MOOC: Methods for Solving Problems (Part the Third)

I’m sure at some point I’ll stop counting them that way. But for now, it stays. #DrunkWithPower

So, we’re still in the thick of the first reading. Today’s overarching topic is ‘Problem Recognition, Definition, and Representation.’

Notes:

Problem recognition, definition, and representation are metalevel executive processes (a.k.a. ‘metacomponents’ in Sternberg’s Triarchic Theory of Human Intelligence)

Robert J. Sternberg (1985)

• ‘Beyond IQ: A Triarchic Theory of Human Intelligence’
• The theory proposes that metacomponents guide problem solving by planning, mentoring, and evaluating the problem-solving process
• This includes such processes as:
  • recognizing the existence of a problem
  • defining the nature of the problem
  • allocating mental and physical resources to solving the problem
  • deciding how to represent information about the problem
  • generating the set of steps needed to solve the problem
  • combining these steps into a workable strategy for problem solution
  • monitoring the problem-solving process while it is ongoing
  • evaluating the solution to the problem after problem solving is completed
• Problem recognition a.k.a. problem finding is one of the earliest stages of problem solving (or the earliest stage)

Getzels (1982)

• Classified problems based on how they were ‘found’
  • three kinds of problems:
    • those that are presented
    • those that are discovered
    • those that are created

• Presented problems
  • one directly given to the solver
  • no need to recognize or find the problem
  • (presumably) stated clearly and just awaits solution
• Discovered problems
  • must be recognized
  • already exists, but not clearly stated or given to the solver
  • solver must gather data (puzzle pieces) to be able to discover a gap(s) in current understanding
  • this helps “discover” the problem
• Created problems
  • those the solver invents
  • does not already exist in the field
  • arguable that this will always produce creative solutions because of problem deviation

Getzels & Csikszentmihalyi (1976)

• artists who spent more time in problem-finding stage were more creative than those who spent less time in the problem-finding stage

Problem Definition

• the aspect of problem solving where scope and goals are clearly stated
• might be easy if the problem statement was prepared for the solver
• some presented problems aren’t clearly stated, requiring the solver to clarify the definition
• discovered problems usually require definition
• defining created problems is challenging since the solver delved beyond/outside the field to create the need for a solution

Problem Representation

• the manner in which information known about a problem is mentally organized
• mental representation is composed of four parts:
  • description of the initial state of the problem
  • description of the goal state
  • set of allowable operators
  • set of constraints
• problem may be represented in various ways (e.g. verbally, visibly, etc)
• even a presented problem may require generation of a new/different representation to be solved

Example: Finding your way to a new location

• It may be easiest for you to follow a map, or
• Maybe you need the directions written out in words, or
• Maybe you need it done in some other fashion (The Google Maps lady tells me where to go while I also look at the map myself, but honestly, the more likely scenario is that my husband is navigating and just tells me where to turn.)

These aspects are not discrete or sequential stages in the problem-solving process

These processes are often interacting with one another, difficult to tease apart

When a problem is represented in a new way, it may also need to be redefined to some extent, or, on the other hand, redefining it may lead to a new representation

Thoughts:

I typed these notes up a little while back. Reading through them now, I realize they’re pretty dry. However, there are some useful nuggets in there. The concept of mentally representing your problem in a very clear and process-focused manner makes a lot of sense. What do we know? What do we not know? What can we do? What can we not do? There’s this grid idea that some people use, presumably based around this quote (fair warning: that’s a political opinion piece to some extent, but it covered the quote fairly well and didn’t throw up a firewall to make me sign in like the NY Times site did… ain’t nobody got time for that) from then-U.S. Secretary of Defense Donald Rumsfeld: known knowns, known unknowns, unknown… I was going to type out all four of the grids, but I honestly got lost in typing the word ‘unknown’ for the umpteenth time. You know that sensation where you use a word SO MUCH that it no longer carries any meaning nor exists as a recognizable thing? I did that with another post where I used the word ‘gallon’ like 40 million times.

So, what do you think? Do you think there’s any way to reliably account for ‘unknown unknowns’? Penn State has adopted the concept of ‘structured analytic techniques,’ which they refer to as a “box of tools” that people can use to account for failures and/or biases in critical thinking. I think there’s merit in having a finite process (or processes) to walk through when you’re wrestling with a problem. While a part of me balks at what could be seen as a surrender of creative thought, another part of me recognizes the merit in the idea, recognizing in it reflections of what we’ve already seen in this MOOC. We aren’t tethering ourselves to a specific idea or mindset, but trying to account for those mindsets and biases we might not even realize we have.

-hxrg