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People differ in the manner they gather, store, and process information when solving a problem.
Students Possess:
A wide variety of problem solving styles and temperaments, including:
Logical Problem Solvers: spatial thinkers who tend to use linear methods. They set a specific goal, determine the steps necessary to achieve that goal, and then embark on the effort to accomplish those steps.
Intuitive Problem Solvers: temporal thinkers who tend to holistic methods. They get a sense of the way they want things to be, determine how things need to be balanced to bring about those changes, and then make adjustments to create that balance.
Flexible Problem Solvers: use both logical and intuitive methods readily.
Some students possess obstacles that impede the problem solving process and often lead to an inability to solve problems correctly. Cognitive psychologists, who study the mental processes associated with processing and understanding information, have identified very common obstacles to problem solving. These obstacles include:
Confirmation Bias: Confirmation Bias is the tendency to search for only the information that supports our ideas. Our initial perceptions and ideas about a problem often shape the search process by which we evaluate these ideas. It is important to maintain objectivity in evaluating ideas so that we are not biased toward our initial perceptions.
Possible Solutions
Insufficiency of Hypotheses. Often when solving problems, a solver seizes upon the first explanation that comes to mind and stops thinking about the problem. This difficulty is related to confirmation bias, but reflects insufficient thought applied to a problem. Many times, the immediate answer is sufficient. Other times, however, only a careful analysis of a situation beyond the immediate response is necessary to ensure a correct solution.
Possible Solutions
Fixation. Fixation is the inability to see a problem
from a fresh perspective. Again, our initial perceptions and structuring
of a problem often determine the approaches we use to solve that
problem. Structuring a problem incorrectly is a prime contributor
to the inability to solve a problem correctly. The adage to see
a problem with "fresh eyes" is a statement of the importance
of viewing a problem from different perspectives.
Two examples of fixation are mental set and functional
fixedness. A mental set is the tendency to approach
a new problem with the same approach that worked previously for
different problems. While part of learning is developing effective
strategies for dealing with problems, the automatic or rote application
of a strategy to a problem can lead a person down the wrong path
and impede problem solving. Much of effective problem solving
lies in knowing which approach to use to solve the problem. Functional
fixedness is the tendency to view physical objects in terms
of their traditional uses. By doing so, we greatly limit the possibilities
for creative uses of objects in nontraditional ways. For example,
a hammer not only can be used for driving or removing nails, but
also serves as an effective paperweight, nutcracker, pendulum
weight, or murder weapon!
Possible Solutions
Other Obstacles. Problem solving can be impaired by biases of personal beliefs, a misunderstanding of information relevant to solving problems, and overconfidence. The solution is to study a problem objectively with all available accurate information and use objective reasoning to achieve a reasonable, sound decision.
Possible Solutions
Problem Solving Elements:
Understanding the Problem define it, consider
how it is similar to other problems previously solved, set goals,
identify variables
Gathering knowledge and information consider which
variables are critical, explore the relationships between variables,
considering different strategies for solving the problem
Generating Possible Solutions possibilities are dependent
on thinking style and skill plus the extent of the knowledge base
Choosing a Solution decision-making skills include developing criteria
to evaluate and rank possible solutions, the ability to identify
faulty premises, and a plan for testing hypothesis
Evaluating the Solution and Making Recommendations
identify alternative means for meeting project goals and generate
the seeds of continuing improvement
Increase Effectiveness when teaching by :
Help students learn to ask thorough questions and seek creative solutions
during the problem solving process.
Debriefings - teachers and students meet together in
a large group to review the problem. During this time, coach students
to reflect on the problem-solving processes used:
Textile Related Examples
At Philadelphia University, Problem Solving is a required class for senior Textile Technology students. In this class, students are provided with a current problem in the textile industry and work on different methods of solving the problem. This task requires development of problem solving skills, which are fostered through various methods. The students are first asked to brainstorm different solutions and write them down, no matter how outlandish they sound. This is performed individually, as a homework assignment so students can consider the problem and different solutions for several days, in order to fully think through the problem. The students and professor then meet and list all the different solutions to the problem. The various options are then discussed in detail, including potential advantages and disadvantages with each solution. Afterwards, the group decides upon the best ideas and proceeds to develop a plan of work and act upon the plan.
For example, one class sought alternatives to sending textile
scraps produced by a local robe manufacturer to a landfill. The
scraps varied in size, shape, and color. Ideas such as utilizing
the scraps for pet bedding, absorbent rags, insulation, mop material,
fire starter/artificial fireplace logs, and patchwork quilt fabric
were explored by the class. These ideas were discussed and narrowed
down based on economic feasibility, complexity of the processes
to convert the scraps for these uses, and marketing potential.
Once the list was narrowed down, the students created a plan of
work detailing how they would convert the scraps to different
usable products, such as a fire starting material/fireplace logs.
The students then commenced with their plan. During their hand-on
problem solving they often thought of alternative methods of accomplishing
their goal. Several of these different ideas were explored to
determine if problems encountered during the conversion process
could be overcome with new methods.
Resources:
-http://scholar.lib.vt.edu/ejournals/JTE/v7n2/wu.jte-v7n2.html#Heppner1
-Tain-Fung Wu, Rodney L. Custer, and Michael J. Dyrenfurth, "Technological and Personal Problem Solving Styles: Is there a Difference?", Digital Library and Archives, Journal of Technology Education, Volume 7, Number 2, Spring, 1996.
-B. Christopher Dougherty and Patti Fantaske, "Chapter 5: Defining Expectations for Problem-Solving Skills", Preparing Competent College Graduates: Setting new and Higher Expectations for Student Learning," Preparing Competent College Graduates: Setting New and Higher Expectations for Student Learning, Elizabeth A. Jones (ed.), volume 5, Number 96, 1996.
-http://www.hawaii.edu/suremath/why1Polya.html
Contains a step-by-step method for problem solving.
-http://mathcounts.org/Problems/strategies.html
Contains problem solving strategies and examples.