STRATEGIES FOR PROBLEM SOLVING INSTRUCTION

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:

Problem Representation: The learner 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.

Solution Planning: This involves 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.

Solution Implementation: During this 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.

Solution Evaluation: During this 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.

1. 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.

1. Introduction

Attention 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 interest.
Instructional 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.
To promote interest show how problem solving in this domain can be helpful in solving everday problems.
To preview the lesson tell students about the problems that they will be going through and preview the strategies that will be employed.

2. Body

To 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

The instructor can use guiding questions or direct statement to focus the learners attention on aspects of the problem, relevant principles or problem solving strategies.
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.
Once 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.
Feedback 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.

3. Conclusion

To 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.
Remotivation 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.

4. Assessment

To 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.

Socratic Dialogue: 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.

Expert Systems: Computer programs that are able to solve problems within a limited domain when given data.

Elaboration Model: This macrostrategy involves the presentation of carefully sequence problem sets.

Simulations: An 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.

Microworlds: Similar 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.

Cognitive apprenticeships: 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.

http://www.pbs.org/kcet/chasingthesun/resources/resources_lesson_2.html

Objective:
Given the four basic principles of flight, students will develop an airplane capable of flight.

1. Introduction

To 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?
To 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.

2. Body

During 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.
To 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.

3. Conclusion

To summarize and close the lesson have the students discuss their results and modifications in both the small group and class setting.

4. Assessment

To 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.
Evaluate the data sheets and analysis for completeness, accuracy, and level of understanding.