Technical Summary: Utility-Preserving De-Identification for Math Tutoring

1. Problem Statement

The sharing of large-scale dialogue data is essential for advancing the science of teaching and learning, yet rigorous de-identification remains a significant barrier. In mathematics tutoring transcripts, a specific challenge known as numeric ambiguity arises. Mathematical expressions (e.g., fractions, dates in word problems, calculation results) frequently share surface-level similarities with structured Personally Identifiable Information (PII) such as dates, phone numbers, or driver's license numbers.

Generic PII detection systems, including industry-standard tools like Microsoft Presidio, often misidentify these mathematical spans as sensitive identifiers. This leads to over-redaction, where core instructional content is stripped from the data, rendering it useless for downstream educational research. Furthermore, there is a lack of domain-specific benchmarks to evaluate PII detection in math tutoring contexts, as original unredacted data is rarely shareable due to privacy regulations.

2. Methodology

The research follows a three-phase workflow to address the research question: How can we accurately detect PII in math tutoring transcripts while preserving the educational utility of the data?

Phase 1: Dataset Construction (MathEd-PII)

Since original unredacted data was unavailable, the authors constructed MathEd-PII, the first benchmark dataset for PII detection in math tutoring.

• Source: 1,000 tutoring sessions (115,620 messages) from a U.S.-based platform, initially redacted by the provider using Microsoft Presidio.
• Human-in-the-Loop LLM Workflow: To create a reliable ground truth without access to original data, the authors employed a three-step process:
  1. Initial Assessment: An LLM evaluated a sample of redacted messages to identify missed PII (false negatives) and incorrect redactions (false positives), inferring plausible original text where necessary.
  2. Human Validation: Researchers manually reviewed LLM outputs, refining prompts iteratively until 95% of identified issues were resolved.
  3. Surrogate Generation: The validated workflow was applied to the full corpus. The system replaced confirmed PII with context-aware, privacy-preserving surrogates and removed labels for content incorrectly flagged as PII.
• Result: A benchmark of 1,000 sessions containing 1,995 validated PII labels, significantly fewer than the 5,263 labels in the original provider dataset, indicating massive over-redaction in the source.

Phase 2: Math Segmentation and Ambiguity Analysis

To investigate the hypothesis that false positives cluster in math-dense regions, the authors developed a density-based segmentation module.

• Math Density Calculation: Messages were scored based on a weighted sum of math vocabulary (derived from K-12 learning components), multi-word phrases, and regular expressions for mathematical patterns.
• Segmentation: Messages exceeding a density threshold became "anchor" messages. Adjacent messages were added to the segment if their semantic similarity (via embeddings) to the segment centroid exceeded a similarity threshold.
• Analysis: This allowed the authors to compare PII detection performance specifically within "Math Segments" versus "Non-Math Segments."

Phase 3: Detection Strategy Evaluation

Four detection strategies were evaluated on the MathEd-PII benchmark:

1. Baseline: Microsoft Presidio (v2.2) with default and custom rules.
2. Basic Prompting: LLMs instructed to identify all PII without domain context.
3. Math-Aware Prompting: LLMs instructed with specific knowledge about math tutoring to reduce numeric false positives.
4. Segment-Aware Prompting: LLMs provided with an explicit label indicating whether a message belongs to a "Math Segment" or "Non-Math Segment."

Six LLMs (including Claude 4.5, GPT-5.2, and Gemini 3 Pro) were tested, with the best performers selected for the advanced prompting strategies. Performance was measured using Precision, Recall, and F1-score, with 95% confidence intervals calculated via bootstrap resampling.

3. Key Results

Failure Analysis (RQ1)

• Numeric Ambiguity Confirmed: False PII redactions are structurally concentrated in math-dense regions.
• Distribution: 55.5% of all false redactions occurred in math-dense segments, which constitute only 36.6% of the corpus.
• Ratio Disparity: In math segments, the ratio of false positives to true PII was approximately 4.88:1. In non-math segments, this ratio was 0.64:1.
• Specific Errors: Generic detectors frequently misidentified mathematical operations (e.g., "9351 / 7") as US Driver Licenses or Course Numbers, and fictional names in word problems (e.g., "If Alex has 5 apples") as real PERSON entities.

Method Evaluation (RQ3)

• Baseline Performance: Microsoft Presidio achieved high recall (78%) but extremely low precision (0.25), resulting in a poor F1-score of 0.379.
• LLM Performance:
  • Basic Prompting: Improved F1 scores significantly (e.g., Gemini 3 Pro: 0.818).
  • Math-Aware Prompting: Further improved precision by explicitly addressing numeric ambiguity (F1: 0.802 for Claude 4.5 Opus).
  • Segment-Aware Prompting: Achieved the highest overall performance. Gemini 3 Pro with segment-aware prompting reached an F1-score of 0.821 (Precision: 0.888, Recall: 0.764).
• Impact on False Positives: The segment-aware approach reduced false positives in critical numeric categories by over 90% (e.g., reducing DATE false positives by 99.5% and eliminating US_DRIVER_LICENSE false positives entirely) while maintaining recall levels comparable to the baseline.

4. Key Contributions

1. Identification of Numeric Ambiguity: The paper establishes numeric ambiguity as a central failure mode in de-identifying math tutoring dialogue, demonstrating that standard tools cannot distinguish between mathematical notation and sensitive identifiers without domain context.
2. MathEd-PII Benchmark: The introduction of the first publicly available benchmark dataset for PII detection in math tutoring, constructed via a novel human-in-the-loop LLM surrogate workflow that allows for rigorous evaluation without sharing original unredacted data.
3. Evidence for Domain-Aware Modeling: Empirical demonstration that utility-preserving de-identification requires domain-aware modeling. Specifically, incorporating mathematical discourse context (via segmentation labels) into LLM prompting substantially outperforms domain-agnostic baselines.

5. Significance and Claims

The authors claim that de-identification for tutoring dialogue cannot be treated as a domain-agnostic preprocessing step. The study provides evidence that preserving analytic utility requires incorporating the specific context of the domain (mathematics).

• Privacy vs. Utility: The work demonstrates that it is possible to achieve high privacy protection (removing true PII) without sacrificing the instructional fidelity of the data (preserving math content), provided that detection systems are aware of the domain.
• Methodological Contribution: The paper offers a replicable workflow for generating high-quality benchmark data in privacy-sensitive domains where original data cannot be shared, using LLMs to generate contextually coherent surrogates.
• Limitations: The authors note that the dataset is limited to a single U.S. platform and that while precision was significantly improved, recall optimization remains an area for future work. They also caution that current reliance on prompting may be brittle across model versions, suggesting future work in fine-tuning specialized models.

In conclusion, the paper argues that for dialogue-based educational data to be shareable and useful, de-identification pipelines must evolve from generic rule-based or model-based approaches to domain-aware strategies that understand the semantic difference between a math problem and a personal identifier.