GM Dashboard: From Logs to Teacher Decisions

Problem

Collaborative math is hard to see

Graspable Math turns algebra into objects you can move: drag the +4 across the equals sign and it becomes −4; drag the 2 away from x and it divides the other side. Its new collaborative whiteboard lets two students work on the same equations at once, like a shared doc, and logs every move.

Collaboration is routine in writing tools and rare in math, so nobody yet knew what it looks like in the data. And a teacher with 30 students cannot watch every pair. What should a dashboard show her?

Solving 2x + 4 = 16 by gestures: dragging +4 across the equals sign, then dividing by 2 — Algebra by gesture: each drag is a logged action.

Graspable Math collaborative whiteboard with an equation and the expression keypad — The collaborative whiteboard, with a Collaborate Live mode for pairs.

Study 1

Study 1: what 448,000 logged actions say about how pairs work

I analyzed 448,025 logged actions and focused on the 504 whiteboards shared by exactly two students (736 students). Sessions ran from minutes to hours, so I normalized each into 12 equal time segments, extracted more than 785 time-series features, reduced them with PCA, and clustered pairs within groups of similar session length.

Slow build, fast startSome pairs warm up to collaboration; others engage from the first minute.
Role swapOne student leads early, then the other takes over.
In sync or lopsidedSome pairs move together; in others, one student does nearly all the work.

Sixteen small line charts of two students’ action counts over normalized session time — Sixteen pairs, sixteen rhythms: action counts for each student across normalized session time.

An honest note: clusters at the individual level were too noisy to interpret. Segmenting by session length is what made the patterns legible.

The patterns were real. The open question was whether a teacher could use them.

Study 2

Study 2: we showed a teacher the chart

Two researchers spent a week in a 6th-grade classroom (43 students) running collaborative activities with the teacher. Our first co-design question, “What superpowers would you want?”, fell flat: she mostly praised the activity. Reframing it as a ranking surfaced her priorities: combined work first, then higher-level thinking, engagement, and feedback.

Then we showed her a chart from Study 1 and asked what she learned and what she would do. Try it yourself:

Actions per time window, one pair. Anonymized demo session.

Are these two students building on each other’s work?

Design

Add an AI layer that reads the log for her

The charts stayed, because they show a whole session at a glance. On top of them we added an AI analysis the teacher can run on any session. It reads the action log and writes three things: how the pair worked together, the moments that may need her (a breakthrough, a struggle, a partner who went quiet), and a recommendation for next time, each with the evidence behind it. For follow-up questions there is a chat about that session, with suggested questions so she never starts from a blank box.

Proactive, not on-demandThe analysis arrives without the teacher having to ask. The chat is there for when she wants more.
Every student appearsThe analysis must mention every active student in its key moments, so a summary never describes only the louder partner.
Uncertainty stays visibleWhen the evidence is ambiguous, the summary offers more than one interpretation, and the panel says plainly that the AI can be wrong.
Logs, not camerasEverything comes from action logs, with no audio or video of children.

GM dashboard AI analysis on a demo session: a priority action, ratings for interaction pattern, activity intensity, and group synchronization, and a key observation with evidence — The AI layer on a demo session: one priority action, three ratings at a glance, and observations that cite the log.

How it works

Keeping the AI close to the log

A raw session log is long and noisy. A preprocessing layer cuts it by 70–80% while keeping each reasoning step, so a sequence like 2x + 3 = 7 → 2x = 4 → x = 2 survives intact. One model analyzes the mathematics, a second turns that analysis into language for teachers, and a validation layer scores each report and reruns weak ones before anything is shown.

Three-layer pipeline: data preprocessing, AI analysis with two model providers, and validation feeding multi-level teacher reports — Preprocess the log, analyze with two models, validate, then explain at three levels of detail.

Impact

From a research pipeline to a tool anyone can try

The dashboard is public with anonymized demo data at gmdashboard.viablelab.org. The work produced a first-author EDM 2024 paper and an AIED 2025 paper (acceptance under 16%), with partners at Graspable Math and Worcester Polytechnic Institute.

if I ran it again

One teacher is a partnership, not a sample, and the AI layer still needs the validation we called for in the paper. While preparing this page I ran the same demo session twice: one report called the pair “partially synchronized,” the next “well-synchronized.” Next I would measure that consistency directly, check reports against human coders, and run a classroom study with several teachers comparing their decisions with and without the summaries.