Mathematical Reasoning

1. Hypothesis

Socratic prompts requiring justification will improve reasoning quality more than worked solutions.

2. Experiment design

Design: diagnostic and adaptive-practice study; baseline, active comparison, calibrated AI condition, user-controlled condition, failure or handback scenario and delayed follow-up Methods: diagnostic assessment; item-level telemetry; worked-example experiments; adaptive-practice trials; interviews; longitudinal progression analysis; pre-registered analysis; active comparison; subgroup and accessibility analysis; delayed retention or longitudinal follow-up; adverse-effect capture; reproducibility testing; participant debrief Independent variables: prompt style; solution visibility; problem type; expertise Dependent variables: reasoning quality; explanation; transfer; confidence Confounders: baseline capability; prior exposure; age; motivation; context; technology access; implementation fidelity Measures: reasoning rubric; explanation completeness; novel-problem score Success criteria: Statistically and practically meaningful improvement; preserved or improved human skill and agency; acceptable burden; no disproportionate subgroup harm; reproducible performance; effective handback, correction and recovery. Failure conditions: No meaningful benefit; gains mask reduced understanding or skill; dependency, fatigue, stress or exclusion exceeds benefit; effects fail to transfer or persist; user control is ineffective; correction or handback fails.

3. Seed result / current evidence

DEFENSIBLE SEED RESULT — NON-EMPIRICAL. The current evidence supports Mathematical Reasoning as a testable research proposition. Problem basis: Current approaches to mathematical reasoning are fragmented, poorly calibrated or insufficiently measured, making it difficult to distinguish real benefit from substitution, novelty or surveillance effects. Directional expectation: If the hypothesis is supported, the intervention condition should improve reasoning quality; explanation; transfer; confidence while avoiding material deterioration in independence, confidence calibration or delayed performance. Proposed observations: reasoning rubric; explanation completeness; novel-problem score. Seed data profile: Evidence Strength 10/100; Confidence 25/100; Maturity 20/100; Overall Health 36/100; Novelty 78/100; Strategic Importance 95/100. Evidence boundary: No validated results yet.; experiments 0, studies 0, participants 0. This is suitable for protocol formation and baseline comparison, not as a finding of effect.

4. Seed conclusion

DEFENSIBLE SEED CONCLUSION — PROVISIONAL. Mathematical Reasoning warrants structured testing because the CSV identifies a defined problem, falsifiable hypothesis, measurable outcomes and relevant literature foundations. The present position is that “Socratic prompts requiring justification will improve reasoning quality more than worked solutions.” is plausible and decision-relevant, but unvalidated. Proceed to controlled testing against the stated success and failure conditions. Confirm, narrow or reject this seed after effect sizes, uncertainty, subgroup outcomes, adverse effects, persistence and handback performance are observed.

Prior-art search performed before starting

PRIOR-ART SEED BASELINE — PARTIAL. The CSV records these literature domains: Number sense; conceptual change; worked-example effect; productive struggle; mathematical anxiety; adaptive practice. It also records: OECD PISA Mathematics — https://www.oecd.org/pisa/; AERO — https://www.edresearch.edu.au/; UNESCO Education — https://www.unesco.org/; NCTM — https://www.nctm.org/. Evidence register status: “Seeded; authoritative source register refreshed; empirical evidence not yet ingested”. This is defensible as a starting prior-art inventory, but not as proof of a completed systematic search because search dates, databases, exact queries, reviewer, result counts, screening decisions, claim mapping and a replayable receipt are absent.

Prior-art material named: Existing literature: Number sense; conceptual change; worked-example effect; productive struggle; mathematical anxiety; adaptive practice. References: OECD PISA Mathematics — https://www.oecd.org/pisa/; AERO — https://www.edresearch.edu.au/; UNESCO Education — https://www.unesco.org/; NCTM — https://www.nctm.org/

Critical gap / next action

Create and attach a dated prior-art search log; lock the protocol; execute the proposed study; link raw data and analysis; then replace the results and conclusion placeholders with evidence-bounded findings.