Four-step heuristic worked example model for mathematical modeling with dialogical fictitious-student examples¶

Design · All designs
Evidence · 2 claims (2 for) · 1 study (1 causal), q3 · 1 of 1 report an effect size · 2 claims rest on one study

Description¶

The article advances a four-step account of mathematical modeling linked to Polya's steps: "(1) understand the problem, (2) mathematize it, (3) work mathematically, and (4) explain the result." Heuristic worked examples are built on this structure, presenting dialogues between two fictitious students who negotiate solutions across the four phases, make realistic attempts, "go a little wrong sometimes, discuss their detours and mistakes, but ultimately demonstrate adequate strategies." This erroneous-elements design is intended to support active processing and sensitize students to pitfalls, while the dialogue simulates expert modeling and scaffolds the problem-solving process.

Design Implications¶

Context¶

Requirements¶

Worked examples segmented into the four modeling sections with a standard strategic scheme across varying surface characteristics
Fictitious students must ultimately solve the problem adequately, since erroneous examples benefited only high-prior-knowledge learners in the cited work

Constraints¶

The study operationalized the model on concrete content areas (basic numeracy, plane geometry, linear functions), so results must be interpreted against those domains
Intervention duration was a single 45-minute period, so effects reflect initial learning rather than comprehensive competency

Target Learners¶

lower secondary school students in Grades 5 and 7

Learning Goals¶

mathematical modeling competency for reality-based tasks
modeling-specific strategy knowledge and metacognitive self-regulation

Claims¶

Examples¶

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Key Sources¶

Hänze, M., & Leiss, D. (2022). Using heuristic worked examples to promote solving of reality-based tasks in mathematics in lower secondary school. Instructional Science. https://doi.org/10.1007/s11251-022-09583-8

Page metadata

Field	Value
`type`	`design`
`id`	`four-step-heuristic-worked-example-model-modeling`
`title`	`Four-step heuristic worked example model for mathematical modeling with dialogical fictitious-student examples`
`description`	`The article advances a four-step account of mathematical modeling linked to Polya's steps: "(1) understand the problem, (2) mathematize it, (3) work mathematically, and (4) explain the result." Heuristic worked exampl...`
`status`	`review`
`generated`	by `process:settle-candidates` on `2026-10-18`
`trust`	unverified — no one has confirmed this page's content
`sources`	1 — `hänze-2022`

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