The Many Templates of Problems
Growing Meta #16
Hi friends,
Do you think of the shape of problems that you solve daily? Choosing your breakfast, designing an experiment, knowing why your neck hurts, proving a theorem, planning a route, figuring out why your phone is not charging…. etc. These are all problems and they, kind of, fall into certain problem templates.
Let’s see what a meta-theory on problems looks like. A professor of education and learning tech, David H Jonassen, wrote a paper in 2000 that later evolved into a book. Without further ado, here’s the highly-cited paper’s summary:
Toward a Design Theory of Problem Solving (2000)
David H. Jonassen
Jonassen saw that there were no typology for problems. Problem solving was not studied from a meta-perspective. So he set out to define the different types of problems that exist. He admits that it’s not perfect.
“The curse of any introductory paper is the lack of depth in the treatment of these issues…… My purpose here is to introduce these issues in order to stimulate discussion, research and development……”
First things first: What is a Problem?
A problem has two properties:
There is an unknown thing
There is a reason to solve it
He goes on discussing instructional design, education and other stuff — I think this definition suffices.
There are two parts to this paper: (1) Aspects to Problem Solving, and (2) Types of Problems.
PART 1: PROBLEM SOLVING
1. What makes a good Problem Solver?
Jonassen believes it depends on three things:
nature of the problem (Problem Variations)
+ the way the problem is represented (Representation)
+ personal skills (Individual Differences)
1.1. So what defines the ‘nature of the problem’?
Jonassen calls them PROBLEM VARIATIONS and he has identified 3 aspects:
1.1.1. Structuredness
Here’s the spectrum: ill-structured <— —> well-structured
Here is a well-structured problem: “given x, y, z, what is w, solve using equation #1.” Here is another “what is the fastest route between x and y, given that I want to pass by z?”.
Most real-world problems are ill-structured: we don’t have all of the elements, there could be different solutions, and often requires judgement (i.e. no correct answer, only optimal).
Researchers have always assumed that students can transfer what they learn from well-structured problems to ill-structured problems, but the research landscape is proving otherwise. Both skills are independent. Ill-structured problems employ different intellectual skills from well-structured ones.
1.1.2. Complexity
Defined by:
number of issues
functions
variables
degree of connectivity between variables
type of functional relationships
stability of the properties over time
More complexity requires more cognitive operation, which could overloads our working memories.
Complexity and structuredness overlap a bit. Ill-structured problems are almost always more complex. But sometimes it’s the opposite: some video games are extremely complex well-structured problems, while “selecting what to wear from our closets for different occasions is a simple ill-structured problem.”
1.1.3. Domain Specificity (Abstract-Situated)
Some problems are within a specific domain (e.g. a law case). Others are quite abstract, they can be applied to several domains (e.g. inferential statistics).
“Graduate students in the probabilistic sciences of psychology and medicine perform better on statistical, methodological, and conditional reasoning problems than do students in law and chemistry, who do not learn such forms of reasoning.”
Now we know 3 aspects within any problem.
1.2. So, what ways can we present a problem?
Jonassen talks about PROBLEM REPRESENTATIONS. He talks about the form of the problem: for example, in math we represent a problem symbolically, in consultancy we narrate the problem with actors and a climax, in programming it is manifested in a thread detailing the error.
He talks about how to represent a problem to learners (in a classroom setting) and talks about how important it is to have high-fidelity in representation.
1.3. And, what makes a good problem solver?
The author identified 7 INDIVIDUAL DIFFERENCES:
Familiarity
How well do you know the problem type? It’s the strongest predictor according to him. It is the product of experience.
I remember doing a lot of IQ tests in my teen days that they became so easy and predictable. The ‘templates’ become clear after many trials. This is the same for all other problems.
Domain and Structural Knowledge
How well do you know the facts around it?
You can be a good analyst, but you would always need to know information surrounding that problem.
Cognitive Controls
How well do you process & reason with information?
Determined with skills such as field independence, cognitive complexity, cognitive flexibility, and category width.
Metacognition
How well are you in being aware with how you learn, in judging the difficulty of a task, in monitoring your understanding, in using information for a specific goal, and in assessing your learning progress?
Epistemological Beliefs
How well do you employ judgement and wisdom in accommodating uncertainty — or recognize your own lack of expertise?
Epistemic beliefs are a person’s belief on what is knowledge, what is not knowledge, what creates it, and how it develops.
Affective and Conative
How well are you unbiased (affective elements)? How well are you motivated (conative elements)?
Affective elements are attitudes and predispositions towards a specific problem. They limit problem solving capacity.
Conative elements are motivational and volitional. Confidence and passion/deep engagement make a person a better solver.
General Problem-Solving Skills
How good is your solution strategy?
Experts use domain-specific, strong strategies are better. Solvers who use weak strategies, such as the general means-ends analysis, are not effective solvers.
We’re done with problem solving. Now to the juicy bit.
PART 2: THE 11 TYPES OF PROBLEMS
Jonassen makes a rough sketch of a TYPOLOGY OF PROBLEM SOLVING. They are sorted from well-structured to ill-structured.
Logical Problems
What is the solution given these constraints?
e.g. Tower of Hanoi. Rubic’s Cube. Divide triangular cake into four equal pieces.🍰😋
Algorithmic Problems
What are the steps to solve a thing?
e.g. Factor quadratic equation. Convert Farenheit to Celsius.
Story Problems
How can I use the information from this story? What algorithm is best suited to solve this problem?
These are other problems disguised as a story.
e.g. How long for car A to overtake car B traveling at different speeds? How many apples does Adam require to satisfy his class?
Rule-Using Problems
What is the process to reach this goal?
e.g. Expand recipes for 10 guests. Calculate many flight hours are required to pay off a 777.
Decision Making Problems
What is the best option in the solution space?
e.g. should I invest in this? how long should this post be?
Trouble-shooting Problems
What is the problem?
e.g. why won’t car start? What is wrong with this modem? Determine why an article is poorly written. Why is there poor logistics to this town?
Diagnosis Solution Problems
What is the cause and the specific treatment to that cause?
e.g. medical diagnoses and treatment. Developing an educational plan for special education students.
Strategic Performance Problems
What series of tactics will get me to my objective?
e.g. flying an airplane. Driving a car in different conditions. Arguing points of law before court.
Case Analysis Problems
What is the solution given these unique properties?
e.g. Harvard business cases. Plan a menu for foreign dignitaries. Evaluate performance of a stock portfolio.
Design Problems
Given an ambiguously specified goal, what is the solution?
e.g. design a vehicle that flies. Make a paper plane. Develop an investment strategy for money market fund.
Dilemma
Given no optimal solution, what is the best solution?
(usually ethical or social problem)
e.g. resolve Kosovo crisis. Negotiate peace between Hutus and Tutsis in Rwanda. Redistribute wealth through tax policies.
The problem types do not seem optimal to me. A lot of them require similar cognitive skills (e.g. in algorithmic and rule-based problems). But it was a satisfying, well-written read.
Keep in mind, this paper was written 20 years ago. In 2011, he wrote a textbook called ‘Learning to Solve Problems: A Handbook for Designing Problem-Solving Learning Environments'.
If you liked this, can you kindly share it with someone who might? Much appreciated!
[1] Jonassen, David H. "Toward a design theory of problem solving." Educational technology research and development 48.4 (2000): 63-85.