Problem solving is
a specialized skill that is performed within a specific content area.
Problem solving is the ability to take previously acquired knowledge,
procedures, principles, and cognitive strategies to solve unencountered
problems. Problem solving can be simple or complex. Simple problem solving
tasks have fewer principles to consider and possess more clarity than
complex problem solving situations. There are two types of problems found
in problem solving: well-defined and ill-defined. Well-defined problems
have clear given and goal states while ill-defined problems have vague,
unknown or situation dependent given and goal states.
To be able to solve
problems within a domain students must be able to apply principles, declarative
knowledge, and cognitive strategies. These types of knowledge are used
to support the four components of cognitive processing in problem solving:
develops a representation of the problem by breaking it down into smaller
problems. In well-defined problems the learner identifies a plan that
could be used to solve the problem.
taking relevant knowledge and using it to develop a method to solve the
problem. In well-defined problems it is making sure you have selected
the correct plan to solve the problem.
stage the learner is testing out the method they have developed to solve
the problem or they are seeing if they have correctly identified the right
plan to solve the problem.
stage the learner confirms whether or not their solution solved the problem.
There are different
conditions in which problem solving can take place but in all conditions
the following stages often occur.
Clarify the given state
2. Clarify the goal state
3. Search for relevant prior knowledge, principles, and cognitive strategies
that will aid in solution.
4. Determine if the conditions and goal state imply a known set of problems.
5. Decompose the problems into known subproblems with subgoals.
6. Determine the sequence for attacking the subproblems.
7. Consider possible solutions to each subproblem.
Here are some ways
that instruction events can be adapted when teaching problem solving.
can be presenting an interesting and challenging problem that students
will learn to solve and by beginning to establish instructional purpose.
Use graphics or a video to present the problem; it will increase student
purpose can be established by the instructors describing the problems
that the students will learn to solve or if they have all ready presented
the problem during the attention getting stage they can show how this
problem is representative of the set of problems to be learned.
promote interest show how problem solving in this domain can be helpful
in solving everday problems.
preview the lesson tell students about the problems that they will be
going through and preview the strategies that will be employed.
activate prior knowledge, instructors should review declarative knowledge
related to this area, review general problem solving strategies, and
review the type and source of principles related to this problem.
The instruction during the information processing stage can be conducted
using either a supplantitive approach or a generative approach. The
approach used depends on the problem solving skills of your students.
The supplantitive approach should be used for inexperienced problem
solvers and the generative approach should be used for experienced ones.
Regardless of which approach is used the following aspects of presentation
of information and processing must take place.
1. Presentation of the problem
2. Recognition of Problem Space
3. Instruction of selecting appropriate principles
instructor can use guiding questions or direct statement to focus the
learners attention on aspects of the problem, relevant principles or
problem solving strategies.
that teachers provide to assist learners could consist of any of the
following: alternate ways or representing a problem, ways of limiting
the numbers of alternative approaches, hints at the form of the solution
or subsolutions, search strategies, monitoring techniques, mental imagery
tactics, job aids or graphics, generic strategies or specific strategies
for representing problems or retrieving solutions for that domain.
students have come up with the solution to an example problem, they
should practice solving problems of similar difficulty. Practice should
be provided so that knowledge can be reorganized and elaborated to support
problem solving, pattern recognition skills become automatic, identification
of subgoals and principles become automatic, and selection and application
of strategies in automatic.
may be provided in the form of hints or guiding questions if the learner
is having difficulty. Feedback should also include comments on the learners
choice of solution and how effective the solution was.
summarize and review the lesson instructors should review the characteristics
of problems that can be solved in a similar manner, summarize effective
strategies for this domain of problems, and suggest methods of remembering
the strategy used.
and conclusion of the lesson can be generated by the learners or provided
by the instructors in the form of a reminder of the what they have learned
in this lesson and how it is useful.
assess problem solving skills the instructor should have the students
solve problems in the area that they have been working in.
There are eight different
macrostrategies that can be used to assist the learning of problem solving.
This is a method of teaching where a student is guided through the
problem solving process through interaction with a expert or mentor who
provides instances and guiding questions.
Computer programs that are able to solve problems within a limited
domain when given data.
This macrostrategy involves the presentation of carefully sequence
activitity that attempts to mimic the essential features of reality but
allows learners to make decisions within this reality without suffering
real world consequences. Simulations are often computer-based.
to a simulation except that instead of being a representation of something
a microworld is constructed by the learner.
Case studies: These
present a realistic situation and require learners to respond as if they
were the person solving the problem.
Problem based learning:
An approach to instruction that structures courses and entire curricula
on problems rather than subject content.
A method of teaching that places a learner in an authentic working
environment as a partial participant
To show an example
of how a strategy to teach problem solving might be used. I have provided
a lesson that teaches problem solving that is located on PBS Teachersource.
Given the four basic principles of flight, students will develop an airplane
capable of flight.
gain student attention and arouse interest use the video segment entitled
"The French Hero" (timecode: 10:50 - 16:00) from episode 1
of "Chasing the Sun." In the segment, French aviator Louis
Bleriot makes many unsuccessful plane flights before finally discovering
a design that helps him become the first person to cross the English
Channel. After the segment, begin a discussion with students about what
they feel makes for a good plane design. Why is it that certain designs
work, while others fail? How important is the process of trial and error
in experimentation? Write some of their responses on the chalkboard.
During the discussion, introduce the four basic principles of flight:
Gravity, Drag, Thrust, and Lift. How does a plane's design influence
its ability to produce lift? How do its engines produce thrust?
establish the instructional purpose and preview the lesson explain to
the class that, like Louis Bleriot, they are going to test several different
airplane designs. After testing and modification of their designs, they
will decide which is the best, and then compete against other students
with their planes.
the process stage, divide the class into groups of four to five students.
Provide instructions on how to construct several different types of
paper airplanes. Have each group work on one design. They will construct
several prototypes and conduct testing within their group. Instruct
the students to create a data chart and record their distances and times
of flight for each of their prototypes during all of their test flights.
The students in each group will select their best plane to submit for
the class competition. One representative from each group will line
up and after a count down of 3-2-1 they will release their planes. After
the test flights, the class will create a new data sheet and record
the flight times and distances for each group's different type of planes.The
students will return to their small groups and make modifications using
the scissors, tape and paper clips. After another round of prototype
testing, the group will select a different student to take their best
entry to the class' final airplane competition.
practice the problem solving have students to develop their own types
of plane using the four principles of flight and have them test their
designs and record the data or have them take their planes outside to
see how wind currents affect their flight designs.
summarize and close the lesson have the students discuss their results
and modifications in both the small group and class setting.
assess the students knowledge of the material have the students turn
in their data sheets and a written analysis of the data they collected.
collected and evaluated for completeness, accuracy and level of understanding.
the data sheets and analysis for completeness, accuracy, and level of