Platform

Standards as the data model. Everything else follows.

Hologram connects grading, mastery, intervention, and audit into one traceable loop built for real classrooms and district review.

Try Hologram with your classFor teachers

Hologram architecturelive loop

01Standards graphState standard to learning components

02Evidence engineEvery rubric score tied to visible work

03Mastery updateBayesian probability per sub-skill

04Intervention planTeacher-reviewed next action

Chapter 01

Single artifact moves through the whole system.

Operating loop

One artifact moves through the whole system.

Teachers approve evidence once. Hologram uses that same approved evidence to update mastery, detect gaps, suggest support, and keep an audit trail.

Draftsubmission to signal

Standard-level evidence appears in the teacher review flow before mastery changes.

3-7learning components

Each standard decomposes into a small set of teachable prerequisite skills.

1source of truth

The approved evidence powers dashboards, tutoring, interventions, and reporting.

Chapter 02

Mastery updates from evidence, not averages.

Mastery engine

Every response updates a mastery probability in real time.

Bayesian Knowledge Tracing runs per standard, per student. The tutor's next question can use the reviewed mastery signal instead of a generic script.

Ms. Chen

7th Grade Math · Period 2 · Quiz 3

Marcus Johnson · 7.RP.A.2

Live

0.18

P(Mastery)

Beginning

BKTModel parameters

P(L₀)Prior knowledge0.18

P(T)Learning rate0.10

P(G)Guess rate0.20

P(S)Slip rate0.10

Session trajectory · 6 responses+0.81

BKT vs naive scoring

Raw % correct5 of 6 responses

83%

Difficulty-weighted avgweighted by item difficulty

79%

BKT estimateaccounts for guess, slip, hint usage

99%

The last two correct were on hard items with no hint. Strong signal of mastery that raw % averages away.

Response streamQuiz 3 · 7.RP.A.2 · 6 items · oldest ↓

Is y = 3x a proportional relationship?Q1 · easy

⏱ 4.8sno hint

P(L|✓) = 0.18·0.9 / (0.18·0.9 + 0.82·0.2) = 0.497
P(Lₙ) = 0.497 + (1−0.497)·0.10 = 0.55

0.18

0.55

+0.37

Find the constant of proportionality: 3 : 12, 5 : 20, 7 : ?Q2 · medium

⏱ 6.3sno hint

P(L|✓) = 0.55·0.9 / (0.55·0.9 + 0.45·0.2) = 0.846
P(Lₙ) = 0.846 + (1−0.846)·0.10 = 0.86

0.55

0.86

+0.31

Graph shows a curve. Is it proportional? Justify.Q3 · hard

⏱ 11.7sno hint

P(L|✗) = 0.86·0.1 / (0.86·0.1 + 0.14·0.8) = 0.435
P(Lₙ) = 0.435 + (1−0.435)·0.10 = 0.49

0.86

0.49

−0.37

Which table represents a proportional relationship?Q4 · medium

⏱ 14.2s1 hint used

hint → effective guess rate: 0.20 → 0.35P(L|✓) = 0.49·0.9 / (0.49·0.9 + 0.51·0.35) = 0.712
P(Lₙ) = 0.712 + (1−0.712)·0.10 = 0.74

0.49

0.74

+0.25

Two recipes use different ratios. Explain when they're proportional.Q5 · hard

⏱ 9.1sno hint

P(L|✓) = 0.74·0.9 / (0.74·0.9 + 0.26·0.2) = 0.928
P(Lₙ) = 0.928 + (1−0.928)·0.10 = 0.94

0.74

0.94

+0.20

Apply proportional reasoning: scaling a recipe for 12 guests.Q6 · transfer

⏱ 5.4sno hint

P(L|✓) = 0.94·0.9 / (0.94·0.9 + 0.06·0.2) = 0.986
P(Lₙ) = 0.986 + (1−0.986)·0.10 = 0.99

0.94

0.99

+0.05

Starting estimate0.18

Final estimate0.99

Change+0.81

Session12 min 18 sec

Compute time< 4 ms/update

Research basis · Hologram’s BKT implementation

Knowledge tracing: Modeling the acquisition of procedural knowledgeCorbett & Anderson (1995)Contextual slip & guess probabilitiesBaker, Corbett & Aleven (2008)Individualized BKTYudelson, Koedinger & Gordon (2013)Deep Knowledge TracingPiech et al. (2015)

Chapter 03

Socratic tutoring activates before students give up.

Study Buddy

The Socratic tutor that asks the right question, never the answer.

When a student gets stuck, Hologram identifies the prerequisite gap and offers a Socratic question tied to the reviewed evidence. It guides discovery instead of handing over the answer.

Student preview · Socratic lesson

A tutor that writes on the whiteboard next to you.

Study Buddy works inside the lesson surface: drawing diagrams, circling evidence, stamping rules, and keeping the full board in view. Marcus drags stickies onto the board, fills blanks in the teacher’s handwriting, and writes back. The example session stays attached to the work, not a detached chat panel.

Marcus Johnson

7th Grade Science · Ridgeline Middle · Period 4

NGSS 5.PS1-4 · prerequisite remediationDid a new substance form?Example student session

Tutor context:quiz evidencecurrent boardteacher-approved goal

Teacher reviewedEvidence historyLesson triggerAudit record

Physical vs Chemical Changes

Ms. Garcia watching

Physical vs Chemical Changes

(from Quiz 3 — let's nail this)

So… what actually happens when stuff changes?

2Watch this — ice cube melting.

solid iceH₂O · (s)

liquid waterH₂O · (l)

water vaporH₂O · (g)

What stayed the same through all three?

PHYSICAL

3Now this — iron + oxygen.

4 Fe + 3 O₂→2 Fe₂O₃

new substance!

rust = iron oxide

CHEMICAL

4Which of these are chemical changes?

butter meltingPHYSICAL
wood burningCHEMICAL
iron rustingCHEMICAL
paper shreddingPHYSICAL
cake bakingCHEMICAL

The rule is:

A change is blank 1 if a blank 2 substance forms. Otherwise it’s blank 3 .

6Which of these are signs a chemical change happened?

7Your turn. Drop each change in the right bucket.

Physical

same stuff, different form

Chemical

new stuff, new properties

Teach it back in your own words.

0 / 40 chars

Mastery unlocked

NGSS 5.PS1-4 — Physical vs Chemical Changes

+0This session

Developingcurrent tier

Chi, VanLehn · Socratic dialogue produces 2× effect size over passive instruction · Cognitive Science, 2014

Built calm

Built as a calm system, not a feature bundle.

Data model

Standards are the primitive.

Rubrics, submissions, mastery updates, and interventions all attach to the same standards graph instead of a loose percentage grade.

Mastery engine

Probability changes with every response.

Each piece of evidence updates a student-standard mastery estimate so teachers see the current signal, not a stale average.

AI grading

Every score needs evidence.

The system drafts standard-level judgments and highlights the visible work behind each recommendation for teacher review.

Audit layer

Every action is traceable.

Teacher approvals, AI suggestions, student actions, and data access produce a record districts can inspect.

District-ready primitives

The platform keeps the hard parts visible.

Teacher review

AI suggestions stay draft until a teacher approves or adjusts them.

Standards trace

Every output can point back to a standard, rubric row, or prerequisite.

Canvas path

Designed for LTI 1.3 launch, roster context, and grade passback.

Audit record

Every meaningful system action can be reviewed later.

See it in your own classroom.

Thirty days, a few classrooms, no production dependency until your team says the workflow earns it.

Try Hologram with your class Read the research

Chapter 02

Mastery updates from evidence, not averages.

Mastery engine

Every response updates a mastery probability in real time.

Bayesian Knowledge Tracing runs per standard, per student. The tutor's next question can use the reviewed mastery signal instead of a generic script.

Ms. Chen

7th Grade Math · Period 2 · Quiz 3

Marcus Johnson · 7.RP.A.2

Live

0.18

P(Mastery)

Beginning

BKTModel parameters

P(L₀)Prior knowledge0.18

P(T)Learning rate0.10

P(G)Guess rate0.20

P(S)Slip rate0.10

Session trajectory · 6 responses+0.81

BKT vs naive scoring

Raw % correct5 of 6 responses

83%

Difficulty-weighted avgweighted by item difficulty

79%

BKT estimateaccounts for guess, slip, hint usage

99%

The last two correct were on hard items with no hint. Strong signal of mastery that raw % averages away.

Response streamQuiz 3 · 7.RP.A.2 · 6 items · oldest ↓

Is y = 3x a proportional relationship?Q1 · easy

⏱ 4.8sno hint

P(L|✓) = 0.18·0.9 / (0.18·0.9 + 0.82·0.2) = 0.497
P(Lₙ) = 0.497 + (1−0.497)·0.10 = 0.55

0.18

0.55

+0.37

Find the constant of proportionality: 3 : 12, 5 : 20, 7 : ?Q2 · medium

⏱ 6.3sno hint

P(L|✓) = 0.55·0.9 / (0.55·0.9 + 0.45·0.2) = 0.846
P(Lₙ) = 0.846 + (1−0.846)·0.10 = 0.86

0.55

0.86

+0.31

Graph shows a curve. Is it proportional? Justify.Q3 · hard

⏱ 11.7sno hint

P(L|✗) = 0.86·0.1 / (0.86·0.1 + 0.14·0.8) = 0.435
P(Lₙ) = 0.435 + (1−0.435)·0.10 = 0.49

0.86

0.49

−0.37

Which table represents a proportional relationship?Q4 · medium

⏱ 14.2s1 hint used

hint → effective guess rate: 0.20 → 0.35P(L|✓) = 0.49·0.9 / (0.49·0.9 + 0.51·0.35) = 0.712
P(Lₙ) = 0.712 + (1−0.712)·0.10 = 0.74

0.49

0.74

+0.25

Two recipes use different ratios. Explain when they're proportional.Q5 · hard

⏱ 9.1sno hint

P(L|✓) = 0.74·0.9 / (0.74·0.9 + 0.26·0.2) = 0.928
P(Lₙ) = 0.928 + (1−0.928)·0.10 = 0.94

0.74

0.94

+0.20

Apply proportional reasoning: scaling a recipe for 12 guests.Q6 · transfer

⏱ 5.4sno hint

P(L|✓) = 0.94·0.9 / (0.94·0.9 + 0.06·0.2) = 0.986
P(Lₙ) = 0.986 + (1−0.986)·0.10 = 0.99

0.94

0.99

+0.05

Starting estimate0.18

Final estimate0.99

Change+0.81

Session12 min 18 sec

Compute time< 4 ms/update

Research basis · Hologram’s BKT implementation

A tutor that writes on the whiteboard next to you.

Standards as the data model. Everything else follows.

Single artifact moves through the whole system.

One artifact moves through the whole system.

Mastery updates from evidence, not averages.

Every response updates a mastery probability in real time.

Every score is a probability —
not a guess.

Socratic tutoring activates before students give up.

The Socratic tutor that asks the right question, never the answer.

A tutor that writes on the whiteboard next to you.

Physical vs Chemical Changes

Built as a calm system, not a feature bundle.

Standards are the primitive.

Probability changes with every response.

Every score needs evidence.

Every action is traceable.

The platform keeps the hard parts visible.

See it in your own classroom.

Standards as the data model. Everything else follows.

Single artifact moves through the whole system.

One artifact moves through the whole system.

Mastery updates from evidence, not averages.

Every response updates a mastery probability in real time.

Every score is a probability —
not a guess.

Socratic tutoring activates before students give up.

The Socratic tutor that asks the right question, never the answer.

A tutor that writes on the whiteboard next to you.

Physical vs Chemical Changes

Built as a calm system, not a feature bundle.

Standards are the primitive.

Probability changes with every response.

Every score needs evidence.

Every action is traceable.

The platform keeps the hard parts visible.

See it in your own classroom.

Standards as the data model. Everything else follows.

Single artifact moves through the whole system.

Mastery updates from evidence, not averages.

Every score is a probability —not a guess.

Socratic tutoring activates before students give up.

Physical vs Chemical Changes

Standards are the primitive.

Probability changes with every response.

Every score needs evidence.

Every action is traceable.

See it in your own classroom.

Standards as the data model. Everything else follows.

Single artifact moves through the whole system.

Mastery updates from evidence, not averages.

Every score is a probability —not a guess.

Socratic tutoring activates before students give up.

Physical vs Chemical Changes

Standards are the primitive.

Probability changes with every response.

Every score needs evidence.

Every action is traceable.

See it in your own classroom.

Every score is a probability —
not a guess.

Every score is a probability —
not a guess.