The Five Ordered Steps of Problem-Solving
Step 2: Generating Options

Step 2: Generating options-- Use an existing ("old" solution) or try a new solution

Use one of two types of existing solutions:

1. Use an algorithm: a problem-solving strategy that--if all the steps are followed correctly--is guaranteed to eventually lead to a solution..

2 Problems with algorithms:
1. They may involve many steps (and doing many steps both (1) takes time and (2) uses up short-term memory's limited space). Because algorithms are often  time-consuming and involve many steps, they are called "inefficient."  Note, however, that although algorithms are inefficient, they are not ineffective: Indeed, they are foolproof formulas.
2. Algorithms only fit problems where there are right answers. Thus, there are algorithms for solving some math problems and playing certain simple games like tic-tac-toe but not for problems with human relationships.
Conclusions about algorithms: Even though algorithms are often called "foolproof formulas", you can go wrong using an algorithm if
1. The algorithm is not the right one for that problem,
2. You skip one of the steps (easy to do when there are many steps),
3. You mess up one of the steps
2. Use a heuristics: a general rule that guides problem-solving, but does not guarantee a perfect solution. You can think of heuristics as mental shortcuts, hunches, or as educated guesses. (Click here for a weather-related heuristic.)
   Examples of useful heuristics:

• Change how  you view the problem
  • Try to solve a simpler version of the problem.
  • Break the big problem into several smaller problems.
  • Make a picture or diagram of the problem.
  • Think of an analogy or metaphor for the problem
  • Imagine the problem solving itself.
  • Think of the problem as an opportunity.
• Use or adapt a solution that has worked in the past.
  • Google it -- or ask an AI program like ChatGPT
  • Ask a friend what to do.
  • Ask "what would (a successful person or someone you admire) do?" For example, you might use Kobe Bryant's approach to problem-solving.
  • Ask "How have I solved similar problems?"
  • Trial and error
• Ask "How could I make the problem worse?" -- then do the opposite.
• Work backwards--Think of the final result you want (i.e., imagine the problem perfectly solved) and then figure out what steps it would take to get that result.
• Math problem heuristics for solving algebra problems
  • Draw a diagram
  • Try out numbers
  • Get rid of fractions
  • Get "x" isolated on one side of the equals sign

     

6 Barriers to generating new solutions

1. Fixation/Set: a rigidity in problem-solving due to wanting to continue to do things the old way.
   Examples:

   • Continuing to try--unsuccessfully--to open a car door with a remote when you could use the key attached to the remote.
   • Wanting to add 20 pounds to a barbell, so waiting until  four 5-pound weights become available when two 10-pound weights are available.
   • Dealing with a problem (e.g., the drug problem) by "doing more of the same"-- even though the same isn't working.
   • If you follow baseball, here is a video of one the biggest mental errors (link to video on twitter, link to video on  youTube) made in the history of major league baseball --and it is due to set. If you want to understand why it was such a bad error (there were several reasons--and see that people don't always forgive errors due to set--click here).
   • Set is sometimes a problem for game show contestants--this may be one example.
   • Functional fixedness: a type of set where we consider only the usual function of an object and overlook other possible uses.
     Ex: Thinking that the only possible use for a brick is to build a wall. (Here, you can see Duncker's Candle Problem--a way of showing the power of functional fixedness).

2. We don't think of as many options as we should. This is partly because short term memory is so limited that we can't think of many options at once (but sometimes, this failure to examine options is due to to laziness and arrogance). One way to get around the problem of not coming up with enough options is to force yourself to write down at least 3 options. For interpersonal problems (e.g., dealing with a messy roommate), you usually have at least three options: (1) Adjust to the situation: Tolerate the mess, (2) Change the situation: Make the roommate clean up, and (3)Avoid the situation: Move out.
3. Putting limits on yourself, such as saying you can't do it (due to learned helplessness, depression, or low self-efficacy) or that you can't change (due to having a fixed mindset rather than a growth mindset).
4. Putting limits on the solution by seeing the problem in win/lose terms when there might be a win/win solution.
5. "All or none" thinking -- Looking only at extreme options ("I will quit school or quit the band") when less extreme options are available (e.g., going to school part time or devoting more time to the band during the summer).
6. Prematurely dismissing options. We reject an idea rather than developing it. Realize that Step 3--the evaluating ideas step--should come after, not during, Step 2--the idea generation step.

Back to Step 1

To Problem-Solving Menu

Back to Lecture Notes Page