1. Read the model first
Each lesson opens with a guided explanation so the learner sees what the core move is before any saved response is required.
Problem Solving Logic
Logic of Problem Solving: Goals, Constraints, and Strategy
How to reason from a problem state to a workable next move
Students learn to formalize practical problems, identify goals and constraints, compare candidate strategies, and justify a plan of action without pretending that every problem has a single certain answer. The unit builds from problem analysis through strategy selection to disciplined revision under new information.
Study Flow
How to work through this unit without overwhelm
2. Study an example on purpose
The examples are there to show what strong reasoning looks like and where the structure becomes clearer than ordinary language.
3. Practice with a target in mind
Activities work best when the learner already knows what the answer needs to show, what rule applies, and what mistake would make the response weak.
Lesson Sequence
What you will work through
Lesson 1
Understanding the Problem Before Solving It
Introduces problem states, goal states, and constraints as the backbone of disciplined practical reasoning, and establishes the habit of describing the problem before proposing a solution.
Start with a short reading sequence, study 1 worked example, then use 15 practice activitys to test whether the distinction is actually clear.
Guided reading1 worked example15 practice activitys
Lesson 2
Building a Structured Problem Map
Teaches students to formalize practical reasoning into goals, constraints, candidate strategies, and a justified next step, using an explicit problem map that can be written down and critiqued.
Read for structure first, inspect how the example turns ordinary language into cleaner form, then complete 15 formalization exercises yourself.
Guided reading1 worked example15 practice activitystranslation support
Lesson 3
Choosing and Revising a Strategy
Explains how to choose between strategies, track tradeoffs, and revise a plan when new information appears, including the discipline of naming revision triggers in advance.
Use the reading and examples to learn what the standards demand, then practice applying those standards explicitly in 15 activitys.
Guided reading1 worked example15 practice activitysstandards focus
Lesson 4
Capstone: Running the Full Problem-Solving Loop
An integrative lesson that asks students to take a real problem description, model it, generate candidate strategies, commit to one, build in revision triggers, and write a short postmortem plan for how they will know whether to revise.
Each lesson now opens with guided reading, then moves through examples and 2 practice activitys so you are not dropped into the task cold.
Guided reading1 worked example2 practice activitys
Rules And Standards
What counts as good reasoning here
Clarify the Goal Before Choosing a Strategy
A strategy cannot be assessed well until the goal state is explicit and specific enough to recognize success.
Common failures
- The learner starts proposing solutions before identifying the actual goal.
- The target outcome remains vague or shifts during the analysis.
Respect Constraints
A proposed solution must fit the relevant time, resource, and rule constraints of the problem.
Common failures
- The plan assumes resources that are not available.
- The solution ignores explicit limitations or requirements.
Compare Options Explicitly
A good practical judgment weighs at least two plausible options before committing to a path.
Common failures
- Only one option is considered.
- The chosen path is asserted without comparison or tradeoff analysis.
Build In Revision Triggers
A good plan names the observations that would justify revising or abandoning it.
Common failures
- The plan has no stopping or revision conditions.
- The reasoner continues executing the plan even when obvious failure signals appear.
Formalization Patterns
How arguments get translated into structure
Problem Map Schema
Input form
practical_problem
Output form
structured_problem_map
Steps
- State the current problem state.
- State the goal state.
- List key constraints and available resources.
- List candidate strategies.
- Compare the strategies against the goal and constraints.
- Choose the best next step and name its revision triggers.
Common errors
- Skipping the constraint analysis.
- Treating a first idea as if it were already the best option.
- Confusing the final goal with the immediate next action.
Decision Matrix
Input form
multiple_candidate_solutions
Output form
criteria_based_comparison
Steps
- Identify at least two candidate strategies.
- Name the criteria for judging them (goal fit, constraint fit, cost, risk, reversibility).
- Compare how each option handles the criteria.
- Identify tradeoffs.
- State the most reasonable current strategy and the conditions that would reopen the comparison.
Common errors
- Choosing without explicit criteria.
- Ignoring obvious tradeoffs.
- Treating a provisional choice as irreversible.
Concept Map
Key ideas in the unit
Problem State
The current situation that must be understood before a reasonable plan can be formed, including what is known, what is unknown, and what has already been tried.
Goal State
The outcome or condition the reasoner is trying to reach, stated clearly enough to tell whether a proposed solution would actually produce it.
Constraint
A limitation, requirement, or condition that shapes which solutions are acceptable — time, budget, rules, resources, or policies.
Resource
Anything the reasoner can draw on to move toward the goal, including time, money, tools, information, or help from others.
Strategy Selection
The process of comparing available approaches and choosing the one that best fits the problem, given the goals and constraints.
Decision Revision
Updating a plan when new information shows that the original path is incomplete, inefficient, or blocked.
Revision Trigger
A specific observation or event that would signal the plan needs to change.
Assessment
How to judge your own work
Assessment advice
- Have I clearly separated the current problem state from the goal state?
- What constraints could block an otherwise attractive solution?
- Could a stranger tell from my description whether the goal has been reached?
- Describing the goal vaguely enough that any action seems acceptable.
- Omitting constraints that are inconvenient to mention.
- What exactly is my next action, and why is it better than the alternatives?
- Do my options genuinely fit the stated constraints?
- Can I name the tradeoff I'm accepting?
- Confusing a broad aspiration with an executable next step.
- Pretending a chosen strategy has no tradeoffs.
- What tradeoff am I accepting by choosing this strategy?
- What future information would make me revise the plan?
- Am I confusing turbulence with real failure?
- Presenting a provisional strategy as if it were certain or final.
- Writing vague revision triggers ('if things go wrong').
- Did I model the state, goal, and constraints explicitly?
- Did I name at least two revision triggers with thresholds?
- Can I say how I will judge whether my strategy worked?
- Letting commitment become stubbornness because no trigger was set.
- Treating the first viable strategy as the only one.
Mastery requirements
- Formalize Problem State
- Compare Strategies
- Name Revision Triggers
- Revise Plan Under New Information
History Links
How earlier logicians shaped modern tools
George Polya
In How to Solve It (1945), developed influential heuristics for understanding problems, planning solutions, carrying out a plan, and looking back. Polya's four-stage approach remains the backbone of modern problem-solving pedagogy.
Herbert Simon
Showed that real problem solving happens under limits of information, time, and attention — 'bounded rationality.' He distinguished 'satisficing' (finding an option that meets the criteria) from 'optimizing' (finding the best option).
Allen Newell and Herbert Simon
Formulated the 'problem space' framework: problem solving as moving through a state space by applying operators from initial state to goal state, subject to constraints.