Word Problem Creation¶

Strategy · All strategies
Evidence · 3 claims (2 for, 1 mixed) · 8 studies (3 causal, 2 quant-synthesis, 2 review, 1 associational), q2–q4 · 1 of 8 report an effect size · 1 claim rests on one study

Description¶

Learners author their own multistep word problems — choosing the operations, contexts, and quantities — and exchange them with peers to solve. Problem creation reverses the usual direction of instruction: instead of interpreting someone else's problem, learners must construct the underlying mathematical structure themselves, then communicate it in readable prose. The strategy integrates mathematics and literacy and can be applied across strands (operations, geometry, statistics, measurement).

Design Implications¶

Writing a problem requires the learner to invert the solution process — to reason backward from a desired answer or relationship to a solvable question — which engages deeper structural understanding than solving alone Problem posing supports learners' understanding of mathematical structure. [+M]. Because learners must anticipate how a reader will interpret their text, the task also builds precision of mathematical language and attention to what information is necessary, extraneous, or misleading.

Context¶

Requirements¶

• Sufficient prior exposure to solved word problems so learners have models of the genre's structure (Demonstration of an example problem and its solution first)
• Tools for writing and computing (paper, calculators), and structured time for drafting, exchanging, solving, and revising
• Clear constraints (allowed operations, number ranges, number of steps) so problems remain solvable at the target level
• A feedback loop in which peer solvers' success or confusion becomes information for the author's revision

Constraints¶

• Without worked models and constraints, learners often produce trivial, ambiguous, or unsolvable problems, wasting the exchange cycle [-M]
• Learners with weak reading or writing fluency may spend most of their effort on prose rather than mathematics, obscuring the math learning goal [~M]
• If authors never see their problems solved, misconceptions embedded in the problems go undetected [-M]
• Backward construction is demanding; for novices it can exceed working memory if operation choice, context, and numbers are all unconstrained Chunking reduces working memory load. [~M]

Implementation Variability¶

• Answer-first variant: give learners an answer and ask them to write the problem that leads to it — a strong structure-reversal format
• Story framing: learners embed the problem in a narrative, integrating literacy goals
• Constraint cards: learners draw required operations or contexts (e.g., "must include division and a unit conversion") to scaffold selection
• Error-hunting variant: peers solve, then critique the problem for ambiguity or missing information, feeding into Peer Discussion

Target Learners¶

• Upper elementary through high school students who have some fluency with the target operations
• Learners who have mastered routine solving and need a task that pushes toward structural reasoning; complete novices benefit more from solving and studying examples first Example–problem sequences reduce cognitive load for novices. [+M]
• Reluctant writers often engage more when writing serves a real audience — a peer who will actually solve the problem (Authentic Audiences & Purposes)

Target Learning Goals¶

• Applying operations in real-world contexts and translating between situations and symbolic expressions
• Understanding problem structure (knowns, unknowns, relationships, necessary vs. extraneous information)
• Mathematical communication and precision of language
• Peer assessment: judging whether a problem is clear, solvable, and appropriately difficult

Instructions¶

1. Model the genre: solve and deconstruct one or two example word problems, naming the parts (context, given information, question, required operations) — Demonstration
2. Set constraints: specify allowed operations, number of steps, and number ranges appropriate to learners' level
3. Learners draft an individual problem and verify it is solvable by solving it themselves — Application and Individual Response
4. Learners exchange problems and solve a peer's problem, noting any ambiguity or errors
5. Authors revise based on solver feedback, then the class discusses what made problems clear or confusing — Peer Discussion

Related Strategies¶

• Problem-solving with worked examples — solving and creating are complementary; creation works best after example study
• Peer review and critique — the exchange-and-revise cycle is a form of structured peer assessment
• Require authors to solve their own created levels before publishing, as a quality filter and a learning act in itself.

Related Elements¶

• Application — authoring is an application task requiring transfer of operations to novel contexts
• Peer Discussion — solver feedback drives revision and surfaces ambiguities
• Demonstration — deconstructing an example problem gives learners the genre model they need before writing

Patterns That Use This Strategy¶

• Cognitively Guided Instruction (CGI for Math) — problem creation aligns with CGI's emphasis on learners' own problem situations and solution strategies
• Case-Based Learning — learner-authored problems are miniature cases grounded in chosen contexts

Examples¶

• Following a Flocabulary math video, students write word problems using the operations taught, then solve classmates' problems; variations include answer-first writing and story-centered problems.
• A middle-school statistics unit where students collect data on a topic of interest and write multistep problems requiring peers to compute means and compare distributions.
• A high-school geometry class where students author problems requiring area and perimeter reasoning about real spaces (classroom, playground), constrained to realistic measurements.

Key Sources¶

• Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM — International Journal on Mathematics Education, 29(3), 75–80.
• Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1–7. doi:10.1007/s10649-013-9478-2
• Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–147). Lawrence Erlbaum.
• Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83(1), 87–101. doi:10.1007/s10649-012-9449-z