Teaching Through Problem Solving

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  • Editorial Feature II
    Teaching and Learning through Problem Solving
    Revised April 9 2003

    Click here for Outline for Problem Solving 

    index
    Teaching Through Problem Solving
    Ways in which We Learn Best
    Steps in Helping Students in the Problem Solving Process
    Assumptions
    Examples


    Teaching Through Problem Solving to top

    We constantly solve problems. In many cases, there is a prescribed way of doing something and we fit our view of the situation and our reactions into that way of thinking and action. At other times, we may feel that the 'rules' do not apply, or that we are facing a new problem and we must then develop our own solution. Or the rules apply but the loss will be too great or the gain too unfair. It is then that we search for an alternative way of dealing with a problem and come up with a previously unused or a novel solution. In so doing, we learn and expand our parameters.

    Teaching through problem solving is not always easy since many of us were taught by remembering facts whether or not they were related to each other, whether or not we were interested in the subject, and in some instances we were taught by rote. In fact, many teachers may say that problem solving in their particular subject area is not possible, not helpful, or only possible in limited parts of the subject matter.

    However, everything that can be taught may be taught from a problem solving point of reference. The rest of this article is dedicated to this idea.

    Ways in which We Learn Best: to top

    It is sometimes helpful to look at the ways in which we learn more rapidly and fully.

    We learn best by solving problems or have a personal stake in the outcome. It is then that we become interested in knowing the parameters, the details, the basis (assumptions) on which the problem is built, and the end results.
    We learn best when we have discovered the answer for ourselves.
    We learn best when we have contributed the answer or have a stake in its presentation.
    We learn best when we have thought out the process by which the answer is achieved.
    We learn best when we have opened ourselves to different possibilities - one of which is a possible answer.
    We learn best when we have come up with a possible answer whether it is correct or not. If our answer is wrong, the 'wrong' answer will cause us to retrace and find out where we went wrong in our thinking and will reinforce the answer.
    We learn best when we have examined our assumptions as to what will support the answer. Assumptions are very often the barrier to our learning and prevents us from achieving.
    We learn best when we have to defend our answer against other potential answers.
    We learn best when we have had to learn the supportive concepts and data which will provide us with the correct answer.
    We learn best when we have a total environmental view of the data we are learning, its supports, its unknowns, or the controversies surrounding it.
    We learn best when we have learned the different ways in which the data and the process of deriving it are used.
    We learn best when we find different ways of arriving at the same answer.

    Steps in Helping Students in the Problem Solving Process to top

    1. Provide the basis for the solving of the problem
    The student is often stymied by the lack of a basis from which to even begin the problem solving process.
         List the possible presumptions to be overcome in solving the problem.
         Identify tools & references needed to help in arriving at a solution.
         Give basic knowledge needed to begin searching for solutions.
         Support off-the-wall suggestions which may have some validity or
         may lead to other possibilities which are valid.
         Breakdown the problem into manageable component parts.

    2. Discover the interest of the students. Many students are not interested in a particular subject. It is the teacher's challenge to illuminate the connection between the topic to be taught and the students interests.

    3. Enter the world of the student. See the material to be learned from the student's viewpoint of what the student wants to do, know, experience.

    4. Allow the student to create a project of personal interest which uses the material to be learned.

    5. Multi-explanations or solutions. There is always more than one explanation for a phenomenon (some have been proven false long ago but were held to be true by the best minds of each preceding age). Alternatively, there is more than one way to interpret what we know, or more than one way to derive a solution. The differences should be brought up and discussed and the students given the task of defending different positions or of deriving the solution from different angles. Today there are many controversies still raging about certain phenomenon. What are they in your particular field?

    6. Learning can be fun. This is a caveat of learning in childhood. Remember some of the ways in which children are taught from a unique and innovative perspective so that learning is actually enjoyable to the child. Translate these to the subject at hand. It is never too late to enjoy the experience of learning no matter how complicated the subject to be taught. We can learn from the simple methods used in the earlier years of childhood. Take a list of teaching techniques from the early years. Look at them from the perspective of the current topic. Which one fits or with a bit of imagination and innovation can be translated or upgraded to fit the current circumstances? It is often surprising the degree to which that which helped us learn the simpler lessons in life are still effective in later years.

    7. We know that many subjects can be learned by rote. The only problem with this method is the incredible boredom of the task and the fact that once learned we have trouble expanding the knowledge to fit new situations. We know the material without knowing the reason for its existence or truthfulness. We do not know the supportive knowledge which helped our predecessors find the solution. There is no fun in learning by rote except the high percentage on our exam grades, or in the presentation before others. But there is little or no expansion of true knowledge.

    I learned by rote parts of the Prologue to Chaucer's Canterbury Tales but to this day have no appreciation of Middle English or how it was transformed into modern day English, or how it limited the world view of those who spoke it, or the ability to rhyme with it, or what other works we still have today which were written in the same format, or how it related to the rest of the work, or to the perspective of the culture which produced it. In fact I did not even know the meaning of the words or the phrases until one day many years later I sat down and repeating it in my head, and attempted to assess its meaning and its true literary value.

    8. Interrelationships - It is important that the student, whatever the project is that has been chosen, make an effort to interrelate the subject of the project with the other topics of the subject matter. This should be more than a simple descriptive relationship and should include ways of integrating the selected topic with the other knowledge learned in the class. Having an individual represent a historical figure in a debate on some topic may help learn everything about one person but all others presented in the class may be a blank for the student at the end of the semester.

    9. Work towards the strengths of each student. It is important that each student realizes and understands the different capabilities brought by different students to a project. No capability or interest should be devalued. In a certain situation, each capability will help solve a specific problem. Collective problem solving should be emphasized over individual problem solving capabilities. Some students cannot see alternative solutions, or any solution at all. When confronted with a potential solution, the student may be able to contribute knowledge from other areas thus increasing interest and adding to the solution of the problem.

    10. Support the discovery of what does not work. This discovery is often as important as the discover of what does work. The student can then be led to appreciate the lessons learned in the process.

    Assumptions to top

    We all believe in a specific order of things. We build our perceptual concepts (assumptions) on the basis of this belief. It is extremely difficult to change our perception because we fit our observations into the framework of this world view. And when a particular fact does not fit, we just say that there is not yet enough data to explain it or to account for its presence. Some of the assumptions which we use about the forces operating in a certain circumstance, the nature of the situation, any moral restrictions, and the probability of a certain outcome are all operating at each juncture in our decision or non decision processes.

    In the development of a problem solving method for teaching any subject, some of the assumptions so often used in developing problem solving techniques are:
       The problem must relate directly to the subject being learned
       The solution must be logically derived from the problem
       The problem must be a real life problem using real information as its base.

    All of these are not necessarily correct. A problem with none of these assumptions can be just as effective. The important point here is the use of or the finding of the answers or data which is to be learned. But even this is not necessary if the problem merely opens up the field, or expands perspective, or creates a more conducive or neutral environment within which thinking and exploring can take place.

    The important point is that our assumptions must be checked and in certain cases overturned in order to produce fruitful predictions and results.

    In the past, many more problems were created by commonly held the assumptions behind real world events.

  • The assumption that the storm pattern of El Nino and La Nina are localized phenomenon and not a worldwide phenomenon precluded any ability to forecast its occurrence.
  • The assumption during the baby boom that the population would continue to grow past the limits of the world to support it (population bomb) was false and precluded the subsequent finding that there were cycles in birth rates worldwide, new farming and marketing methods, changes in birth patterns as populations grow or shrink, etc.
  • The assumption that asbestos was not harmful to the lungs, caused much suffering which is still being paid for.
  • The assumption that wings must flap like the wings of birds in order to fly held up man's age of flight for centuries.

    And on a more personal as well as societal level:

  • The assumption that the findings we come up with are the only possible truth leads us to stake our wealth and lives on inaccuracies which prove costly and in many cases fatal.
  • The assumption that the other side is as stupid as you think they are or are not innovative often leads to disaster (they are usually smarter than you think, and perhaps even more so than you).
  • The assumption that only you have honor which must be defended at any cost, often leads to heightened conflict.

    In general, inaccurate results or predictions were caused by the following limiting assumptions:

    - existence of physical limits
    - limited innovative capacity of man
    - only one way to do something
    - methods used in testing were sufficient to indicate truth
    - limits to acceptability
    - change as straight line process (growth or decrease) and no other form
           (i.e. cyclical, periodic off and on, upper and lower limits
           causing breaks and reforming)
    - strict cause and effect overriding multiple causation and results
    - there is only one type of logic
    - all individuals react to and see the world in the same way
    - form must follow nature
    - thinking limited to a specific set of conditions is usually sufficient
    - reliance on strict cause and effect taking into account too few variables

    Or to put some of the above in a different form, we must reject or scrutinize carefully:
    Any assumption which is culture bound
    Any assumption which assumes that our particular view of the world is true
    Any assumption which accepts the results of testing as true
    Any assumption which causes us to accept answers which will not offend
    Any assumption which assumes that current trends will continue
    Any assumption which assumes that forces are operating within a specific area
    Any assumption which assumes that man is limited in any way
    Any assumption which is based on indeterminate facts

    Examples to top
    This section looks at two different examples for problem solving:
    Example I - The explanation of social structure
    Example II - The disappearance of Neanderthal Man

    Introduction
    One of the problems with problem solving as a teaching method is the inability to break out of our precepts. Since each discipline is often seen as a whole unto itself, it is sometimes difficult to see the relationships between the different disciplines. Particularly when one field, lets say mathematics, does not appear to lend itself well to help in our understanding of one of the 'soft' sciences such as sociology.

    For instance, if we could look at a problem from an economic or a cyclical or a mathematical or a political or geophysical standpoint, we would not only gain new depth in perception but would also discover possible alternative explanations of the problem.

    Throughout the last 200 years, sociologists have looked at sociological phenomena through many different lenses.

    Example I - The Explanation of Social Structure

    Different basic ways of looking at society
    society as a random set of acts
    society as a grand design set at the beginning and played out to the end of time
    society as an innate set of processes or ways of responding (instincts)
    society as a complex set of cyclical processes controlled by reoccurring forces
    society as a recognition and attraction on a genetic level of similarity, power, success, etc.
    society as a collection of single interactions
    society as a process of push and shove throughout time
    society as a creation of a greater power which was set in motion and left or is still operating and guiding
    society as a collection of interactive force fields which cause regional nodes and act off of one another
    society as a playing out of sexual forces and dominance/submissiveness
    society as a set of standard life processes (eating, reproduction, etc.) and the resultant complex of interactions
    society as an evolutionary process of survival of the fittest
    society as a form of follow the leader with the leaders determining the shape and destiny of mankind in any given period
    society as a process of economic/market forces which push and pull the system in different directions producing a complex interplay of action
    society as a constant testing of the limits of nature with changes taking place once a particular movement hits a limit and retracts or falls to start again
    society as a complex set of interacting individual spheres of influence in the rational fulfillment of needs
    society as an interlocking set of primitive rules which are embellished and constantly change by consensus and produce the indeterminate movements of society over time
    society as an experimental process controlled by beings external to the process
    society as a cooperative process of give and take which moves the process along in an attempt to survive against external limits and forces which would destroy the fabric
    society as describable by a set of mathematical equations which we have not yet discovered
    society as a simple set of action and reaction throughout the system creating complex buildups and troughs

    Ways of Working with Example
    Some of these may be far fetched (or not). Select one whether you believe in it or not and defend it against the others or against the main sociological theories of society (past and present) in the following ways:

    1. Indicate the assumptions about man and about social interaction on which the theory is built
    2. Show data or instances which support the view you have selected
    3. Show areas which can not be substantiated but might be 'proved' given certain parameters, findings, research.
    4. Show discrepancies between the other theories and inconsistencies within each theory which would indicate logical or other problems with the theories
    5. Show how your selected theory is superior to the other theories and back it up with examples and solid evidence
    6. Develop at least one test which would help substantiate your theory
    7. Be able to take a test on each of the past or present theories of the field as the semester proceeds to show that you understand the major points of the theories, the major assumptions of man and society on which the theories are built and their strengths and weaknesses (which of course you will use to support your own theory)
    8. Develop and indicate the logical basis for your chosen theory
    9. Give at least 7 rules or ways in which your chosen theory works in society to produce what we observe in the world

    Example II - The Disappearance of Neanderthal Man

    Reasons for the disappearance of one species of man (Neanderthal) living in the same area at more or less the same time as another species - Cro-Magnon Man (anatomically similar to modern man or to put it another way - a name given to modern man, to distinguish him from Neanderthal, living in Europe between 35,000-10,000 B.P.)

  • More aggressive vs less aggressive - the more aggressive tended to survive.
  • Less varied diet which when decreased led to starvation.
  • Less organized living - small groups which were vulnerable against the more organized society of Cro-Magnon (modern) man.
  • Had fir and did not use animal skins and were less able to cope with a hard cold period
  • There was actually never two different species of man.
  • Matriarchal structure could not compete with patriarchal.
  • Lived in caves which were increasingly taken over by modern man and did not have constructed shelter
  • Genetic structure different leading to different reaction to a disease which swept through Europe
  • Less procreation for a number of reasons - genetic, social structure prohibiting multiple partners in a small community and restrictive sexual norms, lower fertility, social prohibition on multiple offspring.
  • Gradual reduction of hunting space through encroachment by modern man on territory
  • Assimilation into the dominant society of Cro-Magnon (modern man)
  • Still exist in isolated pockets (Yeti, Abominable Snowman, Bigfoot, Yowie, Sasquatch.

    See Ways of Working with Example of Example I above and adapt it to the present example

  • HUMANS AND NEANDERTARS WERE CONTEMPORARY
  • Who Were the Neandertals and What Happened to Them?
  • Crypto-bipedal-Primatotolgy ... Sasquatch - The Truth as I Know It Site worth looking at regarding known evidence and current thinking on subject.


    Selective References - General Problem Solving
  • Stanford - An Introductory Handbook for Faculty, Academic Staff-Teaching and Teaching Assistants Revised 2001
    This url will give you the correct url to try for an html version of the above handbook html version
  • Teaching and Learning via the Network Application of "Knowledge Management" Concepts to the Interdisciplinary Area of Biotechnology "...This project will serve as a prototype for the library's role in the application of "knowledge management" concepts to a "problem-solving" instruction model in biotechnology." Universities of Minnesota, Wisconsin-Madison, Indiana University, Iowa State, individuals and staff University of Technology, Sydney
  • Links to a Better Education
    Also see: Description of the scientific method
    Columbia Encyclopedia
  • Problem Solving Program "The Future Problem Solving Program (FPSP) engages students in creative problem solving. Founded by creativity pioneer, Dr. E. Paul Torrance, FPSP stimulates critical and creative thinking skills and encourages students to develop a vision for the future."
    also see: Future Problem Solving Program - US & Non US Programs
    Future Problem Solving Program 2005-06 Topics & Calendar Climate Change/Climate Threat, Freedom of Speech, Nutrition, Healthcare Access, Redistribution of Wealth
  • 21st Century Problem Solving - A modern approach to reliable problem solving across the curriculum. Highly evaluated series of problems for all grades and methods of problem solving in math




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