paths to a solution.

• By definition,________ do not have well-defined problem spaces.

• difficulty is in constructing a plan for sequentially following a series of steps that inch ever closer to their solution.

• 👉 Example:

  • “What career should I choose?” (many possible answers)

  • Need:

    • Domain knowledge

    • Justification skills

    • Different ways to represent the problem

domain knowledge and justification skills

In one study, both___________ proved to be important for solving both ill- and well-structured problems.

regulation of cognition

Additional cognitive and affective factors, including attitudes toward science and _____________, are also important for solving ill-structured problems.

novel/different way

• The ill-structured problems are insight problems because you need to see the problem in a _________

• In particular, you need to see it differently from how you would probably see the problem at first, and differently from how you would probably solve problems in general.

• That is, you must restructure your representation of the problem to solve it.

Insight

• a distinctive and sometimes seemingly sudden understanding of a problem or of a strategy that aids in solving the problem

• reconceptualizing a problem or a strategy in a totally new way.

• they are often the result of much prior thought and hard work

• involved in solving well-structured problems, but it more often is associated with the rocky and twisting path to solution that characterizes ill-structured problems.

• 👉 Example:

  • You’ve been stuck, then suddenly: “Ahh gets ko na!”

  ✔ Even if it feels sudden, it usually comes from:

  • Prior thinking and effort

cannot

Many ill-structured problems______ be solved without the benefit of insight.

Gestaltist and neo-Gestaltist

• includes more than the sum of its parts and may be evidenced b the suddenness of realizing a solution.

• held that insight problems require problem solvers to perceive the problem as a whole

Max Wertheimer

• Gestalt psychologist wrote about productive thinking

• He distinguished productive thinking from reproductive thinking

Productive thinking

• involves insights that go beyond the bounds of existing associations

• new insight (new way of thinking)

Reproductive thinking

• using what you already know

Mental set

• can hinder problem solving

• also termed “entrenchment ”

• a frame of mind involving an existing model for representing a problem, a problem context, or a procedure for problem solving.

• strategy that has worked in the past but that does not work for a particular problem that needs to be solved in the present

• they fixate on a strategy that normally works well in solving many problems but that does not work well in solving this particular problem.

• can influence the solution of routine problems.

• using a strategy that worked before but does not work now

• You fixate on that strategy even if it’s wrong

• 👉 Example:

  • You always solve math using one formula, but the new problem needs a different method—still, you keep using the old one.

Functional Fixedness

• type of mental set

• It involves the inability to see that something that is known to have a particular use also may be used to serve other purposes.

• Involves fixation on a particular use (function) for an object.

• prevents us from solving new problems by using old tools in novel ways.

• You cannot see other uses of an object

  👉 Example:

  You think a coin is only for paying, not for unscrewing something.

Stereotypes

• Another type of mental set is considered an aspect of social cognition.

• beliefs that members of a social group tend more or less uniformly to have particular types of characteristics

• Belief that a group has the same characteristics

👉 Example:
Thinking all students in one course are “good” or “bad” at something.

Transfer

• any carryover of knowledge or skills from one problem situation to another

• Using knowledge from one problem to another

• it can be positive or negative

Negative Transfer

• when solving an earlier problem makes it harder to solve a later one.

• Sometimes an early problem gets an individual on a wrong track.

• Makes solving harder

👉 Example:
You use the wrong old method → leads you to the wrong answer

Positive Transfer

• occurs when the solution of an earlier problem makes it easier to solve a new problem

• Makes solving easier

👉 Example:
You learned one math formula → helps you solve a similar problem

rarely

• Positive transfer across isomorphic problems ____ occurs spontaneously, particularly if the problems appear to be different in content or in content

• Positive transfer is______ if problems look different

• Main challenge = avoiding negative transfer

Incubation

• follows a period of intensive work on a problem.

• It involves laying a problem to rest for a while and then returning to it.

• this way, subconscious work can continue on the problem while the problem is consciously ignored.

• Take a break from the problem

• Subconscious thinking continues

• putting the problem aside for a while without consciously thinking about it—offers one way in which to minimize negative transfer.

• It involves taking a pause from the stages of problem solving.

👉 Example:
You stop studying a hard question, then later the answer suddenly comes to you

Knowledge

• can interact with understanding in problem solving as well.

amount and the organization of knowledge

Experts differ from novices in both the _______________________ that they bring to bear on problem solving in the domain of their expertise.

Experts

• problem solving may be governed by automatic processes.

• Such automaticity usually facilitates the expert’s ability to solve problems in the given area of expertise

• more knowledge + better organization

  Many processes become automatic

  👉 Example:

  An expert solves quickly without thinking too much

novel

• When problems involve novel elements requiring ______strategies, however, the automaticity of some procedures actually may impede problem solving, at least temporarily.

• ✔ But:

  • Automaticity can help (faster solving)

  • But sometimes hurt when problem is new (need new strategy)