IDEAL Problem-Solving Model¶

Strategy · All strategies
Evidence · 1 claim (1 for) · 3 studies (2 causal, 1 quant-synthesis), q3–q4 · 1 of 3 report an effect size

Description¶

IDEAL (Bransford & Steen, 1984) is a general problem-solving system usable across curriculum areas and problem types, named for its five stages:

1. Identify the problem — Learners confirm they know what the problem actually is and whether they have stated it clearly, before attempting a solution.
2. Define terms — Learners check that they understand what each word in the problem statement actually means.
3. Explore strategies — Learners compile relevant information and try out candidate strategies — drawing diagrams, working backward, or breaking a complex problem into manageable units.
4. Act on the strategy — Learners select one of the explored strategies and actually apply it.
5. Look at the effects — Learners ask themselves whether the result is an acceptable solution, closing the loop back to Identify if it is not.

Many other systems for teaching problem-solving exist for specific domains — general problem solving (Burkell, Schneider, & Pressley, 1990; Mayer, 1987; Sternberg, 1988), scientific thinking (Kuhn, 1989), mathematical problem solving (Schoenfeld, 1989), and writing at both the elementary (Harris & Graham, 1992) and adolescent (Applebee, 1984; Langer & Applebee, 1987) levels — but IDEAL's value is its explicit generality: unlike a domain-specific heuristic, it can be taught once and applied across curriculum areas (Pressley, 1995).

Design Implications¶

Context¶

Requirements¶

• A problem complex enough that jumping directly to a solution attempt is likely to fail or waste effort
• Willingness to have learners pause at each explicit stage rather than moving straight from reading a problem to attempting an answer
• Problems rich enough that the Identify and Define phases are non-trivial (ill-structured or multi-step tasks work better than single-step exercises)
• Prompts or graphic organizers that cue each IDEAL phase during early attempts
• Instructor modeling of the full cycle, including revising a failed approach during Look back
• Multiple problems from the same problem class so learners can practice the cycle repeatedly

Constraints¶

• The model's five stages are a general scaffold, not a domain-specific technique — for a specific problem type, a more specialized system (e.g., a mathematical problem-solving heuristic) may add value IDEAL alone does not
• General heuristics show weak transfer when taught in isolation from domain knowledge; learners need content knowledge to Explore meaningfully [-M]
• Overhead of the full cycle can exceed its benefit for simple, well-practiced problem types, where it adds cognitive load without improving solutions [-M]
• Learners may treat the steps as a ritual checklist rather than genuine analysis, especially if the phases are assessed only for completion [-W]
• Less effective for learners who already have strong domain-specific strategies, for whom the general framework is redundant [~W]

Target Learners¶

• Learners across a wide range of curriculum areas who need an explicit, transferable structure for approaching complex problems, rather than a domain-specific technique
• Novices who jump to solutions without representing the problem, producing pattern-matching errors [~M]
• Intermediate learners preparing for transfer to unfamiliar problem types, where the Look back phase builds analogical comparison habits Analogical reasoning improves transfer. [+M]
• Less useful for advanced learners with established domain strategies, who find the general cycle redundant [~W]

Target Learning Goals¶

• Applying a general, teachable problem-solving process to well- or ill-structured problems, per Well-Structured vs. Ill-Structured Problems
• Problem representation: translating a situation into a defined, solvable form
• Metacognitive regulation: planning, monitoring, and evaluating one's own problem solving

Instructions¶

1. Identify — Confirm the problem is correctly and clearly understood before proceeding.
2. Define — Check the meaning of each term in the problem statement.
3. Explore — Gather relevant information and generate candidate strategies (diagrams, working backward, decomposition into subproblems).
4. Act — Choose one strategy from those explored and apply it.
5. Look — Evaluate whether the outcome is an acceptable solution; if not, cycle back to Identify with the new information gained.

Related Strategies¶

• Task Analysis — both decompose a complex task, though task analysis targets prerequisite-skill sequencing rather than in-the-moment problem-solving
• Activating Prior Knowledge — the Explore phase depends on retrieving relevant prior cases and concepts
• Worked examples — a completed IDEAL cycle can be presented as a worked example for learners to study before attempting their own
• Problem-based learning — IDEAL provides the process scaffold that PBL cases often leave implicit
• Teach prompting as a five-part skill (role, task, audience, constraints, justification) with a structured ask-generate-evaluate cycle

Examples¶

• IDEAL in mathematics instruction: a teacher models the full cycle on a non-routine word problem, then students work in pairs on a structurally similar problem using an IDEAL organizer, comparing their representation to the modeled one afterward.
• Writing instruction: students apply Identify/Define to an essay prompt (what is actually being asked?), Explore two possible theses, draft, then Look back by checking the draft against the defined task.
• Engineering design courses: IDEAL maps onto the design cycle; students document each phase in a design notebook, with Look back entries requiring comparison to prior design problems.

Key Sources¶

• Bransford, J. D., & Stein, B. S. (1984). The IDEAL problem solver: A guide for improving thinking, learning, and creativity. W. H. Freeman.
• Pressley, M. (1995). More about the development of self-regulation: Complex, long-term, and thoroughly social. Educational Psychologist.
• Burkell, J., Schneider, B., & Pressley, M. (1990). Mathematics. In M. Pressley & Associates (Eds.), Cognitive strategy instruction that really improves children's academic performance. Brookline Books.
• Mayer, R. E. (1987). Educational psychology: A cognitive approach. Little, Brown.
• Sternberg, R. J. (1988). The triarchic mind: A new theory of human intelligence. Viking Penguin.
• Kuhn, D. (1989). Children and adults as intuitive scientists. Psychological Review, 96(4), 674-689.
• Schoenfeld, A. H. (1989). Teaching mathematical thinking and problem solving. In L. B. Resnick & L. E. Klopfer (Eds.), Toward the thinking curriculum: Current cognitive research (pp. 83-103). ASCD.
• Harris, K. R., & Graham, S. (1992). Self-regulated strategy development: A part of the writing process. In M. Pressley, K. R. Harris, & J. T. Guthrie (Eds.), Promoting academic competence and literacy in school. Academic Press.
• Applebee, A. N. (1984). Contexts for learning to write: Studies of secondary school instruction. Ablex.
• Langer, J. A., & Applebee, A. N. (1987). How writing shapes thinking: A study of teaching and learning. NCTE.
• Arduini-Van Hoose, N. (2020). Problem-solving. In Educational psychology. Retrieved from https://edpsych.pressbooks.sunycreate.cloud. CC BY-NC-SA 4.0.
• Bransford, J. D., & Stein, B. S. (1984). The IDEAL problem solver: A guide for improving thinking, learning, and creativity. W. H. Freeman.
• Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton University Press.
• Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.
• Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15(1), 1–38. doi:10.1016/0010-0285(83)90002-6