Stuck on a Problem? How to Unstick Yourself, Explained

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Stuck on a Problem? How to Unstick Yourself

Educational Psychology · Chapter 2: Memory, Thinking, and the Learning MindSection 2.11 · lesson 16 of 1009 min · free with a free account

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In this lesson

Problem spaces, algorithms, heuristics, and why impasse does useful work.

  • Distinguish well-defined from ill-defined problems
  • Explain the problem space model of Newell and Simon
  • Apply means-end analysis, working backward and analogical reasoning
  • Recognize functional fixedness and mental set as obstacles

Transcript

Everything said in the video, section by section (1,223 words). Read along, or search it.

Memory, Thinking, and the Learning Mind

Stuck on a Problem? How to Unstick Yourself

A student stares at a problem and says they do not know where to start. That sentence is more informative than it sounds. It usually means they have exactly one strategy, and it does not apply here. This section is about building a repertoire instead. We will cover algorithms, and why certainty comes at a price. Then three general heuristics that work when no algorithm exists. We will look at insight, and why being stuck is part of the mechanism. And at two obstacles that only afflict people who already know things. Functional fixedness, and mental set. The goal is a student who can say which strategy they chose, and why.

What Counts

When Routine Procedures Run Out

Problem-solving has a precise definition in cognitive psychology. It occurs when someone encounters a goal they cannot immediately reach. Cannot reach, that is, using routine procedures. If the routine works, it was never a problem in the technical sense. Psychologists split problems into two kinds. Well-defined problems have a clear initial state and a clear goal state. They also specify which operations are permitted. Ill-defined problems lack that structure entirely. The solver must impose organization before any systematic strategy applies. And here is the uncomfortable fact for curriculum design. Most real-world problems, and many academic ones, are ill-defined. So representing a problem is as important a skill as solving one.

Problem Space

Newell and Simon's Search Model

Newell and Simon gave us the dominant model, in the nineteen seventies. It comes from the information-processing tradition. The solver is described as navigating a problem space. A problem space is a mental representation of two things. All the possible states of the problem. And the operators that transform one state into another. Effective solvers search that space strategically rather than exhaustively. They use heuristics and algorithms to reduce how many states they explore. Now here is the finding that matters most for teaching. Experts differ from novices primarily in the richness of their representations. Not simply in their speed. Which means the fix for a struggling solver is rarely to go faster.

Trial And Error

The Simplest Strategy, and Its Place

Trial and error is the simplest strategy there is. Try possible solutions one at a time until one works. It is inefficient for complex problems, and everyone knows that. But inefficient is not the same as worthless. Trial and error is a valid strategy for simple or familiar problems. And it is the foundation of learning by doing. A child working out a puzzle is not doing anything illegitimate. So the teaching error is not letting students use trial and error. The teaching error is letting it remain the only strategy they have. That is what produces a student who tries the same thing repeatedly. They are not being stubborn. They have run out of repertoire.

Algorithms

Certainty, at the Cost of Generality

Algorithms sit at the opposite end. An algorithm is a step-by-step procedure that guarantees a correct solution. Guarantees, provided you follow it correctly. Arithmetic procedures are algorithmic. So are grammatical rules. So is balancing a chemical equation. The advantage of an algorithm is certainty, which is a real advantage. The disadvantage is that it requires specific applicable conditions. And it does not generalize to novel problems. Which creates a particular kind of dependency. A student who only has algorithms is fine until the problem is unfamiliar. Then they have nothing at all. Because the algorithm never told them what to do when no algorithm applies.

Heuristics

Three General Strategies Worth Teaching

Heuristics fill that gap. They are rules of thumb. General strategies that guide search through a problem space efficiently. But they do not guarantee success, and that is the trade. Three of them are worth teaching by name. Means-end analysis is one of the most powerful general heuristics. Identify the difference between the current state and the goal state. Then select an operator that reduces that difference. Repeat. Working backward starts at the goal and reasons toward the start. It is effective when the goal is clear but the path from the start is opaque. Analogical reasoning applies the structure of a solved problem to a new one. A new problem that is structurally similar, even if it looks different. Notice that all three are teachable in any subject.

Key Idea

A Repertoire, Plus the Judgment to Choose

Here is the key idea, and it has two halves. Effective problem-solvers have a repertoire of strategies. And they have the metacognitive awareness to select the right one. The second half is what makes the first half useful. A student with five strategies and no selection skill is not better off. Teaching explicit problem-solving strategies changes what students are. It also means teaching the conditions under which each is appropriate. Students move from passive responders to active, strategic thinkers. But there is a catch in how this gets taught. It cannot be taught by demonstrating solutions. A worked solution shows the strategy being used. It does not show the choice being made, which is the part they need.

Insight

Why Being Stuck Is Part of the Process

Insight is the strangest item in this section. It is the sudden experience of a solution appearing whole. A complete, clear realization. The aha moment. Researchers studying insight found something counter-intuitive about it. Insight often follows a period of impasse. During impasse the solver appears completely stuck. Conventional approaches have failed, and nothing is visibly happening. But something is happening. During impasse, the solver may unconsciously restructure the problem representation. They eventually arrive at a perspective from which the solution is obvious. Which reframes what being stuck actually is. The stuck period is not wasted time. It is where the restructuring happens.

Two Obstacles

Functional Fixedness and Mental Set

Two cognitive obstacles are worth naming, because both are counter-intuitive. Functional fixedness occurs when you can only see an object one way. In terms of its conventional use. That prevents recognizing its potential as a problem-solving tool. Mental set is the tendency to approach new problems with old strategies. Strategies that have worked in the past. It impedes solving whenever a novel approach is actually needed. Now notice what these two have in common. Neither obstacle afflicts someone who knows nothing. Both are produced by successful prior learning. Which means they can get worse with expertise, not better. So teachers should deliberately set problems that require reframing assumptions.

The Repertoire

Six Strategies and When to Use Them

Six strategies, and the useful part is knowing when each applies. Trial and error, for simple, familiar or highly constrained problems. Algorithms, for well-defined problems with a known structure. Means-end analysis, for complex problems with a clear goal. Working backward, when the goal is clear but the path is not. Analogical reasoning, for novel problems similar to ones already solved. And insight, for ill-defined problems that need conceptual reframing. Read that last column again, because it is the teachable part. Students rarely lack strategies entirely. They lack any basis for choosing between the ones they have.

In Practice

Coaching the Strategy, Not the Answer

Watch a teacher coach strategy rather than answer. A physics teacher presents a problem about bridge stability. The default student move is to reach for a formula immediately. She interrupts that sequence deliberately. First, identify what you know and what you need to find. That is means-end analysis, named or not. Second, search for a similar problem you have solved before. That is analogical reasoning. Only then does the formula get applied, as a chosen tool. So the recipe for building problem-solvers is short. Teach strategies explicitly, not just solutions. Ask students to name the strategy they used, and why they chose it. And value the process of reasoning as much as the final answer.

About Educational Psychology at UPI Study

Educational Psychology (Psychology 120) is a self-paced online course of 100 video lessons in 11 chapters, from memory, conditioning and child development to motivation, individual differences, assessment, instruction and educational technology. It carries a NCCRS credit recommendation for 3 semester credits.

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Why students take Educational Psychology with UPI Study

How people learn, and how to teach themEducational Psychology explains how students learn, develop and stay motivated, and how teachers assess and support them. It is a standard course in education and teaching degrees and a common psychology elective.
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130,000+students helped with college creditsACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.

Where the credit goes

Universities that work with NCCRS

Educational Psychology carries a NCCRS credit recommendation. These universities work with NCCRS; some are UPI Study's signed partners. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.

Thomas Edison State UniversityThomas Edison State UniversitySigned partnerUniversity of the PeopleUniversity of the PeopleSigned partnerCharter Oak State CollegeCharter Oak State CollegeSigned partnerStrayer UniversityStrayer UniversitySigned partnerColumbia Southern UniversityColumbia Southern UniversitySigned partnerIndiana TechIndiana TechSigned partnerPenn StatePenn StateWorks with NCCRSSouthern New Hampshire UniversitySouthern New Hampshire UniversityWorks with NCCRSSUNYSUNYWorks with NCCRS +many more cooperating universitiesFind my college →

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FAQ

Questions students ask us

About Stuck on a Problem? How to Unstick Yourself

What is the difference between well-defined and ill-defined problems?
A well-defined problem has a clear starting state, a clear goal and specified permitted operations, like a textbook equation. An ill-defined problem lacks that structure, so the solver must organize and represent it before any systematic strategy can work. Most real-world problems, and many academic ones, are ill-defined, which makes representing a problem as important a skill as solving it.
What is a problem space in Newell and Simon's theory?
In Allen Newell and Herbert Simon's information-processing model, a problem space is a mental representation of all the possible states of a problem and the operators that move from one state to another. Solving means searching that space. Effective solvers search strategically rather than exhaustively, and experts differ from novices mainly in the richness of their problem representations, not simply in speed.
What is the difference between an algorithm and a heuristic in problem solving?
An algorithm is a step-by-step procedure that guarantees a correct answer if followed correctly, like long division or balancing a chemical equation, but it needs specific conditions and does not generalize. A heuristic is a rule of thumb that guides search efficiently without guaranteeing success. Useful heuristics include means-end analysis, working backward from the goal, and reasoning by analogy from a solved problem.
What are functional fixedness and mental set?
Functional fixedness is seeing an object only in terms of its usual function, which hides its potential as a problem-solving tool. Mental set is the tendency to approach new problems with strategies that worked before, even when a new approach is needed. Both come from successful prior learning, so they can grow stronger with expertise. Problems that require reframing assumptions help students overcome them.

About the Educational Psychology course

How many college credits is Educational Psychology?
Educational Psychology (Psychology 120) carries a NCCRS credit recommendation for 3 semester credits. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
How much does Educational Psychology cost and what is included?
$250, paid once, with lifetime access: all 100 video lessons, a practice quiz after each, the graded work and final exam, and an official transcript when you finish. Students who want several courses choose UPI Study PRO instead.
Which universities accept UPI Study credits?
UPI Study has signed partner agreements with universities such as Thomas Edison State University, University of the People and Charter Oak State College, and works with universities such as Penn State, SNHU and SUNY. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities. Use "Find my college" on this page to check yours.
How long does Educational Psychology take?
It is self-paced with no deadlines. The 100 lessons total about 15 hours of video; most students add reading and practice time and finish in a few weeks to a few months, on their own schedule.
How are the exams done?
Quizzes and assignments are online in the course. The final exam is taken online with proctoring; a person on the UPI Study team checks assignments, usually within two days.
How do my credits reach my college?
When the course shows 100% complete, request the official transcript from your dashboard. It is sent to the college you name, and you can send it to more than one. Check your college first with "Find my college" on this page, or ask Athena.

Ready for the full course? Earn 3 credits in Educational Psychology.

100 video lessons, a quiz after each one, and the graded work that earns the credit. Recommended for credit by NCCRS.

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