The document outlines the key steps and considerations in designing problem solving instruction for well-structured versus ill-structured problems. For well-structured problems, it recommends presenting conceptual models, worked examples, and practice problems with support. For ill-structured problems, it suggests articulating the context, constraints, developing case studies, supporting knowledge construction, argument building, and assessing solutions. The overall goal is to help learners effectively solve different types of problems.

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3. Unknown
Solution Problem domain
Problem
Problem-Solving
Problem Type
Process/Schema

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10. Problem schema activated
Construct
No schemas Search for Implement
Problem Succeed Stop
activated Solutions Solution
Representation
Fail

11. Problem schema activated
Construct
No schemas Search for Implement
Problem Succeed Stop
activated Solutions Solution
Representation
Fail
• WHAT DO I NEED TO PRODUCE HERE? WHAT IS AN ACCEPTABLE SOLUTION
GOING TO LOOK LIKE? WHAT ARE THE GIVENS?
• DECOMPOSE PROBLEM STATEMENT AND MAP PROBLEM TO PRIOR
KNOWLEDGE
• IF LEARNER POSSESSES COMPLETE SCHEMA, PROBLEM CAN BE MAPPED ONTO
PROBLEM SCHEMA
• “EXPERTS ARE BETTER PROBLEM SOLVERS BECAUSE THEY RECOGNIZE DIFFERENT
PROBLEM STATES WHICH INVOKE CERTAIN SOLUTIONS” (SWELLER, 1988).

12. Problem schema activated
Construct
No schemas Search for Implement
Problem Succeed Stop
activated Solutions Solution
Representation
Fail
Recall Analogical Means-End Decomposing and
Generate/Test
Problems Analysis Simplifying
•Very natural step; •Isolate goals to •Break down •Least structured
usually 1st be achieved and problem into and weakest
method select means to subproblems method
•Have I achieve goals •Brainstorm
experienced a •What is the most possible solutions
similar problem? important
difference?
Reduce
discrepancies
•Impedes schema
acquisition;
should focus
selectively on
aspects of
problem

13. Problem schema activated
Construct
No schemas Search for Implement
Problem Succeed Stop
activated Solutions Solution
Representation
Fail
• TEST PROCEDURES: IF SOLUTION WORKS, PROBLEM IS SOLVED; IF SOLUTION
FAILS TO WORK, LEARNER GENERATES NEW HYPOTHESIS
• IDENTIFYING CLUES FROM FAILED ATTEMPTS AND USING THEM IS DIFFICULT

14. Designing and Developing Well-Structured
Problem Solving Instruction
 Step 1: Review Prerequisite Component
Concepts, Rules, and Principles
 Step 2:Present Conceptual or Causal
Model of Problem Domain
 Step 3: Model Problem Solving
Performance in Worked Examples
 Step 4: Present Practice Problems
 Step 5: Support the Search for Solutions
 Step 6: Reflect on Problem State and
Problem Solution

15. Identify and Clarify
Articulate Problem Alternative Opinions,
Generate Possible
Space and Contextual Positions, and
Problem Solutions
Constraints Perspectives of
Stakeholders
Assess Viability of
Alternative Solutions by
Implement and Monitor Monitor Problem Space
Constructing Arguments
Solution and Solution Options
and Articulating Personal
Beliefs
Adapt Solution

16. Identify and Clarify
Articulate Problem Alternative Opinions,
Generate Possible
Space and Contextual Positions, and
Problem Solutions
Constraints Perspectives of
Stakeholders
Assess Viability of
Alternative Solutions by
Implement and Monitor Monitor Problem Space
Constructing Arguments
Solution and Solution Options
and Articulating Personal
Beliefs
• DOES A PROBLEM REALLY EXIST? WHAT IS THE NATURE OF THE
PROBLEM?
• MAY HAVE MULTIPLE REPRESENTATIONS OR UNDERSTANDINGS
Adapt Solution
• THINK ABOUT PROBLEM AS REALISTIC SITUATIONS

17. Identify and Clarify
Articulate Problem Alternative Opinions,
Generate Possible
Space and Contextual Positions, and
Problem Solutions
Constraints Perspectives of
Stakeholders
Assess Viability of
Alternative Solutions by
Implement and Monitor Monitor Problem Space
Constructing Arguments
Solution and Solution Options
and Articulating Personal
Beliefs
• CONSTRUCT MULTIPLE PROBLEM SPACES DEPENDING ON SITUATION
• DECIDE WHICH PROBLEM SCHEMA IS MOST RELEVANT AND USEFUL
FOR SOLVING THE PROBLEM (SINNOTT, 1989)
Adapt Solution
• PERCEIVE AND RECONCILE DIFFERENT INTERPRETATIONS OF
PHENOMENA

18. Identify and Clarify
Articulate Problem Alternative Opinions,
Generate Possible
Space and Contextual Positions, and
Problem Solutions
Constraints Perspectives of
Stakeholders
Assess Viability of
Alternative Solutions by
Implement and Monitor Monitor Problem Space
Constructing Arguments
Solution and Solution Options
and Articulating Personal
Beliefs
• MULTIPLE SOLUTIONS BECAUSE THERE ARE MULTIPLE
REPRESENTATIONS OF THE PROBLEM
• GENERATING SOLUTIONS IS A CREATIVE PROCESS AND RELIES ON
UNRELATED THOUGHTS AND EMOTIONS (SINNOTT, 1989)
Adapt Solution

19. Identify and Clarify
Articulate Problem Alternative Opinions,
Generate Possible
Space and Contextual Positions, and
Problem Solutions
Constraints Perspectives of
Stakeholders
Assess Viability of
Alternative Solutions by
Implement and Monitor Monitor Problem Space
Constructing Arguments
Solution and Solution Options
and Articulating Personal
Beliefs
• SOLUTION SHOULD ASSUME FORM OF AN ARGUMENT FOR A
PREFERRED SOLUTION
• SELECT/CONSTRUCT VIABLE SOLUTION, REFLECT, AND JUSTIFY
Adapt Solution

20. Identify and Clarify
Articulate Problem Alternative Opinions,
Generate Possible
Space and Contextual Positions, and
Problem Solutions
Constraints Perspectives of
Stakeholders
Assess Viability of
Alternative Solutions by
Implement and Monitor Monitor Problem Space
Constructing Arguments
Solution and Solution Options
and Articulating Personal
Beliefs
• REFLECT NOT ONLY ON WHAT YOU KNOW, BUT ALSO ON WHAT I
MEANS
• CONSIDER WHAT OTHERS BELIEVE AND DEVELOP ARGUMENTS TO
SUPPORT MENTAL MODEL OF PROBLEM SPACE
Adapt Solution

21. Identify and Clarify
Articulate Problem Alternative Opinions,
Generate Possible
Space and Contextual Positions, and
Problem Solutions
Constraints Perspectives of
Stakeholders
Assess Viability of
Alternative Solutions by
Implement and Monitor Monitor Problem Space
Constructing Arguments
Solution and Solution Options
and Articulating Personal
Beliefs
• MONITOR PERFORMANCE OF ELEMENTS IN PROBLEM TO SEE HOW
THEY PERFORM
Adapt Solution

22. Identify and Clarify
Articulate Problem Alternative Opinions,
Generate Possible
Space and Contextual Positions, and
Problem Solutions
Constraints Perspectives of
Stakeholders
Assess Viability of
Alternative Solutions by
Implement and Monitor Monitor Problem Space
Constructing Arguments
Solution and Solution Options
and Articulating Personal
Beliefs
• TRY OUT SOLUTION IF POSSIBLE
• PROBLEM SOLVERS RECOMMEND SOLUTION AND ADJUST AND
ADAPT IT BASED ON FEEDBACK
Adapt Solution

23. Designing and Developing Ill-Structured
Problem Solving Instruction
 Step 1: Articulate Problem Context
 Step 2: Introduce Problem Constraints
 Step 3: Locate, Select, and Develop
Cases for Learners
 Step 4: Support Knowledge Base
Construction; Cognitive Flexibility Theory
(Spiro, 1987)
 Step 5: Support Argument Construction
 Step 6: Assess Problem Solutions