Geometry teachers described a split in their use of technology for geometric proof. They valued certain digital tools during initial planning and exploration, then reported reverting to pen and paper for formal proof. Teachers attributed that choice to paper's support for diagram annotation and multiple proof-solving approaches. The account describes reported practice, not a causal comparison of ways to teach proof.
The study asked three related questions. It examined which approaches teachers believed best improve students' geometric-proof skills, whether the tools teachers use support a comprehensive proof-solving workflow, and how well the existing tool landscape addresses teachers' needs.
Where teachers said tools fell short
All 18 participants reported teaching students to mark up their proof diagrams. Participants also reported that the proof-specific tools they used did not support diagram annotation, provided limited feedback and oversimplified the proving process.
No reviewed tool covered the full workflow
To assess those reported needs against available software, the researchers reviewed 33 different commercial and research tools across eight categories. The categories included dynamic geometry environments, intelligent tutoring systems, large language models and automatic theorem provers.
The review was a feature-level assessment of what the tools could support, not a test of student performance. No reviewed category or individual tool supported all activities required for geometric-proof instruction. The result is a statement about coverage in the reviewed set, not about whether any tool improves learning.
Four proposals for future tools
The authors propose four guidelines for future proof-education tools: integrate the diagram and proof, generate problems and feedback automatically, support multiple proof formats and reduce accidental complexity.
The recommendations call for linked visual and written proof work, automated generation of problems and feedback, different ways to represent proofs and simpler user experiences. They are design recommendations, and their effects remain untested.
How the evidence was gathered
The interview sample comprised 18 geometry teachers with an average of 19 years of experience, ranging from 3 to 35 years, at public and private schools. Participants were recruited through Facebook posts, email referrals and snowball sampling.
A screening survey received 74 responses. The authors used saturation to determine the interview count and stopped when analysis reached a natural point at which it was no longer revealing new insights.
The study received institutional review board exemption, collected recorded verbal informed consent and conducted remote sessions lasting 50 to 80 minutes.
Interview data were analyzed with inductive thematic analysis using open coding, collaborative theme development, iterative codebook refinement and theoretical saturation.
What the findings do not show
The evidence has a narrow reach. It describes teacher-reported needs and feature coverage in the reviewed tools. It does not establish that digital tools or pen and paper cause better student learning, that the four proposed guidelines improve proof performance or that automated theorem-prover and language-model feedback is accurate or educationally effective.
The recruitment methods were Facebook posts, email referrals and snowball sampling, and they do not by themselves make the teacher group representative. The review covered 33 tools in eight categories, so it cannot establish exhaustive coverage of all available software.
Preprint status and disclosures
The document is an arXiv version 1 preprint dated 25 August 2026 and is marked as a manuscript submitted to ACM.
The work was supported by NSF awards 2447499, 2346174 and 2119007, the NSF Graduate Research Fellowship grant DGE2140739 and the ARCS Foundation Pittsburgh Chapter. The authors reported no financial or non-financial competing interests.
Paper data and sources
Original title: Teaching Geometric Proof with Tech: Pitfalls and Possibilities
Authors: Hwei-Shin Harriman, Wode Ni, Yuchen Jin et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text