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Semantic-Schema Diagnostic for Arithmetic Word Problems

A diagnostic that tags every arithmetic word problem by semantic structure (combine/change/compare, and which quantity is unknown), maps each student's wrong answers to the exact structure that trips them up, and serves targeted practice sets for that structure.

Social SciencesMathematics Education and Teaching Techniques
K-8 math edtech (diagnostics and adaptive practice)

Concept

A diagnostic engine for elementary and middle-school arithmetic word problems. The tool ingests an item bank and automatically tags every story problem with its semantic schema — combine (part-part-whole), change (join or separate), compare — plus which quantity is unknown (result, start, or change unknown) and whether the wording is consistent or inconsistent with the required operation (e.g., "5 more than" phrasing that actually calls for subtraction). Student responses are then aggregated by schema and unknown position rather than by generic skill, yielding a per-student error map ("solves change/result-unknown reliably, fails compare problems with inconsistent language") and a class heat map. From the map the tool assembles targeted micro-practice sets of exactly the failing structure, and gives item writers a coverage report showing which schemas and unknown positions the bank under-represents. The single wedge: operation choice, treated as a measurable, structure-specific skill rather than one generic "word problem" skill.

Why now

The volume's chapter on choosing operations in solving routine story problems [0] establishes that the decisive difficulty in routine story problems is selecting the correct operation, and that this selection is governed by the problem's semantic structure rather than its arithmetic — so practice platforms that tag word problems only by operation or grade level are blind to the actual failure dimension. The volume's chapter on assessing problem solving [0] explicitly calls for a short-term remedy alongside a long-term solution, and a schema-level error map is exactly that kind of implementable remedy: it runs on item banks and response data districts already collect, using a small tagging scheme (a handful of schemas × unknown positions × language consistency) rather than new psychometrics.

Written by GLM · 3 Oct 2026

AI assessment

Backed by 1 paper89

A highly focused diagnostic tool that transforms generic 'word problem' errors into actionable semantic-schema insights for K-8 math platforms.

Evidence strength
4/5
The idea is directly grounded in specific chapters of a comprehensive volume on mathematical problem solving, specifically targeting the identified gap in operation selection and assessment.
Market pull
5/5
The named beneficiaries are the dominant players in the K-8 assessment space who possess the item banks and student data necessary to implement this diagnostic.
Novelty & moat
4/5
While other catalog ideas focus on representation (graphs vs. symbols), this focuses on the semantic structure of the narrative, filling a distinct gap in cognitive diagnostic tools.
Feasibility
4/5
The tagging scheme is small and discrete, making it feasible to implement via a mix of LLM-assisted tagging and simple data aggregation of existing student responses.
Wedge clarity
5/5
The wedge is exceptionally sharp: treating 'operation choice' as a structure-specific skill rather than a general math skill.
Simplicity / focus
5/5
The product is a single, focused diagnostic engine with a clear input (item bank/responses) and output (error map/practice sets).

Scored by Gemma 4 · 3 Oct 2026. Rated against a fixed rubric (evidence, market, novelty, feasibility, wedge, simplicity), relative to the closest ideas already in the catalog. A prior estimate to compare ideas before real-world signal arrives.

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Who benefits

  • Curriculum Associatescompany

    Its i-Ready diagnostic and practice products already drive instruction from K-8 math error data; schema-level subscores would sharpen exactly the word-problem strand where its current diagnostics are coarsest.

  • Renaissance Learningcompany

    Star Assessments and Accelerated Math recommend practice from assessment data; tagging its item banks by semantic schema would make its word-problem recommendations structure-specific rather than generic.

  • NWEAorganization

    MAP Growth reports math subscores to thousands of districts; a schema/unknown-position subscore would give its district clients an actionable breakdown of word-problem failure.

  • Zearnorganization

    Its digital K-5 lessons include extensive story-problem practice; schema tagging would let it route students to the specific problem structures they fail instead of re-teaching whole topics.

Research it builds on

  1. The Teaching and Assessing of Mathematical Problem Solving
    Randall Charles, Edward A. Silver · 2025 · 333 citations
    All ideas from this paper →
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