Problem Solving Logic·Intermediate·4 lessons·47 practice activities·~280 min
Logic of Problem Solving: Goals, Constraints, and Strategy
How to reason from a problem state to a workable next move
What you'll learn
By the end of this unit, you can…
- Formalize problem state.
- Compare strategies.
- Name revision triggers.
- Revise plan under new information.
Lessons
Lesson sequence
- 1Open →
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.
- 2Student Pro
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.
- 3Student Pro
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.
- 4Student Pro
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.
How to study
Three moves that work for this unit
Read the explanation
Each lesson opens with a guided walkthrough — read it before the activity.
Study the worked example
Look at why each step follows, not just what the answer is.
Practice with the target in mind
Know which rule applies and what would make the response weak before you start.
Reference materials
Optional context for the unit. Each lesson surfaces the concepts and rules it uses — these are here when you want the bigger picture.
Concept map (7 terms)
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.
Rules and standards (4)
- 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 (2)
- Problem Map Schema. From practical_problem to structured_problem_map — 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..
- Decision Matrix. From multiple_candidate_solutions to criteria_based_comparison — 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..
Full mastery and assessment guidance
Mastery requirements
- Formalize problem state. Successful Problem Maps · 3_successful_problem_maps
- Compare strategies. Percent Consistent · 80_percent_consistent
- Name revision triggers. Successful Sets · 3_successful_sets
- Revise plan under new information. Successful Revisions · 2_successful_revisions
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.
Historical context (3)
- 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. Structured problem maps, heuristic checklists, and reflective strategy selection.
- 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). Constraint-sensitive planning and realistic decision tools that acknowledge bounded resources.
- 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. The modern language of states, operators, and search in AI and decision analysis comes directly from this framework.