Observations on Problem Solving - Steps in the process. We make decisions constantly which effect our lives and the lives of others.

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  • Editorial Feature
    PURPOSE: To give a method for solving problems

    Index
    Problem Solving  Finding Solutions 
    Example Problem  Possible Solutions  Relevant Sites

    Observations on Problem Solving

    We make decisions constantly which effect our lives and the lives of others. Normally, we do not think about the problem solving process since most of our problems are solved by reaction rather than reflection. The fact that our reaction processes are the result of natural reflexes and the build up over time of small habitual and learned techniques hides the true processes involved. It is only when we are stumped for an answer or find ourselves faced with multifaceted problems demanding more than learned or habitual reaction that we acknowledge the need for more advanced tools.

    The first hurdle to overcome in problem solving is the determination of the different ways in which individuals approach the problem solving process.

    These approaches or dimensions are mutually exclusive giving totally different approaches to the problem - abstract vs. concrete, inductive vs. deductive, focussed vs. field, traditional vs. creative. Each of us falls at a different place along each of these continua or dimensions.

    So how does this help in the problem solving process? When these are combined into a paradigm, each of the categories contains excellent problem solvers albeit totally different in their approach to the process, thus allowing each individual to see what another misses. Which is why all of us need to ask for advice when faced with a major problem, or at least why most of us should. Hopefully we will find someone who comes from a different part of the paradigm and can shed light where we cannot see.

    If we surround ourselves with those who fit into our corner of the paradigm created by the different categories, than we are severely limiting our ability to find the most creative solution much less define the problem with maximum clarity.


    Steps to Problem Solving       return to top

    The following is not so much a discussion of the problem solving process as it is a listing of the steps we often go through in finding solutions to a problem.

    Finding the Problem

    Be sure that the problem is defined correctly. Many problems have been solved only to find that the real problem still exists. Or worse, that the solution produced more serious problems than existed prior to the solution. Finding and defining the problem correctly is in fact the most difficult process.

    To illustrate this, take any problem with which people are familiar and ask 5 people what in fact is the real problem. And while you are at it, ask also what the solution is. Aside from some overall agreement relative to certain points, you will get back 5 basically different answers. If these are combined along with 10 other answers, you may have the basis for a start in defining the 'real' problem and even some insight into a possible solution.

    Many problems, if stated correctly, become easy, or at least easier, to solve.

    Assess whether the problem is in fact the problem or only part of a larger problem. We can take it as axiomatic that every problem is only part of a larger problem. However, in order to find any solution at all to a current problem, it is necessary to define some limits which relate to the problem as it presents itself in a current well defined situation.

    Always assess the causes of the problem. Make a chart of the problem and all of its probable causes. Solution is often found by analysis of the causes.

    Brain storming. This involves the suggestion of random access thoughts which are put forward whether fanciful or not on what the problem is and how to solve the problem. Out of far flung and ridiculous ideas often come some solutions not otherwise contemplated.

    Association mapping - map all of the relevant factors - all the possible causes, all possible entities effected by the problem and how effected, all possible effects of solutions, all possible attendant factors (environmental, physical, psychological, economic, social) which surround the problem. In this way, it is possible to come up with associations and links never thought of leading to better definition of the problem and a more creative solution.

    Dealing with the Problem
    Once you have the correct problem(s):

    1  Break the problem into its subparts to more easily understand the whole.

    2  Map the relations between the subparts (see http://www.mindtools.com/page2.html Excellent full explanation of powerful pen and paper techniques to problem solution including critical path analysis, decision trees, force field analysis, etc.)

    Finding the Solutions       return to top

    Assess basic physical, social, etc. principles in the attempt to find a possible solution

    For instance, in looking for a solution to a problem in the physical world, list all of the possible connections between the problem and the following physical principles: adhesion, friction, leverage, gravity, rhythm, floatation, suction, lift, vacuum, static electricity, action-reaction, Bernoulli to name a few.

    In looking for a solution to a social problem, list connections and associations between parties involved, institutions, norms, laws, economic and social trends or cycles, and impacting environmental factors as a start.

    Look for multiple solutions. Just finding one solution which works does not mean that it is the best solution.

    Find solutions to the sub parts which together will solve the over all problem.

    Set priorities as to which solutions will be tried according to time, space, ease, etc. depending on the type of problem.

    Assign dependency between the different parts of the problem and solutions. The solving of certain parts of the problem or the use of specific solutions may make other solutions unnecessary.

    Maintain constant feedback to assure that the solving of the sub problems does not impact negatively on the overall solution.

    Set priorities in the timing for the solution of the sub problems. There is often a time dependency between solution of the different sub problems (see http://www.mindtools.com/page2.html)

    Factors to take into consideration in assessing a solution

    usability
        ease of use
        ease of learning to use
        amount of time in using (speed)
        activity of those using
        reliability
    universality 
        universality of use
        culture specificity
        all possible ways it can be used
        possible future uses
    sophistication
        technology needed
        knowledge needed to use
    target user population
        activity of those using
        preferences
        abilities and limitations
    production
        replicability
    repair/replace
        amount of time to fix
        replaceable parts
        accessibility of replacement parts
        availability of parts
        ease of repair
        knowledge needed to repair
    support
        maintenance
        other things needed to use it
        availability of resources needed
    completeness of solution
        comprehensiveness
        degree to which solves problem
        how long will it last
        how well it solves the problem
    safety
        to users
        to repairers
        when discarded
        to future generations 
    among others

    Assumptions are always a big stumbling block to the solution of a problem

    The limits of our knowledge, the restrictions placed upon us by culture, habits, and learning, all limit the degree to which we can define and implement a solution.

    However, much more important than the above limitations, are the limitations placed upon us by our assumptions. Our assumptions are made up of what we know or think is true, and of what works and doesn't work. If we assume that individuals will do specific things or certain types of action and reaction will occur in any situation, then we will often be in error.

    Problem       return to top

    You are in a room with 4 other people and there is a ping pong ball inside a 6-7cm (2.5-3 inches) high steel pipe sealed tight to the floor (but not through the floor), with a diameter almost the same size as the ball. Nothing else is in the room. Mission - to get ping pong ball out of pipe within 30 minutes with no damage to pipe, ball, room, or people. (author of problem idea: unknown)

    How to do this? Can you think of more than one possible way even if in the end it might not work? Make a list of possible solutions before reading further.

    What is the problem? 
    Before we get to the 14 possible solutions and the 8 solutions which were rejected for one or more reasons, lets look at the problem itself.

    The problem as outlined here appears to be fairly clear.

    But are there other factors to take into account which in fact are part of the problem?

    1  One such factor is the five people. How will they react and who will lead the group. If the self appointed leader thinks he knows the answer and refuses to let the group express its collective thoughts, than this presents a problem toward finding the best solution or perhaps any solution at all.

    2  If some of the group refuse to participate or even interrupt the process, then the possible solutions are reduced.

    3  If unforeseen and interfering environmental factors are present which are not part of the presenting problem, than the progress of the solution may be impeded.

    4  If social or cultural norms, or sensitivities are impinged, then some solutions may not be possible.

    Physical principles which might have an effect on the solution

    Assess the physical principles impinging on this particular problem. As a short list, the following physical principles may have an effect on the outcome: adhesion, friction, leverage, gravity, rhythm, floatation, suction, lift, vacuum, static electricity, action-reaction, Bernoulli

    Assumptions
    If we assume that: Everyone will work together, the physical details of the problem are what they appear to be on their face, laws of causality as we understand them operate, each of us is capable of finding a solution, the best leader will be either self appointed or selected by consensus, there is an easy answer, the time is sufficient, etc. we may not solve the problem.

    According to the stated problem, what is permitted and what is not permitted?

    1  no mention that the people did not have normal clothing and things in pockets, hair, etc. which could be used.
    The rules indicate no damage to pipe, ball, room, or people, but damage or disassembly of other materials - clothing, things in people's pockets, etc. were not mentioned and can be broken apart or destroyed.
    3  No mention was made of non communication with the outside. (can arrange for something to be done by someone outside) 
    4  No mention was made of construction of room. (could be a stand alone tool shed)
    5  No mention was made as to the construction and material of floor. (could be wood)
    6  No mention was made as to the gender of the individuals in room.

    Assess the causes of the problem

    The causes in the present case would appear to be fairly straight forward.

    Why are you trapped with 4 other people (some of whom you don't like) in a room with a ping pong ball in the first place? You agreed to do this. Not a problem - solve it and get out.

    Physical 
    Gravity keeps the ball at the bottom of the pipe.
    Small space on either side of the ball precludes picking it up and also hampers extracting it by other means due to space constrictions such as friction of ball against walls of pipe.

    Constrictions 
    Time constriction
    Lack of tools
    Non damage to pipe, ball, room, or people
    All the normal ways of extracting things are not possible (in this case can not turn the pipe over, reach in and grab it with your hand, knock the bottom of the pipe to get it out the other side...)

    Consequence Analysis

    Before acting, it often helps to rate the consequences of an act. Consequences are often more important than the solution itself. (See appendix below)


    The Possible Solutions       return to top

    Number in parentheses indicates intuitively assessed probability that the method will work in present circumstances
    1(low) to 10 (high) 
    1  adhesion - strand of hair and gum or other quick drying viscous substance to attach to ball and lift (10) 
    2  suction - using mouth (10)
    3  friction - two pieces of cloth stuffed on either side of ball and lifted very slowly (6)
    4  friction and leverage - two pieces of very thin hard material used like chop sticks (may have to split something someone has in pocket)(8)
    5  gravity and displacement - pile up small pieces of something under the ball by dropping in on top and jumping or blowing to settle them below ball (3)
    6  floatation - liquid available - saliva (5)
    7  sling - thread from cloth put under ball by rolling ball and lifting (6)
    8  Bernoulli - very fast movement (blowing) over top of pipe. Ball is probably too heavy for this to work but no harm in trying (6) [teacher's guide]
    9  static electricity - felt or wool rubbed produces an electro- static charge which clings to ball. (4)
    10  rhythm action/reaction - all jumping in rhythm on wood floor to bounce it out or jumping down from a height - actually might work even though wood floor is not that pliable, and the surface of the floor actually touching the ball is quite small. (2)
    11  action-reaction - bounce the ball within the pipe with something long enough to contact the ball and every time make it bounce higher - walls of pipe fairly close and the friction of the ball hitting the walls would probably make this unfeasible. Worth a try however. (2)
    12  Conservation of Momentum - drop an object which has more elasticity than ball from a height directly onto the ball and the reaction of the ping pong ball will be enough to get it out of the pipe.

    Methods thought of and rejected

    1  chemical reaction to create a foam and lift it out - no materials
    2  super cold to float it out - ha!
    3  mold growth beneath ball - time restriction and fact that mold growth would also encapsulate ball and restrict its movements
    heating up base of pipe on theory that pipe expands and hot air rises thus lifting the ball with it. Several reasons this would not work:
    - lack of fuel and ignition and the fact that materials can not be destroyed as in combustion.
    - it is possible that the ball will expand faster than the pipe
    - ball too heavy for the lift of hot air. 
    - hot air will flow upwards unevenly creating a binding of the ball to one side 
    5  have crane lift room and turn it on its side allowing the ball to roll out. No one said you couldn't communicate with the outside world. And if the operation is done carefully there will be no damage to pipe, ball, room, or people. Assumes room is stand alone (i.e., tool shed) and well built. 
    6  wait for rain on the assumption that there are windows through which water can be collected, or no ceiling to the room and use water to float ball - not enough time. 
    7  physchokenetic levitation - takes someone with psychokinetic abilities and even so that would be a stunning feat.
    8  Magnetic, diamagnetic and superconductor levitation - these take materials probably not carried by the average person. However, they are options. [maglev.html]

    Comments, additional methods, criticisms welcomed email

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    Appendix
    Rate from 1 to 10 (1=low 10=high)

    Solution# 1 2 3 4 5 6 7 8 9


    Possibility of success
    Truth fairness justice
    Positive outcome
    Positive side effects
    Negative outcome*
    Negative side effects
    Best overall solution
    Your preference**

    *positives and negatives do not necessarily add up to 100%
    **assess why these are your preferences. They may have nothing to do with the best solution.
    return to solutions

    Problem Solving References return to top

    20 Ways to Foster Creativity in Your Students, Laura C. Mohr, High School Science Teacher, St. Louis, Missouri http://www.enc.org contact at lmohrlmohr@yahoo.com

    Ideas for Creativity and Innovation - Techniques, keeping mentally fit, and helpful creative resources. A number of very good links http://www.vistaprint.com/marketing-article-detail.aspx?pid=920

    http://www.mindtools.com/page2.html Excellent full explanation of powerful pen and paper techniques to problem solution including critical path analysis, decision trees, force field analysis Problem Solving and Analytical Techniques * Brainstorming - Generating Options * Critical Path Analysis - Planning and Scheduling Complex Tasks * Decision Trees - Powerful Quantitative Analysis of Decision Impact * Force Field Analysis - Analysis of all Pressures For and Against Change * PMI - A Powerful Enhancement to Pros and Cons * SWOT Analysis - Analysing your Strengths, Weaknesses, Opportunities and Threats

    Whelmers http://www.mcrel.org/whelmers/whelm22.asp pingpongbaseball dropped together

    Teacher's Guide1A worksheet produced by the Native Access to Engineering Programme Concordia University, Montreal Worksheet 7 FLIGHT Teacher's Guide

    maglev.html, Magnetic, diamagnetic and superconductor levitation http://www.geocities.com/Area51/Shire/3075/maglev.html excellent links to a number of experiments done in the areas of serious levitation research. Work being done by a number of governments, universities, and private individuals on levitation systems for trains, rocket launchers, etc.

    http://www.fortbragg.k12.ca.us/AG/PhysSci/bernouli.html Very nice series of experiments on Bernoulli's Principle from the Fort Bragg Unified School District

    http://www.usfirst.org/ FIRST inspires in young people, their schools and communities an appreciation of science and technology, and of how mastering these can enrich the lives of all. Corporate America provides economic and professional support to FIRST. Many Fortune 500 companies have significantly helped FIRST grow and are committed to its continued progress. Government organizations such as NASA are key partners in this worthwhile cause. FIRST represents a cooperative team effort by students, teachers, communities, corporations, and our government. FIRST Robotics Competition This competition is our longest-standing program, involving more than 20,000 high school students in the United States, Canada, Brazil, and the UK. FIRST LEGO League Starting with the FIRST LEGO League, our Jr. Robotics program introduces science and technology to elementary and middle school students using real-world challenges and hands-on learning. FIRST Place Through our mentor workshops and student classes, FIRST Place provides the environment to inspire and educate others in field science and technology.



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