Complexity of Problem Solving

Most people would agree that problem solving is an essential 21st century literacy skill, I think. Dr. David Jonassen spoke at the Texas Tech College of Education last week on the topic of problem solving, and specifically presented on the subject, “Designing Learning Environments for Troubleshooting.” His presentation is available as a podcast, and is about an hour and 18 minutes long.

Dr. Jonassen is the director of the Center for the Study of Problem Solving at the University of Missouri. He also was involved with a PT3 project at the University of Missouri which resulted in the creation of the online resource KITE: Knowledge Innovation for Technology in Education. KITE is a searchable online database offering “over 1000 stories of technology integration at your fingertips.” The teacher interviews are available in full-text transcribed format, rather than audio or video files. This makes the database records richly searchable.

I agree with Dr. Jonassen that many people oversimplify the rich complexities involved in authentic problem solving. I highly recommend listening to his podcast presentation if you are interested in the topic of problem solving in education. He suggests a great framework for thinking about different types of problem solving as well as different problem solving strategies. I really like his idea of using “design assignments” to encourage higher order thinking skills and problem solving. This dovetails nicely with ideas from the book “A Whole New Mind: Moving from the Information Age to the Conceptual Age” by Dan Pink which I finished reading recently. Design is one of the six key senses and skills Pink identifies as more important than ever in the 21st century.

Here are my notes that I took during Dr. Jonassen’s presentation (please forgive the typos, this is not very edited):

David Jonassen

7 Feb 2006

http://kite.missouri.edu/
http://csps.missouri.edu/
http://tiger.coe.missouri.edu/~jonassen/

assumption seems to be that we solve all problems the same
– Jonassen’s work differs from that

People’s affective responses to problems, connotations to problem solving people feel very loathsome about

design is one of the most complex forms of problem solving
– in engineering now they are preferring to talk about “opportunities” rather than problem solving

I have been accused of being overly cognative

major impediment: people don’t like to talk about problems
– if you admit you have a problem, you often lose capital in the organization
– this is a difficulty when you have people

people get paid to solve problems
– no one gets paid to write in blue books or to memorize
– memorization certainly is part of people’s jobs, even with actors

Well-Structured problems
– parameters of problem specified in problem statement (like problems stated in a textbook)
– applies limited number of rules and principles organized in a predictive and prescriptive arrangement
— those are not

— problems contain an unknown, real world problems typically have real world answers

– regulaar and well-structured domain knowledge
– possess correct, convergent answers
– possess comprehensible solutions where the relationship between decision chociess and all problem states is known, or

David is more interested in Ill-Structured problems
– have vaguely defined or unclear goals and unstated constraints
– often different goals or expecations, or unstated constraints, lead to difficulty in problem solving
– possess multiple solutions, solution paths, or no solutions at all (no consensual agreement on the appropraite solution)
– possess multiple criterai for evaluating solutions
– possess less manimpulable parameters
– no prototypic cases
— even fiating something like law on abortion does not make the problem go away
– uncertainty about which concepts, rules and priciples necessary for solutions

Often people cannot tell you why they don’t like a piece of art or something designed architechturally

most unstructured problems are multi-disciplinary
– can’t therefore be solved just using proces (economic, environmental, regulatory, affect, etc are involved)
– engineers by themelves can often not solve the problem!

continuing ill-structured problems
– often requires learners or problem solvers to express opinions and judgement, many people have problems with this!!!

is some research (we disagree based on cognative requirements) to solve well-structured versus ill-structured problems (
– tends to be a relationship but not necessarily

playing chess is a well-structured environment but very complex, because there are virtually an infinite number of possible moves

Abstractness/Situatedness
– overlaps…

Static – dynamic
– the very wicked problems are dynamic, they are a moving problem
– like Heisenburg effect
– do variables change over time?

Independence of problems

Now talking about problem typology (not a taxonomy)
– logic problems (one can argue that these are just logic problems, not problems like “tower of hanoi”
– alogrithms- factoring equations is an example, converting F to C, calculating speed
– story problems: how long does it take for car A to pass car B, etc
– rule using: outcome is info, like searching online catalog for best resources, rewriting a story in first person, trying to apply a set of rules for applying your performance in a given context, trying to figure out how to use a telephone or subway in a foreign country
– decision making problems: should I move to take another job, what car should i buy, where should my child go to college, etc (it wouldn’t be a problem if it didn’t have more than one possible solution)
— best way to get to the Interstate during rush hour
– troubleshooting: this is the one we all probably understand the most: why can’t I connect online, detwrmine why a newspaper article is poorly written, identify communication breakdowns in a committee
— most people don’t have schema for how a car works
— psychiatrists are troubleshooters, why is milk production down on a dairy farm
— something is broken and we need to isolate the problem

diagnosis solution
– more complex that troubleshooting
– virtually any type of medical diagnosis is in this genre
– how should i study for the final exam
– identifying and treating turfgrass problems on a golf course
– develop individual plan of instruction for special education students
– decide how to make an unconrollable horse rideable
– helping Johnny to read

Strategic performance
– situational awareness: flying an airplace on a combat mission
– driving a car in differnent conditions (driving a new car at night in the rain in an unknown city in a foreign country where you can’t read the road signs)
– managing an investment portfolio
– moving to the next level in pokeman game
– teaching in a live class
– arguing points of law before a court
– air traffic controllers at a busy airport

Case / System analysis
– case studies
– Harvard business cases
– everyday, real world problems that require system / policy analysis
– render judgement in a tort case

Design problems
– some of the most complex
– designing
– most of lit comes from engineering and architechtural
– most empirical is engineering design
– write a short story: compose a fugue, design a bridge
– make a paper airplane, design a dog house, design a vehicle that flies

Janet Kollatard has term “learning by design”
– doing design as an activity to engage students in higher order thinking and meaningful learning

other examples
– developing curriculum for school; plan marketing campaign for new internet company
– design a can crusher
— study at Penn State found those students using the Perry Scale of epistimological belief development progressed as far in 1 year as a student typically does in 4 years of college
— these students were living ambiguity
— for some problems there can see to be an infinite set of solutions, but after doing a constraint analysis only a subset can be possible

Dilemmas
– should abortions be banned
– resolve Middle East crisis
– negotiate peace between Hutus and Tutsis in Rwanda
– redistribute wealth through graduated taxation
– usually are in ethical, social, and moral dilemmas

This typology gives a context for our discussion now about

Everyone has an opinion about education
– no child left untested legacy
– somehow that is supposed to make those students accountable
– unfortunate
– Dave Berliner at Univ of AZ gives talk that shows that high stakes testing is having the exact opposite effect it is supposed to have

reality is: we are not able to know how well students can think
– David argues the only kind of thinking you can reliably assess (not just valid) is memorization
– that is why we are stuck focusing on memorization, looking for high correlation coefficients
– the more complex your activities, the more subjective it becomes

We are already seeing a diminuization of student writing skills and discourse skills because they are bubbling
– that notion of accountabiilty is going to come back to haunt us

Problems like school accountability and military in iraq require “historical reasoning”
– historical reasong and other unnatural act” by Weisburg, got his degree at Stanford
– Weinburg argues that history can only be understood economically, culturally, etc– can’t be understood chronologically
— history is by its very essence inter-disciplinary

We are going to have to address these inter-disciplinary problems and issues

Outsourcing of engineering to India will be a huge problem
– in few years we’ll have

Troublehshooting is a little more constrained, and limited
– requires domain knowledge, system device knowledge

from textbooks: students learn some theoretical domain knowledge, but if they don’t connect it to concrete experience it is pretty useless

it is only when an idea is embedded in some context that it has meaning
– a theory only makes sense when you can apply it in a context

Peformance and procedural knowledge

strategic knowledge is important
– trial and error
– exhaustive
– topographic
– split half
– functional discrepancy detection
– this are heuristics that can help

Experiential knowledge: this is the most valuable
– case based reasoning comes in here

what groups compose the system? key question

Need procedureal knowledge about how to conduct various tests

Historical approeaches to troubleshooting instruction
– procedureal demonstration
– conceptual (content) instruction
– rule based approaches
— expert systems
– simulations
– intelligent tutoring system

people were interpeting the wrong question, not providing incorrect information in an IRS 800 number analysis

Cognative porcesses in troubleshooting
– identify fault symptoms (what is wrong with the system?)
– constuct a model of the problem space
— describe goal state and subsystem
– diagnosis process
– resolve fault
– add to knowledge base

Architecture David has developed, coming out in EdPsych Review in 1 month on troubleshooting

– Case library: archive of previous cases (since the first thing you do when you hae a problem, you try to remember a similar sitatuion and apply same solution, or adapt it)
– System Model layers
– diagnoser

when anthropological study of refrigeration troubleshooting in grocery stores, found that individual repair folks would always call someone else on the cell phone, and inevitably a story would come out of that

PT3 grant for Missouri was to develop teacher stories:
http://kite.missouri.edu/
– lots from Texas
– transcribed stories, indexed them, put them into a library
– knew from experience that teachers are most interested in grade and subject

This uses the nearest neighbor alorithm, is google-like

– now is saying we teach by stories more than teaching by theories
– goal is to supplant lack of experiences of novices with expert experiences

If I want to figure out how to use appropriate technologies (integrate them) then a case library can be helpful
– can be used in problem based learning environments
– what we are really doing here is sharing stories

functional layer: what are cause/effect relationships between different components of the system

12 v battery is really a 14 v batter

Air Force calls it PARI model, developed at Brooks AFB
– what am I going to do first?
– involves actions, hypothesis, probability, and interpretation
– is actually a pretty dumb system, it is just raising state flags

This is just a theory now, but it gets at the idea of integrated knowledge
– big difference between experts and novices is that experts can represent what they know in multiple ways
– big part of the problem is us: assessment is the achillies heel of education
– anything that is worth knowing cannot be assessed using just 1 method

heuristic: generic, generalized kinds of strategies
– when people troubleshoot things, the more experiences they have the more they represent a solution as an exemplar not a heuristic
– novice troubleshooters start out with a weak conceptual model
– organization of what they know is based more around conceptual ideas
– as you progress from novice to expert that flips upside down: expert diagnostician can diagnose very quickly and expertly, because they use their experience more than a logical sequence

We call these illness scripts or schemas in medicine
– diagnostic process is more pattern recognition than following logic
schema: linked to direct experiences, exemplars

David thinks

Main arbiter of being an “expert” is experience
– Dreyfus and Dreyfus stage model goes through phases, there is a transitional phase but those are not actually discrete

example of thoracic xrays
– radiology specialists can identify right away
– experiment showed flashing xray for 1/4 of a second, just below perceptual time
– some experts can’t explain how they knew that but they can

A solution to not having experience as novice teachers:

-graduated clinical experiences is one way to address this, start students in the classroom early

reform is not going to come from novice teachers

how do you reform education:
1- quickest way is to eliminate compulsory education, that would create the biggest change that you could ever do (this is naive, it would create social and economic chaos, because schools provide a custodial function that Jakes talked about many years ago)

2- changing schools requires changing society
– have to change the mindsets of people with whom you work
– that is a phenomenally complex process

it is wrong to expect to foment revolution with novice teachers
– power plays a huge role

have to somewhow convince part of society to change

concept of a public education is so ingrained, it will really take a revolution to do this

assessment
– is depth versus breadth problem
– can’t afford to cover the curriculum and use multiple versions of assessment

“Learning to Solve Problems” book
– suggest problem based learning and rubrics to assess
— in engineering (ABET) says they have to move to problem based learning models
– many engineering faculty don’t know how to assess learning outcomes they want students to display

it is hard work and time consuming to assess more authentically

argumentation is one of the best ways to solve ill-structured problems
– notion of component-conceptual skills

Example of Pysics Mechanisms
– similar to force-motion assesment

sample question
– asking people to argue for an answer on multiple choice exam
– many know how represent relationships mathematically, but not explain it
– hardest thing is to get physics teacher to teach physics without using formulas,

could we use “willingness to fail” as important element in definition of “expert”
– fear of failure really constrains acquisition of knowledge for teachers and principles in years 1, 2 and 3

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