Problem Solving¶

Strategy · All strategies
Evidence · 3 claims (1 for, 1 mixed, 1 against) · 7 studies (4 causal, 2 quant-synthesis, 1 review), q2–q4 · 2 of 7 report an effect size

Description¶

Problem solving involves designing activities that require learners to come up with solutions — ways of dealing with issues or challenges they can apply back on the job. Learners are presented with a problem (ideally authentic and ill-structured), investigate it, and construct, test, and defend a solution. The process of determining a solution is where deep learning occurs: learners must organize knowledge around the problem's structure rather than recall isolated facts Hmelo-Silver's review of problem-based learning [+M].

Design Implications¶

Problem solving works because generating a solution forces retrieval, elaboration, and integration of knowledge — but only when learners have sufficient prior knowledge to search productively. Unguided problem solving with novices can overload working memory and produce minimal learning Minimal guidance during instruction is less effective for novices than guided instruction. [-S]. The design task is therefore to structure the problem, the scaffolds, and the debrief — not just to present a challenge and step back.

Context¶

Requirements¶

• An authentic problem with genuine stakes and multiple defensible approaches; well-structured problems (single correct answer, known procedure) reduce the activity to routine exercise
• Sufficient prior knowledge, activated before or during the task (Activation)
• Access to resources learners can consult: reference material, data, or experts
• A facilitator who coaches rather than lectures, and a structured debrief that consolidates what the solution process taught (Coaching, Class Discussion)
• Assessment criteria that evaluate solution quality and reasoning, not just outcome match (Assessment)

Constraints¶

• Novices without domain schemas engage in means-ends search that consumes working memory without building knowledge Cognitive overload degrades learning when element interactivity exceeds working memory capacity. [-S] — pair early problem solving with worked examples or strong scaffolds
• Ill-structured problems with no debrief leave learners with fragmented, idiosyncratic takeaways; the learning is in the comparison and consolidation, not the struggle alone
• Problems far removed from learners' context produce engagement without transfer; relevance is a precondition, not a nice-to-have
• Group problem solving without individual accountability allows free-riding and dilutes each learner's generative effort

Implementation Variability¶

• Problem-based learning (PBL): problem precedes instruction; learners identify knowledge gaps, then learn to fill them (medical education model)
• Productive failure: learners attempt problems before instruction, then compare their solutions to canonical ones; exploration prior to instruction can deepen subsequent learning even when initial attempts fail Prior activation and exploration can prepare learners to learn from instruction. [~M]
• Case-based problem solving: learners analyze and resolve problems embedded in real cases (Case Studies)
• Worked-example-to-problem fading: full solutions are progressively faded into independent problem solving as expertise grows

Target Learners¶

• Intermediate learners with foundational knowledge who can search productively; pure novices need scaffolding or worked examples first Minimal guidance is less effective for novices but beneficial as expertise develops. [~S]
• Adult and professional learners, for whom authentic job-relevant problems supply motivation and transfer context
• Less effective for learners with no relevant prior knowledge, who lack the schemas needed to constrain search

Target Learning Goals¶

• Applied and transfer goals: using knowledge to handle novel, ill-structured situations (Application of Knowledge)
• Strategic and metacognitive goals: monitoring one's own solution process, recognizing when an approach is failing
• Integration goals: connecting concepts across topics as the problem demands, rather than learning them in isolation

Instructions¶

1. Select or construct an authentic problem aligned to performance goals; verify it is ill-structured enough to require reasoning, not recall.
2. Activate relevant prior knowledge before or at the start of the attempt (Activation).
3. Present the problem with necessary resources and constraints; for novices, provide a worked example of a similar problem first.
4. Have learners investigate, generate, and test candidate solutions — individually or in accountable groups (Application).
5. Facilitate with questions and hints rather than answers (Coaching); escalate support only when learners stall.
6. Debrief: compare solution approaches across learners or against an expert solution, and name the principles the problem illustrated (Class Discussion).
7. Follow with a second, structurally similar problem to consolidate the schema (Analogical Reasoning).

Related Strategies¶

• Case-Based Learning — problems embedded in narrative cases; supplies the authenticity problem solving needs
• Productive Failure — a specific sequencing of problem solving before instruction

Related Elements¶

• Coaching — the facilitation stance that keeps problem solving guided without taking over
• Application — the generative act at the core of the strategy
• Case Studies — a common vehicle for delivering the problem
• Assessment — rubrics must evaluate reasoning and solution quality, not just correctness

Patterns That Use This Strategy¶

• Case-Based Learning — the Harvard method centers discussion on resolving a real problem
• Cognitive Apprenticeship — problem solving is the phase where learners act with coaching support
• Anchored Instruction — the anchor is a rich problem context (e.g., the Jasper Woodbury series)

Affordances¶

• Active Learning — problem solving is a maximal form of active learning: learners generate, test, and revise rather than receive
• Cognitive Load Management — well-designed problems manage element interactivity through scaffolds and resource access; poorly designed ones exceed working memory
• Analogical Reasoning — solving a sequence of structurally similar problems builds the schema that enables transfer

Examples¶

• Problem-based learning in medical education — small groups work through a patient case (e.g., Maastricht University's PBL curriculum), identifying learning issues before consulting resources; see Hmelo-Silver (2004).
• Jasper Woodbury Problem Solving series — video-anchored mathematical adventure problems requiring students to plan trips and budgets (https://peabody.vanderbilt.edu).
• Harvard Business School case method — students must take a position and defend a decision on a real management problem in every class session.

Key Sources¶

• Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48(4), 63–85. doi:10.1007/BF02300500
• Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235–266. doi:10.1023/b:edpr.0000034022.16470.f3
• Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75–86. doi:10.1207/s15326985ep4102_1
• Kapur, M. (2008). Productive failure. Cognition and Instruction, 26(3), 379–424. doi:10.1080/07370000802212669
• Sweller, J., van Merriënboer, J. J. G., & Paas, F. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10(3), 251–296. doi:10.1023/a:1022193728205